MODECO, modelling study on the role of energy communities in the energy transition.
Date: 2023-05-04
Institutions: Joint Research Centre
Subjects: electrical energy, energy consumption, energy efficiency, energy policy, energy production, energy saving, energy supply, price of energy

MODECO – Modelling study on the role of 
energy communities in the energy 
transition  

Jiménez Martínez, M., Igualada L., Valdés Martín, 
R., Farriol Salas, A., Heredia Julbe, P., Noris, F., 
García Muñoz, F., Corchero, C. 

 2023 

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JRC132896 

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doi:10.2760/118421  KJ-03-23-143-EN-N 

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How  to  cite  this  report:  Jiménez  Martínez,  M.,  Igualada  L.,  Valdés  Martín,  R.,  et  al.,  MODECO  –  Modelling  study  on  the  role  of  energy 
communities in the energy transition, Publications Office of the European Union, Luxembourg, 2023, doi:10.2760/118421, JRC132896 

Ares(2023)2767878

MODECO 

MODECO 

Modelling study on the role of energy 
communities in the energy transition 

Service Contract no. 942132-IPR-2021 

April 2023 

Authors: Jiménez Martínez, M., Igualada L., Valdés Martín, R., Farriol Salas, 
A., Heredia Julbe, P., Noris, F., García Muñoz, F., Corchero, C. 

        Service Contract no. 942132-IPR-2021  
        Modelling study on the role of Energy Communities in the energy transition 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Contents  

Abstract ....................................................................................................................................................................................................................................................................... 1 

Acknowledgements .......................................................................................................................................................................................................................................... 2 

Executive summary .......................................................................................................................................................................................................................................... 3 

1 

Introduction..................................................................................................................................................................................................................................................... 8 

1.1  Objectives ........................................................................................................................................................................................................................................ 10 

1.2  Report scope.................................................................................................................................................................................................................................. 11 

2  Case studies definition ..................................................................................................................................................................................................................... 12 

2.1  Selected target regions ...................................................................................................................................................................................................... 12 

2.1.1 

Climatic differences ............................................................................................................................................................................................. 13 

2.1.2 

Regionalized cost of capital ......................................................................................................................................................................... 15 

2.2  Definition of Energy community archetypes ................................................................................................................................................. 16 

2.2.1 

Number and type of members .................................................................................................................................................................. 18 

2.2.2 

Energy carriers .......................................................................................................................................................................................................... 19 

2.2.3 

Available investment options ..................................................................................................................................................................... 20 

2.3  Economic scenarios ................................................................................................................................................................................................................ 22 

2.3.1 

Energy prices calculation ................................................................................................................................................................................ 23 

2.3.2 

Use-of-Network charges ................................................................................................................................................................................. 23 

2.3.2.1 

Time-of-Use tariff ................................................................................................................................................................................... 25 

2.3.2.2 

Peak power tariff ...................................................................................................................................................................................... 26 

2.3.2.3 

Bandwidth tariff......................................................................................................................................................................................... 26 

2.3.3 

Taxes .................................................................................................................................................................................................................................. 27 

3  Modelling of Energy communities ......................................................................................................................................................................................... 29 

3.1  Energy demand simulation ............................................................................................................................................................................................. 29 

3.1.1 

Non-residential and residential users ................................................................................................................................................ 29 

3.1.1.1 

Electrical baseload demand ........................................................................................................................................................... 29 

3.1.1.2 

Adjustment for space cooling demand in Spain ......................................................................................................... 31 

3.1.1.3 

Heat demand ................................................................................................................................................................................................ 32 

3.1.2 

Industrial users ......................................................................................................................................................................................................... 35 

3.1.2.1 

Ambient temperature dependent users .............................................................................................................................. 35 

3.1.2.2 

Ambient temperature independent users ......................................................................................................................... 37 

3.2.1 

Heat pumps’ flexibility potential .............................................................................................................................................................. 40 

3.3  Electric vehicles .......................................................................................................................................................................................................................... 41 

3.3.1 

Private charging stations (non-smart charges) ......................................................................................................................... 41 

3.3.2 

Community-led charging points (V2G) .............................................................................................................................................. 43 

3.3.3 

Community’s CO2 emissions......................................................................................................................................................................... 46 

4  Models description ................................................................................................................................................................................................................................ 47 

4.1  Power system model............................................................................................................................................................................................................. 47 

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4.1.1  Model adaptation to the reference ESES ........................................................................................................................................ 50 

4.2 

Investment model .................................................................................................................................................................................................................... 51 

4.2.1 

Representative day’s selection .................................................................................................................................................................. 51 

4.2.2  Objective function .................................................................................................................................................................................................. 52 

4.2.3 

Key model constraints ....................................................................................................................................................................................... 53 

4.2.4 

Energy balance equations .............................................................................................................................................................................. 55 

4.2.5 

Energy assets modelling ................................................................................................................................................................................. 56 

4.3  Operational model ................................................................................................................................................................................................................... 58 

4.3.1  Objective function .................................................................................................................................................................................................. 58 

4.3.2 

Balance equations ................................................................................................................................................................................................. 58 

4.3.3 

Energy assets modelling ................................................................................................................................................................................. 59 

4.3.4 

Calculation of CO2 emissions ...................................................................................................................................................................... 62 

5  Energy communities’ description ............................................................................................................................................................................................ 63 

5.1  Business park ............................................................................................................................................................................................................................... 63 

5.1.1 

Business park: Heat demand ....................................................................................................................................................................... 64 

5.1.2 

Business park: Electrical demand ........................................................................................................................................................... 65 

5.2 

Industrial polygon .................................................................................................................................................................................................................... 67 

5.2.1 

Industrial polygon: Heat demand ............................................................................................................................................................ 68 

5.2.2 

Industrial polygon: Electrical demand ................................................................................................................................................ 70 

5.3  Rural town ....................................................................................................................................................................................................................................... 70 

5.3.1 

Rural town: Heat demand............................................................................................................................................................................... 71 

5.3.2 

Rural town: Electrical demand ................................................................................................................................................................... 72 

5.4  Urban district ................................................................................................................................................................................................................................ 74 

5.4.1 

Urban district: Heat demand ....................................................................................................................................................................... 75 

5.4.2 

Urban district: Electrical demand ............................................................................................................................................................ 77 

5.5  Virtual community ................................................................................................................................................................................................................... 79 

5.5.1 

Virtual community: Heat demand .......................................................................................................................................................... 80 

5.5.2 

Virtual community: Electrical demand ............................................................................................................................................... 81 

6  Energy price scenarios ...................................................................................................................................................................................................................... 84 

6.1  Power system indicators ................................................................................................................................................................................................... 84 

6.2  Marginal prices ........................................................................................................................................................................................................................... 85 

6.3  Energy tariffs ............................................................................................................................................................................................................................... 88 

7 

Investment model results .............................................................................................................................................................................................................. 91 

7.1  Tariff structures: TOU, Peak power, Bandwidth ........................................................................................................................................... 91 

7.1.1 

Business park ............................................................................................................................................................................................................. 91 

7.1.2 

Industrial polygon .................................................................................................................................................................................................. 96 

7.1.3 

Rural town .................................................................................................................................................................................................................. 100 

7.1.4 

Urban district ........................................................................................................................................................................................................... 103 

7.1.5 

Virtual community .............................................................................................................................................................................................. 107 

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7.2  Sensitivity tests ....................................................................................................................................................................................................................... 111 

7.2.1 

Sensitivity to different price rates ...................................................................................................................................................... 112 

7.2.2 

Sensitivity to different discount rates ............................................................................................................................................. 114 

8  Operational model results .......................................................................................................................................................................................................... 117 

8.1  Local generation mix .......................................................................................................................................................................................................... 117 

8.1.1 

Emitted and avoided CO2 emissions ............................................................................................................................................... 122 

8.2  Economic benefits ................................................................................................................................................................................................................ 126 

8.2.1 

Avoided energy costs ...................................................................................................................................................................................... 127 

8.3  Energy costs ............................................................................................................................................................................................................................... 133 

8.3.1 

Disaggregated energy payments ......................................................................................................................................................... 133 

9  Conclusions ............................................................................................................................................................................................................................................... 138 

References .......................................................................................................................................................................................................................................................... 141 

Definitions ........................................................................................................................................................................................................................................................... 149 

List of boxes...................................................................................................................................................................................................................................................... 152 

List of figures .................................................................................................................................................................................................................................................. 153 

List of tables ..................................................................................................................................................................................................................................................... 157 

Annexes ................................................................................................................................................................................................................................................................. 160 

Annex 1. Mathematical Formulation for MODECO’s Investment Model ......................................................................................... 160 

Annex 2. Mathematical Formulation for MODECO’s Operational Model ........................................................................................ 180 

Annex 3. Technical parameters for energy assets in the investment and operational models .............................. 196 

Annex 4. Gap values obtained for the scenarios executed in the EC investment model ............................................... 208 

Annex 5. Gap values obtained for the scenarios executed in the EC operational model .............................................. 210 

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Abstract  

This report assesses the influence on the operational and investment decisions of five representative Energy 
Community  typologies (in  Germany  and  Spain)  of  a  variety  of  external  factors,  namely  energy  taxes,  levies 
and  tariff  schemes.  In  particular,  four  schemes  were  tested:  No  Charges,  Time-of-Use  (TOU),  Subscription 
Bandwidth and Peak power. The study indicates that none of the evaluated tariff structures poses significant 
barriers  to  Energy  communities’  future  expansion.  As  long  as  investment  and  operational  costs  are 
competitive  against  electricity  prices,  communities  will  have  incentives  to  form  and  invest  in  the  energy 
assets  that  better  fit  their  demand  and  geographical  conditions.  The  TOU  tariff,  however,  could  lead  to 
overinvestments  in  batteries  under  certain  pricing  conditions.  The  introduction  of  power-based  charges,  e.g. 
Bandwidth  and  Peak  power,  avoids  this  pitfall  even  in  future  scenarios  with  high  price  differentials.  The 
Bandwidth  tariff  also  offers  an  opportunity  to  adapt  Use-of-Network  charges  to  a  future  system  with  high 
prosumers  participation  as  it  ensures  higher  grid  cost  recovery.  Another  interesting  alternative  is  the 
Portuguese  regulation  in  which  partial  charges  are  always  applied  to  self-consumption.  Considering  the 
impacts  of  self-generation  while  still  recognizing  its  benefits  is  relevant  as  the  study  shows  that  self-
consumption is the largest economic benefit in the short-term, but energy arbitrage and electricity sales will 
become relevant incomes for future Energy communities. 

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Acknowledgements 

The authors would like to thank JRC staff Stamatios Chondrogiannis, Georg Thomassen and Rade Cadenovic 
for  their  valuable  feedback  and  support  through  this  work.  The  report  also  benefitted  from  insights  and 
feedback from our colleague Josh Eichmann. 

Authors 

Catalonia  Institute  for  Energy  Research  (IREC):  Jiménez  Martínez,  Mariana;  Igualada,  Lucía;  Valdés 
Martín, Roger; Farriol Salas, Albert; Heredia Julbe, Pol; García Muñoz, Fernando; Corchero, Cristina. 

R2M Solution Spain: Noris, Federico 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

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Executive summary 

Policy context 

As  part  of  the  European  Commission’s  ambitious  Greenhouse  Gas  (GHG)  emissions  reduction  targets,  the 
Clean Energy for all European Package introduced the concept of Renewable Energy Communities and Citizen 
Energy Communities. Several Energy communities across Europe have been created and support the energy 
transition  efforts  towards  greater  utilization  of  renewable  energy  sources,  decarbonisation  of  the  energy 
system  and  energy  democratisation  (e.g.,  energy  poverty,  energy  justice)  with  significant  social  elements 
associated  with  them.  Since  there  is  a  great  variety  of  already  existing  energy  community  projects,  it  is 
becoming increasingly important to analyse different use cases and understand which best practices to follow 
for  new  implementations  and  policies.  The  differences  between  the  legislative  framework,  the  user 
engagement  practices,  and  the  potential  revenue  streams  represent  a  valuable  resource  for  defining  the 
needed boundary conditions for the implementation of energy community projects at a national and European 
level.  

Considering the novelty and complexities of these participating structures, it is important to assess the impact 
of a variety of factors on the energy communities’ operational and investment  decisions that  will influence 
their further deployment and penetration. This varies depending on, for instance, the community typology, the 
geographic  location  (e.g.  weather  and  legislative  framework)  and  trends  for  several  factors  including  the 
technology’s  performance  and  costs,  and  available  energy  prices.  One  major  element  is  the  legislative  and 
regulatory  framework,  including  energy  taxes,  tariffs  and  levies that  are  placed  upon  the  energy  generated 
and  used. Within  the  above  context,  the  JRC  contracted  R2M  and  IREC  to  assess  the  impact  of  policy  and 
regulatory  instruments  (e.g.  network  tariffs  and  energy  taxes)  on  the  expected  operational  and  investment 
decisions  made  by  different  Energy  community  types.  MODECO  stands  out  for  being  one  of  the  initiatives 
contributing  to  the  development  of  technical  tools  that  support  better  understanding  the  implications  of 
Energy communities in the energy future of Europe. 

Work scope 

The scope of this work is to analyse how investment and operational decisions within Energy communities are 
affected  by  different  tariff  structures  through  the  evaluation  of  four  scenarios.  These  tariff  scenarios  are 
formed  by  considering  a  dynamic  price  obtained  from  a  Unit  Commitment  and  Economic  Dispatch  (UCED) 
reflecting  a  future  energy  transition  scenario  and different  Use-of-Network  charges  (i.e.,  No  Charges,  Time-
Of-Use  [TOU],  Bandwidth  subscription,  Peak  power  based)  during  a  16-year  period  (2025-2040).  Taxes  are 
also  applied  except  in  the  No  Charges  case,  which  is  only  used  for  comparative  purposes.  Additionally,  we 
explore the sensitivity to the TOU tariff structure by using an annual flat rate instead of the dynamic prices, 
and a Power Purchase Agreement (PPA) for industrial users; as well as different discount rates. 

In particular, we consider five Energy community archetypes (i.e. Business park, Industrial polygon, Rural Town, 
Urban District, Virtual community) in two European regions (i.e., Germany and Spain). The number and type of 
members considered for each archetype is defined based on existing European Energy communities and the 
archetype intrinsic characteristics. Electricity, natural gas and heat are present in all archetypes, while we only 
consider  biomass  for  the  Rural  town  and  green  hydrogen  for  industrial  users.  The  potential  investments 
considered  are  combined  heat  and  power,  hydrogen  electrolyser,  hydrogen  storage  tank,  solar 
photovoltaics  (ground-mounted  and  on  rooftop),  wind  turbines,  batteries  and  vehicle-to-grid 
charging points. The use of Heat pumps and non-smart electric vehicle chargers are also considered for the 
community  energy  modelling  but  not  as  part  of  the  investment  decisions.  Depending  on  the  archetypes’ 
characteristics some energy assets are disregarded as a viable investment option (e.g. wind turbines on land-
restricted  areas).  Based  on  existing  data  regarding  national  conditions  for  renewable  asset  financing  in 
European countries, we considered different Weighted Average Cost of Capital values for Germany and Spain.  

We assumed that each community acts as a single economic entity with one interconnection point with the 
external  energy  markets.  For  the  Virtual  community,  the  Portuguese  regulation  for  virtual  self-consumption 
happening  at  the  same  or  different  voltage  levels,  the  only  of  its  kind  so  far  in  Europe,  is  used  as  an 
inspiration to define the applicable rules to this archetype. Under these rules, partial Use-of-Network charges 
are  applied  to  self-consumption  by  the  Virtual  community,  the  only  in  which  members  are  not  within 
geographical proximity. In the rest of archetypes, self-consuming implies avoiding taxes and Use-of-Network 
payments.  The  considered  dynamic  energy  prices  scenarios  are  based  on  the  results  obtained  from  the 
wholesale market module. We consider selling prices to be always equal to the regional marginal price while 
electricity purchased costs depend on the applicable tariff structure scenario. 

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To  assess  how  Energy  communities  would  invest  and  operate  under  such  conditions,  we  executed  three 
optimization models, namely the UCED, the investment and the operational models. The investment 
and operational models are specifically designed for MODECO and suited to Energy community applications, 
while the UCED model corresponds to an existing model adapted using an external Energy System Evolution 
Scenario  (ESES)  as  reference.  The  Distributed  Energy  scenario  from  ENTSO-ES’  Ten  Year  Network 
Development  Plan  2022,  which  considers  a  high  future  usage  of  wind  and  solar  technologies  and  the 
dismantling of all nuclear and carbon-based  power plants, is used for this purpose. Possible impacts of the 
effect on energy prices of the war in Ukraine and other geopolitical unstable areas are not considered and are 
outside the scope of the present work, although adaptations from the selected ESES were done to incorporate 
higher gas prices.  

To  model  the  behaviours  and  assumptions  of  the  different  archetypes  across  the  range  of  scenarios 
considered, the following steps are implemented:  

1.  Simulate the energy demand and resources for both residential and non-residential (tertiary and 
industrial)  users. This includes electricity baseload, heat  demand as well as heat pump and electric 
vehicles usage (via private and public charging stations).  

2.  Define economic scenarios and select the model’s economic and technical parameters based on 

existing literature. 

3.  Adapt ESES to the selected UCED model.  
4.  Develop and execute investment and operation models using the outputs from items #1 and #2 
as inputs. For the investment model, this included an algorithm for selecting a set of representative 
days from each evaluated year. 

The  proposed  investment  model  contains  a  series  of  constraints  to  avoid  excessive  surplus  generation  and 
energy arbitrage activities, prioritizing self-consumption. We proposed this set of constraints considering that, 
according to current European Directives, Energy communities’ primary objective is not to generate financial 
profits  but to create economic, social and environmental benefits.  However, the following question remains: 
what  is  the  balance  between  prioritizing  economic  benefits  rather  than  financial  profits  in  the 
Energy  community’s  context?  We  consider  this  feature  a  key  characteristic  differentiating  Energy 
communities  from  other  types  of  energy  investors  that  needs  to  be  clearly  delimited  in  future  models,  for 
example by incorporating different business models in the community archetypes. This becomes a relevant 
issue  as  current  directives  also  encourage  a  level  playing  field  for  communities  and  larger 
participants, mandating members to allow the participation of Energy communities in all market activities, 
which makes delimiting this balance harder. 

Key conclusions 

Our  results  show  that  under  most  pricing  conditions  the  three  evaluated  tariffs  (TOU,  Bandwidth,  Peak 
Power)  result  in  similar  investment  decisions  for  the  Energy  communities.  Specially,  investments  in 
generation assets are not significantly affected by the Use-of-Network charges applied, meaning that at the 
end of the 16-year period the communities have a similar technological mix regardless of the tariff, although 
the  year  at  which  they  installed  the  assets  slightly  varies  from  case  to  case.  In  particular,  investments  in 
renewable energies (solar, wind) are mostly driven by the trade-off between investment and operational costs 
and  electricity  market,  and  the  community’s  demand  behaviour  and  spatial  restrictions.  Similarly,  at  the 
considered costs, CHP installations tend to be done early, regardless of the tariff, to replace boilers and supply 
the community’s heat demand. 

When the price curves have hours with extreme low and high prices, Energy communities under a TOU tariff 
invest in significantly larger storage capacity that remains unutilized most of the time and is only profited in 
this  particular  hours.  This  indicates  that  storage  investments  are  more  sensitive  to  price  variations 
under  a  TOU  tariff  with  pure  energy-based  charges.  We  did  not  observe  a  similar  response  when 
considering  the  Peak  power  or  Bandwidth  models,  which  indicates  that  power-based  components  avoid 
overinvestments even  when  wide  price spreads are present. We corroborated the high sensitivity of  battery 
investments to electricity price differences by using a flat rate instead of the dynamic market price. Under this 
scenario, battery installations were reduced drastically while for other types of technologies a similar power 
was  installed.  No  sensitivity  tests  were  conducted  on  the  Peak  power  or  Bandwidth  models,  but  we 
recommend it for future analysis. 

The TOU and Peak power tariffs resulted in higher economic benefits for Energy communities although which 
tariff offers the highest gains is influenced by regional costs: in Germany the highest benefits are associated 
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to  the  TOU  and  in  Spain  to  the  Peak  power  scheme.  In  both  regions,  the  Bandwidth  model  offered  the 
least benefits. Furthermore, for the Bandwidth model, Energy communities were not able to reduce as much 
costs  as  in  other  tariffs  given  that  we  assumed  the  contracted  power  to  be  a  fixed  value  for  the  16-year 
period,  not  subject  to  optimization.  We  consider  that  including  the  contracted  bandwidth  as  a  variable  in 
future investment optimization models will be advisable to get a better picture of this tariff’s potential effects 
on future communities. 

The Subscription Bandwidth model also considers penalizations for power injections and withdrawals beyond 
certain  limits.  In  most  of  the  evaluated  scenarios,  the  communities’  energy  assets’  operations  avoided 
incurring  in  excess  penalizations  as  the  proposed  investment  model  follows  a  cost  minimization  approach. 
However,  in  the  cases  in  which  extremely  high  peak  prices  are  registered,  the  communities  bear  the 
penalizations costs as the potential revenues are significantly higher. This situation happens just a few hours 
per  year,  but  the  exceeding  power  is  significantly  larger  than  the  contracted  bandwidth.  To  prevent  this 
outcome, we suggest testing the utilization of scalable penalizations with different prices depending 
on the percentage of power exceeded above the contracted bandwidth and not a fixed cost. 

The proposed Bandwidth model is the only that poses a cost over energy injections, including the monthly fee 
per contracted bandwidth and the associated penalizations to excess energy injections. This becomes relevant 
in scenarios in which energy communities significantly reduce their electricity grid consumption but are active 
generators and use the grid to provide surplus electricity to the market pool. Our results, for instance, show 
that in the archetypes with lower demand (Business Park, Rural Town, Urban district), small or no 
charges  at  all  would  be  paid  by  communities  under  the  TOU  o  Peak  power  tariff.  Generally, 
generation is not subjected to Use-of-Network charges as these are imposed to consumption points.  In the 
future  grid,  however,  when  energy  prosumers  –  including  Energy  communities  –  become  more  numerous, 
associating  part  of  the  costs  to  generation  as  done  in  the  Bandwidth  model  is  an  interesting 
alternative to ensure the recovery of grid costs. 

Another interesting feature is the application of the Portuguese regulation on self-consumed energy in the 
Virtual community. In this archetype, members are not located in close proximity but share energy assets such 
as  batteries  and  local  generation  technologies.  In  this  case,  the  self-generated  energy  has  Use-of-Network 
charges associated with its consumption but with a discount over the full cost paid by users consuming from 
the market pool. The applicable discount depends on the voltage level in which both load and generation are 
located  as  well  as  the  energy  flow  direction.  By  using  these  rules,  Energy  communities  always  pay  for 
network  usage,  even  when  self-generating.  Our  results  indicate  that  their  usage  makes  battery 
investments  less  attractive  than  when  no  charges  are  associated  with  self-generation.  We,  however, 
recommend  performing  a  sensitivity  test  using  the  same  scenario  but  no  charges  associated  with  self-
consumption,  as  well  as  evaluating  different  user  types  to  better  understand  these  rules’  implications  on 
Energy communities.  

Overall,  our  study  indicates  that  none  of  the  evaluated  tariff  structures  poses  significant  barriers  to  the 
expansion  of  Energy  communities.  As  long  as  investment  and  operational  costs  are  competitive  against 
electricity  prices,  communities  have  an  incentive  to  form  and  invest  in  self-generation  assets.  Storage 
installations will be also encouraged to promote energy injections and withdrawals in convenient times for the 
power system operation. Purely energy-based tariffs (TOU), however, could lead to overinvestments in storage 
units that would be only used for a few hours annually. The introduction of power-based charges, e.g. in the 
Bandwidth and Peak power models, seems to avoid this pitfall even in future power scenarios in which wide 
price  differences  are  present.  In  particular,  the  Bandwidth  tariff  presents  an  opportunity  to  adapt  Use-of-
Network charges to a future system with high prosumers participation as it ensures higher grid cost recovery. 
This becomes especially relevant as our study shows that not only self-consumption, but energy arbitrage and 
electricity sales will become relevant activities. Another interesting alternative in this regard is the Portuguese 
regulation  in  which  partial  charges  are  applied  to  self-consumption  taking  place  at  the  same  or  different 
voltage levels. 

Main findings 

The investment model’s decisions are based on a set of representative days for the entire 16-year evaluation 
period.  The  representative  days  selected  have  a  strong  influence  on  the  final  investment  decisions 
made  by  the  communities,  particularly  in  the  TOU  tariff  model.  In  general,  total  investments  tend  to  be 
larger  in  the  German  than  Spanish  communities  due  to  more  favourable  economic  conditions  (higher 
marginal prices, lower investment costs) as well as larger energy, and in particular heat demand. A significant 

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economic  parameter  is  the  selected  WACC,  which  showed  significant  differences  between  South  and 
Central-West  regions  and  is  based  on  a  European-level  study  of  financing  conditions  for  renewable 
energies  (wind,  solar)  and  different  member  countries.  This  not  only  highlights  the  importance  of  using 
country-specific  data  to  better  represent  the  economic  context  affecting  Energy  communities,  but  also  the 
importance of counting with such information at the European member level. 

The Business park archetype invests in gas-fuelled CHP, rooftop solar photovoltaics, V2G charging stations 
and  batteries.  The  community  in  Spain  invests  in  larger  sums  than  the  same  archetype  in  Germany.  The 
Bandwidth and the No Charges scenarios result in the largest investments, while the TOU and the Peak-power 
scenarios  have  the  lowest  investments.  Interestingly,  installed  batteries  in  Spain  are  much  greater  than  in 
Germany largely due to the low electricity purchase price and the high selling price registered in Spain during 
certain hours from the selected representative days. In the Peak power scenario, batteries are mostly charged 
with  excess  on-site  production  with  limited  charging  from  the  grid  due  to  the  extra  costs  associated  with 
rising peak demand. This characteristic reduces the number of V2G-capable chargers and the storage capacity 
installed.  In  the  TOU  scenario  –  with  different  representative  days  and,  thus,  price  curves  –  grid  battery 
charging  is  less  favourable  due  to  the  price  curves’  characteristics,  limiting  the  opportunities  for  energy 
arbitrage  and  leading  to  lower  storage  capacity.  The  TOU  scenario  in  this  archetype  is  associated  with  the 
lowest CHP, storage and the highest V2G-capable charging points. 

For the Industrial polygon, there are the smallest regional differences in heat and electricity demand and 
therefore in investments across locations. These communities mostly invest in PV solar rooftop, wind turbines, 
V2G-capable chargers, batteries and gas-fuelled CHP. The installed CHP is constant across the different tariff 
scenarios and so are the PV solar rooftop and wind turbines that corresponds to the maximum installable and 
allows  for  energy  arbitrage  by  leveraging  the  installed  storage  capacity.  The  only  exception  is  the  Spanish 
polygon under a Peak power tariff in which less storage and CHP capacity is installed. Under the Bandwidth 
model,  the  Spanish  community  does  incur  some  penalizations  for  excess  energy  withdrawal  and  injections, 
but these are small. For the Peak Power tariff case, ground-mounted solar is installed in Spain in addition to 
the wind capacity put on land in all other scenarios, although its capacity is small in comparison to the wind 
farms. 

The Rural town communities invest in wind, PV solar (land and rooftop), gas-fuelled CHP, batteries and V2G-
capable chargers. In Germany there are significant variations across tariffs, with the TOU scenario having the 
largest  investments  mostly  for  CHP  and  storage,  while  in  Spain  the  profiles  vary  less  and  result  in  lower 
investments.  In  the  Peak  power  tariff,  batteries  are  used  to  store  excess  local  energy  at  times  in  which 
demand  and  prices  are  low  to  discharge  at  higher-priced  hours  or  when  demand  peaks  occur.  The  CHP  is 
aligned  with  the  thermal  demand  in  all  scenarios,  except  for  the  TOU  scenario.  In  Spain,  the  lowest  CHP 
capacity  is  installed  under  the  TOU  tariff,  while  in  Germany  the  opposite  is  observed. The  largest  wind 
capacity  is  observed  for  the  TOU  scenario  in  Spain.  In  this  region,  no  solar  is  installed  despite  its  better 
radiation  levels  as  the  wind  profile  better  matches  the  community’s  demand  curve  and  the  high-priced 
periods.  Similar  to  what  happens  in  other  archetypes,  these  differences  can  be  attributed  to  the  selected 
representative days’ price curves. 

In  the  Urban  district  archetype,  investments  occur  in  gas-fuelled  CHP,  storage  and  PV  solar  rooftop  as 
ground  renewable  generation  is not  allowed.  V2G-capabl  chargers  are  also  installed  but  in  a  small  number 
(five) that remains constant across scenarios. In Germany, investments are significantly greater than in Spain 
to cover the larger heat and electricity demand. For the No Charges scenario, the investments in Germany are 
the lowest while in Spain are the greatest. Such variations result from differences in the price curves from the 
selected representative days. The main differences across tariffs are associated with decisions regarding CHP 
and storage, as the amount of solar rooftop installed remains fairly constant across scenarios using the same 
representative  days.  For  the  TOU  scenario,  storage  in  Germany  is  much  greater  than  in  Spain,  due  to  the 
existence of wide price spreads, leading to increased CHP extra capacity.  

The  Virtual  community  invests  in  storage,  PV  solar  (land  and  rooftop),  wind  turbines,  and  V2G-capable 
chargers  with  greater  investments  in  Germany  than  in  Spain,  especially  for  the  Peak  power  scenario.  This 
archetype presents the most V2G chargers, also used as storage, due to the larger influence area considered, 
which  results  in  a  higher  number  of  electric  vehicles  circulation.  For  the  Power  peak  in  Germany,  the  main 
difference is associated with the installed storage (used mainly to lower summer demand peaks as wind load 
factor is lower during this summer) and solar on the ground. As happens in the Rural town, wind is preferred 
over  solar  in  the  Spanish  community  as  the  wind  generation  profile  offers  a  better  match  with  high-priced 
hours. 

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With  the  considered  economic  assumptions,  biomass-fuelled  CHP  and  green  hydrogen-related  assets 
(electrolyzer,  storage  tank)  do  not  result  in  profitable  investments.  Solar  and  wind  installations 
depend  on  energy  prices,  technological  costs  and  land  space  restrictions.  Due  to  its  higher  marginal  prices, 
renewable energy investments take place earlier in the German than the Spanish region. Under future system 
scenarios  with  high  shares  of  renewables, local  generation  might  not  always  result  in  carbon  offsets  when 
natural gas-fuelled CHP technologies are installed and compared to importing energy from the electricity grid.  

We  observed  that  using  a  Peak  power  tariff  encourages  investments  in  renewable  sources  that  match 
demand curves (for instance, solar photovoltaics in the German Rural town) even when batteries are installed. 
This tariff also encourages self-consumption and disincentives grid electricity purchasing for battery charging 
to  be  resold  at  later  times.  The  TOU  tariff  is  the  most  sensible  to  price  curve  selection,  resulting  in 
significantly larger energy storage investment when wide price spreads are present (German Rural town and 
Urban district).  

Regardless  of  the  region  or  archetype,  the  No  Charges  scenario  results  in  the  largest  economic  value  for 
most scenarios, while the Bandwidth model tends to result in the lowest. Despite these opposite trends, both 
tariffs  result  in  similar  investment  decisions.  In  the  Bandwidth  scenario,  Energy  communities  operate  their 
assets  looking  to  avoid  penalizations  as  much  as  possible,  except  when  there  is  a  significant  amount  of 
surplus energy during high-cost periods or opportunities to perform energy arbitrage in contexts in which wide 
price  spreads  are  present.  We  observed  this  in  the  German  Rural  town  and  Urban  district,  and  the  Spanish 
Industrial polygon but to a minimum extent. 

We studied the impact of different energy prices, namely dynamic (baseline), flat and PPA under a TOU 
structure for four archetypes (all except Business park) as a sensitivity analysis. For Flat rate prices, storage 
investments are reduced as low as zero for the  Industrial polygon and Virtual community storage assets to 
the selected price curve, highlighting the high risk level and price exposure of these assets, which might not 
be  assumed  by  real  Energy  communities  despite  the  potential  high  revenues  calculated  by  the  investment 
model. For the PPA fixed price, investments are reduced for the Industrial polygon, the only case in which it is 
considered, but not as significantly as with the Flat rate. This as the PPA price results in lower purchase prices 
for 2040 than the Flat rate, providing a larger margin with the high selling prices registered at the end of the 
period.  An  additional  sensitivity  analysis  of  different  discount  rates  is  done  for  the  German  base  cases, 
considering larger WACC. A higher discount rate slightly reduces the investments in energy assets as revenues 
are reduced considering the present value of future cash flows. 

Regardless  of  the  tariff  or  archetype,  self-consumption  represents  the  largest  economic  benefit  in 
2025  and  2030  for  all  scenarios  modelled,  although  electricity  sales  take  place  in  all  cases.  The  latter 
meaning  that  with  the  assumed  energy  prices,  surplus  energy  sales  result  in  an  economically  attractive 
activity up to different levels. In 2040 when peak prices rise considerably but off-peak are actually cheaper, 
electricity  sales  become  a  more  significant  revenue  source  for  all  communities.  At  the  end  of  the 
evaluation period, energy arbitrage activities also tend to become more relevant, which is why batteries show 
a higher usage at the later years. 

Related and future JRC work 

The  present  study  adds  a  technical  perspective  to  previous  reports  commissioned  by  JRC  regarding  Energy 
communities  in  Europe.  It  also  benefits  from  previous  research  conducted  by  the  institute  regarding  the 
modelling  of  the  European  power  system  and  whose  outcomes  are  used  in  MODECO  to  model  future 
electricity prices. Although the findings in this work contribute to better understanding the impact of different 
tariff  structures  on  future  Energy  communities’  investment  and  operational  decisions,  it  also  opens  new 
questions  to  be  answered  by  future  research,  which  will  require  rethinking  some  features  of  the  proposed 
operational and investment models. 

Quick guide 

In this document, we discuss the key assumptions used to simulate the Energy community archetypes, build 
the community investment and operational models and design the tariff scenarios. A extended description of 
the  obtained  results  upon  which  we  based  our  conclusions  is  also  presented.  We  also  include  a  brief 
description  of  the  models  while  the  complete  mathematical  formulation  can  be  found  in  Annexes  so  other 
modellers can build on them for further analysis.  

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1 

Introduction 

As  part  of  its  climate  change  mitigation  strategy,  the  European  Union  (EU)  has  pledged  to  raise  its  2030 
Greenhouse Gas (GHG) emissions reduction target to at least 55% compared to 1990 levels. To achieve this 
goal,  the  European  Commission  has  set  specific  targets  for  the  energy  sector  as  it  is  responsible  for  more 
than 75% of the EU’s GHG emissions. Among the most important are the binding target of reaching at least 
32% of renewable energy in the EU’s gross final energy consumption by 2030, which might be increased up 
to 40% to help in achieving the overall GHG emissions reduction goal (European Commission, n.d.-c).  

Europe’s climate goals are expected to unlock important investments in renewable energy assets at different 
levels.  To  ensure  European  citizens  are  an  active  part  of  this  transition,  the  climate  and  energy  framework 
contemplates specific figures to promote their participation in the energy markets, for instance, individual and 
collective  self-consumption,  or  Energy  communities.  The  “Energy  community”  figure  was  first  introduced  in 
European  legislation  through  the  Clean  Energy  for  all  Europeans  Package,  where  the  concepts  of  “Citizen 
energy  communities”  and  “Renewable  energy  communities”  were  defined  (European  Commission,  n.d.-a). 
These figures show a series of commonalities, as can be seen from the definitions shown in the table below, 
but  also  key  differences  such  as  the  geographical  and  technological  constraints  applicable  to  Renewable 
energy communities. 

Table 1. Definition of Renewable and Citizen energy community in the European legislation 

Article 2(16) Recast Renewable Energy 
Directive 

Article 2(11) Recast Electricity Market 
Directive 

“Renewable energy community” 

“Citizen energy community” 

A legal entity: 

A legal entity that: 

(a) which, in accordance with the applicable national 
law, is based on open and voluntary participation, is 
autonomous,  and 
is  effectively  controlled  by 
shareholders  or  members  that  are  located  in  the 
proximity  of  the  renewable  energy  projects  that  are 
owned and developed by that legal entity; 

(b)  the  shareholders  or  members  of  which  are 
natural  persons,  Small  and  medium  enterprises  or 
local authorities, including municipalities; 

(c)  the  primary  purpose  of  which  is  to  provide 
environmental,  economic  or  social  community 
benefits  for  its  shareholders  or  members  or  for  the 
local  areas  where  it  operates,  rather  than  financial 
profits. 

The  directive  further  states  that  Renewable  energy 
communities  shall  be  entitled  to  produce,  consume, 
store  and  sell  renewable  energy,  including  through 
renewables power purchase agreements. 

Source: Obtained from (Frieden et al., 2020). 

(a) is based on voluntary and open participation and 
is effectively controlled by members or shareholders 
that  are  natural  persons,  local  authorities,  including 
municipalities, or small enterprises; 

(b)  has  for 
to  provide 
its  primary  purpose 
environmental,  economic  or  social  community 
benefits  to  its  members  or  shareholders  or  to  the 
local areas where it operates rather than to generate 
financial profits; and 

in  generation, 

(c)  may  engage 
including  from 
renewable sources, distribution, supply, consumption, 
aggregation,  energy  storage,  energy  efficiency 
services  or  charging  services  for  electric  vehicles  or 
provide  other  energy  services  to  its  members  or 
shareholders. 

Furthermore, the Directive on common rules for the internal electricity market (EU 2019/944) laid out a series 
of rules to enable consumers’ participation – individually or through Citizen energy community – in all energy 
markets,  either  by  generating,  consuming,  sharing  or  selling  electricity,  or  associated  services  such  as 
flexibility  products.  The  revised  Renewable  energy  directive  (2018/2001/EU)  built  on  these  precedents  by 
mandating  EU  countries  to  enable  the  participation  of  renewable  self-consumers  and  Renewable  energy 
communities in all available support schemes for larger participants (European Commission, n.d.-a). 

Among others, the policy framework for the emergence of community-based energy business models at EU 
level is set, offering new opportunities for citizens and SMEs on how to satisfy their energy needs. In fact, by 
2019, the Joint Research Centre (JRC) had already identified 3,500 renewable energy cooperatives – a type of 
Energy communities – in 9 European member states, most of which were located in Germany and Denmark, 

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two  countries  with  strong  traditions  of  community  ownership  and  social  enterprises.  The  most  common 
activity performed by these communities is energy generation, although electricity supply, energy efficiency, 
distribution, electro mobility, consumption and sharing, flexibility and storage, and financial services are also 
provided.  Among  a  sample  of  European  Energy  communities  studied  by  JRC,  solar  is  found  to  be  the  most 
widespread  energy  source  (38%),  followed  by  wind  (19%),  biomass  (17%),  biogas  (15%),  and  hydro  (4%). 
Examples of Energy communities included Photovoltaic (PV) solar energy systems installed in school buildings 
or  farm  rooftops;  small  biomass  installations,  heat  pumps,  solar  thermal  and  district  heating  networks  for 
communities in colder climates; or community-owned wind farms (Caramizaru and Uihlein, 2019). 

More recently, European policies favouring citizen-driven energy projects have already prompted an important 
number  of  pilots  to  test  innovative  business  models  and  investment  schemes  for  Energy  communities  in 
different  contexts  and  member  states.  Some  examples  are  the  LIGHTNESS  Project  that  promotes  the 
formation of Citizen energy communities in seven pilot sites spread among five countries  (Project Lightness, 
n.d.);  the  DECIDE  initiative  that  works  towards  the  implementation  of  seven  Energy  communities’  pilots 
providing different energy services in seven European member states (DECIDE Project, 2020); and the COME 
RES Project that focuses on advancing Renewable energy communities by supporting the installation of pilots 
with community PV, on-shore wind, storage and integrated energy solutions in nine European countries (COME 
RES Project, 2020). In the  future, a further growth in  Energy  communities’ initiatives can be expected given 
that  the  potential  for  citizens’  energy  participation  is  very  large  with  projections  suggesting  that  prosumer 
citizens could produce twice as much power as nuclear power stations produce now, accounting for 1558 TWh 
(≈ 77.90B€), see  below. 

Figure 1. Power production and services by energy citizens per member state expected in 2050 

Source: (Arybilia et al., 2018) 

Under  this  context,  Energy  Communities  present  a  tremendous  opportunity  to  simultaneously  accomplish 
several important objectives including: i) increasing renewable energy penetration, ii) energy savings, iii) self-
consumption of locally generated energy, iv) citizen empowerment and participation, v) tackle energy poverty, 
vi) ensuring energy security, vii) local economy benefits, viii) job creation, ix) environmental awareness, and x) 
education of future generations; these co-benefits ultimately support decarbonisation of different sectors of 
the economy needed to achieve the ambitious EU targets mentioned above. There are several kinds of Energy 
communities  including  residential,  industrial,  tertiary,  island  (both  geographical  and  energy  islands)  with 

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specific needs and challenges. Importantly, users can contribute to a usable implementation of solutions for 
local energy trading.  

Considering the novelty and complexities of these participating structures, it is important to assess the impact 
of  a  variety  of  factors  on  the  operational  and  investment  decisions  of  the  energy  communities  that  will 
therefore  influence  their  further  deployment  and  penetration.  This  varies  depending  on,  for  instance,  the 
typology  of  the  energy  community,  the  geographic  location  (e.g.,  weather  and  legislative  framework)  and 
trends for several factors including technology performance, costs penetration and energy prices. One major 
element is the legislative and regulatory framework, including energy taxes, tariffs and levies on the energy 
generated and used.  

However,  a  lack  of  tools  analysing  the  viability  of  Energy  community-led  investments  under  different 
economic conditions is identified, particularly under the perspective of policy makers that want to assess the 
potential  impact  that  energy  regulatory  decisions  might  have  on  these  new  market  participants.  The 
MODelling study on the role of Energy COmmunities in the energy transition (MODECO) aims to help closing 
this gap by developing a set of simulation and optimization tools to analyse long-term investment decisions 
at  the  community  level  within  an  energy  transition  context  and  under  different  economic  scenarios.  In 
particular,  the  project  looks  to  shed  some  light  on  the  effect  that  different  energy  pricing,  tariff  and  taxes 
structures  would  have  on  the  investment  decisions  made  by  Energy  communities  under  different  local  and 
regional contexts. 

1.1 

 Objectives 

MODECO’s objective is to analyse how investment and operational decisions within Energy communities are 
affected  by  the  usage  of  different  energy  pricing,  Use-of-Network  tariff  and  tax  designs  during  a  16-year 
period (2025-2040). The considered options for each case are the following: 

—  Pricing structures: Dynamic pricing (based on wholesale market), Power-Purchase-Agreement (PPA) and 

Flat rate. 

—  Use-of-Network charges: Time-of-Use (TOU), Bandwidth subscription model; and Peak power-based. In 
all cases in which Use-of-Network charges are applied, taxes on electricity are also added based on the 
current fiscal structure used in each analysed location. 

—  No  Charges:  As  a  comparison  point,  a  scenario  without  any  charges  or  taxes  is  also  tested  in  the 

investment model. 

The  described  economic  conditions  are  evaluated  over  five  Energy  community  archetypes  designed 
considering  typical  configurations  across  European  projects  (Task  1).  Furthermore,  the  impact  of  different 
Weighted  Average  Cost  of  Capital  (WACC)  on  the  Energy  communities’  investment  decisions  are  tested 
through  a  sensitivity  analysis.  The  Energy  community  design  includes  delimiting  the  type  and  number  of 
members in each archetype, the expected hourly electricity and heat demand registered in each year of the 
studied period, and the energy carriers and technologies supplying this demand in the analysis starting year 
(2025).  

For each archetype, a set of potential energy investments are selected considering the available space and 
resources on a case  by  case basis. The  five selected archetypes are analysed in two countries representing 
two  different  European  regions  (South-West  and  Central-West).  As  the  communities  interact  and  are 
embedded  within  the  regional  electricity  markets, a  reference  Energy  System Evolution  Scenario  (ESES)  are 
selected  for  modelling  the  wholesale  electricity  market.  The  potential  growth  and  participation  of  Energy 
communities as a whole is also considered in the wholesale market participants. 

Afterwards, three optimization models are used to test how the Energy community archetypes would behave 
under the different economic circumstances analysed. The first consists of a Unit Commitment and Economic 
Dispatch (UCED) model representing the wholesale electricity market in each target location. The hourly prices 
obtained from this model are then used as an input to the scenarios using the Dynamic pricing structure as a 
base case, and also to calculate the Flat rates used in a sensitivity analysis. The PPA price is calculated with 
the  annual  long-term  average  unit  cost  of  energy  from  the  generation  units  included  in  the  modelled 
wholesale  markets.  The  second  model  consists  of  a  long-term  community  investment  decision  tool  that 
allows selecting the type of technologies most suitable to each Energy community archetype, as well as the 
optimal installation year. The third is an operational model allowing to see in hourly detail how the installed 
energy technologies will function in three target years: 2025, 2030 and 2040. 

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1.2  Report scope 

Modelling is a robust tool to forecast and assess the impact of different policies on the potential penetration 
of Energy Communities across a range of typologies,  configurations and scenarios. This report  presents the 
results  of  extensive  modelling  and  assessment  aimed  at  shedding  light  on  the  implications  of  different 
legislative  and  policy  frameworks  on  the  deployment  of  Energy  Community  as  a  structure  to  foster energy 
transition  while  enabling  active  participation  of  users.  For  this  purpose,  a  Unit  Commitment  and  Economic 
Dispatch  (UCED)  model  as  well  as  an  investment/expansion  model  are  created  and  used  to  model  the 
different  scenarios  considering  Heating  &  Cooling,  Transport  and  Gas  sectors.  White-box  models  populated 
with real data from previous projects and information from established sources were used, such as ENTSO-E 
(2021a)  Ten-Year  Network  Development  Plan  (TYNDP).  were  used.  For  operational  decisions,  three  target 
years were considered, while for investment/expansion a 16-year timespan was used. The models considered 
the interrelations between the wholesale system/market and the "individualistic" operational, and investment 
decisions  of  the  Energy  Communities  archetypes.  Different  types  of  electricity  contracts,  network  tariff, 
energy contracts/pricing per energy carrier were modelled to execute targeted sensitivity analysis.  

The  methodology  and  results  from  this  process  are  presented  in  this  document.  The  main  assumptions 
considered  for  the  community  archetypes  design  and  the  construction  of  the  economic  scenarios  are 
presented  in  Chapter  2,  while  Chapter  3  contains  the  specific  methodology  for  the  simulation  of  the 
communities’  electrical  and  thermal  demand.  Chapter  4  describes  the  main  features  of  three  optimization 
models developed, the inputs used, the  constraints and  outputs expected including the assumptions  for the 
different assets considered. The diagram above summarizes the correlation among the different models and 
the main inputs and outputs.  Chapter 5 describes in  detail the five Energy Community archetypes,  namely 
Urban  district,  the  Rural  town,  the  Business  Park,  the  Virtual  Community  and  the  industrial  polygon.  The 
descriptions include the types, numbers and features of the buildings as well as the energy assets  included. 
The  heat  and  electricity  demand  are  presented  for  as  the  base  case  without  local  energy  investments.  
Chapter 6 illustrates the Energy Prices scenarios, penetration of renewable energy sources, associated CO 2 
emissions, marginal prices and energy tariffs for both countries and time horizons. The results obtained from 
the  execution  of  the  investment  model  are  discussed  in  Chapter  7,  while  Chapter  8  presents  the  results 
from the Operational model. Finally, the project’ main outcomes and conclusions are summarized in Chapter 
9. 

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2  Case studies definition 

The case studies analysed within the MODECO initiative use the Energy System Evolution Scenario (ESES) as 
their  reference,  ESES  is  largely  based  on  the  Distributed  energy  scenario  from  the  well-known  TYNDP 
developed by ENTSO-E (2021a). The TYDNP 2020 edition is selected as it is the most complete recent version 
available.  In  addition  to  the  Distributed  Energy  Scenario,  two  additional  story  lines  –  National  trends  and 
Global  ambition  –  are  included  in  the  TYNDP  2020  (ENTSO-E,  2021a).  However,  the  Distributed  energy 
scenario  is  preferred  for  this  project  as  it  specifically  considers  the  active  participation  of  prosumers  and 
distributed resources in the future energy systems, which makes it more relevant for the analysis carried out 
in MODECO project, which focuses on projects driven by Energy community. The storyline given by ENTSO-E 
describing the selected scenario is presented below. 

Distributed  energy,  a  full  energy  scenario  as  well  compliant  with  the  1.5° C  target  of  the  Paris 
Agreement,  presents  a  decentralised  approach  to  the  energy  transition.  On  this  ground,  prosumers 
actively participate in a society driven by small scale decentralised solutions and circular approaches. 
Distributed energy reaches carbon neutrality by 2050 (ENTSO-E, 2021a). 

Some  relevant  differences  between  the  Distributed  Energy  and  the  National  Trends  scenario  –based  on 
current Member States National Energy and Climate Plans as well as on EU climate targets – are expected to 
impact on the energy prices obtained by MODECO’s wholesale market model and, therefore, in the investment 
and operational decisions taken by the modelled communities. One of the most critical is the high CO 2 price 
considered in the Distributed energy scenario for 2030 (53 €/ton), which almost doubles  that considered for 
the  National  trends  scenario  (28  €/ton)1  (ENTSO-E,  2021a).  The  higher  carbon  price  impacts  on  the 
technological mix considered for the target regions in 2030 and 2040, which have a higher share of low or 
non-emitting sources such as renewable energies. The specific future mix considered for each target region is 
explained in the next section. 

2.1  Selected target regions 

The  Energy  community  archetypes  developed  within  MODECO  project  are  evaluated  in  the  South-West  and 
Central-West  European  regions,  with  two  representative  countries  being  analysed,  namely  Spain  and 
Germany. As explained before, Germany is a country with a long-term tradition of community-owned projects, 
being the European member state with more Energy community initiatives in place. Spain, on the other hand, 
is a more recent player in the development of citizen-led energy projects, but has some prominent examples, 
such as the energy  cooperative Som Energia, included in  the Energy community  projects evaluated in JRC’s 
2019 report (Caramizaru and Uihlein, 2019).  

From  the  modelling  perspectives,  the  two  selected  countries  offer  an  interesting  contrast  as  their  regional 
weather  conditions  reflect  on  distinct  consumption  patterns,  which  are  expected  to  translate  into  different 
investment  choices  even  when  the  same  Energy  community  archetypes  and  tariffs  are  considered. 
Furthermore, the assumptions made by ENTSO-E in its TYNDP 2020 reflect differently on the future energy 
mix for both countries. As can be seen in  Figure 2 and Figure 3, both the German and Spanish systems will 
rely heavily on solar Photovoltaic (PV) and wind energy by 2030 and 2040. Nonetheless, the Spanish energy 
mix  englobes  substantial  fossil-fuelled  power  in  the  form  of  Combined  Cycle  Gas  Turbines  (CCGT)  even  by 
2040 whereas the German  system will  have a lower  share of traditional technologies  in comparison to the 
total power installed as it will phase out not only nuclear but most of its fossil fuels-driven technologies with 
the exception of CCGT. 

1 By the end of 2021, the average price for future carbon credits in the European Union Emission Trading System  – known as European 
Union Allowances (EUA) -  was 52 euros per tonne (Qin et al., 2021). Analysts estimate that carbon credits will reach average prices of 
85.22 euros per tonne in 2022 and 94.23 euros per tonne in 2023 (Twidale, 2022), which are significantly higher than the carbon price 
defined in the Distributed energy scenario, despite considering more aggressive prices than in the base case. 

12 

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Figure 2. Installed power by technology in Germany in 2025, 2030 and 2030 for selected reference scenario  

CCGT:  Combined  Cycle  Gas  Turbines;  FCEL:  Fuel  Cell;  GAST:  Gas  Turbines;  HDAM:  Hydro-reservoirs;  HPHR:  Open-loop  hydro  pumped 
storage;  HPHS:  Closed-loop  hydro  pumped  storage;  HRDT:  Hard  coal-fuelled  generators;  HROR:  Hydro  Run-of-River;  LIGT:  Lignite-fuelled 
generators,  OCGT:  Open  Cycle  Gas  Turbines;  OILT:  Oil-fuelled  generators;  ORES:  Other  Renewables;  OTHT:  Other  non-renewables 
(combined heat and power); PHOT: solar photovoltaics; WTOF: wind offshore; WTON: wind onshore; BATS: batteries. 

Source: Own elaboration with data from (ENTSO-E, 2021b). 

Figure 3. Installed power by technology in Spain in 2025, 2030 and 2030 for selected reference scenario  

BATS:  batteries;  CCGT:  Combined Cycle  Gas  Turbines;  CSPP: Concentrated Solar  Power;  HDAM:  Hydro-reservoirs;  HPHR: Open-loop  hydro 
pumped storage; HPHS: Closed-loop hydro pumped storage; HRDT: Hard coal-fuelled generators; HROR: Hydro Run-of-River; LIGT: Lignite-
fuelled  generators,  NUC:  Nuclear;  ORES:  Other  Renewables;  OTHT:  Other  non-renewables  (combined  heat  and  power);  PHOT:  solar 
photovoltaics; WTON: wind onshore. 

Source: Own elaboration with data from (ENTSO-E, 2021b). 

2.1.1  Climatic differences 

Hourly  geographically  aggregated  weather  data  published  by  the  Open  Power  System  Data  (Open  Power 
System Data, 2020) is preferred for the local temperature at the Energy community case studies representing 
both  target  regions.  This  dataset  is  mostly  used  for  national-level  simulations  to  represent  the  population-
weighted  mean  weather  within  a  given  country,  but  it  is  used  in  this  case  to  represent  a  random  location 
within the target regions. The provided values are aggregated by Renewables.ninja using the NASA MERRA-2 
reanalysis as explained by the dataset authors (Open Power System Data, 2020). Hourly temperature values 
from the year 2007 are used for the base year calculations explained in this report. 

As  can  be  seen  in  the  figure  below,  the  reported  mean  monthly  air  temperatures  for  Spain  (Mean_ES)  are 
higher than those registered in Germany (Mean_DE) throughout the year; which indicates that the weather in 
Spain is significantly warmer than in the German case. The regions’ temperatures get closer during the first 
transition  season  in  April  and  May,  when  the  German  values  rise  considerably,  even  reaching  maximum 
temperatures  (Max_DE)  similar  to  Spain  (Max_ES),  while  the  mean  values  grow  apart  during  the  second 

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transition  season  as  the  minimum  values  registered  in  Germany  (Min_DE)  during  Autumn  get  considerably 
lower after the summer whereas in Spain the temperature drop takes place in winter.  

Figure 4. Monthly mean, maximum and minimum air temperature values registered in each target region 

Mean_DE:  Mean  hourly  temperature  registered  per  month  in  Germany;  Min_:  Minimum  hourly  temperature  registered  per  month  in 
Germany;  Max_DE:  Maximum  hourly  temperature registered  per  month  in  Germany; Mean_ES:  Mean  hourly  temperature  registered per 
month in Spain; Min_ES: Minimum hourly temperature registered per month in Spain; Max_ES: Maximum hourly temperature registered 
per month in Spain. 

Source: Own elaboration with 2007 data from (Open Power System Data, 2020). 

Looking  at  the  mean  hourly  temperature  registered  each  season  (Figure  5),  it  is  notable  that  mean  hourly 
temperatures  in  the  German  case  rarely  exceed  22ºC,  even  in  the  summer,  whereas  in  Spain,  22ºC  are 
registered most hours of the day in the summer season, reaching values above 25ºC around midday. On the 
contrary, winter mean temperatures in Germany are below 5ºC for all hours in winter, while in Spain, all hours 
registered  temperatures  above  this  same  value.  The  observed  differences  will  impact  the  Cooling  Degree 
Days (CDD) considered for each case and, thus, the electricity demand for space cooling purposes. Similarly, 
the colder temperatures registered in the German winter season will influence the heat demand calculated for 
the  Energy  community  archetypes  located  in  this  region,  which  is  significantly  higher  than  in  Spain  that 
experiences  more  temperate  winters.  The  summer,  winter  and  transition  seasons  shown  in  Figure  5  are 
defined  in  accordance  with  the  selected  methodology  for  electricity  load  modelling  as  will  be  explained  in 
Chapter 3. 

The differences in the solar irradiation and wind speed resources presented in each region are also observable 
through  the  load  factor  curves  for  each  technology  that  are  used  in  MODECO  to  model  solar  PV  and  wind 
speed  generation.  These  curves  are  part  of  the  European  Resource  Adequacy  Assessment  (ERAA)  2021 
Climatic Database (ENTSO-E, 2022) and are used in the selected ESES reference model to simulate solar and 
wind  generation  in  each  European  country.  As  seen  in  Figure  6,  solar  resources  are  considerably  higher  in 
Spain  than  in  Germany,  particularly  during  the  winter  season  when  it  is  cold  but  with  clear  skies  in  the 
southern country.  

Onshore wind (Figure 7), on the other hand, shows different trends depending on the season. In winter, wind 
speeds are considerably higher in Germany than Spain as indicated by the load factor curves. However, in the 
summer and transition periods, wind resources are more favourable in Spain, especially in the evening hours 
when values increase considerably, which is not the case of the German region, where the load factor curve 
has  less  pronounced  peaks  across  all  seasons.  It  must  be  noted  that  offshore  wind  is  not  considered  an 
available  technology  within  MODECO’s  Energy  community  case  studies,  meaning  it  is  not  included  in  the 
options  available  at  the  communities’  investment  portfolios.  Nonetheless,  offshore  wind  is  relevant  in 
Germany’s future energy mix as observed in  Figure 2 and will impact on its wholesale market prices, which 
will serve as an economic signal for the defined energy communities in this location. 

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Figure 5. Mean air temperature per hour registered each season in the analysed regions 

Source: Own elaboration with 2007 data from (Open Power System Data, 2020). 

Figure 6. Mean solar load factor per hour registered each season in the analysed regions 

Source: Own elaboration with data from (EERA, 2022). Data corresponds to TYNDP market nodes DE07 and ES06.  

Figure 7. Mean wind load factor per hour registered each season in the analysed regions 

Source: Own elaboration with data from (ENTSO-E, 2022). Data corresponds to TYNDP market nodes DE07 and ES06.  

2.1.2  Regionalized cost of capital 

In addition to the climatic and energy system difference, different Weighted Average Cost of Capital (WACC) 
are assumed for the target  regions based on the findings of a recent study on  renewable energy  financing 
conditions  in  Europe  (Roth  et  al., 2021).  This  document  draws  conclusions  from a  series of  surveys and  in-
depth  interviews  with  renewable  energy  project  developers,  bankers,  financial  experts  and  other  key 
stakeholders  in  the  renewable  energy  financing  sector.  In  general  terms,  the  report  found  that  there  are 
significant  differences  in  the  WACC  reported  in  European  member  states,  although  an  overall  reduction  in 

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reported WACC has been observed at the EU level in comparison with previous years  (Roth et al., 2021). This 
does not consider the recent significant increase in material costs resulting from the increase of energy prices 
and geopolitical instability from certain regions suppliers of important raw materials.   

Regarding  the  two  target  countries,  the  report  found  that  Germany  is  one  of  the  European  markets  with 
lowest  reported  WACC  while  Spain  has  an  average  WACC  within  Europe.  However,  Spain  is  one  of  the 
countries  with  a  higher  spread  between  minimum  and  maximum  WACC  values,  whereas  Germany  has  the 
narrowest gap. The report associates this trend to the wider range of investors present in the Spanish market, 
which are characterised by different return expectations (Roth et al., 2021). 

From the technologies of interest to  MODECO, only PV solar and onshore  wind are included in this analysis 
(wind offshore  is not  considered  in  any  of  the  investment  options  for  the  Energy  community  case  studies). 
However,  the  findings  can  be  extrapolated  to  other  technologies  as  the  WACC  varies  little  from  the 
technological  perspective  and  is  mostly  dependent  on  location.  This is explained  by  the  study’  findings  that 
show  that  country  risk  is  the  main  driver  of  WACC,  although  experience  with  renewables  is  also 
significant (experiences of a country with deployment of renewables tend to reduce cost of capital)  (Roth et 
al., 2021). 

In MODECO, the minimum WACC values reported for wind onshore for Spain and Germany in the AURES 2021 
study (Roth et al., 2021), which can be seen in the following table, are used as the default discount rate for 
the investment model. The presented values are the same reported for PV solar in Spain, and that no data for 
solar  is  available  for  Germany.  However,  the  same  values  are  assumed  for  all  technologies  as  data  from 
countries  reporting  values  for  both,  PV  solar  and  onshore  wind,  show  strong  similarities  between  both 
technologies. This might be explained by the reliance on balance sheet financing and the investment portfolio 
diversification approach taken by some market players, which benefit from applying a more general WACC to 
different  technologies  (Roth  et  al., 2021).  To  test  the  effect  of  using  a  different  discount  rate,  a  sensitivity 
analysis is run on the German archetypes considering the maximum WACC value instead of the base case. 

Table 2.  Minimum and maximum WACC values considered for each target region 

Country 

Minimum WACC 

Maximum WACC 

Germany 

Spain 

1.3% 

3.0% 

2.5% 

9.0% 

Source: Own elaboration with data from (Roth et al., 2021). 

2.2  Definition of Energy community archetypes 

As  mentioned  before,  five  Energy  community  archetypes  are  designed  as  part  of  the  MODECO  initiative, 
looking to replicate typical contexts found in European communities: Urban district, Rural town, Business 
park, Industrial polygon and Virtual community. All of the proposed Energy community archetypes can be 
considered  Citizen  energy  communities  within  the  European  legislation  framework,  as  gas-fuelled  is 
considered a potential investment.  

For those archetypes where geographical proximity is a constraint, it is assumed that all members inside the 
community  are  neighbours  and  interconnected  through  a  shared  electrical  network  (public  or  private), 
theoretically  considering  only  one  interconnection  point  with  the  external  energy  market  (Figure  8).  In  this 
way, only the net electricity injected and consumed through this point is considered in the calculations of the 
obtained  revenues  for  excess  energy  sold,  the  energy  purchasing  expenses  and  the  avoided  costs  by 
community thanks to self-consumption.  

Although  in  reality  peer-to-peer  trading  or  differentiated  internal  energy  prices  could  take  place  among 
energy  community  members,  these  possibilities  are  not  assessed  in  this  work  as  it  is  assumed  that  under 
perfect market conditions the overall welfare gained by the community remains the same regardless of how 
this is distributed among members, thus, it is considered that the community acts as a single economic entity. 
A similar assumption is made for gas, considering that the community buys all gas from a bulk provider to be 
later distributed among its  members at a fixed  price.  This is relevant in those  cases  where  heat-and-power 
investments are considered. 

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Figure 8. Community-energy market interaction considered for all archetypes except the Virtual community 

Source: Own elaboration. 

In  the  scenarios  in  which  Use-of-Network  tariffs  are  considered,  the  Portuguese  regulation  for  self-
consumption (Regulamento do Autoconsumo nº. 8/2021, RAC 8/2021) is used as inspiration to define the rules 
applicable within the MODECO analysis (ERSE, 2021). Under the Portuguese regulation, Use-of-Network tariffs 
applicable to self-consumption through the public network result from the Use-of-Network tariffs applicable 
to  consumption  deducted  from  the  tariffs  applied  to  the  voltage  levels  upstream  of  the  generation 
interconnection voltage. In the occurrence of reverse flows upstream to the generation interconnection level, 
these are not computed in the Use-of-Network tariffs. Finally, in cases where the generation is interconnected 
at  a  voltage  level  downstream  of  the  load  voltage  level  connection,  the  tariffs  applicable  to  the  self-
consumed  energy  correspond  to  those  applicable  to  the  case  where  both  are  at  the  same  voltage,  with  no 
reverse flows between voltage levels. The applicable rules from RAC 8/2021 are summarised in Table 3. 

In the Urban district, Rural town and Business park archetypes, Case 1 applies as  all non-industrial loads 
are  assumed  to  be  in  the  low  voltage  network  and  within  the  same  neighbourhood.  For the  Industrial 
polygon,  Case  2  (Table  3)  is  used  as  industrial  users  are  assumed  to  be  connected  at  the  medium 
voltage level. In all these cases, generation assets can only be connected at the same voltage level as the 
loads due to the assumed geographical vicinity constraints. The Virtual community is the only case in which 
the  geographical  limits  are  relaxed  as  it  is  assumed  that  members  and  generator  assets  inside  this 
archetype  are  not  necessarily  neighbours.  In  this  archetype,  it  is  assumed  that  full  Use-of-Network 
tariffs are applicable to all energy produced and consumed by the community. 

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Table 3.  Summary of the rules applied to self-consumption under the Portuguese normative 

Scheme 

Use-of-Network charges applicable 
to self-consumption 

Case 1. Load and generation at the same level – LV 

Case 2. Load and generation at the same level – MV 

Case 3. Load and generation at different voltage levels  – upstream 
generation 

Case  4.  Load  and  generation  at  different  voltage 
downstream generation 

levels  – 

Load network access charges– network 
usage (MV) – network usage (HV) 

Load network access charges –network 
usage (HV) 

Load network access charges –network 
usage (HV) 

Load network access charges– network 
usage (MV) – network usage (HV) 

*LV = Low Voltage, MV = Medium Voltage, HV = High Voltage 
Source: Own elaboration based on RAC 8/2021 (ERSE, 2021). 

2.2.1  Number and type of members 

The  number  and  type  of  members  considered  inside  each  archetype  is  defined  based  on  existing  European 
Energy  community  initiatives  and  the  archetype’s  intrinsic  characteristics;  for  instance,  it  is  assumed  that 
households  in  the  Urban  district  archetype  are  all  located  in  Multi-family  buildings.  Four  general  dwelling 
types  are  considered  within  the  archetypes  design:  Multi-family  buildings,  Single-family  buildings,  Non-
residential  buildings,  Mixed  buildings  and  Industrial  buildings.  Non-residential  buildings  englobe  commercial 
and  public  dwellings,  and  Mixed  buildings  refer  to  mostly  residential  dwellings  in  which  the  first  floor  is 
dedicated to commercial activities. The exact number of households and businesses per building is indicated 
as part of the Energy community case studies definition and will be described in Chapter 4. 

It must be noted that the number and type of buildings considered for each Energy community archetype is 
the  same  regardless  of  the  region  considered.  Nonetheless,  different  energy  consumption  patterns  are 
observed for the same Energy community archetype due to regional differences driven by climatic conditions. 
In particular, energy demand for space heating and cooling is highly dependent on the outdoor temperature 
registered,  which  highlights  the  importance  of  the  temperature  data  selection  in  the  final  results  obtained 
from  the  case  studies  simulation.  The  applicable  building  types  per  Energy  community  archetype  are 
summarized in Table 4. 

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Table 4.  Number and type of building in each archetype for year 2025 

Archetype 

Business park 

Industrial polygon 

Rural town 

Urban district 

Virtual community 

Type of buildings* 

MFB 

SFB 

NRB 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

MB 

✓ 

✓ 

✓ 

✓ 

IB 

✓ 

*MFB = Multi-family building, SFB = Single-family building, NRB = Non-residential building, MB = Mixed building, IB = Industrial building. 
Source: Own elaboration. 

2.2.2  Energy carriers 

Different energy carriers are considered for each Energy community archetype. Electricity, natural gas and 
heat are present in all communities. However, biomass is only considered for the Rural town archetype, and 
green  hydrogen  is  assumed  to  be  available  only  for  industrial  users.  The  electricity  price  assumed  by  the 
energy communities are defined based on the economic scenarios described in Section 2.3. Prices for natural 
gas, biomass and green hydrogen are defined using different sources.  

For  natural  gas,  two  different  prices  are  considered:  a  retail  price  for  the  Energy  communities,  and  a 
wholesale price for the gas-driven generators  considered in the  wholesale energy market module. The 
natural gas price for the Energy communities is assumed to vary on a daily basis following the behaviour 
of the price index reported for the Iberian market (MIBGAS-ES index) in 2019 (Mercado Ibérico del Gas, 2020). 
The  daily  price  vector  is  adjusted  per  user  using  the  bi-annual  values  reported  for  residential  and  non-
residential  consumers  in  Germany  and  Spain  in  Eurostat  database  (Eurostat,  2022).  Finally,  the  yearly 
variation in the natural gas price is defined based on the annual gas prices considered in the reference ESES 
and representing the wholesale price. The retail price vectors are available at the associated database. 

The  biomass  prices  are  assumed  to  be  mostly  stable  throughout  the  year,  so  only  yearly  updates  are 
assumed.  These  are  defined  based  on  the  projections  made  by  the  Heat  Roadmap  Europe  (HRE4,  n.d.) 
initiative  for  2030  and  2050  (Duić  et  al.,  2017).  Pricing  regional  differences  are  considered,  assuming  that 
biomass prices in Spain are similar to those reported for Greece as no specific information is provided for this 
country. The projected values for MODECO cases are summarised in the following table. 

Table 5 Biomass prices considered for Germany and Spain in the target years [EUR/MWh] 

Biomass type 

Country 

2025 

2030 

2040 

Woodchips 

Pellets 

Germany 

29.65 

30.90 

33.71 

Spain 

26.20 

27.31 

29.79 

Germany 

36.35 

34.23 

38.49 

Spain 

36.37 

38.74 

38.26 

Source: Own elaboration with data from (Duić et al., 2017). 

Future green hydrogen prices are dependent on the future costs of electricity and electrolysers, as well as the 
efficiency levels and the operating lifetime reached by the latter. The cost component with the largest impact 
on green hydrogen’s production cost is the cost of renewable electricity used to power the electrolyser unit, 
while  the  second  is  the  electrolyser’s  investment  cost.  The  International  Renewable  Energy  Agency  (IRENA, 

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2020)  projects  that  by  2040  green  hydrogen  could  cost2  between  25.08  €/MWh3  and  75.26 
€/MWh4assuming electricity prices of 21.4 €/MWh and 69.6 €/MWh, respectively. Similarly, the International 
Energy  Agency (IEA, 2020) estimates that by 2050, green  hydrogen  could  cost5 between 27.17  €/MWh and 
68.96 €/MWh, under electricity prices of 20 €/MWh and 60 €/MWh. 

An analysis performed by the International Council on Clean Transportation (ICCT) for the cost of renewable 
hydrogen towards 2050 estimates future hydrogen production costs by using a discounted cash flow model 
and three common technologies: Alkaline, Proton Exchange Membrane (PEM) and solid oxide electrolyser. The 
electrolyser  system is assumed  to  be  connected  to  the  grid  and  consume  energy  from  a  renewable  energy 
producer  under  a  PPA  agreement.  The  production  cost  is  calculated  per  country  considering  different 
renewable electricity prices based on projected Levelized Costs of Electricity (LCOE) for wind power generation 
in  2030  and  2050  (Zhou  and  Searle,  2022).  The  resulting  hydrogen  prices  for  2025,  2030  and  2040  are 
shown in Table 6 for Germany and Spain.  

Table 6 Green hydrogen prices for Germany and Spain in the target years [EUR/MWh] 

Original prices 

Country 

2025 

2030 

2040 

Germany 

29.65 

30.90 

33.71 

Spain 

26.20 

27.31 

29.79 

Source: Own elaboration with data from (Zhou and Searle, 2022). 

The original prices obtained by the ICCT study (Zhou and Searle, 2022) are close to those projected by IRENA 
(25.08 €/MWh) and IEA (27.17 €/MWh) under optimistic electricity pricing conditions (20-22 €/MWh). From the 
cost assumptions used in MODECO (see Annex database) the LCOE for wind power in 2025 is 25.53 €/MWh 
and 31.33 €/MWh for high and low capacity turbines in Germany; while for Spain is 24.94 €/MWh and 30.93 
€/MWh, respectively. The LCOE from low-capacity turbines are within the optimistic price scenarios from IEA 
(2020) and IRENA (2020), which result in similar hydrogen prices to those projected by the ICCT. In 2030 and 
2040  the  costs  from  this  technology  decreases  for  both  technologies,  which  would  result  in  a  downwards 
trend  for  hydrogen  prices  instead  of  the  rising  trend  proposed  by  ICCT.  Moreover,  within  MODECO 
assumptions, solar energy is expected to become a key technology for both regions (Figure 2 and Figure 3), 
which  would  indicate  that  a  mix  of  solar  and  wind  energy  costs  must  be  taken  into  account  into  the 
calculation of future hydrogen prices instead of just wind as in the ICTT methodology. Still, the prices shown in 
Table 6 are considered to be a fair assumption, although in future analysis more robust approaches would be 
recommended. 

2.2.3  Available investment options 

The potential investment options shown in Table 7 differ per Energy community archetype based on available 
resources  and  available  land  space.  Only  investments  in  renewable  energy  assets  and  Combined  Heat  and 
Power (CHP) are considered. For some of the technological categories, some sub-categories are defined. The 
Capital (CAPEX) and Operational (OPEX) expenses associated to wind, solar photovoltaic (PV) and batteries are 
taken  from  the  cost  projections  for  low-carbon  and  storage  technologies  made  by  the  European  Joint 
Research  Centre  (JRC)  (Tsiropoulos  et  al.,  2018b)  and  the  costs  for  thermal  technologies  are  based  on 
projections  made  by  the  HRE4  (n.d.)  project.  Non-smart  chargers  and  individual  heat  pumps  are  considered 
individual investments made according to expected adoption trends and not decided by the community as a 

2 The costs are approximately values taken from “Figure ES2. Cost of green hydrogen production as a function of electrolyser deployment, 
using an  average  (USD  65/MWh) and a  low  (USD  20/MWh) electricity  price,  constant  over the  period 2020-2050”,  available  at  (IRENA, 
2020). As in the original source these are given in USD/kg H2, values are converted using a Low Heating Value of 51.2 kWh/kg H2 and a 
currency value of 1 USD = 1.07 EUR. 
3 Electrolyser initial cost of 696 €/kW, discount rate of 8% and a stack lifetime of 80,000 hours (IRENA, 2020). 
4 Electrolyser initial cost of 1000 €/kW, discount rate of 8% and a stack lifetime of 80,000 hours (IRENA, 2020). 
5  Hydrogen  produced  from  low-carbon  electricity  sources  reported  by  (International  Energy  Agency,  2020)  is  considered  as  green 
hydrogen. To convert to desired units, the same Low Heating Value and currency value from previous calculations are used. 

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joint  investment.  The  rest  of  technologies  are  part  of  the  investment  portfolio  from  which  the  Energy 
community can invest based on their expected return under the different economic scenarios evaluated. 

Table 7 Technologies considered in each Energy community archetype as potential investment options 

Type 

Technology 

Characteristics 

Archetype 

Urban  Business  Rural 

Industrial  Virtual 

Wind Energy 

Medium  specific  capacity  (kW/m2), 
medium hub height (100m) 

High specific capacity (kW/m2), low 
hub height (50m) 

Solar 
Photovoltaics 
(PV) 

Land PV (utility scale) 

Rooftop PV flat surface 

Power 

Li-ion 
batteries 

Stationary storage system (energy-
designed, C-rate 0.25) 

Stationary  storage  system (power-
designed, C-rate 2) 

Electrolyzer 

PEM 

Non-smart 
chargers* 

V2G Smart 
chargers  

Heat & 
Power 

Small CHP 

Unidirectional EV charger 

Bidirectional EV charger 

CHP - Biomass (woodchips) 

CHP - Gas engine 

Air-to-air heat pumps 

Heat pumps* 

Air-to-water heat pumps 

Heat 

Ground sourced heat pumps 

Boilers* 

Natural gas boilers 

Others 

Hydrogen 
storage 

Hydrogen storage 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

✓ 

*Private investments decided exogenously based on assumptions and not as an outcome of the investment model. 
Source: Own elaboration. 

The proposed costs for solar PV, on-shore wind and Li-ion batteries are compared against those assumed by 
the  references  ESES  in  Table  8.  In  the  data  originally  reported  by  JRC  for  onshore  wind  and  PV  solar 
(Tsiropoulos et al., 2018b), operation and maintenance  costs are assumed as a fixed  fraction of the CAPEX 
over the entire lifetime of the technology, and the fraction is based on literature review and expert validation. 
The report does not specify whether this fraction includes both fixed and variable operation and maintenance 
costs, but it is assumed it does. The ESES documentation (ENTSO-E, 2020), on the other hand, indicates that 

21 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
the  provided  values  correspond  to  “Fixed  VOM”  or  fixed  variable  operation  and  maintenance  costs,  but  no 
further explanation of the concepts included is provided. 

Table  8  Comparison  of  CAPEX  and  OPEX  values  proposed  by  MODECO  against  ESES’  assumptions  for  available 
technologies 

Technology 

Source 

2030 

2040 

CAPEX 
[€/kWe] 

OPEX 
[€/kWe] 

CAPEX 
[€/kWe] 

OPEX 
[€/kWe] 

On-shore  wind  –  Medium 
specific capacity 
On-shore  wind 
specific capacity 

–  High 

Solar PV – Land  

Solar PV – Rooftop  

JRC 
ESES 
JRC 
ESES 
JRC 
ESES 
JRC 
ESES 
JRC* 
ESES 
JRC* 
ESES 

1,190 
1,066 
960 
1,066 
450 
439 
500 
439 
892 
500 
191 
500 

35.7 
21 
28.8 
21 
7.7 
9 
12.5 
9 
17.8 
11 
3.8 
11 

1,140 
915 
920 
915 
370 
319 
410 
319 
656 
379 
141 
379 

34.20 
21 
27.6 
21 
6.29 
8 
10.25 
8 
13.1 
10 
2.8 
10 

Li-ion batteries – energy 
designed  
Li-ion batteries – power 
designed 
*Original data was given in €/kWh, but these are converted to €/kWe using the C-rate values. OPEX are assumed to be 2% of the CAPEX as 
reported by Tsiropoulos et al. (2018a) as no data was provided in Tsiropoulos et al. (2018b). 
Source: Own elaboration with data from Tsiropoulos et al. (2018a), Tsiropoulos et al. (2018b) and ENTSO-E (2020). 

For on-shore wind, the initial investment costs considered by JRC are slightly higher than those considered in 
the reference ESES, except for the values projected by 2030 for the high specific capacity model. CAPEX costs 
are always higher when considering the JRC values for on-shore wind technologies. In the case of solar PV, 
the investment costs projected by JRC are higher for all cases than the assumptions taken in the reference 
ESES. Solar OPEX costs assumed by JRC are lower than in the ESES when considering PV installations on land 
(utility scale), but higher when considering installations over rooftops. Nonetheless, it must be noted that the 
ESES does not differentiate between systems’ arrangements, and when considering the average OPEX costs 
for both land and rooftop installations, the obtained values are closer to that reported by the ESES.  
As happens with solar PV technologies, the reference ESES does not differentiate between battery types. Thus, 
the  values  are  higher  or  lower  depending  on  the  specific  technology  considered  as  the  JRC  source  offer 
differentiated values depending on the battery type. For energy-designed storage systems, the CAPEX values 
projected by JRC are much higher than in the ESES, but for power-designed systems the opposite is true. For 
OPEX  values  a  similar  trend  is  observed  when  considering  the  actual  values,  but  in  percentage  terms,  the 
operation and maintenance costs considered by the ESES represent close to 2% of the CAPEX as proposed for 
the JRC values. 
The  higher  disaggregation  in  the  JRC  database  is  preferred  for  the  MODECO  analysis  as  it  offers  more 
possibilities for the communities’ investment portfolios, which might result in interesting insights than using 
the  general  categories  defined  in  the  reference  ESES,  which  were  thought  for  a  larger  scale  (Europe-wide). 
Moreover, it is considered that the values proposed by JRC do not divert greatly from the ESES assumptions, 
particularly considering solar and wind energy technologies. Still, the differences between both sources must 
be taken into account when analysing the results. 
The specific cost considered for each year and technology can be consulted in the associated database. 

2.3  Economic scenarios 

MODECO  evaluates  how  different  economic  conditions  affect  the  investment  and  operational  decisions  of 
Energy  communities  under  different  local  and  regional  contexts  that  influence  the  associated  costs  to 
electricity  consumption.  The  evaluated  energy  prices  scenarios  are  based  on  the  results  obtained  from  the 
wholesale  market  module  developed  as  part  of  the  project  and  whose  design  will  be  discussed  in  the  final 
report.  Nonetheless,  the  conceptualization  behind  each  energy  pricing  scenario  and  the  methodology  to 
calculate them are specified in this report at least in general terms. On the other hand, the approach to set 
the  costs  applicable  to  the  network  tariff  and  taxes  scenarios  considered  is  explained  in  this  section  in 
addition to its conceptual definition. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

22 

 
 
 
To evaluate the impact of different tariff structures on Energy communities’ investment decisions, three tariff 
scenarios (TOU, Peak Power, Bandwidth) are defined considering three different structures for Use-of-Network 
charges:  
—  Energy-based charges (TOU): Network costs are recovered through the application of a charge based 
on consumption volume. The applicable charge is different depending on the time of the day as it follows 
a Time of Use (TOU) structure.  

—  Peak-power  based  model  (Peak  Power):  Use-of-Network  costs  are  charged  to  users  based  on  their 

peak power consumption. The charge is applied on a monthly basis 

—  Bandwidth  model  (Bandwidth);  Users  pay  a  fixed  fee  for  a  symmetrical  kW-band.  The  subscription 
allows users to freely used the contracted bandwidth; this fee is set as a monthly cost paid for kW-band 
contracted.  Energy  consumed  or  injected  beyond  this  limit  are  subjected  to  a  penalization  cost  that 
depends on the excess volume and duration.  

In all of these cases,  dynamic prices changing  by the hour according to  market conditions are considered, 
and taxes are applied following the applicable rules in each region. To  serve as a comparison point, a case 
without  any  charges  and  taxes  is  also  tested  (No  Charges)  using  dynamic  prices.  A  sensitivity  test 
(TOU_Flat)  is  run  for  the  TOU  tariff  structure  considering  the  use  of  an  annual  flat  rate  instead  of  the 
dynamic prices. For the industrial polygon archetype, a variation of this case is additionally tested, considering 
that  the  community  has  a  bilateral  contract  with  a  fixed  price  established  for  the  16-year  period  analysed 
(TOU_PPA).  The  process  and  assumptions  used  to  calculate  each  of  the  tariff  components  (active  energy 
price, Use-of-Network charges and taxes) are explained in the following sections. 

2.3.1  Energy prices calculation 

—  The dynamic price represents the case in which the community buys energy directly from the wholesale 
market, and thus, the energy price obtained from MODECO’s wholesale market modules for Germany and 
Spain is directly used as input for this case. Thus, the dynamic prices used in scenarios TOU, Bandwidth 
and Peak Power, as well as the No Charges correspond to the resulting price vector from the UCED model. 
The  flat  rate  can  be  interpreted  as  a  fixed  price  contract  between  an  electricity  supplier  and  the 
community. The flat rate price used in the TOU_Flat scenario is calculated for each year and country as 
the weighted average from the marginal prices obtained.  

—  Finally, the PPA scenario represents a long-term contract, where the community acquires electricity 
from  a  power  generator  at  a  fixed  price,  which  is  calculated  based  on  a  long-term  average  cost.  This 
scenario is only applied to the Industrial polygon archetype, which is the community type where this type 
of contracts is expected to be more common. The fixed energy cost applied during the 16-year period is 
defined  considering  the  fixed  and  variable  operational  costs  from  renewable  and  efficient  gas-based 
generators6 in the wholesale market, including the annualized capital expenditure. The cost data is taken 
from the database available at the documentation from the TYNDP scenarios published in 2020 (Entso-E, 
2021),  except  for  the  investment  costs  for  solar,  wind  and  Combined  Heat  and  Power  (CHP)  that  are 
obtained  from  (Tsiropoulos  et  al.,  2018b).  As  a  result  of  this  process,  active  energy  costs  of  52.44 
EUR/MWh  and  38.35  EUR/MWh  are  obtained  for  Germany  and  Spain,  respectively.  As  this  scenario 
represents a long-term contract with a generator, the same active energy cost is applied throughout the 
16-year period.  

—  The resulting energy tariffs for each case are presented and discussed in Chapter 6.  

2.3.2  Use-of-Network charges 

As  previously  explained,  three  types  of  tariffs  based  on  existing  and  theoretical  schemes  are  tested  in 
MODECO’s  Energy  community  archetypes.  The  first  corresponds  to  the  TOU  scheme,  where  different  prices 
are set for different periods that can be determined in advance for a determined period (static Time-of-Use) 
or  determined  in  real  time  based  on  actual  system  conditions  (dynamic  Time-of-Use)  (IRENA,  2019).  
MODECO’s TOU tariff is considered static and has two different pricing periods  – peak and off-peak – which 

6  The  specific  generation  technologies  considered  for  this  calculation  are  solar  photovoltaics,  concentrated 
solar  power,  onshore  wind,  offshore  wind,  combined-cycle  gas turbines,  and  combined  heat  and power.  The 
generic unit that englobes all renewable generators in the selected ESES reference scenario is also included.  
23 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
                                                        
 
are  defined  for  each  region  based  on  the  regional  wholesale  module  parameters  (demand  and  available 
generation).  The  off-peak  hours  correspond  to  the  time  slot  with  the  less  system  constraints,  whereas  the 
peak  period  is  set  during  the  higher  congestion  hours.  The  hours’  classification  is assumed  to  be  known  by 
users in advance and will be updated every five years based on the regional system evolution.  

The  second  tariff  scenario  consists on  a  Peak  Power  scheme,  where  users  pay  a  fixed  price  based  on  the 
maximum  power  demanded  each  month  (€/kW-peak)  as  suggested  in  (Koski  et  al.,  2019).  Finally,  the 
Bandwidth  subscription  scenario  is  based  on  the  bandwidth  tariff  model  proposed  by  ENEXIS,  a  Dutch 
Distributor  System  Operator  in  (E.DSO,  2020).  Under  this  mode,  customers  subscribe  to  a  symmetrical  kW-
band and pay a fixed monthly fee for using the contracted power for both energy injections and withdrawal 
from the grid. Consumption or feed-in outside the contracted limit is possible, but an exceedance fee must be 
paid  considering  the  amount  of  power  exceeded  and  the  duration.  Thus,  the  exceedance  is  set  as  €/kWh 
above the contracted power limit. In this sense, not only the energy consumption must be known for the Peak 
Power Based and Subscription Based scenarios, but also the registered power at each time step.  

The  Use-of-Network  charges  considered  in  each  scenario  are  based  on  the  costs  associated  with  the 
distribution  and  transmission  networks  reported  for  Germany  and  Spain.  For  transmission  costs,  the  Unit 
Transmission Tariffs calculated by ENTSO-E in 2019 are used as a base cost. The defined values are  22.52 
€/MWh  for  Germany,  and  9.33  €/MWh  for  Spain  (Entso-E,  2020).  It  is  assumed  that  all  users  pay  for 
transmission  costs,  directly  or  through  their  DSO,  which  passes  the  cost  to  its  customers  via  distribution 
network fees. 

Distribution tariffs, on the other side, apply  differently to those connected to the  distribution grid in Low 
Voltage (< 1kV), Medium Voltage (1 kV-36 kV) and High Voltage (> 36 kV) level according to the ranges used 
in  (Eurelectric  Union  of  the  Electricity  Industry,  2013)  and  based  on  the  values  proposed  by  the  European 
standardisation  bodies  CEN/CENELEC.  The  total  cost  to  recover  via  distribution  tariffs  is  based  on  the  data 
reported  in  the  Study  on  tariff  design  for  distribution  systems  commissioned  by  the  European  Commission 
Directorate General for Energy in 2015  (Ref-e et al., 2015). A more updated version containing similar data 
could not be found. According to the European Agency for the Cooperation of Energy Regulators (ACER), Spain 
updated its tariff methodology for the 2020-2025 period and Germany has amended its own constantly, with 
last changes being introduced in 2019 and 2020 (ACER, 2021). Thus, the numbers used for this analysis are 
not completely up to date, but present a fair understanding of the cost associated with distribution activities 
in both countries. 

Within  MODECO,  consumers  pay  for  the  costs  corresponding  to  the  voltage  levels  used  to  supply  them 
electricity. This means that users at the low voltage level (e.g. those in the Business park, Urban district, Rural 
town  and  Virtual  community)  pay  for  the  costs  associated  to  the  low  voltage,  medium  voltage  and  high 
voltage networks, but users connected at the medium voltage level (Industrial polygon) only pay for the costs 
associated with the medium and high voltage networks. Thus, it is necessary to disaggregate the total costs 
to recover per voltage level. This is done by dividing the total allowed revenues – without transmission costs, 
taxes and levies – between the circuit length corresponding to each level and reported in (Ref-e et al., 2015). 

 Afterwards,  the  Unit  Distribution  Tariff  applicable  to  consumers  connected  at  each  level,  is  calculated  by 
dividing the disaggregated cost to recover between the total electricity flowing into that circuit, this includes 
the  energy  delivered  into  each  level  plus  the  energy  delivered  in  upstream  circuits.  This  means  that  high 
voltage costs are  divided into energy delivered at low,  medium and high  voltage, but  low voltage costs are 
only allocated among users connected to the low voltage network. As disaggregated electricity delivered data 
is not available for Germany, the same energy shares per connection point as in Spain is assumed, calculating 
the  corresponding  volume  per  voltage  level  using  the  number  of  connection  points  and  the  total  electricity 
delivered  reported  for  the  German  case.  The  final  distribution  costs  to  recover  and  the  resulting  Unit 
Distribution Tariff per country and voltage level are summarized below. 

Table 9 Regional data used to calculate the applicable Unit Distribution Tariff per voltage level 

Country 

Voltage 
level 

Connection 
Points 

Circuit 
length 
[km] 

Electricity 
delivered 
[MWh/year] 

Cost to recover 
[€/year] 

Unit 
Distribution 
Tariff 
[€/MWh] 

Germany 

HV 

3,923 

31,380 

98,380,118 

       586,251,250  

1.25 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

24 

 
 
Country 

Voltage 
level 

Connection 
Points 

Circuit 
length 
[km] 

Electricity 
delivered 
[MWh/year] 

Cost to recover 
[€/year] 

Unit 
Distribution 
Tariff 
[€/MWh] 

MV 

LV 

72,336 

280,345 

141,587,507 

    5,237,495,429  

21.83 

39,714,305 

383,202 

229,632,375 

    7,159,102,975  

31.18 

Total 

49,934,777 

694,927  469,600,000  12,982,849,654 

Spain 

HV 

MV 

LV 

2,572 

96,084 

49,127,000 

276,343,969 

105,591 

509,866 

70,703,000 

1,466,408,498 

28,592,609 

1,156,785 

114,669,000 

3,326,990,532 

-  

1.18 

12.24 

29.01 

Total 

28,700,772  1,762,735  234,499,000 

5,069,743,000 

-  

Source: Own elaboration with data from (Ref-e et al., 2015). 

Within  MODECO,  a  community  in  Germany  that  is  connected  at  the  low  voltage  level  would  pay  Use-of-
Network tariffs equivalent to the sum of the Unit Distribution Tariff (low, medium and high voltage) plus the 
Unit Transmission Tariff. This is equivalent to paying 76.77 €/MWh or 7.68 €cents/kWh, which is close to the 
7.71 €cents/kWh reported to be paid by German households in 2020 (BDEW, 2020). For Spain, the network 
tariffs for low voltage users would be 42.43 €/MWh or 4.24 €cents/kWh; this value, however, is not directly 
comparable  to  existing  prices  as  Spain  recovers  its  network  costs  through  a  combination  of  energy  and 
power-based charges (ACER, 2021). 

The values obtained through this process and shown in Table 9 are used to define the applicable charges in 
each of the network tariff scenarios evaluated in this study. The specific methodology followed in each case is 
explained in the following sections.  

2.3.2.1  Time-of-Use tariff 

As explained, TOU tariffs are energy-based charges that have different values depending on the time of the 
day.  The  peak  and  off-peak  periods  are  defined  for  2025,  2030,  2035  and  2040,  considering  five-year 
updates. For each year, the following steps are applied, differentiating between target regions: 

1.  Per  each  hour  of  the  day,  the  difference  between  demand  and  available  renewable  generation  is 

calculated, identified as “residual demand”. 

2.  The mean residual demand per hour registered during each season (i.e. winter, transition, summer) is 

calculated. 

3.  For each season, the 8 hours of the day with the largest mean values are classified as “peak” and 

the rest as “off-peak”. 

4.  The demand registered during peak and off-peak hours is added for the entire year to identify the 

total demand share associated with each period. 

5.  The  total  costs  to  recover  per  voltage  level  (Table  9)  are  divided  into  “peak  costs”  and  “off-peak 
costs”  depending  on  the  demand  share  corresponding  to  each  period  and  calculated  in  the  step 
before. The same is done to the electricity delivered per voltage level. 

6.  Finally, the costs are allocated considering the principle used in (Li et al., 2022) to define Time-of-
Use  tariffs  for  an  integrated  community  energy  system,  which  states  that  the  costs  of  satisfying 
base  demand  (“off-peak”  in  this  case)  should  be  allocated  to  both  periods  while  the  costs  of 
satisfying peak demand should be allocated to peak hours only. For instance, a consumer connected 
to  the  low  voltage  network  would  pay  the  following  distribution  tariffs  for  unit  of  consumption 
(€/MWh) during peak and off-peak hours: 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

25 

 
 
Eq. 1 Use-of-Network charges applicable to users in medium voltage networks during off-peak hours 

𝑇𝑎𝑟𝑖𝑓𝑓𝑜𝑓𝑓−𝑝𝑒𝑎𝑘 =

𝐷𝑖𝑠𝑡.  𝐶𝑜𝑠𝑡𝑠𝐿𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐿𝑉

+

𝐷𝑖𝑠𝑡. 𝐶𝑜𝑠𝑡𝑠𝑀𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝑀𝑉

+

𝐷𝑖𝑠𝑡. 𝐶𝑜𝑠𝑡𝑠𝐻𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐻𝑉

Eq. 2 Use-of-Network charges applicable to users in medium voltage networks during peak hours  

𝑇𝑎𝑟𝑖𝑓𝑓𝑝𝑒𝑎𝑘 =

𝐷𝑖𝑠𝑡.  𝐶𝑜𝑠𝑡𝑠𝐿𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐿𝑉

+

𝐷𝑖𝑠𝑡.𝐶𝑜𝑠𝑡𝑠𝑀𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝑀𝑉

+

𝐷𝑖𝑠𝑡.𝐶𝑜𝑠𝑡𝑠𝐻𝑉,𝑜𝑓𝑓−𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐻𝑉

                                 +

𝐷𝑖𝑠𝑡.𝐶𝑜𝑠𝑡𝑠𝐿𝑉,𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐿𝑉,𝑝𝑒𝑎𝑘

  +

𝐷𝑖𝑠𝑡.𝐶𝑜𝑠𝑡𝑠𝑀𝑉,𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝑀𝑉,𝑝𝑒𝑎𝑘

  +

𝐷𝑖𝑠𝑡.𝐶𝑜𝑠𝑡𝑠𝐻𝑉,𝑝𝑒𝑎𝑘
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑𝐻𝑉,𝑝𝑒𝑎𝑘

The  value  of  the  charges  applied  during  peak  and  off-peak  hours  are  the  same  through  the  year,  but  the 
hours classified as peak and off-peak vary according to the season. The resulting values from this process will 
be  discussed  in  the  final  report,  in  alignment  with  the  inputs  considered  for  the  wholesale  market  module. 
Nonetheless, the steps to  calculate the applicable  costs per period ensure that these  are differentiated and 
that Use-of-Network tariffs in peak hours are more expensive than in off-peak time slots. 

2.3.2.2  Peak power tariff 

Under this scenario, network costs are recovered through a  capacity-based charge (€/kWe) that is applied 
over the maximum power registered by each user during the billing period (assumed as one month). Thus, for 
this  case,  it  is  necessary  to  transform  the  estimated  Unit  Transmission  Tariff  and  Unit  Distribution  Tariff 
charges  into  capacity-based  values.  In  this  case,  it  is  defined  that  the  price  per  kWe  is the  same  for  users 
connected in low voltage than in  medium or high  voltage. Per each voltage level, the  applicable charge  per 
kWe  is  calculated  using  the  assigned  costs  to  recover,  the  number  of  connection  points  and  the    typical 
contractual  powers  defined  by  (Ref-e  et  al.,  2015)  for  the  following  customer  groups:  households  (6  kW), 
users  in  medium  voltage  (220  kW)  and  large  industrial  users  (400  kW).  The  first  are  assigned  to  the  low 
voltage category, the second to the medium voltage level and the last to the high voltage level. The obtained 
costs per kWe are defined below. 

Table 10 Applicable capacity-based charges per country and voltage level. 

Country 

Voltage 
level* 

Connection 
Points 

Typical contracted 
power considered 
[kW] 

Capacity-based 
charge  
[€/kW-month] 

Germany 

Spain 

HV 

MV 

LV 

HV 

MV 

LV 

3,923 

72,336 

6 kW 

220 kW 

39,714,305 

4000 kW 

2,572 

105,591 

6 kW 

220 kW 

28,592,609 

4000 kW 

*LV = Low Voltage, MV = Medium Voltage, HV = High Voltage 
Source: Own elaboration with data from (Ref-e et al., 2015) 

2.3.2.3  Bandwidth tariff 

3.11 

30.53 

33.04 

2.24 

7.50 

9.11 

The bandwidth tariff scheme consists of a fixed price per month that customers pay and allows them to inject 
and extract energy from the public network. When this limit is surpassed, a penalization fee (€/kWh) is applied 
considering  the  amount  and  duration  of  the  power  exceeded.  As  it  is  assumed  that  users  try  to  avoid 
penalization  fees,  the  applicable  charges  per  kWe  contracted  must  be  enough  to  recover  the  applicable 
network costs. Thus, the charged values are defined considering the cost to recover on a monthly basis and 
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the number of connection points at each voltage level, whereas the penalization fees are defined as equal to 
the sum of the applicable Unit Transmission Tariff and Unit Distribution Tariff. The proposed values per region 
and voltage level are defined in the table below: 

Table 11 Applicable contracted bandwidth cost and penalization fees per country and voltage level. 

Country 

Voltage 
level 

Connection 
Points 

Contracted 
bandwidth cost  
[€/kWe month] 

Penalization 
fees  

[€/kWh] 

Germany 

Spain 

HV 

MV 

LV 

HV 

MV 

LV 

3,923 

72,336 

39,714,305 

2,572 

105,591 

28,592,609 

*LV = Low Voltage, MV = Medium Voltage, HV = High Voltage 
Source: Own elaboration with data from (Ref-e et al., 2015) 

2.3.3  Taxes 

12.45 

18.49 

18.50 

8.95 

10.11 

10.12 

0.024 

0.046 

0.077 

0.011 

0.023 

0.052 

Energy taxes are considered excise taxes as these are paid by the seller but passed to the buyers as part of 
the final cost. Excise taxes come in two forms,  ad  valorem and per  unit, which will be evaluated as part of 
MODECO economic scenarios. Ad valorem taxes are levied as a percentage of the good’s value, whereas in the 
per unit option these are paid per unit of a good sold  (Lyndon et al., 2020). Two general energy taxes types 
are  considered  in  this  analysis  following  the  classification  proposed  by  the  Organization  for  Economic 
Cooperation  and  Development  (OECD,  2020)(Organisation  for  the  Economic  Cooperation  and  Development 
(OECD), 2020): 

—  Fuel excise tax: All excise taxes that are levied on fuels and that are not carbon taxes. 

—  Electricity excise tax: All excise taxes that are levied on electricity.  

In the case of fuel excise taxes, different values are defined per energy carrier according to the current taxes 
imposed on each fuel in Germany and Spain. The values considered to define the theoretical taxes are based 
on  the  OECD’s  estimations  that  are  set  in  per  unit  basis  (€/GJ)  and  are  in  turn  calculated  considering  the 
applicable  normative  in  each  country  and  the  energy  content  of  the  taxed  products,  to  have  a  comparable 
value for all energy sources (OECD, 2020). 

In Spain, the main applicable taxes on energy usage are the Tax on Hydrocarbons (per unit) that applies to 
liquid and gaseous fuels, including  bio fuels, as well as to coal tar, crude oil, waste oils and coal and coke-
related gases; the Special Tax on Coal (per unit), which applies to coal and coke products except for peat; 
and  the  Special  Tax  on  Electricity,  an  ad  valorem  tax  applied  to  electricity  consumption  by  end  users. 
Industrial cogeneration is also subjected to the latter tax (OECD, 2019b), but it is not the case for MODECO’s 
industrial communities. For Germany, only two taxes are considered, the Energy Tax (per unit) applicable to 
specific  uses  of  liquid,  gaseous  and  solid  fuels  and  biofuels  and  the  Electricity  Tax  (per  unit),  which  is 
charged to certain electricity consumption usages (OECD, 2019a). 

For all evaluated scenarios, except the No Charges case, the current situation in each country is considered. 
This  means  that  for  Spain,  per  unit  taxes  are  applied  to  fuels  while  electricity  is  taxed  via  an  ad  valorem 
charge.  In  Germany,  both,  fuels  and  electricity  are  taxed  using  per  unit  charges.  The  applicable  charges  to 
each energy carrier are defined based on the OECD tax report for 2019, where effective energy tax rates in 
€/GJ  are  calculated  for  member  countries  –  including  Germany  and  Spain  –  using  data  on  actual  taxation 
schemes and total energy consumptions per energy carrier (OECD, 2020). The applicable values used in this 

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27 

 
 
report for natural gas and electricity are listed in the table below. It must be noted that, as happened with the 
natural gas prices, taxes on this fuel are differentiated per final usage.  

Table 12 Per unit taxes applicable to energy carriers of interest according to OECD data. 

Energy carrier 

Usage 

Germany 

Spain 

Electricity 

Residential, commercial, 
industrial 

2.85 €/GJ 

1.44 €/GJ* 

Natural gas 

Residential, commercial 

1.53 €/GJ 

0.65 €/GJ 

Natural gas 

Industrial 

0.60 €/GJ 

0.30 €/GJ 

* Not used in the final scenario; substituted for an ad valorem tax of 5.11% 
Source: Own elaboration with data from OECD (2020). 

To incorporate the ad valorem tax in the Spanish case, the per unit value tax shown in Table 12 is substituted 
by a charge of 5.11% calculated on the total energy costs paid by the user, which corresponds to the actual 
tax currently in place in Spain. This is applied over the cost of energy consumed plus the power-based costs in 
the  scenarios  in  which  these  are  considered  (bandwidth  and  peak  power-based).  By  using  the  proposed  ad 
valorem tax, the annual amount of money recovered via taxes stays similar as in the per unit case (calculated 
considering the total amount of energy  consumed and the mean electricity price  charged to  residential and 
non-residential  consumers  (Eurostat,  2022)).  This was expected  as the  OECD’s  values  used  for  the  per  unit 
taxes  are  based  on  the  actual  revenues  collected  by  existing  energy  taxes  in  Germany  and  Spain  (OECD, 
2020).  

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28 

 
 
 
 
 
 
3  Modelling of Energy communities 

This  chapter  focuses  on  the  definition  and  modelling  of  the  case  studies  representing  the  defined  Energy 
community  archetypes  for  the  two  target  regions  (Germany  and  Spain).  The  methodology  to  model  the 
communities’  electricity  and  heat  demand,  accounting  for  the  weather  differences  between  the  selected 
target regions is explained in the following section. Additionally, further details are provided for the modelling 
of  Electric  Vehicles  (EV)  and  Heat  Pumps  (HP),  and  the  consideration  of  these  assets’  demand  response 
potential. The results obtained from this process are used as inputs in the operational and investment models 
developed as part of MODECO and are presented and discussed in Chapter 5, following the description of the 
optimization models in Chapter 4. 

3.1  Energy demand simulation 

In MODECO project, the electricity base load refers to the electricity demand from users related to heating 
or EV usage, as the latter are modelled separately and added to the baseload demand to get the community’s 
final electricity consumption. The purpose of having disaggregated demand for electrical heating and EV is 
to  account  for their  potential  usage  for  demand  response  services,  which  are  considered  in  the  operational 
and investment models. Due to the mathematical formulation used to represent demand response and smart 
EV  charging,  the  models  require  visibility  over  the  electrical  consumption  associated  to  these  assets  to 
perform this task. As described in the next sections, different methodologies are applied according to the type 
of user considered (residential, non-residential, and industrial). The reasons for this are the different energy-
weather  relations  and  the  lack  of  in-depth  information  for  industrial  consumers.  Similarly,  heat  demand 
refers to all the thermal energy consumed by the users for space and water heating services, independently 
of the heat source. Later, it is assumed that a part of this heat demand is served by electrical heat pumps 
while  the  rest  is  obtained  by  gas-driven  equipment.  As  happened  with  the  electricity  baseload  modelling, 
different  methodologies  are  applied  to  non-residential  and  residential  buildings,  and  to  industrial  users,  as 
information on the latter is scarce. 

3.1.1  Non-residential and residential users 

Energy demand from residential and non-residential buildings has been widely studied in the literature. Thus, 
a number of open data and detailed models are available to simulate electricity and heat demand from these 
users.  In  particular,  detailed  models  representing  different  typologies  of  residential  and  non-residential 
consumers  in  Germany  are  found  useful  to  MODECO  purposes.  Nonetheless,  as  these  models  are  built  for 
colder climates, adjustments are needed to incorporate the effect of  space cooling, which is relevant in the 
case  of  warmer  regions  such  as  Spain.  The  implementation  of  the  German  models  in  the  corresponding 
Energy community archetypes, including the proposed adjustments for the Spanish case, are explained below. 

3.1.1.1  Electrical baseload demand 

The load shape for non-residential and residential (Multi-family and Single-family) buildings are based on the 
electrical standard load profiles developed by the German Association of Energy and Water Industries7 (BDEW, 
2017) that represent different customer groups (Table 13) for which similar consumption behaviours can be 
assumed).  As  the  electrical  standard  load  profiles  were  built  based  on  consumption  data  from  German 
customers, it is assumed that electricity usage for heating and cooling is not considered, as heat demand is 
practically fully covered by fossil fuels (Entranze Project, 2008) and cooling demand is minimal as shown by 
the  European  Building  Stock  Observatory’s  data  on  energy  consumption  of  space  cooling  by  member  state 
(European Commission, n.d.-b) .   

7 In German: Bundesverband der Energie-und Wasserwirtschaft. 

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Table 13 Type of customer represented in the electrical standard load profiles developed by BDEW 

Profile 

Customer group description 

Examples 

H0 

G0 

G1 

G2 

G3 

G4 

G5 

G6 

L0 

L1 

L2 

Private households. 

Private households. 

General  purpose  industrial  profile,  defined 
as  a  weighted  mean  of  all  commercial 
customers. 

Assigned if none of the profiles G1 to G6 apply. 

Industrial  profile  for  businesses  which 
operate on weekdays from 8 to 18 o’clock. 

Offices,  workshops, 
administration facilities, doctor’s office 

kindergartens, 

public 

Industrial  profile  for  businesses  which 
operate mostly during the evening. 

Street  lights,  gas  stations,  evening  restaurants 
and 
their  peak 
facilities 
consumption is not during the weekend). 

recreational 

(if 

Industrial  profile  for  continuous,  relatively 
uniform  demand,  including  a  noticeable, 
continuous peak demand. 

Purification  plants,  drinking  water  pumps, 
communal facilities in residential complexes, cold 
storage warehouses. 

Industrial  profile  for  continuous,  relatively 
uniform  demand,  including  a  noticeable, 
continuous peak demand. 

Shops, hairdressers. 

Industrial profile for bakeries with baking in 
house  which  typically  start  operating  at  3 
o’clock during weekdays and at midnight on 
Saturdays. 

Bakeries with in-house baking facilities. 

Industrial  profile  for  businesses  with  a 
strong consumption focus during weekends. 

Youth clubs, cinemas, restaurants, petrol stations 

General purpose agricultural profile, defined 
as  a  weighted  mean  of  all  agricultural 
customers. 

Assigned 
if  the  energy  provider  does  not 
differentiate  between  agricultural  customers 
according to the profiles L1 and L2. 

Agricultural profile for dairy farms and side-
line stockbreeding businesses. 

Dairy farms, side-line stockbreeding farms 

Agricultural  profile  for  businesses  with  a 
mixture of household and farming. 

Assigned  if  neither  L1  nor  time-of-the-day-
independent industrial profiles apply. 

Source: Translated English version from the table reported by Bock (2019). 

Each of the electrical standard load profiles listed above contains 9 representative daily curves for three day 
types – weekday, Saturday, Sunday – and 3 seasons: “Winter”, “Summer” and “Transition”. As power (kW) data 
is provided using 15-minute time steps, hourly electricity consumption is calculated before building a yearly 
vector. The representative daily curves are adjusted considering that the base year starts on Monday and each 
season covers the following periods as done in the BDEW’s H0 example (BDEW, 2017): 

—  1st January to 20th March – “Winter” 

—  21st March to 14th May – “Transition” 

—  15th May to 14th September – “Summer” 

—  15th September to 31th October – “Transition” 

—  1st November to 31th December – “Winter” 

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National holidays are not taken into account in this process. 

Once  the  yearly  vector  is  formed,  the  data  is  normalized  and  multiplied  by  the  corresponding  annual 
electricity  consumption  in  kilowatt-hour.  For  Multi-family  and  Single-family  buildings,  the  annual  demand 
(Table  14)  is  based  on  the  households’  mean  electricity  demand  reported  for  Spain  and  Germany,  and 
differentiated between multifamily and Single-family units. The mean annual consumption per household in 
both countries was obtained from the Spanish Transmission System Operator (Red Eléctrica de España, n.d.), 
and  from  the  German  Federal  Statistical  Office  (German  Federal  Statistical  Office,  2020),  respectively.  To 
differentiate  between  households  in  Single-family  and  Multi-family  buildings,  it  is  assumed  that  the  latter 
have an annual consumption 7% lower than the national average while Multi-family units had a consumption 
16%  larger,  assuming  a  similar  relation  to  that  reported  in  the  SECH-SPAHOUSEC  project,  a  national-level 
analysis performed in Spain in 2011 (Proyecto SECH-SPAHOUSEC, 2011). In the case of Spain, the estimated 
demand for space cooling is subtracted from the base load value as this will be allocated later. Considering 
the data reported by SECH-SPAHOUSEC, this demand is considered as 5% of the annual electricity demand. 

Table 14 Annual electricity demand from Single-family and Multi-family units without considering space cooling 

Country 

National average 

Single-family units  Multi-family units 

Germany 

3,113 kWh/year 

3,611 kWh/year 

2,895 kWh/year 

Spain 

3,108 kWh/year 

3,606 kWh/year 

2,890 kWh/year 

Source:  Own  elaboration  with  data  from  Red  Eléctrica  de  España  (n.d.);  German  Federal  Statistical  Office  (2020)  and  Proyecto  SECH-
SPAHOUSEC (2011). 

For  Single-family  buildings  the  yearly  demand  is  equal  to  the  set  value  for  Single-family  units,  whereas 
demand for Mixed  buildings and Multi-family buildings is obtained  by multiplying the  value for  Multi-family 
units by the number of households assigned to each building.  

For  non-residential  buildings,  a  different  approach  is  needed  as  energy  demand  varies  greatly 
depending  on  the  economic  sector  considered.  As  no  comprehensive  data  was  found  for  Spain  or 
Germany, the results from a study conducted in Hellenic non-residential dwellings (Droutsa et al., 2020) was 
used as a reference to define yearly electricity demands for the Non-residential buildings considered in each 
archetype. This reference provides a database with Energy Use Intensity (EUI) values – provided in kWh/m2 – 
for different building types, differentiating among energy usage for heating, cooling, domestic water heating 
and  lighting.  For  the  construction  of  the  electricity  base  load,  the  EUI  values  for  lighting  are  used  as  a 
reference.  No  regional  differentiation  is  considered.  The  EUI  values  for  the  different  building  types  can  be 
consulted in the attached database. 

3.1.1.2  Adjustment for space cooling demand in Spain 

As the used load shapes are based on consumption data from German customers, electricity usage for space 
cooling  is  not  clearly  incorporated,  which  results  in  a  lower  summer  consumption  than  expected  for  the 
Spanish  case  studies.  Thus,  a  correction  method  is  used  to  incorporate  this  consumption  in  the  modelled 
communities’ electricity baseload demand. First, CDD are  calculated for the  base year, following  Eq. 3 from 
Eurostat  methodology  (Eurostat,  2021)  and  a  TBaseline  of  22ºC  as  considered  by  the  European  Environment 
Agency (Crespi et al., 2020), and being suitable for Spain as reported by (Pablo-Romero et al., 2021). 

Eq. 3  Calculation of Cooling Degree Days 

If 𝑇𝐷 ≥   𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 Then [CDD =   𝑇𝐷 − 𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒], 𝐸𝑙𝑠𝑒 [𝐶𝐷𝐷 = 0] 

The  daily  mean  air  temperature  (TD)  is  calculated  for  each  day  using  the  corresponding  24  hourly  values 
reported in the input weather data for each region. The daily CDD results obtained from . 

Eq.  3  are  then  added  to  obtain  the  total  CDD  registered  in  the  base  year  (CDDSpain).  This  value  is  used  to 
estimate ElSpain, the specific electricity demand in kWh per square meter of fully cooled floor area in the non-
residential buildings considered in the Spanish case studies, using a linear equation proposed in (Aebischer et 
al., 2007) for locations in temperate and Mediterranean cities (Eq. 4). 

Eq. 4 

 Specific electricity demand for fully cooled floor areas in kWh/m2 

𝐸𝑙𝑆𝑝𝑎𝑖𝑛 = 12.7 + 0.013 ∗   𝐶𝐷𝐷𝑆𝑝𝑎𝑖𝑛 

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As not all the area in non-residential buildings is fully cooled, the obtained ElSpain value is adjusted for each 
building  using  the  reported  EUI  values  for  space  cooling  in  the  Hellenic  buildings  database  (Droutsa  et  al., 
2020).  This  is  done  by  assuming  that  the  building  type  with  the  highest  EUI  for  space  cooling  has  a  70% 
share of its area fully cooled (SCshare) – which is the maximum value reported in  (Aebischer et al., 2007) for 
Non-residential dwellings – and the rest are adjusted accordingly. In this way, the yearly electricity demand 
for  space  cooling  in  Non-residential  buildings  (ElSpace_cooling)  is  estimated  using  the  resulting  values,  the  floor 
area (Area in m2) and the number of floors per dwelling (NFloors), as shown in Eq. 5. 

Eq. 5 Electricity demand for space cooling in Spanish buildings 

𝐸𝑙𝑆𝑝𝑎𝑖𝑛_𝑐𝑜𝑜𝑙𝑖𝑛𝑔 = 𝐸𝑙𝑆𝑝𝑎𝑖𝑛 ∗ 𝑆𝐶𝑆ℎ𝑎𝑟𝑒 ∗ 𝑁𝑓𝑙𝑜𝑜𝑟𝑠 ∗ 𝐴𝑟𝑒𝑎 

The space cooling demand per dwelling is allocated through the users’ yearly vector by assigning a share of 
the annual demand to each day, proportional to the daily CDD registered by applying Eq. 3. For households, 
the same  process is applied  but the annual electricity demand for space  cooling is estimated based on the 
data  reported  in  the  SECH-SPAHOUSEC  (2011)  and  set  as 5%  of  the  total  household  electricity  demand  as 
explained before. For Single-family units the electricity usage for space cooling is estimated as 190 kWh/year 
and for Multi-family units, 152 kWh/year. 

3.1.1.3  Heat demand 

The  heat  demand  of  the  non-residential  and residential  users is  modelled  by  adapting  the  2006  guidelines 
(BGW, 2006) and the gas standard load profiles methodology defined by the German Federation of the Gas 
and  Water  Industry  (BGW)  and  the  German  Association  of  Local  Utilities  (VKU)  in  2016  (BDEW,  2016).  The 
2016 methodology uses Eq. 6to calculate the daily heat demand for a given customer, using the consumer’s 
expected daily consumption8 (KW), the corresponding h-Wert or h-value – h(θ) – and a weekday factor (F) to 
adjust  daily  consumption  according  to  the  day  of  the  week.  The  weekday  factors  provided  in  the 
methodological  guidelines  are  differentiated  by  building  category  and  can  be  consulted  in  MODECO’s 
database. 

Eq. 6 Daily heat demand for a given customer 

𝑄𝑑𝑎𝑦(θ) = KW ∗ ℎ(𝜃) ∗ 𝐹 

The  customer  value,  KW,  is  calculated  using  the  user’s  specific  consumption  between  two  meter  readings, 
usually  corresponding  to  monthly  or  bi-monthly  consumption,  and the  h-values  registered  during  this  same 
period.  As  there  is  no  monthly  or  bimonthly  information  available  regarding  typical  buildings  heat 
consumption,  the  KW  value  is  set  to  one.  Later  the  vector  is  normalized  and  adjusted  to  the  heat  annual 
demand for each consumer, which can be more easily accessed. 

To obtain the h-value, Eq. 7 is applied considering the original sigmoid function and the linear function added 
to the original methodology in 2016 to improve demand distribution during the year. The coefficients A, B, C, 
D, mH y bH are given for the different building types listed in Table 15. To align these values with the electrical 
standard load profiles used for the definition of the electrical baseload demand, each building considered in 
the  Energy  community  case  studies  must  be  assigned  a  building  category  and  a  standard  load  profile.  The 
applicable  coefficients  to  each  building  type  can  be  consulted  in  the  associated  database.  The  original 
methodology  provides  different  coefficients  for  buildings  located  in  windy  and  no  windy  locations.  For 
MODECO,  it  is  assumed  that  all  Energy  community  case  studies  are  located  in  windy  locations  (meaning 
average wind speeds above 4 m/s) and only those values are presented in Annexes.  

Eq. 7 Calculation of the h-Wert or h-value using a mix from the sigmoid and linear functions 

ℎ(𝜃) = [

𝐴

1 + (

𝐵
𝜃 − 𝜃0

)𝐶

] + [max {

𝑚𝐻 ∗ 𝜃 + 𝑏𝐻
𝑚𝑊 ∗ 𝜃 + 𝑏𝑊

}] + 𝐷 

8 The customer value (KW) must be specified individually for each consumer (metering point) based on actual metered consumption and 
related temperature data. The methodology specifies that KW values must be calculated for an average daily temperature of 8ºC when 
the h-value is equal to 1 (BDEW, 2016). 

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Table 15 Building types considered in the gas standard load profiles methodology 

Category 

Building type description 

EFH 

Single-family building. 

MFH 

Multi-family building. 

GMK 

Buildings in the metal and automotive sector. 

GHA 

Retail and wholesale. 

GKO 

Local authorities, credit institutions and insurance companies. 

GBD 

Other operational services. 

GGA 

Restaurants. 

GBH 

Accommodations. 

GWA 

Laundries, dry cleaning. 

GGB 

Horticulture. 

GBA 

Bakery. 

GPD 

Paper and printing. 

GMF 

Household-like business enterprises. 

GHD 

Total load profile for Non-residential buildings. 

Source: Translated English version from the table in (BDEW , 2016). 

To account for the thermal inertia in the sigmoid function part of the h-value equation, the geometric series 
approach (Eq. 8) is used, while the mean daily temperatures (TD, TD-1, TD-2, TD-3) are obtained using the 24 hour 
values  for  each  corresponding  day  as  done  to  calculate  the  daily  CDD.  The  reference  temperature  (θ0)  is 
defined as 40ºC as in the original methodology. 

Eq. 8 Temperature geometric series 

θ =

𝑇𝐷 + 0.5  ∗   𝑇𝐷−1 +   0.25 ∗  𝑇𝐷−2 + 0.125 ∗   𝑇𝐷−3
1 + 0.5 + 0.25 + 0.125

The intraday consumption is modelled by using the hourly factors (SF) defined for each building category in 
the gas standard load profiles methodology and provided in the 2006 documentation from BGW (BGW, 2006). 
In  this  previous  version,  there  were  11  classes  considered  for  residential  buildings  representing  the 
percentage of old (built prior to 1978)  and new buildings (built after 1978) present in the area whose heat 
demand  is  being  modelled.  As  the  2016  methodology  applied  in  MODECO  does  not  contemplate  these 
categories, the hourly factors for class 11 – corresponding to the German average – were considered for all 
residential members. The hourly factors are also differentiated by the temperature range in which the daily 
mean temperature is located. The exact  values applicable to each building  category and temperature range 
can be consulted in MODECO’s database. 

Finally, the  resulting  vector is normalized  and adjusted  to  the  building’s annual  heat  demand  in  kWhth/year. 
For Spanish households, the annual heat demand is set assuming the same shares per usage – Space Heating 

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33 

 
 
 
 
 
(SH),  Domestic  Water  Heating  (DWH),  Space  Cooling  (SC),  and  Others  –    as  reported  by  the  Spanish 
government  in  2011  for  households  in  Single-family  and  Multi-family  buildings  (IDAE,  2014).  For  German 
residential buildings, it is  assumed that space heating demand is 3.04 larger  than in  Spain  given 
the space heating unit consumption per dwelling reported for both countries in the Entranze Project database 
(Entranze Project, 2008), and that heat demand for domestic water heating is similar to Spanish households. 
The final values resulting from this process are shown in Figure 9, and can be consulted in the Annex data. 

The obtained values for Germany were compared against the shares of space and domestic water heating in 
total  residential  consumption  reported  by  the  Entranze  Project  (Entranze  Project,  2008).  To  do  so,  the 
weighted national average was calculated considering the number of Single-family and Multi-family buildings 
reported  in  the  same  source.  This  calculation  showed  that  the  suggested  total  heat  demands  are 
representative  for  the  German  national  average,  although  demand  for  space  heating  seems  to  be  slightly 
overestimated. 

Figure 9. Annual energy consumption in MWh/year per household (Single-family and Multi-Family buildings) and region 
disaggregated by end usage 

Source: Own elaboration with data from Entranze Project (2008) and Proyecto SECH-SPAHOUSEC (2011). 

For Non-residential  buildings,  the  EUI  values for  space  and  domestic  water  heating  reported  in  the  Hellenic 
building database was used as a reference to define the annual heat demand values for each case. As Greece 
(GR)  has  lower  Heating  Degree  Days  (HDD)  than  Spain  or  Germany,  the  values  are  adjusted  with  a  similar 
approach to that used by (Aebischer et al., 2007) to account for heat demand under different HDD conditions 
using Eq. 9. As can be seen, the specific heat demand per Hellenic building type (EUIHeat, GR) – equal to the sum 
of  the  specific  energy  demand  for  space  heating  (EUISH,  GR)  and  domestic  water  heating  (EUIDWH,  GR)  –  is 
adjusted considering the share of the building’s heat demand that varies proportionally to the number of HDD 
(αBuilding) and the HDD in Greece and the target region. This share is roughly estimated by dividing EUIsH by the 
specific  energy  demand  for  DHW,  as  water  heating  is  less  dependent  on  climatic  conditions  as  stated  in 
(Aebischer et al., 2007). 

Eq. 9 Calculation of specific heat demand for space heating in kWh/m2 

𝐸𝑈𝐼𝐻𝑒𝑎𝑡,𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 = 𝐸𝑈𝐼𝐻𝑒𝑎𝑡,𝐺𝑅 ∗ 𝛼𝐵𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ∗ (

𝐻𝐷𝐷𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛
𝐻𝐷𝐷𝐺𝑅 − 1

) 

The HDD for each location – including Greece – are calculated using Eq. 10 from the Eurostat methodology 
(Eurostat,  2021)  with  a  TBaseline  of  15.5ºC  as  indicated  by  the  European  Environmental  Agency  (Crespi  et  al., 
2020), and the weather data from the Open Power System Data  (Open Power System Data, 2020) used in 
other calculations and presented in Section 2.1.1. 

Eq. 10 Calculation of Heating Degree Days 

If 𝑇𝐷   ≤   𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 Then [HDD  =   (𝑇𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒   −   𝑇𝐷)] Else [HDD  =  0] 

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34 

 
 
 
3.1.2 

Industrial users 

Heat consumption in industrial processes differs from customer to customer as there are a wide range 
of individual needs for process, water and space heating. Consequently, industrial heat load profiles are more 
diverse  than  for  residential  and  Non-residential  buildings,  having  users  with  nearly  constant  demand 
throughout  the  year  to  load  profiles  with  significant  seasonality  (Jesper  et  al.,  2021).    Moreover,  unlike 
residential and non-residential dwellings, recent data indicates that there is no generalized relation between 
heat and electricity usage in industrial consumers as this relation depends on the type of process itself. For 
industries with a high proportion of ambient temperature independent (process) heat demand, there seems to 
be  a  correlation  between  both  energy  carriers.  However,  for  consumers  whose  heat  demand  is  highly 
dependent on ambient temperature, little or no correlation between both carriers exist (Jesper et al., 2022). 

Consumers whose heat demand depends on ambient temperature are most frequent even in the secondary 
sector, for instance, manufacturing and assembly of goods such as wood furniture manufacturers. Industries 
in  which  space  heating  is  a  relevant  heat  sink  are  usually  within  this  category.  On  the  contrary,  some 
economic  divisions  like  basic  metals  or  the  food  industry  are  not  influenced  significantly  by  ambient 
temperature  due  to  the  nature  of  their  processes.  For  instance,  the  first  requires  high  temperatures  (> 
500 ºC) that are practically not affected by ambient temperature changes, while food industries rely on hot 
water  for  most  of  its  processes  (e.g.  cooking,  cleaning,  steaming,  sterilization,  and  hot  water)  that,  as 
explained previously, are temperature independent (Jesper et al., 2021). 

Considering the above, separate methodologies are used for modelling the energy demand of industrial users 
depending on their process type. For users with ambient temperature dependent processes, a methodology to 
calculate  heat  demand  based  on  ambient  temperature  is  proposed  to  maintain  a  regional  differentiation 
between communities in Spain and Germany.  This means that the profiles generated for this type of users 
are  specific  to  each  target  region.  Hourly  electricity  demand  is  taken  from  real  users’  data  as  little  or  no 
relation between both is assumed for this type of customers. 

On the other hand, users with heat demand not affected by ambient temperature are modelled based on an 
existing  database,  called  JERICHO-E,  that  provides  estimated  hourly  energy  consumption  data  for  seven 
energy  intensive  industries  in  Germany  (Priesmann  et  al.,  2021).  Both,  process  heat  and electricity  demand 
are taken from this database to ensure a relation is maintained between both carriers as field data seems to 
corroborate (Jesper et al., 2022). Demand for space  heating and cooling is modelled separately considering 
these are temperature-related and they can be served  by electrical heat pumps. The consideration of these 
users in the Industrial Polygon, the only archetype in which they are included, is relevant for MODECO as this 
type  of  industries  –  chemical  and  refineries,  steel  manufacturers,  other  industries  with  high  heating 
requirements – are expected to be the main consumers of green hydrogen (IRENA, 2022).  

More details about the methodologies proposed for both types of industrial customers is provided in the next 
sections.  

3.1.2.1  Ambient temperature dependent users 

The total annual electricity demand for the industrial users within this category is defined based on an open 
data  set  of  50  small  and  mid-size  enterprises  with  industrial  operations  in  Germany.  This  dataset  contains 
15-minute power data for an entire year, so hourly energy values are calculated before being introduced in 
the model (Brauer, 2020). Loads are classified into 5-days and 7-days consumption schedules so they can be 
matched  with  the  time  series  from  suitable  heat  clusters  as  schedule  is  one  of  the  determinants  for  heat 
demand in this category as will be explained in this section. Additionally, loads with annual consumption over 
5 GWh are extracted from the sample and classified as high energy users to be used as reference values for 
the ambient temperature independent users. 

The daily heat demand for the industrial users is estimated through a linear regression model adaptable to 
different  customer  groups  and  daily  temperature  values  (Eq.  11).  The  model  is  based  on  a  sample  of  566 
large-scale  natural  gas  consumers  and  is  differentiated  by  weekday  and  weekend  consumption,  and  usage 
cluster. The original sample consisted of 797 consumers, but 231 were excluded because of missing data or 
not presenting a linear relation between natural gas consumption and heat demand as the model parameters 
were defined on gas meter readings. According to the authors, the found  cluster correlations are almost as 
accurate as individual correlation (Jesper et al., 2021). 

Eq. 11 Linear regression model to estimate industrial users’ heat demand 

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35 

 
 
𝑄𝑑
𝑄𝑑

= ℎ𝑙𝑖𝑛(𝑇𝑎𝑚𝑏) = {

max(0,
max(0,

𝑚ℎ ∗ 𝑇𝑎𝑚𝑏 + 𝑏ℎ) 𝑖𝑓 𝑇𝑎𝑚𝑏 <   𝑇ℎ𝑙
𝑚𝑤 ∗ 𝑇𝑎𝑚𝑏 + 𝑏𝑤) 𝑖𝑓 𝑇𝑎𝑚𝑏 ≥   𝑇ℎ𝑙

} 

To simulate a  user’s  heat demand, the weekday and weekend cluster applicable to each customer  must be 
indicated. To assign a cluster to the industrial users inside the Energy community archetypes, the distribution 
per economic division found by the model authors is considered. In working days (Figure 10), the authors of 
the study found out that Cluster 0 and Cluster 1 are most likely to better represent a customer if industrial 
production is the dominant activity. On the other hand, Cluster 2 and Cluster 3 are most likely for consumers 
where  assembly,  logistics,  general  administration,  research  and  development,  sales  or  service  are  the  main 
activities  in  the  site.  Weekend  distribution  shows  similar  trends  and  the  data  is  available  in  the  attached 
database (Jesper et al., 2021). 

The  cluster  assignment  can  be  explained  in  most  cases  by  the  users’  heat  sink  and  their  respective  time 
schedules. The authors found that dependency of heat demand on mean daily ambient temperature increases 
from  weekday  cluster  0  to  cluster  3  and  weekend  cluster  0  to  cluster  4,  thus,  existing  a  weaker  relation 
between temperature and heat demand in industrial customers with heavily industrialized processes (Jesper 
et  al., 2021).  As this  model  is selected  to  represent  temperature  dependent  users,  only  weekday  clusters 2 
and 3, and weekend clusters 2, 3, 4 are used to create industrial profiles in MODECO. 

Additionally, it was found that users in weekend cluster 3 have a reduced heat load, which indicates a 5-day 
production schedule. In contrast, the rest of the clusters – all weekday clusters and weekend clusters 2 and 4 
–  show  similar  demand  levels,  which  makes  them  suitable  for  customers  producing  seven  days  a  week. 
Weekend  cluster  2  and  cluster  4  can  also  be  used  for  industrial  customers  with  5-day  production  days,  if 
space  heating  is  the  main  heat  use  and  room  temperature  is  not  reduced  on  the  weekends  (Jesper  et  al., 
2021). As mentioned, this characteristic is taken into account when matching the heat load with an electricity 
time  series  (i.e.  heat  loads  built  with  weekend  cluster  three  parameters  are  only  matched  with  five-week 
schedule electrical loads). 

Figure 10. Distribution of companies per working day cluster in each economic sector 

Source: Obtained from Jesper et al. (2021). 

Daily water and space heating requirements for these users are calculated using the same methodology as 
for residential and Non-residential buildings. In this case, the GMK profile  – buildings in the automotive and 
metal sector – is always used as it is assumed to be representative of industrial users. The resulting values 
are  subtracted  from  the  previously  obtained  daily  demand  to  separate  process  heat  from  these  other 
applications. The hourly behaviour for space and domestic water heating is obtained using the weekday and 
hourly  factors  applicable  to  this  building  type,  except  that  for  seven-day  schedules  all  days  are  treated  as 
weekdays. 

Hourly  loads  for  process  heat  are  constructed  using  information  from  the  U.S.  National  Renewable  Energy 
Laboratory  (NREL)  regarding  process  heat  load  shapes  (McMillan,  2019).  Specific  loads  are  selected, 
maintaining  consistency  between  the  process  represented  and  the  sector  to  which  the  simulated  industrial 
user belongs and that is linked to the clusters used to model heat demand. To do so, each load shape from 

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36 

 
 
 
the  NREL  database  is  assigned  an  economic  sector  from  the  Nomenclature  of  Economic  Activities  (NACE) 
system used in the clustering model (Jesper et al., 2021), suitable to its indicated North American Industrial 
Classification  System  (NAICS)  code.  Moreover,  as  the  NREL  database  differentiates  between  industries  by 
number  of  employees,  only  those  with  less  than  250  employees are  considered  as  the  modelled  users are 
assumed to be small and mid-size enterprises in consistency with the used source for the electrical load.  

In  the  case  of  the  Spanish  industrial  users,  a  load  correction  associated  with  space  cooling  will  be  done 
following the same process explained for residential and Non-residential buildings. 

3.1.2.2  Ambient temperature independent users 

The  electrical  demand  for  the  industrial  users,  considered  only  in  the  industrial  polygon  and  business  park 
archetypes  is  designed  based  on  the  JERICHO-E  database  that  contains  comprehensive  data  on  energy 
consumption  patterns  for  heat,  cold,  mechanical  energy,  information  and  communication,  and  light  in  high 
special and temporal resolution. The model was originally developed for Germany and can be disaggregated 
by sector – residential, industrial, commerce and mobility – using a combination of bottom-up and top-down 
approaches  and  multiple  open  data  sources  such  as  weather  time  series  and  standard  load  profiles 
(Priesmann et al., 2021).  

To  model  the  industrial  electricity  load,  the  authors  of  JERICHO-E  use  8  Industrial  Standard  Load  Profiles 
(ISLP)  representing  the  following  sectors:  food;  glass,  ceramic,  and  stones;  automotive,  chemical,  paper, 
mechanical  engineering;  iron  and  steel;  and  other  industries  (Priesmann  et  al.,  2021).  The  load  shapes  for 
chemical, paper, and iron and steel are used in MODECO to simulate the electricity and heat consumption of 
four  large  industrial  users  within  these  categories.  The  normalized  heat  and  electricity  hourly  demand  is 
presented in the Figure 11 for the 3 analysed seasons (winter, summer, transition) although the original load 
profiles contain individual data for the 8760 hours in a year and are inputted as such in the models. 

The database permits disaggregating the electricity and heat load shapes by end  use. Although its  share in 
the  final  energy  consumption  is  low,  as  it  is  practically  fully  related  to  the  process  requirements,  space 
heating and cooling demand is not included in the total energy consumption curve to maintain methodological 
consistency. Instead, it is modelled as for ambient temperature dependent users, which means that there will 
be slight differences between Spanish and German users in this category. The annual energy demand used to 
adjust the normalized curve for these users is defined based on the annual consumption from the industrial 
users classified as high energy consumers as explained above. Heat process demand is assumed to follow the 
same shape, and have a total annual demand equal to 48% of the registered annual electricity demand as 
reported  in  a  study  (Jesper  et  al.,  2022)  evaluating  the  relation  between  both  energy  carriers  in  industrial 
consumers. 

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37 

 
 
Figure 11. Hourly curves showing total energy demand (heat and electricity) for selected industrial standard load profiles 
from the JERICHO-E database [data adjusted to 1000 MWh/day] 

Source: Own elaboration with data from (Priesmann et al., 2021). 

3.2  Heat pumps  

Since the starting year (2025), it is assumed that a share of the communities’ total heat demand is already 
served by electric heat pumps. Differentiated values are assumed for Germany and Spain and based on the 
share of space heating unit consumption per dwelling (kWh/dwelling) supplied by  electricity reported in the 
Entranze  database  for  residential  buildings  in  European  member  states  (Entranze  Project,  2008).  As  no 
differentiated data was found for Non-residential buildings, the same distribution is assumed for this group. 
Therefore, in the Spanish case studies it is assumed that 18% of the heat demand from residential and Non-
residential buildings is supplied by electric  heat pumps by 2025,  while in  Germany this share is just 4% as 
most  heat  demand  is  met  by  fossil  fuels  combustion.  Every  year,  it  is  assumed  that  the  amount  of  heat 
served  by  heat  pumps  grows  by  2.6%  in  comparison  with  the  previous  year,  in  line  with  the  electrification 
rates assumed by the ESES for 2030 and 2040. 

To  calculate  the  electricity  demand  associated  with  the  heat  load  served  by  electrical  heat  pumps,  a 
methodology  similar to that  used  by  (Heitkoetter et al., 2021) and   (Ruhnau et al., 2019) is applied.  As the 
heat  pumps’  Coefficient  of  Performance  (COP)  varies  with  ambient  temperature,  hourly  COP  values  for  Air 
Sourced Heat Pumps (ASHP), Ground Sourced Heat Pumps (GSHP), and Water Sourced Heat Pumps (WSHP) are 
calculated  based  on  the  quadratic  regression  of  manufacturer  data  used  by  (Heitkoetter  et  al.,  2021)  and 
described in Eq. 12. 

Eq. 12 Calculation of hourly COP values for different heat pump types 

𝐶𝑂𝑃𝑡

𝐻𝑃 =   {

6.08 − 0.09 ∗  𝛥𝑇 + 0.0005 ∗  𝛥𝑇2, 𝐴𝑆𝐻𝑃
10.29 − 0.21 ∗  𝛥𝑇 + 0.0012 ∗  𝛥𝑇2, 𝐺𝑆𝐻𝑃
9.97 − 0.20 ∗  𝛥𝑇 + 0.0012 ∗  𝛥𝑇2, 𝑊𝑆𝐻𝑃

} 

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38 

 
 
 
The  values  for  ΔT  (𝑇𝑠𝑖𝑛𝑘 − 𝑇𝑠𝑜𝑢𝑟𝑐𝑒)  comprise  all  possible  combinations  of  source  and  sink  temperatures 
applicable  to  each  heat  pump  type.  The  applicable  sink  and  source  temperature  for  each  heat  pump 
technology are listed in the table below. 

Table 16 Sink and source temperature applicable to considered heat pump technologies 

Type 

Tsource 

Tsink 

ASHP 

Air 

Radiator heating, floor heating, water heating 

GSHP 

Ground 

Radiator heating, floor heating, water heating 

WSHP 

Water 

Radiator heating, floor heating, water heating 

*ASHP = Air Sink Heat Pump; WSHP = Water Sink Heat Pump; GSHP = Ground Sink Heat Pump; 
Source: Own elaboration with data from Heitkoetter et al., (2021). 

For air and ground source temperature, hourly data from Open Power System Data (2020) are used, while for 
water source a constant ground water temperature of 10 ºC is assumed as in  (Heitkoetter et al., 2021). For 
the calculation of sink temperatures, the approach of Ruhnau et al. (2019) is applied, considering 50ºC as the 
heat sink temperature for water heating  –  value based on German  field measurements and  considered the 
same for Spain – and Eq. 13 to calculate hourly values in the case of radiator and floor heating. 

Eq. 13  Hourly sink temperatures used for radiation and heating applications 

𝑠𝑖𝑛𝑘 =   {

𝑇ℎ

40 º𝐶 − 1.0 ∗   𝑇ℎ
30º𝐶 − 0.5 ∗   𝑇ℎ

𝑎𝑚𝑏, 𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟 ℎ𝑒𝑎𝑡𝑖𝑛𝑔
𝑎𝑚𝑏, 𝑓𝑙𝑜𝑜𝑟 ℎ𝑒𝑎𝑡𝑖𝑛𝑔       

} 

Subsequently,  the  obtained  COP  time  series  are  used  to  calculate  a  weighted  average  for  the  different 
technologies  considering  different  market  shares  for  Germany  and  Spain.  For  the  German  case,  the  shares 
proposed by (Heitkoetter et al., 2021) are considered: 55% ASHP, 39% GSHP, and 6% WSHP. In the case of 
Spain, a larger usage of ASHP is considered – 90% ASHP, 8% GSHP, 2% WSHP – as market sources show it is 
by far the dominant heat pump technology in the country (Observ’ER, 2021).  

Finally, hourly weighted average COP are used to calculate the electrical load (𝐸𝑙𝐻𝑃) from heat pumps’ usage 
by applying Eq. 14 considering that  𝑥𝐻𝑃 is the share of the community’s heat load (𝑄ℎ) that is supplied via 
electrical heat pumps.  

Eq. 14 Electrical demand associated to heat pumps operations Electrical demand associated to heat pumps operations 

𝐸𝑙𝐻𝑃 =

𝑄ℎ ∗   𝑥𝐻𝑃
𝐶𝑂𝑃ℎ

The investment and operation and maintenance costs associated with the different types of heat pumps are 
obtained from the HER4 cost database (HRE4, n.d.). The values for 2030 and 2040 are shown in the following 
table. CAPEX is assumed constant during the 16-year period, while the CAPEX values considered for each year 
can  be  consulted  in  the  associated  database.  For  comparison,  the  cost  of  the  natural  gas  boilers  is  also 
presented  in  Table  17.  This  information  is  also  used  in  the  Total  Cost  of  Ownership  analysis  and  the 
investment model as an input for decision-making regarding the potential installation of Combined Heat and 
Power (CHP) units. 

As investment costs are given in € per heat pump and boiler unit, the given values are transformed to € per 
heat  unit  (kWh-year),  assuming  that  this  equipment  is  sized  to  cover  the  households’  entire  space  and 
domestic water heating demand. Thus assuming that one unit is able to generate the annual heat demand for 
single-family  and  multi-family  buildings,  respectively,  which  permits  to  estimate  the  cost  per  heat  unit 
generated by each thermal technology. As no specific data is provided for commercial buildings, it is assumed 
that the investment cost is equal to  33% of the estimated cost for  residential users (considering the  mean 
value  between  single  and  multifamily  homes),  maintaining  the  relationship  presented  in  the  work  of 
Heitkoetter et al. (2021) for domestic and commercial applications. 

Table 17 CAPEX, OPEX and useful life considered for heat pumps and boilers used in residential users 

Technology 

Type 

User 

2030 

39 

2040 

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type 

CAPEX 
[€/unit] 

OPEX  
[% 
CAPEX] 

Life 
[years] 

CAPEX 
[€/unit] 

OPEX [% 
CAPEX] 

Life 
[years] 

ASHP 

WSHP 

Heat pumps 

10 
15 
20 
20 
20 
20 
25 
*ASHP = Air Sink Heat Pump; WSHP = Water Sink Heat Pump; GSHP = Ground Sink Heat Pump; SFH = Single-family home; MFH = Multi-
family home. 
Source: Own elaboration with data from HRE4 (n.d.). 

1570 
10 
7000 
15 
20  105020 
11050 
20 
20  186080 
2490 
20 
19440 
25 

1660 
7830 
116990 
12900 
206350 
2760 
21560 

9.8% 
2.1% 
0.7% 
1.3% 
0.4% 
6.6% 
2.8% 

9.8% 
2.1% 
0.7% 
1.3% 
0.4% 
6.6% 
2.8% 

All 
SFH 
MFH 
SFH 
MFH 
SFH 
MFH 

Natural 
gas 

Boiler 

GSHP 

3.2.1  Heat pumps’ flexibility potential 

As  previously  mentioned,  the  electrical  demand  associated  with  heat  pump  operation  is  considered  in  the 
optimization  models  as  an  electrical  consumption  profile.  Given  that  heat  pumps  can  shift  their  operation 
without greatly affecting users’ comfort by taking advantage of the building thermal inertia, the participation 
of  these  items  in  Demand  Side  Response  (DSR)  programs  is considered, assuming  there  is a  portion  of  the 
heat pumps electrical demand that can be increased or decreased as required. To implement it in MODECO 
models, some considerations have been taken from Heitkoetter et al. (2021) as explained. 

In  DSR,  heat  pumps’  flexible  operation  must  consider  some  established  limits  that  are  associated  with  the 
equipment technical restrictions as well as socio-economic factors that account for users’ comfort. Regarding 
technical restrictions, it is considered that the load decrease share for these assets is 0%, whereas the load 
increase  share  is 75%.  Additionally, the  use  of  a  flexible share  parameter representing  socio-technical  load 
shifting  potential  restrictions,  e.g.,  the  social  acceptance  or  the  regulation  framework  can  hamper  the 
implementation of load shifting, is included as done by Heitkoetter et al. (2021). This is considered to be 40% 
in all cases as defined for Germany by the authors.  

At every time step, the potential amount of up and down flexible energy has to be within the maximum load 
increase  and  the  maximum  load  decrease.  Both  bounds  are  calculated  by  multiplying  the  calculated  heat 
pumps’ electrical demand at each hour by the load increase and load decrease share values. Additionally, it is 
multiplied by the flexible share parameter mentioned above to obtain the available amount of flexible energy 
at each time step. Moreover, the time frame of management, which is the maximum duration that loads 
can be postponed or preponed, is also incorporated as a constraint for the model.  This value is set at  3 
hours for all heat pump types (residential, commercial) as proposed by Heitkoetter et al. (2021). 

Finally,  three  different  costs  associated  to  heat  pumps  participation  in  DSR  are  assumed  in:  1)  a  specific 
investment  cost  for  information  and  communication  technology  (ITC)  components;  2)  annual  fixed  costs 
caused by maintenance works and the electricity consumption of the ITC components; and 3) variable costs 
reflecting compensations for losses in production and comfort (Heitkoetter et al., 2021). These costs differ for 
domestic  and  commercial  heat  pumps  as  shown  in  the  following  table;  but  no  differences  are  assumed 
between  target  regions.  It  is  also  assumed  that  these  costs  –  as  well  as  the  load  shifting  parameters  – 
remained the same during the studied period. 

Table 18 Installation and operation costs of equipment for heat pump’s participation in DSR programs 

Heat pump category 

Investment cost 
[€/MW] 

Fixed cost 
[€/MW/year] 

Variable cost for 
DSR [€/MWh] 

Residential 

Commercial 

62,000 

20,000 

12,000 

600 

10 

10 

Source: Own elaboration with data from Heitkoetter et al. (2021). 

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3.3  Electric vehicles 

Electricity  demand  associated  to  electric  vehicles  is  modelled  differently  for  private  charging  points 
(households and work stations) and Community-led stations as the second type allows for smart charging 
and  participates  in  demand  response  programs,  via  Vehicle-to-Grid  (V2G),  so  its  modelling  must  permit 
optimizing  the  vehicles’  charging  and  discharging  at  these  points.  Electrical  usage  from  private  charging 
points,  on  the  other  hand,  is  perceived  by  the  model  as  part  of  the  Community’s  electricity  demand.  The 
methodology  and  assumptions  considered  in  each  case  are  explained  in  the  following  sections,  while  the 
specific data inputted in each case can be consulted in the associated database. 

3.3.1  Private charging stations (non-smart charges) 

The  number  of  non-smart  domestic  and  commercial  charging  points  available  in  each  archetype  by  2025, 
2030 and 2040 is defined exogenously considering the following assumptions, 

—  For the starting year (2025), it is assumed that there are 56 passenger cars per 100 inhabitants in each 
archetype,  as  reported  at  the  European  level  in  (ACEA,  2022b),  or  1.29  passenger  cars  per  household 
assuming a population density of 2.3  persons per household based on the average European household 
size (Eurostat, 2022); 

—  The number of EV belonging to commercial fleets owned by community members is defined on a case-

to-case basis. 

—  The total cars fleet (including both domestic and commercial vehicles) inside the communities is assumed 

to increment by 1.2% each year, as reported by (ACEA, 2022b) for the EU. 

—  The percentage of EV within the total vehicles fleet is based on the electrification rates set by the ESES 
reference  model  for  the  transportation  sector  in  2030  (7%)  and  2040  (24%).  For  2025  a  similar 
backwards trend is assumed for 2025 as observed in Figure 12. It must be noted that currently less than 
1%  of  the  total  vehicles  fleet  are  electric  in  both  Germany  (0.8%)  and  Spain  (0.3%)  (Robinson  and 
Erickson, 2016). 

—  From  the  total  number  of  EVs  owned  by  community  members  (residential  and  non-residential),  it  is 
assumed that all commercial EVs have their own private charging station, but only 50% of residential EV 
owners have a private charging point at home in the Business park, Urban district and Virtual community 
archetypes.  In  the  Rural  town  case,  this  number  is  assumed  higher  (60%)  as  single-family  houses  are 
more likely to have access to home charging facilities as reported by (Hensley and Knupfer, 2018). 

—  All the charging points owned by community members are assumed to be non-smart. 

—  Additionally,  it  is  assumed  that  some  public  non-smart  chargers  are  already  installed  inside  each 

archetype based on the number of electrical chargers currently available in Europe. 

Figure 12. EV share in total passenger cars fleet per year 

Source: Own elaboration based on electrification rates assumed for the transportation sector in the ESES 

The final number of non-smart charging points considered in each archetype are summarized in the following 
table per usage category and year. 

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Table 19 Number of non-smart charging stations considered in each archetype by year and owner category. 

Archetype 

Category 

Number of  installed charging points 

2025 

2030 

2040 

Domestic 

Business park 

Business 

Public 

Domestic 

Industrial polygon 

Business 

Public 

Domestic 

Rural town 

Business 

Public 

Domestic 

Urban district 

Business 

Virtual 
community 

Public 

Domestic 

Business 

Public 

4 

22 

2 

- 

25 

2 

4 

4 

1 

10 

14 

2 

27 

50 

8 

7 

22 

4 

- 

25 

4 

9 

4 

2 

21 

14 

4 

54 

50 

16 

28 

22 

6 

- 

25 

6 

34 

4 

4 

79 

14 

6 

207 

50 

32 

Source: Own elaboration with data from Eurostat (2020) and the selected ESES. 

The electrical load associated with the usage of the private charging points is  modelled using the Electric 
Vehicle  Charging  Infrastructure  Simulator  (ELVIS),  an  open  source  software  developed  at  the 
Distributed  Artificial  Intelligence  DAI-Laboratory  from  TU  Berlin  university  (DAI-Laboratory,  2020).  For  each 
private non-smart charging point category, the assumptions summarized in Table 20 are used as inputs to the 
model.  Similarly,  the  relative  charging  frequency  of  start  charging  time  per  hour  of  the  day  reported  by 
(Corchero  García,  2015)  for  European  domestic  and  business  users  is  used  to  indicate  the  model  the  most 
likely initial charging hour per day. It is assumed that one charging per day is the most common frequency for 
all users as reported by (Quiros-Tortos et al., 2018).  

Table 20 Assumptions considered for charging stations for domestic and business use 

Data 

Domestic 

Business use 

Station power rating 

Average initial SOC  

3.7 kW 

58.6% 

11.0.kW 

62.7% 

Average parking time 

5 hours 

5 hours 

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Source: Own elaboration with data from Corchero García (2015). 

In addition to these parameters, the model requires basic information from the vehicles that charge energy at 
each point. In MODECO, 5 EV generic types (Table 21) are considered based on the characteristics of existing 
EV models and  provided  by  the  Emobpy  open  source  model  (Gaete-Morales et  al.,  2021).  For  simplification 
purposes,  one  EV  type  is  assigned  to  one  charging  point  even  in  work  stations.  In  2025,  the  EV  types  with 
lower  battery  capacity  (35.8  kWh)  are  used  as  default  models,  while  in  future  periods,  cars  with  larger 
capacities are favoured, representing technological improvements. In all cases, a 95% charging efficiency is 
assumed. 

Table 21 Assumptions for standard EV models considered 

EV generic 
model 

Power 

Capacity 

EV_Model_1 

100 kW 

35.8 kWh 

EV_Model_2 

386 kW 

60 kWh 

EV_Model_3 

386 kW 

70 kWh 

EV_Model_4 

386 kW 

90 kWh 

EV_Model_5 

386 kW 

100 kWh 

Source: Own elaboration with data from Gaete-Morales et al. (2021). 

3.3.2  Community-led charging points (V2G) 

In addition to the non-smart EV chargers operating inside the community and privately owned by homeowners 
or  businesses,  smart-charging  stations  with  V2G  capabilities  are  considered  an  available  technology  at  the 
Energy communities’ potential investments portfolio. These community-led EV charging points are expected to 
provide electricity to EV owners from the community without access to private charging points, as well as to 
external  EVs  that  are  circulating  in  the  community’s  area  and  are  in  need  of  recharging  their  batteries.  A 
summary of the EV charging assumptions is provided in Figure 13. 

Figure 13. Economic assumptions considered for smart and non-smart EV charging stations 

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Source: Own elaboration. 

All  smart  charging  stations  are  considered  to  have  a  capacity  of  11  kWe  and  be  located  in  public  points 
(parking, streets) accessible to all vehicles circulating inside the community area. The investment cost for the 
starting  year  is  set  at  4,500  euros  per  installed  charger  based  on  data  from  the  European  Federation  for 
Transport and Environment (EFTE, 2020). This source considers the investment costs to remain similar up to 
2030 as it estimates that only fast chargers will experience a cost decline in the next 16 years. However, the 
2022  European EV Charging  Infrastructure  Masterplan estimates that by 2030, EV chargers  between 4 and 
22 kWe capacity will have an initial cost of 125 €/kWe (ACEA, 2022a), which translates into an investment of 
1375  euros  per  charging  point  in  MODECO  scenario.  This  drop  in  price  is  considered  to  take  place  in  the 
current analysis. However, from 2030 to 2040, prices are assumed to remain the same as originally assumed 
in  (EFTE,  2020).  Operation  and  maintenance  costs  are  assumed  to  be  10%  of  CAPEX  based  on  data  from 
(Nationale Plattform Elektromobilität, 2015) and lifetime is considered 10 years as reported in  (Hecht et al., 
2020). 

The number of external EV assumed to be circulating daily inside each archetype is related to the number and 
size  of  Non-residential  buildings9  considered  in  each  case,  as  these  vehicles  are  assumed  to  be  owned  by 
commuters that live outside the community area but work there. It is assumed that the percentage of workers 
owning  an  EV  is  equal  to  the  value  considered  for  community  residential  members;  in  the  same  fashion,  a 
similar annual growth is assumed. For the Virtual community archetype, the obtained number is tripled as it is 
assumed that workers from non-residential buildings that are close to the Virtual community members might 
also use these chargers.  

The final number of community and external EV circulating in each archetype is shown in the following table, 
whereas  the  number  of  employees  considered  per  non-residential  building  is  available  at  the  associated 
database. On weekends, the employees from business with typical Monday-to-Friday schedules (for instance, 
offices)  are  assumed  to  charge  elsewhere  and  are  not  accounted  for  in  the  circulating  units.  Although  it  is 
possible  for  a  fraction  of  the  community  members’  EVs  to  shift  some  of  their  charging  from  their  private 
charger to a community-owned station, this is ignored as it is assumed most of them will continue using their 
own charger as it is most comfortable. 

The decision to install or not a smart charging point will depend on the economic benefits obtained by using 
the  EV  as  storage  to  optimize  the  communities’  energy  management,  as  well  as  on  the  potential  revenues 
obtained  from  providing  charging  services  to  the  EVs  circulating  inside  the  community.  In  this  sense,  it  is 
assumed that, when possible, the community uses locally generated energy to provide this service, but users 
always  pay  a  charging  fee  equivalent  to  what  they  would  have  paid  in  regular  public  chargers,  minus  a 
discount of 5% that is defined based on the willingness to pay value reported by (Ensslen et al., 2018) for this 
application  and  obtained  through  a  survey  for  German  and  French  EV  owners.  This  means  that  the  smart 
charging cost must be 95% the cost of the alternative regular charging to be attractive to the users.  

Table 22 Number of EV circulating in the energy communities per year disaggregated by owner type 

Archetype 

Owner 

2025 

2030 

2040 

Number of  circulating EV per category 

Business park 

Community 
members 

WD* 

WK* 

WD 

WK 

WD 

WK 

29 

29 

36 

36 

78 

78 

External 

37 

10 

74 

21 

287 

80 

9  Non-residential  buildings  are  classified  into  micro,  small,  medium  and  large.  The  considered  number  of  employees  per  category  are 
based on the classification used by the European Commission (Eurostat, 2015). In particular, the following values are assigned: micro (5 
employees), small (30 employees), medium (100 employees), large (250 employees).  

44 

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Archetype 

Owner 

Number of  circulating EV per category 

Industrial 
polygon 

Rural town 

Urban district 

Virtual 
community 

Community 
members 

External 

Community 
members 

External 

Community 
members 

External 

Community 
members 

25 

25 

25 

25 

25 

25 

73 

11 

4 

34 

11 

58 

11 

2 

34 

2 

146 

117 

563 

450 

18 

18 

60 

60 

8 

55 

22 

4 

55 

31 

14 

172 

172 

3 

84 

13 

103 

103 

157 

157 

464 

464 

External 

56 

18 

112 

36 

434 

137 

*WD = Working days, WK = Weekend 
Source: Own elaboration with data from Eurostat (2020) and the selected ESES. 

The  alternative  charging  cost  is  calculated  using  Eq.  15  from  the  methodology  proposed  in  (Ensslen  et  al., 
2018),  setting  a  reference  charging  price  based  on  the  cost  of  charging  at  non-smart  stations  at  the 
applicable wholesale hourly price (pt). This reference price is the same for all hours of the year and is based 
on the average cost associated with immediately charging all EVs arriving at the station points (without smart 
management).  The energy required by each EV at each hour (et,x) is defined as shown in Eq. 16 considering 
the mean SOC at initial and departure times explained before, and the technical characteristics assumed for 
the  EVs’  batteries  (particularly  the  battery’s  capacity,  Eb,  and  charging  efficiency,  effcharging)  and  the  public 
station chargers. In the original article (Ensslen et al., 2018), the number of chargers is known, but as this is 
not  the  case  here,  the  calculation  of  the  reference  price  is done  considering  that  there  is always a  charger 
available  for  an  upcoming  EV.  This  is  considered  a  fair  assumption  as  the  reference  price  is  just  an 
approximation  to  the  alternative  cost  of  charging  that  same  EV  in  a  non-smart  station,  which  might  be 
located at any point.  

Eq. 15 Reference charging price 

∑

𝑝𝑟𝑒𝑓 =  

8760
𝑡=1
∑

∑
8760
𝑡=1

𝑋
𝑥=1
𝑋
∑
𝑥=1

𝑝𝑡 ∗ 𝑒𝑡,𝑥
𝑒𝑡,𝑥

Eq. 16 Energy required to charge an EV battery 

𝑒𝑡𝑥 =  

(𝑆𝑂𝐶𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 − 𝑆𝑂𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙) ∗ 𝐸𝑏
𝑒𝑓𝑓𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔

In  MODECO  operational  and  investment  models,  it  is  assumed  that  all  EVs  arrive  and  leave  with  the  same 
SOC values. Thus, the energy needed to charge the EVs in a non-smart charger is the same for all vehicles. 
Therefore,  once  the  reference  price  is  set  (pref),  it  is  possible  to  calculate  a  service  cost  (Scost)  that  can  be 
directly applied to each EV connecting into the Energy community’s chargers as stated in  Eq. 17. The users’ 
willingness  to  pay  is  accounted  for  in  these  costs,  discounting  5%  to  the  resulting  reference  price.  This  is 
viewed as an incentive  for  users to participate in  smart charging instead of  regular charging, which implies 
more intensive battery use. This service cost is used in the operational and investment models to estimate the 
economic gains of the Energy community through the provision of  EV charging services. The extra costs and 
benefits associated with the actual smart energy charging and discharging are accounted for in the model as 
part of the total energy that the community injects and extracts from the grid. 

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45 

 
 
 
 
 
 
 Eq. 17 Service cost applied to EV connecting to V2G charging stations 

𝑆𝑐𝑜𝑠𝑡 = 0.95 ∗   𝑝𝑟𝑒𝑓 

3.3.3  Community’s CO2 emissions 

The  Carbon  Dioxide  (CO2)  emissions  associated  to  the  community’s  energy  usage  are  calculated  for  the 
different electricity and heat sources prior to the installation of any energy asset. The emissions associated to 
the baseload electrical demand and EV usage is calculated based on the CO2 emissions from the energy mix 
used  in  each  evaluated  region,  and  obtained  from  the  UCED  model  execution.  In  the  case  of  heat,  the  CO2 
emissions  associated  to  Heat  pump  operation  is  calculated  on  a  similar  fashion,  based  on  the  electrical 
consumption from these assets obtained with the methodology explained in Section 3.2. 

The  emissions  associated  to  boiler  usage  are  calculated  through  the  volume  of  natural  gas  consumed  by 
these  units,  which  is obtained  by  multiplying  the  annual  heat  energy  provided  by  these  assets to  cover the 
community’s demand not supplied by heat pumps (MWh), plus efficiency losses, by the conversion factor from 
volume  to  energy  provided  by  the  European  Union  of  the  Natural  Gas  Industry  (Eurogas).  This  factors 
indicates that 1 m3 of natural gas is equal to 10.83 kWh (Eurogas, 2011), considering the gas gross calorific 
value. No conversion from gross to net calorific value is done as it is assumed that the substituted boilers are 
able to capture latent heat as most modern gas-based technologies do (Eurogas, 2011). The Greenhouse Gas 
Emissions  (GHG)  associated  to  natural  gas  burned  in  fuel  -based  boilers  is  estimated  using  the  default 
emissions  factors  for  stationary  combustion  in  the  residential  sector  from  the  Intergovernmental  Panel  on 
Climate Change  guidelines  (Chernova, 1966), presented in Table  23. To convert the  GHG factors from TJ to 
MWt  the  heat  unit  equivalents  from  Eurogas  are  considered,  assuming  gross  calorific  values  due  to  the 
reasons  explained  above  (Eurogas,  2011).  Methane  (CH4)  and  Nitrous  Oxide  (N2O)  are  converted  to  CO2 
equivalent considering typical conversion factors10. 

Table 23 GHG emission factors for natural gas combustion in the residential sector 

GHG 

CO2 

CH4 

N2O 

kg GHG/TJ 

Kg GHG/MWt 

56100.0000 

201.9438 

5.0000 

0.1000 

0.0179 

0.0004 

Source: Own elaboration with data from Eurogas (2011) and Chernova (1966). 

Finally,  the  avoided  CO2  emissions  from  boiler  substitution  by  heat  pumps  is  calculated  considering  the 
difference between the CO2 emissions associated to the electricity consumed by heat pump operation and the 
CO2 emissions calculated considering that the same heat would be supplied by boilers. The latter is calculated 
following the same steps used for the boilers actively used by the community. 

10 The emission of 1 kg of nitrous oxide (N2O) equals 298 kg of CO2 equivalents, and the emission of 1 kg of methane (CH4) is equal to 25 
kg CO2 equivalents (Statistics Netherlands, 2023). 

46 

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4  Models description 

As  mentioned  before,  three  optimization  models  are  used  in  MODECO  to  evaluate  the  impact  of  different 
energy tariffs in the investment and operational decisions of Energy communities. The key outputs and inputs 
to each model are summarized in Figure 14, while the specific values inputted to each case can be found in 
the  Annex  database.  As  observed  in  Figure  14,  the  models  are  interlinked  as  the  outputs  from  one  model 
serve as inputs in another. Specifically, the main output from the UCED model are the hourly marginal prices, 
which  are  used  to  build  the  energy  price  scenarios  tested  in  the  investment  model.  Similarly,  the  installed 
capacity  per  technology  and  year  decided  by  the  investment  model  are  used  as  inputs  for  the  operational 
model, in which the optimal operation of such assets is decided. Finally, the results from the investment and 
operational  models  are  used  to  modify  the  inputs  to  the  UCED  model,  before  re-executing  to  evaluate 
changes in the hourly marginal prices obtained.  

In the following sections, the main features from each model are described. Particular focus is given to the 
investment  and  operational  models,  as  these  are  developed  specifically  for  MODECO.  For  the  UCED  model, 
which was externally developed, only a general description is presented. 

4.1  Power system model 

The selected UCED model representing the entire European power system is built by the Joint Research Centre 
(JRC) using the object-based modelling toolbox PyPSA, an open source toolbox based on Python for simulating 
and  optimizing  modern  power  systems  that  include  features  such  as  conventional  generators  with  unit 
commitment, variable wind and solar generation, storage units, coupling to other energy sectors, and mixed 
alternating and direct current networks. PyPSA can calculate the linear optimal power flow, which is the least-
cost  optimization  of  power  plant  and  storage  dispatch  within  network  constraints,  using  the  linear  network 
equations, over several time steps. The project is maintained by the Department of Digital Transformation in 
Energy Systems at the Technical University of Berlin and further details be consulted in (Brown et al., 2018) . 

One  key  characteristic  is  that  the  model  covers  all  Europe,  including  Germany  and  Spain,  and  is  based  on 
ENTSO-E  (2020)  terminology,  which  permits  adapting  it  to  the  reference  ESES  with  minor  modifications.  In 
particular, it is considered an advantage that power plants are aggregated according to type – based on fuel, 
class,  efficiency,  etcetera  –  avoiding  the  need  to  have  data  for  each  specific  unit  in  the  European  power 
system  and  being  able  instead  to  use  general  technical  parameters  per  type  as  done  in  the  analysis  by 
ENTSO-E (2020). Other important aspects are that flows  between zones are based on NTC time series, and 
that demand response is modelled according to the ERAA methodology, where, similar to dispatchable power 
plants, energy is “generated” by reducing demand. 

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Figure 14. Schematic diagram of the optimization models used within MODECO project 

Source: Own elaboration. 

49 

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4.1.1  Model adaptation to the reference ESES 

As the selected UCED model was already based on ENTSO-E terminology, only a few parameters are changed 
to  consider  the  evolution  of  the  power  system  contemplated  in  the  reference  ESES  used  in  MODECO.  The 
capacity  installed  per  type  of  technology  in  2025,  2030  and  2040  is  defined  according  to  the  distributed 
energy  scenario’s  data  available  at  the  documentation  from  TYNDP’s  2020  edition  (ENTSO-E,  2021).  The 
considered capacities per technology and year can be seen in Section 2.1. 

In addition to the power plants capacity, the Demand Side Response (DSR) capacity per country and the cost 
associated with using it are also taken from the reference ESES database  (ENTSO-E, 2021). Finally, the fuel 
and CO2 emissions costs are also based on the values from the TYNDP 2020 scenarios. However, the costs 
for natural gas and CO2 emissions are updated based on recent data, as current prices are much higher than 
those  projected  in  the  reference  ESES,  even  though  an  increasing  trend  is  also  considered  in  the  reference 
scenario. Therefore, the prices registered in 2021 for natural gas (Eurostat, 2022) and carbon permits (Ember, 
2022) in the European Union are used as the starting cost in 2025, while a similar relative increase to that 
reported in the original ESES is assumed for 2030 and 2040. The results from this process are shown in Table 
24, while the rest of the fuel costs can be consulted in (ENTSO-E, 2021). 

Table 24 Indicators associated with solar PV and Energy communities. 

Year 

2025 

2030 

2040 

Natural gas cost [EUR/GJ] 

Carbon emissions cost 
[EUR/tCO2] 

Original 

Modified 

Original 

Modified 

6.46 

6.91 

7.31 

11.96 

12.79 

13.54 

23 

53 

100 

54 

124 

235 

*Used for the UCED model executions whose results are used and presented in this document. 
Source: own elaboration with data from Eurostat (2022), Ember (2022) and ENTSO-E (2021b). 

In order to avoid the occurrence of several hours per year in which demand is not met and the energy price is 
set  as  the  Value  of  Lost  Load  (VOLL),  the  capacity  of  gas-based  generation  (CCGT,  OCGT,  GAST)  originally 
considered in the reference ESES for all countries is expanded by 60% in 2040 in comparison to 2030. This 
was proposed after testing the model with the original inputs, which led to a high percentage (over 50% of 
hours in the year) of scarcity events reported for Germany in 2040. These findings do not necessarily reflect 
those obtained by ENTSO-E for the distributed energy scenario presented in the TYNDP 2020 report (ENTSO-E, 
2021a), as the model and technical parameters used are not the same. Given that MODECO’s objective is not 
to study resource adequacy in the future power system, expanding the available gas capacity is proposed as a 
simple way to ensure enough generation is available to cover demand at most of the annual hours. As would 
be further explained in Chapter 7, this modification managed to reduce the number of  hours in which load is 
not met to 16 for Germany’s 2040 system. In those cases, the VOLL was set as 3,000 €/MWh  as this is the 
price cap set for day-ahead markets in Europe up to the beginning of 2022. 

All  the  models’  macro  parameters  are  inputted  directly  in  the  Python  code  whereas  the  component  data  is 
imported  through  CSV  files  and  hdf5  tables.  Once  all  inputs  are  introduced  to  the  model,  its  resolution  is 
performed in two steps:  

1. 

2. 

 Seasonal  Hydro  Optimization  to  determine  the  minimum  storage  levels  through  a  temporal 
aggregation of the energy volumes based on a predefined resolution. 
 Rolling Horizon Dispatch Optimization. The  storage bounds are  fed to the model as a  lower bound 
for the reservoir levels.  

Once  these  steps  are  completed,  the  yearly  optimization  of  the  power  system  is  done  and  the  results 
analysed. As seen in  Figure  14, in addition to the hourly  marginal prices, the CO2 emissions and volume of 
energy dispatched per type of technology, renewable energies curtailed, and Energy Not Served (ENS) are also 
obtained for further analysis. 

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4.2 

Investment model 

The  investment  model  is  implemented  in  the  GAMS/CPLEX  solver  as  a  Mixed  Integer  Linear  Programming 
problem  (MILP).  The  temporal  scope  of  the  model  is  16  years,  and  its  temporal  resolution  is  hourly.  The 
potential investments included in the model are shown in Table 7. As explained before, not all energy assets 
are available to all archetypes; for instance, biomass-fuelled CHP is only considered in the Rural town case. In 
that case, the technologies that are not available are left out of the potential investments portfolio and do not 
form  part  of  the  investment  decision  process  for  that  archetype.  As  observed  in  Table  7  some  of  the 
technologies  have  subcategories  with  two  available  options.  These  are  represented  using  a  common 
modelling approach but specific costs and operational parameters (see Annex database). 

4.2.1  Representative day’s selection 

Due to the complexity of the model, in the optimization process it is not possible to consider 8760 hours as 
time steps for each year. Thus, a set of representative days per month are selected, reducing the amount of 
data inputted to the model. This is a common approach used in other similar models, such as the investment 
problem targeted in (Nahmmacher et al., 2016). The outcome of running the model for a different number of 
days selected, ranging from 1 to 100 representative days for a single year, was compared. As expected, the 
more number of days used, the more the results tend to approach the outcome using all representative days. 
However, the authors found that by using six representative days, the model output diverged in less than a 
4% from the solution with the 100 representative days. The conclusion is that the number of days selected 
has to be determined by analysing the trade-off between computational time and the solution’s accuracy.  

The specific process used in MODECO is based on the methodology proposed by  (Nahmmacher et al., 2016) 
and  it  is  applied  for  every  month  of  the  years  between  2025  to  2040  to  each  specific  case  (country, 
archetype, tariff scenario) considering a number of key variables influencing investment decisions: electricity 
purchase price (€/kWh), wind load factor, solar load factor, electricity demand (kWe), and thermal demand11 
(kWt).The methodology that the authors follows is based on the hierarchical clustering algorithm developed by 
(Ward, 1963) and can be observed with full detail in (Nahmmacher et al., 2016). On a fast note, the algorithm 
proceeds as follows:  

1.  Normalize all the time series considered. 

2.  Apply the clustering algorithm: 

(a)  For  every  historical  day  𝒅  a  vector  𝑽𝒅  is  created,  which  incorporates  all  values  of  the 
variables considered in that day. The dimension of this vector is the number of time slices 
multiplied by the number of variables considered.  

(b)  Initially, set the clusters 𝑪𝒅 = [𝑽𝒅 ] as a cluster containing the vector 𝑽𝒅,  
(c)  Compute the centroid 𝑪̅𝒅 of each cluster 𝑪̅𝒅 as the mean value of vectors in cluster, 
(d)  Compute the distance between clusters (metric = Euclidean distance), by using the centroid 

𝑪̅𝒅 as the representative value for the cluster. 

(e)  Join the two clusters where the minimum distance between clusters is obtained. 
(f)  Update the centroid of each cluster. 
(g)  Repeat steps (c) to (f) until only one cluster remains. 
(h)  Choose  a  number  of  representative  days  selected.  This  means  to  select  the  step  of  the 
process  where  the  desired  number  of  representative  days  corresponds  to  the  number  of 
clusters at hand. 

(i)  For each cluster 𝑪𝒅, choose the closer vector 𝑽𝒅 to the centroid 𝑪𝒅 as the representative day 

for the cluster, 

(j)  Define  a  weight  𝝎𝒅    to  each  cluster  𝑪𝒅, to  each  cluster  𝑪𝒅, as  the  number  of  vectors  𝑽𝒅  

that it contains. 

3.  Scale back the time series using the weight 𝝎𝒅 assigned to each day. 

11 The thermal demand variable  is not considered in the Virtual community archetype as CHP  installations are not considered a viable 
investment option.  

51 

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Finally, in this study case, two days per month are selected, with a total of 24 days being considered for every 
year. The investment planning’s scope is 16 years, and each day is composed by 24 time-slices, meaning that 
the  optimization  algorithm  is  executed  for  a  total  of  9216  time  steps.  This  number  of  days  has  been 
determined  after  comparing  the  behaviour  of  the  optimization  algorithm  with  a  different  number  of  days. 
When selecting more than two days per month, the optimization algorithm did not reach a solution within an 
acceptable  gap  and  time  (see  Box  1).  It  is  worth  mentioning  that  the  computational  power  and  the  time 
available in order to study the model heavily influences this selection, and in other contexts a greater number 
of days could have been selected.  

Box 1.  Defining “close enough” optimal solutions under limited testing times 

The  GAMS/CPLEX  solver,  in  which  MODECO’s  investment  and  operational  models  are  built,  permits  to  set 
criterions to stop the optimization process even when the optimal solution (BP) is not found. For this study, the 
Optcr  parameter  is  used  as  a  primary  option,  considering  acceptable  a  solution  with  Optcr  of  0.1%.  This 
entails that the CPLEX solver will  stop finding an optimal solution when the objective function value of the 
current  best  solution  (BF)  is  within  that  tolerance  level  [(|𝐵𝑃 − 𝐵𝐹|)/(1.0𝑒 − 10 + |𝐵𝐹|)   < 𝑂𝑝𝑐𝑡𝑟].  This 
reduces solution time as the solver stops not looking for better solutions.  

Although this tolerance level is reached in most of the results presented in this report, the solver was not able 
to find a solution within this range for some scenarios in a reasonable time (< 24 hours) to finalize this study. 
In  these  cases,  the  process  stop  criteria  was  changed  to  a  time  limit,  registering  the  theoretical  difference 
between the found and the best possible solution, refer as gap in this document. Given that the gap registered 
for  these  cases  was  significantly  large  (>10%),  an  additional  constraint  was  imposed  to  these  scenarios, 
defining  the  objective  function  as positive.  This change  managed  to  lower the  registered  gap  to  acceptable 
levels for most cases, but not all as will be discussed in Chapter 7. In these cases, the results are discussed 
after warning the reader about this issue to be interpreted with caution. 

More information about the solver parameters can be consulted in GAMS documentation (McCarl, 2016). 

4.2.2  Objective function 

The model’s objective function (Eq. 18) is designed to minimize the difference between economic benefits 
and  energy  costs  for  the  community.  The  general  form  of  the  model’s  objective  function  is  shown  in  the 
equation below. 

Eq. 18 Objective function for the investment model. 

𝐹  =   −𝐵𝑒𝑛 +   (𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓 + 𝐶𝑜𝑠𝑡𝑖𝑛𝑣 + 𝐶𝑜𝑠𝑡𝑜𝑝 + 𝐶𝑜𝑠𝑡𝑑𝑟 +   𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 +   𝐶𝑜𝑠𝑡𝑔𝑒𝑛), 𝑡𝑎𝑟𝑖𝑓𝑓 𝜖 {𝑇𝑂𝑈, 𝑃𝑃, 𝐵𝑊} 

The  first  term  Ben  accounts  for  all  the  benefits  obtained  in  the  16-year  period  as  compensation  for  the 
injection  of  surplus  energy  from the  Energy  community  to  the  distribution  network  and the  provision  of  EV 
charging  services.  The  rest  of  the  terms  are  all  the  costs  related  to  meeting  the  community’s  thermal  and 
electrical  demand  in  that  same  period,  whether  it  is  by  generating  it  locally  through  the  energy  assets 
installed or purchasing it from the grid. The specific definition for each term can be consulted in Table 25. 

𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓 is modeled differently depending on the tariff scenario; the rest 
The cost of purchasing electricity 𝐶𝑜𝑠𝑡𝑏𝑢𝑦
of the terms in the objective function equation are handled equally regardless of the tariff scenario imposed. 
Scenarios with Energy-based charges only (TOU, TOU_Flat, TOU_PPA, No Charges) are modelled considering 
a price vector specifying the hourly cost of electricity, which is then multiplied by the electricity purchased at 
each time step. As explained before, the hourly prices values are calculated according to the energy price case 
(dynamic, flat rate, PPA) plus taxes and Time-of-Use charges in the applicable scenarios. For the Bandwidth 
tariff scenario, a similar approach is used, but an additional charge is imposed to the consumed and injected 
power above the established limits. In this case, the price vector consists of the marginal prices plus taxes, as 
the  network  costs  are  recovered  through  fixed  monthly  costs  that  the  users  pay  for  their  contracted 
bandwidth power. This fixed cost is not included in the optimization as is not subjected to changes within the 
modelled variables. Finally, in the Peak power case, the same price vector as in the Bandwidth tariff is used, 
but  an  additional  charge  is  imposed  over  the  maximum  power  registered  by  the  community  on  a  monthly 
basis.  

To  incorporate  the  effect  of  time  in  the  value  of  money,  all  cash  inflows  and  outflows  in  future  years  are 
brought to a present value by using the discount rate considered in each scenario. This is done by multiplying 

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1

all costs and revenues by the term 

(1+𝑅)𝑦−1 , where R  is the discount rate and y is the number of time periods 
(years) since the starting year. We did not incorporated avoided energy costs as an explicit cash flow in the 
objective  function  as  this  benefit  is  already  implicit  in  the  minimization  of  the  electricity  purchased  costs 
𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓. Therefore, if the objective function is positive, meaning there are higher costs than benefits, it 
𝐶𝑜𝑠𝑡𝑏𝑢𝑦
does not mean that the proposed investments necessarily result in economic losses for the community as the 
avoided costs also need to be taken into account as an economic benefit. 

Table 25 Definition of the cost terms used in the investment model’s objective function 

Cost term 

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓 

𝐶𝑜𝑠𝑡𝑖𝑛𝑣 

𝐶𝑜𝑠𝑡𝑜𝑝 

𝐶𝑜𝑠𝑡𝑑𝑟 

𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 

𝐶𝑜𝑠𝑡𝑔𝑒𝑛 

Description 

It accounts for the total cost of electrical energy purchased in the evaluated timeframe. 
Three  different  types  of  electrical  purchase  costs  are  considered,  depending  on  the 
scenario  category:  Energy-based  (EB)  for  No  Charges,  TOU,  TOU_Flat  and  TOU_PPA 
scenarios,  Bandwidth  (BW)  and  Peak  Power  (PP)  for  the  Bandwidth  and  Peak  power 
scenarios, respectively. 

Total investment costs from all the energy assets installed in the 16-year period. It is 
computed by multiplying the capital expenses associated with each technology type for 
the  capacity  installed.  As  most  assets  have  a  useful  lifespan  beyond  16  years,  the 
equivalent  annual  investment  costs  from  these  years  are  discounted  from  the  total 
investment sum. In the case of the technologies that have a useful life lower than the 
investment period (V2G chargers and Electrolyser), the replacement cost is considered.  

Total  fixed  operational  expenses  –  defined  as  an  annual  fixed  sum  dedicated  to  the 
equipment’s  operation  and  maintenance  –  expected  in  the  16-year  period.  It  is 
calculated  using an OPEX factor equivalent to a percentage of the asset’s investment 
cost. The used factors for each technology can be consulted in the Annex database. 

Variable  costs  associated  with  the  activation  of  demand  response,  which  depends  on 
the total volume of energy shifted. 

Total  cost  associated  with  fuel  purchasing  for  the  operation  of  CHP  units  and  boilers. 
Note that three types of fuels are considered in MODECO  – natural gas, hydrogen and 
biomass – but not all are available for all archetypes (2.2.2). 

Use-of-Network  tariffs  applied  to  all  energy  produced  in  the  Virtual  Community 
archetype. The rest of archetypes are exempt from this cost given the network charges 
rules for physically closed generation and demand explained in Chapter 2. 

Source: own elaboration. 

4.2.3  Key model constraints 

As listed below, a set of general constraints are used in the investment model to serve different purposes: 

—  Time decision constraint. With the objective of reducing computational stress, the annual investments are 

always decided in the first hour (time step) of each year. 

—  Electrical  oversizing  constraint.  The  installed  storage  power  cannot  be  larger  than  the  local  power 

generation installed by the community. 

—  Storage oversizing constraint. The installed capacity from heat generation assets (boilers and CHP) cannot 
be  higher  than  15%  above  the  maximum  thermal  energy  demanded  by  the  community  in  the  16-year 
period.  

—  Rooftop  surface  constraint.  The  total  area  occupied  by  PV  solar  systems  installed  in  rooftops  cannot 

exceed the total area available at the community’s rooftops. 

—  Land surface constraint. The total area occupied by ground-mounted solar PV systems, wind turbines and 
hydrogen tanks cannot be higher than the total land surface available at the community for this purpose.  

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—  Thermal  oversizing  constraint.  The  installed  capacity  from  heat  generation  assets  (boilers  and  CHP) 
cannot be higher than 15% above the maximum thermal energy demanded by the community in the 16-
year period.  

The  surface  constraints  are  implemented  to  reflect  the  physical  limitations  typically  encountered  in  the 
defined archetypes regarding the surface availability to installed energy assets  such as those  considered in 
MODECO. In particular, it is important to consider that ground-mounted PV solar and wind turbines compete 
for the same area as both need to be in open air spaces. Hydrogen tanks are also expected to be installed in 
open air surfaces, which is why their area is also taken into consideration for the land surface constraint. CHP, 
electrolyzer and batteries are not contemplated in this limitation as it is assumed that they can be installed in 
other available spaces, such as already existing facilities like a warehouse. In the case of the rooftop surface 
constraint, only the area from solar PV systems installed in rooftops is considered. 

The  rest  of  constraints  limit  the  amount  of  power  generation  and  storage  that  can  be  installed  inside  the 
community. These limits,  however, are based on arbitrary decisions interpreting the definition of Renewable 
and Citizen energy communities that indicates that generating financial profits  must not be the community’s 
main  purpose  although  they  are  able  to  provide  economic  benefits  to  their members,  shareholders or local 
areas in which they operate. Within MODECO, it is assumed that installing excess generation capacity with the 
sole purpose to sell energy in the wholesale market should not be promoted as it would be a financial profit-
led  activity.  Still,  it  is  reasonable  that  communities  could  generate  excess  energy  at  some  hours  in  which 
demand is low and stored in batteries to be consumed at later times, when it is needed. A reasonable limit to 
ensure  this  is  to  limit  power  generation  capacity  to  the  community’s  peak  demand  as  proposed  in  the 
electrical oversizing constraint.  

The  storage  capacity  is  also  restricted  to  fit  the  maximum  local  generation  capacity  installed  (storage 
constraint), preventing the installation of numerous storage units to act as stand-alone batteries that charge 
at  low-priced  periods,  increasing  the  community’s  demand  to  re-sell  energy  later  during  peak  priced  hours. 
Notably, a first  version of the model  did not include such constraint and  with the future reference  scenario 
prices,  it  led  to  extremely  high  storage  installations  that  were  financed  through  energy  arbitrage  revenues 
obtained  at  specific  days  towards  the  end  of  the  evaluation  period.  Nonetheless,  it  is  relevant  that 
communities could still engage in energy arbitrage up to a certain extent, which supported battery usage for 
increasing self-consumption. This is important considering that grid flexibility is also an important benefit that 
communities could provide to the system. 

Finally,  the  thermal  oversizing  constraint  restricts  the  heat  generation  capacity  of  CHP  units  to  the 
community’s  peak  thermal  demand  as  wasted  heat  production  is  considered  misaligned  to  sustainable  and 
efficient energy usage, which goes against the provision of environmental benefits and towards maximizing 
financial  gains.  In  this  case,  however,  the  power  generated  could  be  larger  than  the  community’s  demand, 
thus  generating  surplus  electricity  to  be  sold  to  the  grid.  As  noted,  a  15%  margin  is  considered  to  provide 
some operational flexibility. 

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Box 2 Drawing the line between economic benefits and purely financial profit generation 

Three  of  the  investment  model  constraints  were  proposed  based  on  the  principle  that  Energy  communities 
should  not  engage  in  energy  activities  with  the  sole  purpose  to  generate  financial  profits.  Nevertheless, 
representing such nature into an optimization model that could be applied to different archetypes and regions 
presents new conceptual challenges. In national regulations, communities’ investments might be constraint by 
rules  such  as  those  currently  applied  to  collective  self-consumption  in  Spain  (Ministerio  para  la  Transición 
Ecológica,  2019)  which  limits  the  number  of  members  that  can  be  part  of  it  to  a  certain  geographical 
extension (maximum of 2 km between furthest participants) and provides larger financial incentives to energy 
that is released (generated or discharged) at the same time as demand. However, a generic model like that 
designed  for  MODECO  cannot  rely  on  such  specific  rules.  Still,  it  must  reflect  the  difference  between 
community-led energy investments and those guided by maximizing financial profits, especially as the latter 
are also expected to be risk takers while communities would probably follow a more conservative investment 
strategy. The proposed set of constraints seems to fit this purpose to a certain extent, but as will be seen in 
Chapter 7, they might need some further thought to better reflect communities’ nature in contexts in which 
prices  promote  the  installation  of  purely  merchant  projects.  Nonetheless,  the  question  of  whether  or  not 
communities should  be  assumed,  or even  encourage, to  take  part  in  these  activities remains,  particularly  if 
they  represent  potential  benefits  for  the  whole  system,  for  instance,  by  providing  flexibility  services  or 
contributing  to  shifting  demand  to  hours  when  more  generation  is  available.  This  is  a  relevant  point 
considering  that  the  internal  electricity  market  directive  (EU  2019/944)  and  the  revised  renewable  energy 
directive  (2018/2001/EU)  mandate  EU  countries  to  allow  the  participation  of  Energy  communities  on  all 
market activities, accessing the same support schemes as larger participants. So, where is the line between an 
energy investment led by profit and one whose main purpose is to return economic, environmental or social 
benefits?  Reaching  a  consensus  over  this  aspect  might  help  to  improve  the  design  of  models  such  as  that 
proposed  by  MODECO.  Another  important  aspect  is  the  incorporation  of  different  business  models  into  the 
Energy community archetypes proposed in this study, for  instance, energy cooperatives might  have more in 
common with traditional energy investors than a group of neighbours looking to become self-sufficient and 
reduce their energy bills. 

4.2.4  Energy balance equations 

The mathematical formulation for the investment model can be consulted in Annex 1 while a summary of the 
balance equations applied in the investment model are presented in this section. These are used to maintain 
an  equilibrium  between  the  different  energy  flows,  including  energy  generated  and  consumed  within  the 
Energy community’s boundaries, and that imported and exported from outside. This balance includes not only 
electrical but also thermal energy flows, and the energy carriers that might be potentially used to generate 
heat and power (natural gas, hydrogen and biomass).  

Electrical power balance.  In the electrical power balance, at each hour, the constraint indicated in Eq. 19 
must be satisfied. The term for the electrical power generated by assets [𝐸𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑] is calculated from all 
the generation assets that can be potentially installed in each archetype and which were described in Table 7. 
This includes solar and wind generation, CHP electrical generation, and power discharged from batteries or EV 
through the V2G charging points. The electrical power consumed by assets [𝐸𝑃𝑎𝑠𝑠𝑒𝑡𝑠] is defined by the power 
charged  by  storage  devices  (batteries  and  EV)  and,  in  the  case  of  the  industrial  polygon,  the  electricity 
consumed by the electrolyzer. The electrical demand [ED] refers to the electricity needed by the community to 
satisfy  its  members’  demand,  which  considers  the  community’s  electrical  load  modelled  and  the  shifting 
possibilities  offered  by  the  Demand  Side  Response  (DSR)  characteristics  considered.  Finally,  the  electrical 
power bought [𝐸𝑃𝑏𝑜𝑢𝑔ℎ𝑡] and electrical power sold [𝐸𝑃𝑠𝑜𝑙𝑑] refer to the electricity imported and exported from 
the grid to complement the local generated electricity to satisfy the community and the assets’ demand. 

Eq. 19 Electrical power balance 

𝐸𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 + 𝐸𝑃𝑏𝑜𝑢𝑔ℎ𝑡 =  𝐸𝐷 + 𝐸𝑃𝑠𝑜𝑙𝑑 + 𝐸𝑃𝑎𝑠𝑠𝑒𝑡𝑠 

Heat balance. The thermal energy balance is satisfied at each hour given the constraint indicated in  Eq. 20. 
The thermal power generated by assets [𝑇𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑] term is calculated from the thermal energy generated 
by  CHP  units  and  boilers,  while  the  thermal  demand  [TD]  corresponds  to  the  heat  demanded  by  the 
community  to  meet  its  water  and  space  heating  requirements,  plus  the  process  heat  in  the  case  of  the 

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Industrial polygon. This balance is not considered for the Virtual community archetype as investments in CHP 
units are not considered a possibility in this case. 

Eq. 20  Thermal balance 

𝑇𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑇𝐷 

Fuel balance. The balance for the supply and demand of the fuels used by the community are given by Eq. 
21, Eq. 22 and Eq. 23 for natural gas, biomass and hydrogen, respectively. In the natural gas balance, the fuel 
consumption from CHP and boilers [𝐶𝐻4𝑎𝑠𝑠𝑒𝑡𝑠 ] must be equal to the gas bought [𝐶𝐻4𝑏𝑜𝑢𝑔ℎ𝑡 ] as it is the only 
source possible. A similar equation is applied to  biomass, a fuel only available in the  Rural town archetype. 
Lastly, the  hydrogen  balance  considers  that  the  hydrogen  stored  in  the  hydrogen  tank  or  consumed  by  the 
community’s  boilers  and  CHP  [𝐻2𝑎𝑠𝑠𝑒𝑡𝑠 ]  must  be  equal  to  that  bought  from  outside  [𝐻2𝑏𝑜𝑢𝑔ℎ𝑡 ]  plus  the 
internally  produced  hydrogen  by  the  electrolyzer  [𝐻2𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑]  in  those  cases  in  which  this  equipment  is 
available (Industrial polygon). 

Eq. 21 Hydrogen balance 

Eq. 22 Biomass balance 

Eq. 23 Hydrogen balance 

𝐶𝐻4𝑏𝑜𝑢𝑔ℎ𝑡   = 𝐶𝐻4𝑎𝑠𝑠𝑒𝑡𝑠  

𝐵𝐼𝑂𝑏𝑜𝑢𝑔ℎ𝑡 = 𝐵𝐼𝑂𝑎𝑠𝑠𝑒𝑡𝑠 

𝐻2𝑏𝑜𝑢𝑔ℎ𝑡   + 𝐻2𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 = 𝐻2𝑎𝑠𝑠𝑒𝑡𝑠  

4.2.5  Energy assets modelling 

The  mathematical  formulation  of  the  energy  assets  considered  in  MODECO  is  done  based  on  standard 
approaches used in the literature and can be consulted in Annex 1. For most energy assets, a similar approach 
is  used  in  the  investment  and  operational  models,  except  when  adaptations  are  needed  to  take  into 
consideration that the capacity installed in the investment model is unknown at the start of the optimization 
or that representative days are used instead of the whole year vector. The values used for all the technical 
parameters required can be consulted in the Annex database associated with this report. 

Wind  turbines  and  Solar  PV.  Both  systems  are  modelled  considering  the  load  factor  curves applicable  to 
each  country.  The  hourly  generation  is  then  obtained  by  multiplying  the  hourly  load  factor  by  the  asset’s 
installed capacity, which is defined as a variable.  

Electrical storage assets are represented with a modified approach to the typical equation (Eq. 24) used to 
model batteries in which the State of Charge (SOC) is represented as a percentage (%) of the total capacity, 
which  results  in  a  nonlinear  model  as  the  installed  capacity  is  unknown.  To  avoid  non-linearity,  instead  of 
modelling  the  SOC  (%),  the  approach  used  in  MODECO,  models  the  energy  (kWh)  inside  the  battery  (e)  as 
shown in Eq. 25.  

Eq. 24 Traditional approach used for modelling electrical storage 

𝑖𝑛𝑠𝑡 = 𝑆𝑂𝐶𝑡−1 ∙ 𝑒𝑡−1
Eq. 25 Proposed approach to avoid nonlinearity when modelling electrical storage 

𝑖𝑛𝑠𝑡   + 𝐶𝐻𝐴𝑅𝐺𝐼𝑁𝐺 𝑃𝑡 −   𝐷𝐼𝑆𝐶𝐻𝐴𝑅𝐺𝐼𝑁𝐺 𝑃𝑡 

𝑆𝑂𝐶𝑡 ∙ 𝑒𝑡

𝑒𝑡 = 𝑒𝑡−1 + 𝐶𝐻𝐴𝑅𝐺𝐼𝑁𝐺 𝑃𝑡 −   𝐷𝐼𝑆𝐶𝐻𝐴𝑅𝐺𝐼𝑁𝐺 𝑃𝑡 

Note that the maximum charging/discharging power of the battery cannot be known in advance, as it depends 
on the capacity installed as a result of the investment decisions made. Thus, the charging/discharging power 
given to the Electrical Storage is limited by the product of the C-rate and the current installed capacity and 
not  by  a  maximum  charging/discharging  power,  which  avoids  nonlinearity  problems.  The  C-rate  gives  a 
relation  between  the  capacity  installed  and  the  maximum  charging/discharging  power  available.  It  must  be 
noted that the battery can only charge or discharge at a given time step, as a restriction is imposed to avoid 
the simultaneity of these two activities. 

As the  investment  model  is  applied  to  a  certain  number  of  representative  days in  the  year,  the  investment 
strategy and the assets management is not decided over a continuous time period. Thus, a constraint is set to 
define the initial SOC of the battery in the first time step as equal to  50% on a daily basis. The SOC of the 
battery at the end of each day is also set to a predefined value (50%) as, without this constraint, the model 
would try to discharge the battery at the final time steps of each day to sell electrical surpluses to the grid. 

Hydrogen tank. For this asset type a similar problem to the electrical storage is found as the pressure level 
(Pa) of the tank must be modelled while having the tank’s volume as a variable, which results in a nonlinear 

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equation  when  the  typical  approach  is  used.  Let  𝑞𝑡,  𝑣𝑖𝑛𝑠𝑡  be  the  pressure  level  of  the  tank  and  the  total 
volume  installed,  respectively,  then  the  pressure  inside  the  tank  is  typically  modelled  as  shown  in  Eq.  26 
where K is a constant given  by two  parameters (mean temperature inside the  vessel  and the universal gas 
constant).  

Eq. 26 Traditional approach used for modelling hydrogen tank storage 

𝑞𝑡 =   𝑞𝑡−1 + 𝐾 ∙

𝐻2 𝑖𝑛𝑓𝑙𝑜𝑤𝑡 − 𝐻2 𝑜𝑢𝑡𝑓𝑙𝑜𝑤𝑡
𝑣𝑖𝑛𝑠𝑡

As observed in the equation above, the volume of the tank divides the hydrogen inflow/outflow. Given that all 
these  three  are  variables,  it  results  in  a  nonlinear  model.  To  solve  this  problem,  instead  of  modelling  the 
pressure level (Pa), the quantity of Hydrogen (mol) inside the tank is used, which ensures linearity. Let  𝑚𝑜𝑙𝐻2 
be the mols inside the tank, the following equation is proposed: 

Eq. 27 Proposed approach to avoid nonlinearity when modelling the hydrogen storage tank 

𝑚𝑜𝑙𝐻2,𝑡 = 𝑚𝑜𝑙𝐻2,𝑡−1 + 𝐻2 𝑖𝑛𝑓𝑙𝑜𝑤𝑡 − 𝐻2 𝑜𝑢𝑡𝑓𝑙𝑜𝑤𝑡 
In order to bound the moles of hydrogen inside the tank by the installed volume 𝑣𝑖𝑛𝑠𝑡, a constraint to limit the 
maximum hydrogen inflow/outflow is applied using the product from the C-rate and the tank volume. The C-
rate gives a relation between the volume installed and the maximum possible inflow/outflow of hydrogen. The 
initial and final state of the tank’s pressure is imposed through a set of constraints for the start and end of 
each day. The initial state value is applied as non-continuous days are used, while defining a minimum tank’s 
pressure  for the  final  state  prevents  the  tank  from fully  discharging  at  the  end of  each  day.  Similar to  the 
electrical storage case, the tank cannot simultaneously charge and discharge hydrogen at a given time step. 

Electrolyzer  is  modelled  by  assuming  a  linear  relation  between  power  consumption  and  hydrogen 
generation.  The  maximum  power  consumed  by  the  electrolyzer  at  each  time  step  (hour)  is  limited  by  the 
power installed. 

V2G charging stations. As the number of V2G chargers installed is a variable in the investment model, the 
input curves with the number of vehicles connecting and disconnecting at each time step are built assuming a 
high  number  of  chargers  available.  These  are  then  interpreted  by  the  model  as  the  number  of  vehicles 
wanting to connect and leave the station. For the individual EV, the following assumptions are made: 

—  All  the  EVs  considered  are  assumed  to  have  the  same  battery  capacity  𝐸𝑏  each  year.  This  battery 
capacity  is  calculated  considering  a  mean  value  from  the  typical  sizes  in  current  and  future  EV 
models. More information about these assumptions can be consulted in Section 3.3.2. 

—  All the vehicles are assumed to arrive at the station with the same state of charge 𝑆𝑂𝐶𝑖𝑛𝑖 and leave 

at the same state of charge 𝑆𝑂𝐶𝑓𝑖𝑛. 

—  The EV’s SOC has to be in a certain range [𝑆𝑂𝐶𝑚𝑖𝑛, 𝑆𝑂𝐶𝑚𝑎𝑥]. 
—  All  EVs  are  assumed  to  stay  connected  at  the  charging  station  for  time  periods  between  3  and  7 

hours with a mean charging duration of 5 hours as reported by (Corchero García, 2015). 

To reduce computational stress, all the batteries from the vehicles connected to the V2G points are treated as 
a  single  unit  whose  total  power  and  capacity  is  the  sum  of  all  the  batteries  in  the  connected  EV  pool.  The 
charging and discharging power of the battery pool is limited by the product between the number of vehicles 
connected and the maximum charging/discharging power of each V2G charger. It must be noted that each of 
𝑚𝑎𝑥    that  limits  the  power 
the  V2G  chargers is assumed  to  have  a  maximum  charging/discharging  power  𝑃𝑉2𝐺
that  can  be  delivered  to  the  vehicle.  Constraints  to  limit  the  upper  and  lower  bounds  of  the  battery  pool’s 
energy levels are applied using the number of vehicles connected at time t, the vehicles that want to connect 
at  t  and  the  vehicles  that  want  to  leave  at  time  t-1,  as  well  as  constraints  applied  to  the  individual  EV 
regarding  their  SOC  levels  and  explained  above.  The  specific  constraints  used  and  its  mathematical 
formulation can be consulted in this document’s Annex. 

Combined Heat and Power (CHP).  A simplified  model  considering a linear relation between the heat and 
power  production  of  the  CHP  units  is  selected  for  the  investment  model.  The  linear  relation  is  established 
through  a  conversion  factor  specific  to  each  CHP  subtype  [𝐶𝐻𝑃𝑔𝑎𝑠, 𝐶𝐻𝑃𝑏𝑖𝑜𝑚𝑎𝑠𝑠].  The  use  of  more  detailed 
approaches, such as that applied in the operational model, is discarded as it adds complexity as the installed 
capacity is a variable in this case. In the proposed linear model, the following constraints are applied: 

—  The CHPs cannot generate more electrical power than the nominal power installed. 
—  The CHP’s state (on/off) at each time step is controlled via a binary variable. 

57 

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—  CHPs are considered to be always on at the first time step of each day. 
—  The CHPs can only be switched off and on once per day; respecting minimum up and down times is 

obliged. 

—  A  linear  relation  between  electrical  power  generated  and  fuel  consumption  is  established  using  a 
conversion factor specific to  each fuel. Note that   𝐶𝐻𝑃𝑔𝑎𝑠 can consume both  hydrogen and natural 
gas, although not at the same time, while 𝐶𝐻𝑃𝑏𝑖𝑜𝑚𝑎𝑠𝑠 can only consume biomass. 

Boilers. The same model is applied to the two boiler categories considered in MODECO: regular and industrial. 
It considers that a linear relation exists between the thermal power produced and the fuel consumed at each 
time step. As assumed for the CHP equipment, the communities’ boilers can be fuelled by hydrogen or natural 
gas, but not simultaneously.  Only one fuel can be used at each time step. Finally, a constraint is applied to 
limit the maximum thermal power produced by the boilers to the total boiler capacity installed each year. 

Demand  Response.  In  MODECO,  demand  response  is  provided  by  heat  pumps,  which  are  considered  a 
flexible  load  within  the  modelled  communities.  Within  the  model,  demand  response  operations  are 
constrained  by  an  upper  and  lower  limit  for  increasing  or  decreasing  the  heat  pump's  demand.  These  are 
defined  based  on  the  percentage  of  customers assumed  to  be  willing  to  participate  in  the  provision  of  this 
service and the technical restrictions associated with heat pumps. If the increase or decrease is higher than 
the limit, customers’ needs will not be satisfied. Additionally, an upper limit for the consecutive hours that the 
demand response service might be used is imposed. If demand response is used for large periods of times, 
there is a risk that customers' needs won’t be fulfilled causing a future loss of profit.  For similar reasons, a 
maximum  number  of  times  that  demand  side  response  can  be  activated  per  day  is  set  as  an  operational 
constraint.  

The assumptions made for demand response and the energy assets considered in the investment model can 
be consulted in Chapter 3. 

4.3  Operational model 

The  goal  of  this  model  is  to  obtain  the  optimal  energy  planning  of  the  communities'  energy  assets  at  an 
hourly level in an annual horizon, by minimizing its operational costs. The mathematical model is classified as 
a  Mixed  Integer  Linear  Problem  (MILP)  as  integer  and  binary  variables  are  needed  to  describe  the  energy 
asset’s operational modes. As such, the objective function and all the constraints needed are linear. Contrary 
to  the  investment  model,  the  operational  model  is  executed  individually  for  each  target  year  and  scenario 
considered  in  this  analysis.  This  permits  to  use  the  8760  time  steps  in  a  year  without  the  need  to  select 
representative  days.  The  operational  model  outputs  the  optimal  usage  of  the  technology  for  every 
combination of year, archetype, and energy tariff scenario studied in this project, indicating the corresponding 
energy  production,  energy  usage,  heat  produced,  biomass  consumed,  gas  consumed,  hydrogen  produced, 
hydrogen consumed, emissions and marginal prices for technology. The key inputs and outputs used for the 
operational model are presented in Figure 14. 

4.3.1  Objective function 

The  objective  function  used  in  the  operational  model  consists  of  the  minimization  of  the  difference 
between  the  economic  benefits  and  costs  associated  with  the  community’s  energy  management  in  the 
evaluated  year  (Eq.  28).  Aside  from  a  shorter  time  horizon,  the  main  difference  when  compared  to  the 
objective function used for the investment  model is that the investment  costs (𝐶𝑜𝑠𝑡𝑖𝑛𝑣) are  not included in 
the function as this is no longer a variable to be optimized. Moreover, as CHP is modelled with more detail in 
this case (see Section 4.2.5), the equipment’s start-up cost is computed as a specific term (𝐶𝑜𝑠𝑡𝐶𝐻𝑃). The rest 
of the components are the same as in the investment model, which also includes the differentiation between 
the purchase electricity costs depending on the tariff structure evaluated. 

 Eq. 28 Objective function for the operational model 

𝐹  =   −𝐵𝑒𝑛 +   (𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓 + 𝐶𝑜𝑠𝑡𝑜𝑝 + 𝐶𝑜𝑠𝑡𝑑𝑟 +   𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 +   𝐶𝑜𝑠𝑡𝑔𝑒𝑛 + 𝐶𝑜𝑠𝑡𝐶𝐻𝑃) , 𝑡𝑎𝑟𝑖𝑓𝑓 𝜖 {𝐸𝐵, 𝑃𝑃, 𝐵𝑊} 

4.3.2  Balance equations 

The  balance  equations  used  for  the  operational  model  are  similar  to  those  described  for  the  investment 
model in Section 4.3.2. The specific equations applicable to this model can be consulted in Annex 3. 

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4.3.3  Energy assets modelling 

All the energy assets that can be potentially installed in the Energy communities are modelled and included in 
the operational model (see Table 7). Nonetheless, these are only activated if their availability in the evaluate 
year has been decided by the investment model. Note that some of the energy assets are only considered a 
potential investment for some specific archetypes, for instance, the biomass-fuelled CHP is only available for 
the Rural town archetype. Given that a generic operational model is used for all cases, the technologies that 
are not considered in one archetype are simply not activated as happens with the assets that were not part of 
the  investment  decisions  made.  In  the  following  paragraphs,  a  brief  explanation  of  the  modelling  approach 
used for each energy asset is given while the specific mathematical formulation can be found in Annex 2.  

Solar PV and wind turbines. No further explanation is given as they are represented as in the investment 
model using the load factors applicable to each technology and location and the installed capacity, which in 
this case is not a variable but a given input. 

V2G charging stations. To model a charging point with V2G capabilities, the state of charge (SOC) of the EV 
battery should be included in the operational model as an available and accessible data to be able to decide 
when  the  EV  battery  should  be  charged  or  discharged  to  meet  both  the  EV  owner  needs  and  Energy 
community  interests.  The  charging  and  discharging  modes  are  decided  using  binary  variables  to  model  the 
bidirectional  operation  of  these  chargers,  and  when  a  binary  variable  is  introduced,  the  model  becomes  a 
combinatorial problem with a harder computational requirement. This is not a problem per se, except when a 
large  number  of  charging  points  are  considered  as  the  computational  time  required  to  find  the  optimal 
solution might be too large to be feasible. To avoid this problem, the operation model proposed for MODECO 
is inspired by the authors of (Quiros-Tortos et al., 2018) that suggest using an aggregated solution in order to 
reduce the number of binary variables in the operational model.  
The assumptions made for V2G charging points model following this approach are listed below:  

—  All  electrical  vehicles are  aggregated  to  form  a  single  pool  of  electrical  batteries that  act  as a  storage 
unit, hence the energy and power capacities of the EVs are also aggregated by category. This includes all 
types of EVs considered in each archetype. Thus, the number of EVs per type connected at the V2G points 
must be known to calculate the aggregated batteries capacity available for every single hour. 

—  The optimization model decides the behaviour of the aggregated pool for every time step. The time steps 
have been defined on an hourly basis according to the specifications made for both the operational and 
the investment models. Then, if the pool starts charging or discharging at the beginning of a time interval 
with a determined power value, it is supposed that this operation point is the same during the whole hour.  
—  The battery capacity values will be in line with the values defined for the reference models described in 
Table 21. The number of vehicles per model is decided following the technological evolution assumed for 
private  charging  points.  In  2025,  mostly  EV  with  low  capacities  are  considered,  whereas  for  future 
timespans, the number of EVs with larger capacities increments. This is in line with (Gaete-Morales et al., 
2021) that states that the typical EV battery size in 2010 was 30 kWh; today 60 kWh is not an exception 
anymore and by 2030 the battery capacity for new vehicles will be over 80kWh.  

—  The  maximum  state  of  charge  and  depth  of  discharge  of  the  entire  vehicle  pool,  as  well  as  the 
efficiencies remain constant. These maximum states of charge and depth of discharge will be calculated 
as  the  average  of  the  current  values  for  this  technology,  since  they  are  quite  stable  values  over  time, 
whereas efficiencies will be considered 95% as for private charging points.  

—  Corchero  Garcia  (2015)  reported  statistical  data  from  several  European  electric  vehicles  and  charging 
points monitored during three years. Based on their results for EVs of private use, it can be assumed for 
this work that the initial SOC for every electrical vehicle connecting to the charging station at every time 
is considered to be 58% and the request SOC at departure time is considered to be 84% (Corchero García, 
2015). 

Apart  from  assumptions  and  parameters  values,  the  model  has  some  constraints  explained  below  whose 
mathematical formulation can be consulted in Annex 2:  

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1.  Two constraints aggregating all available energy and the power capacities of all EVs in a particular 
time. Specifically, the capacity of each EV type is multiplied by the number of this EV type connecting 
in each hour. 

2.  All EVs that arrive or depart at time interval t are assumed to do so at the start of the interval and 
remain in that state without any further cars arriving or departing until the start of the next period. 
Note that the main input for this model is the number of electrical vehicles of each considered type 
arriving or departing at every period of time.  

3.  The  energy  balance  equation  of  the  aggregated  battery  pool  illustrates  the  fact  that  all  the  EVs 
connecting  or  disconnecting  at  a  certain  time  period  have  the  same  energy  levels  across  their 
batteries. 

4.  The energy level of the pool is not allowed to surpass the maximum SOC defined, or be inferior to the 

minimum SOC established.  

5.  The last set of constraints ensure that the upper and lower power limits for charging and discharging 

at every time step cannot be surpassed.  

Electrical  storage.  As  the  electrical  storage  capacity  is  known  from  the  start,  batteries  can  be  modelled 
using  the  typical  approach  shown  in  Eq.  24  without  any  particular  assumptions  needed.  Nonetheless,  the 
following set of constraints must be taken into consideration: 

—  The  energy  level  of  charging  and  discharging  cannot  surpass  the  battery’s  upper  operational  limit. This 

ensures safety operation and expands the battery’ life expectancy.   

—  Discharge and discharge cannot be performed simultaneously. A real battery can only perform one action 

at a time.   

—  The electrical storage SOC fluctuates according to the operational needs but cannot exceed the maximum 
and minimum operational levels. These limits are defined based on the batteries’ technical characteristics 
and can be consulted in the Annex database. 

—  Efficiency losses are incorporated when charging and discharging the battery, this represents that some 

energy is lost when using the battery as happens in real storage systems. 

—  Final SOC is considered equal to the battery’s initial SOC. Without this constraint, the model will empty all 
the batteries to sell electricity before the day is over and no battery capacity will be available for the next 
start.  

Combined Heat and Power (CHP). As the installed CHP capacity is known, more complex approaches can be 
used to represent the features of this equipment in the operational model. In this case, the heat and power 
production of the CHP unit is not defined through linear relations but by the equipment’s feasible operating 
region, which is represented through a trapezoid (Figure 15) delimited by four operational points (A, B, C, D). 
Although other approaches are found in the literature, for instance using more operational points, the feasible 
operating region considered in MODECO is the same as suggested by the authors of (Mansouri et al., 2020).  

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Figure 15. Feasible operational region for a CHP unit given four operational points 

Source: (Mansouri et al., 2020) 

As  explained  before,  the  CHP  units  can  be  operated  using  gaseous  fuels  –  natural  gas  or  hydrogen  –  or 
biomass (pellets). In both cases, the same modelling approach is applied although the values used to define 
the operational points are specific to each fuel category (gases, biomass). The general constraints considered 
for this technology are: 
A set of constraints representing the operational points forming the unit’s feasible operating region and the 
relation between heat and power conversion at each point: 

— An upper and lower limit for energy and heat production that cannot be surpassed. These are related to 
the operational points and are defined to ensure safety operational boundaries and avoid negative impacts 
on the units’ useful life expectancy. 

— An  upper  limit  for  power  and  heat  related  to  the  gas,  hydrogen  and  biomass  consumed.    As  explained 
before, these constraints vary depending on the CHP used, the parameters of each raw material consumed 
is different.   

— As  done  in  the  investment  model,  the  operational  model  contemplates  the  possibility  to  shut  down  the 
equipment if their operation is not economically feasible and restart it at a later period. However, in this 
case, minimum up and down times are considered to restrict the number of times this can happen in a day 
in addition to the shutdown costs. 

Additionally, the proposed model permits to take into account the costs associated  with the shut  down and 
following restart of the machine (𝐶𝑜𝑠𝑡𝐶𝐻𝑃). The CHP’s shutdown is assumed to have null costs but the start-
up  costs  are  valued  as  equal  to  the  costs  of  the  extra  fuel  required  to  warm-up  the  engines,  which  is 
calculated as the required fuel to operate the machine during 10 minutes at nominal power. 

Electrolyzer. This equipment produces hydrogen through a chemical  reaction initiated by electrical current. 
This  hydrogen  produced  is  able  to  fill  the  hydrogen  tank  or  be  used  as  a  raw  material  for  the  CHP.  The 
constraints applied are: 
—  An  upper  and  lower  limit  for  the  hydrogen  produced.  This  equation  is  to  ensure  safety  and  ensure  the 

electrolyzer maintains its useful life expectancy. 

—  The  maximum  power  cannot  exceed  the  renewable  energy  production.  It  must  be  noted  that  the 
electrolyzer  is  assumed  to  be  only  powered  by  renewable  energy  as  only  green  hydrogen  usage  is 
considered in MODECO’s energy communities.  

—  A loss of efficiency production is considered. These losses reflect on less hydrogen produced per energy 

consumed.   

Hydrogen  storage  tank.  The  hydrogen  tank  can  be  filled  with  the  hydrogen  produced  by  the  electrolyzer 
and be later used as fuel in the CHP or boiler units. The considered constraints for this technology are:  

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—  An upper and lower limit for the storage of the hydrogen. It’s not feasible to fill the tank more than the 

tank capacity. This constraint guarantees that the hydrogen doesn’t exceed the capacity.   

—  An upper and lower limit of charging and discharging storage. This equation is to ensure safety and make 

the hydrogen tank have a longer life expectancy of use. 

—  The gas pressure inside the tank cannot exceed an upper limit. This equation is also to ensure safety and 

prolong the life expectancy of the tank.   

—  The final pressure of the tank must be the same as the initial pressure. Without this constraint, the model 

will empty the tank and no hydrogen will be available to use after the last time step.  

—  A hydrogen balance equation, between the tank, the boiler, the CHP, the hydrogen available in the tank 

and the charging and discharging hydrogen.   

—   
Boilers. Boilers, regular and industrial, are included in the operational model following a similar approach to 
the investment module. The only difference is that the total thermal capacity installed is not a variable but a 
given input. 
—   
Demand  response.  Demand  response  is  modelled  as in  the  investment  model  as  no  investment  decisions 
are  made  through  the  optimization  model.  Instead,  the  parameters  associated  to  this  feature  are  defined 
exogenously as done for the investment model. 

4.3.4  Calculation of CO2 emissions 

The  emissions  from  the  operation  of  the  local  generation  assets  is  calculated  considering  the  emissions 
factors associated to each available fuel (Table 26). From the considered energy assets, only CHP lead to CO2 
emissions when operated with natural gas or biomass. As the operational model outputs the hourly electrical 
generation  per  asset,  the  aggregated  annual  values  are  used  to  calculate  the  CO2  emissions  associated  to 
local generation by multiplying the electrical production by the corresponding emission factor. In the Industrial 
polygon, which considers the usage of green hydrogen, it is assumed that the gas-fuelled CHP uses natural 
gas and hydrogen in the same proportion as the entire community’s balance, as the model outputs the total 
fuel consumption for all the community assets, including boilers. 

Table 26 CO2 emission factors associated to natural gas, hydrogen and biomass combustion 

Fuel 

kg CO2/MWt 

Natural gas 

Hydrogen 

Biomass 

201.94 

0.00 

10.53 

Source: Own elaboration with data from UK Department for Business, Energy and Industrial Strategy (2023) and Chernova (1966) 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

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5  Energy communities’ description 

The electricity and heat loads obtained for each Energy community case study are presented in this section, 
highlighting the regional differences between Germany and Spain, as well as the observed evolution during 
the studied period (2025-2040). It must be remembered that the demand from smart EV charging points is 
not yet included as its installation will be decided by the investment model. Also, the final behaviour from the 
heat  pumps  fleet  might  be  different  in  the  final  results  due  to  changes  induced  by  the  DSR  program 
considered. 

5.1  Business park 

The Business park archetype is also located within an urban context, but contrary to the Urban district case, 
practically  all  energy  loads  are  driven  by  Non-residential  buildings,  with  a  high  presence  of  office 
buildings and associated services. In particular, 35 dwellings are considered to be part of this community, but 
only  seven  are  Mixed  buildings  with  some  floors  dedicated  to  residential  spaces,  which  results  in  a  lower 
number of households than in the Urban district case. In the ground floors of these dwellings, services such as 
restaurants and coffee shops can be found. From the rest of buildings, sixteen correspond to offices, four to 
hotels, three banks, two supermarkets, two fitness centres and one kindergarten. All services are thought to 
serve an urban space with a large presence of employed people. 

Table 27 Business park indicators 

Indicator 

Total number of dwellings 

Number of MFB 

Number of SFB 

Number of NRB 

Number of MB 

Number of IB 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

35 

0 

0 

28 

7 

0 

35 

35 

35 

35 

35 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

28 

28 

28 

28 

28 

7 

0 

7 

0 

7 

0 

7 

0 

7 

0 

Total rooftop area [m2] 

15,700 

15,700 

15,700 

15,700 

15,700 

15,700 

Total land area [m2] 

- 

- 

- 

- 

- 

- 

Number of households 

150 

150 

150 

150 

150 

150 

Non-smart charging points 

24 

28 

49 

24 

28 

49 

Annual electricity demand 
[GWh] 

9.22 

9.43 

9.88 

9.95 

10.08 

10.42 

Annual heat demand [GWh] 

17.32 

17.05 

16.69 

16.56 

16.46 

16.34 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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Table 28 CO2 emissions associated with energy usage in the Business park archetype 

CO2 emissions [ton/year] 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total 

4301 

3969.27 

3685.92 

3084.35 

2778.6 

2622.22 

Electricity usage [%] 

22.69 

22.25 

28.01 

11.99 

9.35 

18.35 

Boiler usage [%] 

77.31 

77.75 

71.99 

88.01 

90.66 

81.65 

Displaced by heat pumps 

145.88 

345.07 

717.59 

630.93 

827.9 

1188.72 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.1.1  Business park: Heat demand 

The  large  presence  of  Non-residential  buildings  is  evident  in  the  distribution  of  monthly  heat  demand  per 
sector, as heat demand from residential is minimal inside the community, even in the German region (Figure 
16) where the larger  heat demand considered per  household makes is  presence  more evident in the Urban 
district  and  Rural  town  archetypes.  Furthermore,  fewer  differences  are  observed  between  the  Spanish  and 
German  cases  as  heat  demand  among  Non-residential  buildings  in  both  regions  is  less  distant  than  per 
residential users. Still, heat demand in the German Business park is significantly larger, particularly driven by 
higher  requirements  in  the  winter  months,  with  the  exception  of  January,  when  Spanish  Non-residential 
buildings  demanded  more  heat  due  to  an  especially  cold  winter.  This  trend  is  also  observable  in  other 
archetypes, as all use the same temperature data as reference. 

Figure 16. Monthly heat demand per sector in the Business park archetype in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

The  observed  hourly  demand  (Figure  17)  for  this  archetype  follows  a  similar  shape  to  the  Urban  district 
archetype, but indicates a steeper peak during morning hours (around 7:00 am). This can be explained by the 
large number of dwellings with business hours’ operations such as banks and offices. The winter evening peak 
is also more visible here than in the Rural town archetype, following a similar shape to the Urban district case. 

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This  peak  practically  disappears  in  the  transition  period  and  is  inexistent  in  the  summer,  where  evening 
heating is not required and people tend to spend more time outside. 

Figure 17. Mean heat consumption reported in 2025 in the Business park archetype in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.1.2  Business park: Electrical demand 

The daily electricity demand in the Business park follows a similar shape to the Urban district, but it must be 
noted that demand is far larger in this archetype than in the previous two cases. In the Spanish region, it is 
also  relevant  that  the  peak  winter  demand  is  practically  at  the  same  level  as  the  summer  peak  demand 
(Figure ). In the Urban district case, the summer peak demand – mostly driven by space cooling requirements 
– represents the highest daily demand in the year. This is also due to the higher heating requirements from 
Spanish  Non-residential  buildings  than  from  residential  users,  more  relevant  in  previous  archetypes,  which 
translates into higher electricity demand in the winter thanks to the 18% heat pumps usage considered in this 
region.  In  Germany  (Figure  ),  on  the  contrary,  less  differences  are  observed  among  the  Urban  district  and 
Business park load shapes. 

Figure 18. Daily electricity demand per sector in the Business park archetype in Spain [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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Figure 19. Daily electricity demand per sector in the Business park archetype in Germany [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

As  happened  with  heat  demand,  electricity  consumption  in  the  Business  park  peaks  during  morning  hours 
(around  11:00  am)  but  a  few  hours  later  than  for  heat.  Electricity  demand  starts  increasing  rapidly  after 
7:00am,  which  coincides  with  the  observed  heat  demand  and aligns  with  the  business hours’  operations  of 
Non-residential  buildings  from  the  sectors  considered  in  this  archetype.  It  is  relevant  to  observe  that  the 
summer  demand  in  Spain  remains  practically  the  same  than  in  the  transition  season,  whereas in  Germany, 
summer  electricity  demand  is  clearly  lower  in  the  Summer.  This  can  be  explained  by  the  space  cooling 
requirements that are particular to the Spanish case and take place during the summer months. 

Figure 20. Mean electricity consumption reported in 2025 in the Business park archetype in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

The number of EV charging points considered in the Business park is larger than for the two previous cases, 
but its contribution to the community’s total electrical load is insignificant given the presence of large energy 
users such as hotels. The annual heat and electricity demand evolution follow a similar shape to the Urban 
district  archetype,  with  annual  reductions  in  the  community’s  heat  demand  in  addition  to  larger  usage  of 
electrical heat pumps, and can be consulted in the attached database. 

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66 

 
 
 
 
5.2 

Industrial polygon 

The  industrial  polygon  archetype  presents  a  series  of  characteristics  that  are  particular  to  this  case.  For 
instance,  the  use  of  a  different  member  classification  (Type  1:  Ambient  temperature  dependent;  Type  2: 
Ambient temperature independent) instead of the residential and non-residential categories used so far  for 
the previous archetypes. However, this does not  mean that Non-residential buildings are not present in this 
case as some of the Type 1 members can be classified as such (for instance, warehouse or industrial offices). 
Still, as a different approach is used, the Type 1 and Type 2 classification is preferred. 

Table 29 Industrial polygon indicators 

Indicator 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total number of dwellings 

Number of Type 1 buildings 

Number of Type 2 buildings 

50 

39 

11 

50 

39 

11 

50 

39 

11 

50 

39 

11 

50 

39 

11 

50 

39 

11 

Total rooftop area [m2] 

33,800 

33,800 

33,800 

33,800 

33,800 

33,800 

Total land area [ha] 

Non-smart charging points 

Annual electricity demand 
[GWh] 

50 

25 

50 

25 

50 

25 

50 

25 

50 

25 

50 

25 

373.48 

373.48 

373.46 

372.96 

372.96 

372.94 

Annual heat demand [GWh] 

782.49 

782.49 

782.48 

770.67 

770.67 

770.65 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Table 30 CO2 emissions associated with energy usage in the Industrial polygon archetype 

CO2 emissions [kton/year] 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total 

195.87 

195.87 

195.87 

166.91 

166.91 

166.91 

Electricity usage [%] 

21.81 

21.81 

21.81 

9.22 

9.22 

9.22 

Boiler usage [%] 

78.19 

78.19 

78.19 

90.78 

90.78 

90.78 

Displaced by heat pumps 

3.71 

3.71 

3.71 

2.89 

2.89 

2.89 

Source: Own elaboration based on MODECO’s methodology and assumptions 

As shown in Table 29, 39 out of the 50 industrial users belong to the Type 1 category, which means that their 
heat load is related to the ambient temperature, and thus, presents regional differences. From these, only six 
have a 5-days working schedule, whereas the rest operates all week. The type of industries represented within 
this  group  varies  among  manufacturing  of  motor  vehicles,  electrical  equipment,  furniture  and  machinery; 
wholesale  and  retail  trade;  transportation  companies;  and  warehousing.  The  full  list  of  industries  can  be 
consulted in the associated database. 

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From the  eleven  industrial  users belonging  to  the  Type  2, three  belong  to  the  chemical  sector,  three  to  the 
food  industry,  two  produce  glass,  and  the  rest  three  iron,  paper  and  vehicles.  It  is  important  to  note  that 
despite being outnumbered by the Type 1 users, this group represents over 90% of the electrical demand in 
the  Industrial  polygon  and  a  similar  share  of  the  total  heat  demand.  Thus,  few  regional  differences  are 
observed  in  this case  even  at  the  hourly  level  as  will  be  explained  in  the  following  sections.  Also,  electrical 
demand  from  heat  pump  usage  is  minor  as  most  heat  demand  in  the  Industrial  polygon  corresponds  to 
process heat, in particular, high temperature heat (>400 ºC). 

5.2.1 

Industrial polygon: Heat demand 

As observed in Figure 21 heat demand from Type 2 members represents the main heat consumption in the 
industrial polygon. As the consumption from these industries is not directly related to ambient temperature, a 
similar mean hourly consumption is maintained across seasons. Heat demand starts to increase at 4:00 and 
shows a  peak  consumption  between  10:00  and  11:00  in  the  morning  during  winter,  transition  and summer 
periods. Although hardly visible due to its small share in comparison to Type 2 load, the consumption of Type 
1 users is at its minimum in summer,  when higher temperatures are reached, and maximum during winter. 
Furthermore, the difference between regions only impacts Type 1 load, which is higher in Germany than Spain. 
Looking at monthly data per industrial user category (Figure 22), it is also observed that Type 1 heat demand 
follows a more pronounce seasonal pattern than that of Type 2 users, but here is still some impact of season 
on Type 2 demand, being slightly higher in winter than summer months. This is due to the fact that even Type 
2 users use heat for space and water heating purposes, although the main share goes to other applications 
related to their own industrial processes. As an example, the monthly results for the German case in 2025 are 
shown in Figure 22. The Spanish industrial polygon behaves pretty  similarly. The results can be consulted in 
the associated database. 

Figure 21. Mean heat consumption reported in 2025 in the Industrial polygon archetype 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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68 

 
 
 
 
 
 
Figure 22. Monthly heat demand per sector in the industrial polygon in 2025

Source: Own elaboration based on MODECO’s methodology and assumptions 

In Figure 23, the process heat from the German case is divided per temperature range, using the applicable 
shares per industry. Given the industry mix defined, the resulting shares are similar between low (<100 ºC), 
medium (100-400 ºC) and high heat (>400 ºC) temperature ranges. As part of MODECO initiative, it would be 
assumed  that  only  heat  demand  for  space  and  water  heating  can  be  supplied  by  electrical  heat  pumps. 
Process heat could only be supplied by burning natural gas or green hydrogen at the industrial site. 

Figure 23. Monthly heat demand by temperature level in the Industrial polygon in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

69 

 
 
 
 
5.2.2 

Industrial polygon: Electrical demand 

Contrary  to  industrial  heat  demand,  which  is  partially  affected  by  ambient  temperature  and  thus  presents 
regional differences, electrical load is practically the same for both target regions (Figure 24). Although there 
is  some  demand  for  heat  and  space  cooling,  this  goes  unnoticed  due  to  the  larger  demand  from  Type  2 
industrial consumers, whose processes have high electricity usage intensity. Similarly, no visible difference is 
observed  across  seasons,  which  is  expected  as  electrical  demand  associated  with  heat  pumps  is  also 
negligible when compared to the processing electrical demand. The demand associated with EV charging is as 
well negligible when compared against the users’ baseload. 

Figure 24. Mean electricity consumption reported in 2025 in the Industrial polygon archetype (Others include EV and heat 
pump electrical consumption) 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.3  Rural town 

The Rural town archetype is characterized by the presence of single-family residential dwellings, as 48% 
of the buildings in this community are classified as such (with rooftop area of 90 m2). As shown in Table 32, 
this  means  that  there  is  a  larger  number  of  dwellings  than  in  the  Urban  archetype  but  a  lower  number  of 
households,  making  more  significant  the  energy  demand  from  Non-residential  buildings.  The  presence  of 
Single-family buildings also reflects in the rooftop space area, whose average value per dwelling is lower than 
in the Urban archetype.  In addition to the 34 Single-family buildings, there are 19  Multi-family buildings, 7 
Mixed  buildings and  11 Non-residential buildings. The commercial and services considered in this archetype 
are  similar  to  those  found  in  the  Urban  district  (supermarket,  drugstore,  bakery,  etcetera),  but  sizes  are  in 
general  smaller.  The  only  exception  are  four  buildings  where  farming  activities  are  carried  out,  as  this  are 
particular  of  the  Rural  town  archetype.  In  this case,  only  six  charging  points are  considered  for  the  starting 
year (2025), two for household users and four for business usage. 

Table 31 Rural town indicators 

Indicator 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

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Indicator 

Germany 

Spain 

Total number of dwellings 

Number of MFB 

Number of SFB 

Number of NRB 

Number of MB 

Number of IB 

71 

19 

34 

11 

7 

0 

71 

19 

34 

11 

7 

0 

71 

19 

34 

11 

7 

0 

71 

19 

34 

11 

7 

0 

71 

19 

34 

11 

7 

0 

71 

19 

34 

11 

7 

0 

Total rooftop area [m2] 

16,060 

16,060 

16,060 

16,060 

16,060 

16,060 

Total land area [ha] 

Number of households 

Non-smart charging points 

Annual electricity demand 
[GWh] 

Annual heat demand 
[GWhthermal] 

100 

151 

6 

100 

151 

10 

100 

151 

31 

100 

151 

6 

100 

151 

10 

100 

151 

31 

2.57 

2.66 

2.87 

2.78 

2.84 

3.02 

7.19 

6.72 

6.09 

5.85 

5.70 

5.49 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Table 32 CO2 emissions associated with energy usage in the Rural town archetype 

CO2 emissions [ton/year] 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total 

1672.19 

1490.57 

1308.25 

1071.74 

957.24 

897.58 

Electricity usage [%] 

17.43 

18.34 

25.94 

10.41 

8.87 

19.82 

Boiler usage [%] 

82.57 

81.66 

74.06 

89.59 

91.13 

80.18 

Displaced by heat pumps 

60.36 

135.46 

260.06 

222.14 

285.07 

396.18 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.3.1  Rural town: Heat demand 

In  the  Rural  town  archetype,  heat  demand  from  Non-residential  buildings  is  more  significant  in  the 
community’s total load. As expected, heat demand is larger in winter months than in warmer seasons, and is 
larger in Germany than in Spain. When observing hourly heat demand per final usage, the same trend as in 
the Urban district is observed regarding heat pump usage, as the adoption rate is also assumed to be larger in 
Spain (18%) than in Germany (4%). However, in this archetype, the heat demand peak registered at morning 
hours is more pronounced than in the Urban district archetype, which is related to the dairy farms considered 
in this energy community type and that have a considerable demand for water and space heating. 

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Figure 25. Monthly heat demand per sector in the Rural town archetype in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Figure 26. Mean heat consumption reported in 2025 in the Rural town communities in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

The  annual  changes  in  heat  demand  throughout  the  studied  period  behave  similar to  the  Urban  district,  so 
these graphics are not shown but can be found in the associated database. 

5.3.2  Rural town: Electrical demand 

In  terms  of  electricity  consumption,  similar  trends  are  observed  in  the  daily  demand  curves  for  Germany 
(Figure 27) and Spain (Figure 28), being flatter in the first case. The demand for space cooling is identifiable 
in  the  energy  communities’  Spanish  archetypes,  as  well  as  the  slightly  higher  demand  in  winter  associated 

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with the heat pump operations. As happened with heat demand, the electricity consumption peaks registered 
at  morning  and  evening  times  are  more  noticeable  in  this  archetype  than  in  the  Urban  district,  due  to  the 
presence  of  agricultural  activities.  Electrical  demand  from  EV  charging  is  less  significant  than  in  the  Urban 
district,  which  was  expected  as  the  number  of  charging  points  is  lower  (Figure  29).  As  happens  with  heat 
demand,  the  evolution  of  the  electrical  demand  from  202  to  2040  behaves  similarly  to  the  Urban  district, 
with  progressive  increments  associated  with  heat  pumps  increasing  usage  and  more  EV  charging  units 
installed. 

Figure 27. Daily electricity demand per sector in the Rural town archetype in Germany [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Figure 28. Daily electricity demand per sector in the Rural town archetype in Spain [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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Figure 29. Mean electricity consumption reported in 2025 in the Rural town communities in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.4  Urban district 

The Urban district archetype is formed by 35 dwellings, 18 of which are residential (Multi-family), 
10  Mixed  buildings  and  7  Non-residential  buildings  representing  different  services and  businesses  that 
can be found in urban neighbourhoods. In the ground floors of the Mixed buildings, the following services are 
found: one bakery, one drugstore, one hair salon, one bank, two restaurants, two offices, and two retail shops. 
In  the  Non-residential  buildings there  are  three  offices,  a  healthcare  clinic,  a  library,  a  fitness  centre  and  a 
supermarket.  Sixteen  of  these  buildings  are  small-sized,  sixteen  mid-sized  and  three  large-sized,  adding  a 
total  of  12,300  m2  of  rooftop  space.  The  total  households living  in  the  residential  and Mixed  buildings are 
426, and 5 of them own an EV and its corresponding charging point. Additionally, seven EV charging stations, 
with two charging points each, are installed in the supermarket and used for its delivery vehicles. A summary 
of the Urban district archetype is presented below. 

Table 33 Urban district indicators 

Indicator 

Total number of dwellings 

Number of MFB 

Number of SFB 

Number of NRB 

Number of MB 

Number of IB 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

35 

18 

0 

7 

10 

0 

35 

18 

0 

7 

10 

0 

35 

18 

0 

7 

10 

0 

35 

18 

0 

7 

10 

0 

35 

18 

0 

7 

10 

0 

35 

18 

0 

7 

10 

0 

74 

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Indicator 

Germany 

Spain 

Total rooftop area [m2] 

12,300 

12,300 

12,300 

12,300 

12,300 

12,300 

Total land area [ha] 

- 

- 

- 

- 

- 

- 

Number of households 

426 

426 

426 

426 

426 

426 

Non-smart charging points 

19 

23 

44 

19 

23 

44 

Annual electricity demand 
[GWh] 

3.16 

3.25 

3.46 

3.42 

3.47 

3.63 

Annual heat demand [GWh] 

8.22 

7.47 

6.44 

6.05 

5.80 

5.46 

Source: Own elaboration based on MODECO’s methodology and assumptions 

 Table 34 CO2 emissions associated with energy usage in the Urban district archetype 

CO2 emissions [ton/year] 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total 

1924.28 

1671.07 

1410.73 

1123.62 

983 

906.9 

Electricity usage [%] 

17.91 

19.12 

27.42 

11.69 

9.72 

Boiler usage [%] 

82.09 

80.88 

72.58 

88.31 

90.28 

21.1 

78.9 

Displaced by heat pumps 

68.97 

150.51 

275.4 

229.26 

290.19 

394.89 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.4.1  Urban district: Heat demand 

In the German case (Figure 30), the urban district distinguishes for a similar representation from residential 
and  non-residential  heat  consumption,  being  slightly  higher  for  residential  users  as  the  heat  demand  per 
household in this region is high and residential dwellings are more numerous than Non-residential buildings. 
In the Spanish region (Figure 30), Non-residential members consume more heat than residential users as they 
have  higher  energy  intensity  per  square  meter  for  space  heating  purposes.  Comparing  both  regions,  it  is 
noticeable  that  heat  demand  in  the  summer  is  similar  for  both  regions  as  it  is  practically  associated  with 
domestic  water  heating  consumption.  Nonetheless,  in  winter,  it  is  clear  that  in  German  households,  heat 
consumption is much larger than in the Spanish case. 

Looking at the heat consumption per season and source (Figure 31), the gradual decrease in heat demand as 
temperature  gets  higher  is  observed  in  both  regions.  Also,  it  is  clear  that  heat  demand  is  higher  in  the 
morning,  mostly driven  by Non-residential buildings, although another  peak is identified in the evening. The 
heat  share  covered  by  heat  pumps  is  considerably  lower  in  the  German  Urban  district,  despite  the  higher 
overall heat demand, as heat pumps usage share is significantly lower in Germany (4%) than Spain (18%).  

The  refurbishment  rate  considered  for  the  Urban  district  community  reflects  lower  heat  demand  in  future 
years  in  comparison  with  2025  for  both  target  regions  (Figure  32).  Similarly, the  higher  heat  pumps  usage 
rate  assumed  for  both  regions,  results  in  a  larger  heat  share  supplied  by  these  technologies.  As  will  be 
explained  in  the  following  section,  this  also  reflects  in  larger  electrical  consumption  associated  with  heat 
pumps operation. 

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Figure 30. Monthly heat demand per sector in the Urban district archetype in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Figure 31. Mean heat consumption reported in 2025 in the Urban district communities in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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Figure 32. Annual heat consumption and associated CO2 emissions for the Urban district archetype 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.4.2  Urban district: Electrical demand 

Regarding  electricity  consumption,  residential  and  Non-residential  buildings  contribute  similar  shares  to  the 
community  total  demand  in  both  regions.  In  Germany  (Figure  33),  electrical  load  has  a  flat  behaviour 
throughout  the  year,  with  slightly  higher  consumption  in  winter.  This  is  expected  as  no  cooling  demand  is 
considered  and  space  heating  is  mostly  supplied  by  natural  gas  equipment.  On  the  other  side,  increased 
electricity demand for space cooling is observable in the Spanish Urban district  during the summer months 
(Figure 34). Similarly, a higher demand in winter is observed in this region in comparison with other seasons 
and with the German case (Figure 35). This is due to the consideration of a larger share of heat pumps’ usage 
for  space  heating  applications,  which  transforms  into  higher  electricity  demand  in  winter.  Electricity 
consumption from EV charging is low in comparison to baseload demand as few charging points are available 
in the starting year (2025). 

Figure 33. Daily electricity demand per sector in the Urban district archetype in Germany [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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Figure 34. Daily electricity demand per sector in the Urban district archetype in Spain [2025] 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Figure 35. Mean electricity consumption reported in 2025 in the Urban district communities 

Source: Own elaboration based on MODECO’s methodology and assumptions 

In the evolution of the Urban district’s electricity demand, the increasing electrical demand from heat pumps’ 
operations is observable as  expected by the larger  share of heat that is supplied  by  this technology as the 
usage rate increases in both regions. To a lesser extent, the electrical demand associated to EV charging also 
increases with time, although its contribution to the community’s total demand is still minimal, even in 2040. 
As  observed  from  the  following  figures,  annual  electricity  demand  in  the  Spanish  case  is  higher  than  in 
Germany, which is associated to space cooling and space heating needs supply via heat pumps. 

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Figure 36. Annual electricity consumption and associated CO2 emissions for the Urban district archetype 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.5  Virtual community 

Similar to the Business  park  case, the  Virtual community  shares  common traits with the Urban  district 
archetype,  as  it  is  located  within  an  urban  context  and  has  members  with  similar  characteristics  to  those 
included in the Urban district case. Nonetheless, the Virtual community lack of vicinity boundaries permit to 
include a larger number of members than in the other Energy community archetypes. The higher number of 
members is observable in the annual electricity demand  reported in this case, which is more aligned to the 
Business  park  case,  even  though,  residential  dwellings  are  the  most  numerous  group  in  this  case.  Heat 
demand  is  even  larger  in  the  Virtual  community  than  in  the  Business  park,  but  this  demand  cannot  be 
supplied by a shared asset as members are located on different points and heat cannot be shared “virtually” 
as electricity can. 

As mentioned before, residential dwellings are the most common within the Virtual community members as 
53 out of 100  members are Multi-family dwellings, 24 are Mixed buildings and just  23 are Non-residential 
buildings. Among the last group, there are banks, offices, cinemas, fitness centres, museums, libraries, hotels, 
primary  schools,  secondary  schools,  shopping  malls,  supermarkets  and  universities.  As  happens  with  the 
members’  number,  the  lack  of  geographical  boundaries  also  permits  more  diversification  in  the  type  of 
members included in the community. The number of EV charging points is also more significant as it is not 
restricted to a specific area but can include charging stations located in any point of the city. 

Table 35 Virtual community indicators 

Indicator 

Germany 

Spain 

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Indicator 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total number of dwellings 

100 

100 

100 

100 

100 

100 

Number of MFB 

Number of SFB 

Number of NRB 

Number of MB 

Number of IB 

53 

0 

23 

24 

0 

53 

0 

23 

24 

0 

53 

0 

23 

24 

0 

53 

0 

23 

24 

0 

53 

0 

23 

24 

0 

53 

0 

23 

24 

0 

Total rooftop area [m2] 

34,100 

34,100 

34,100 

34,100 

34,100 

34,100 

Total land area [ha] 

300 

300 

300 

300 

300 

300 

Number of households 

1,118 

1,118 

1,118 

1,118 

1,118 

1,118 

Non-smart charging points 

63 

67 

88 

63 

67 

88 

Annual electricity demand 
[GWh] 

8.95 

9.18 

9.60 

9.60 

9.72 

10.01 

Annual heat demand [GWh] 

21.23 

19.24 

16.55 

15.52 

14.87 

13.98 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Table 36 CO2 emissions associated with energy usage in the Virtual community archetype 

CO2 emissions [ton/year] 

Germany 

Spain 

2025 

2030 

2040 

2025 

2030 

2040 

Total 

5043.17 

4369.64 

3677.16 

2911.48 

2537.8 

2336.16 

Electricity usage [%] 

19.15 

20.29 

28.46 

12.56 

10.37 

21.61 

Boiler usage [%] 

80.85 

79.71 

71.54 

87.44 

89.63 

78.39 

Displaced by heat pumps 

177.98 

387.6 

706.97 

587.7 

743.2 

1009.53 

Source:  Own elaboration based on MODECO’s methodology and assumptions 

5.5.1  Virtual community: Heat demand 

As observed in Figure 37, heat demand from residential users is the most relevant load in the German Virtual 
community, whereas in Spain, Non-residential buildings represent the principal heat consumers. As happened 
in  other  archetypes,  there  are  few  differences  at  the  monthly  scale  between  one  archetype  and  other 
regarding  the  curve  shape.  Nonetheless,  at  the  hourly  level  (Figure  38),  it  is  possible  to  identify  different 
trends.    However,  this  archetype’s  behaviour  is  highly  similar  to  that  of  the  Urban  district,  as  the  main 
difference  between  these  two  is  not  the  type  of  dwellings  but  the  number  and  absence  of  physical 
constraints,  which  will  strongly  influence  the  investment  decisions  of  the  Virtual  community  in  comparison 
with the other urban archetypes. 

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Figure 37. Monthly heat demand per sector in the Virtual community archetype in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

Figure 38. Mean heat consumption reported in 2025 in the virtual community archetype in Germany and Spain 

Source: Own elaboration based on MODECO’s methodology and assumptions 

5.5.2  Virtual community: Electrical demand 

The daily electricity demand from the Virtual community follows a similar trend to the Urban district, although 
with a larger overall demand. Instead, the monthly electrical loads are shown to highlight the flatter shape of 
the German case, which is also observed in previous archetypes. Also, it is relevant to observe that in terms of 
electricity  consumption,  residential  and  Non-residential  buildings  follow  a  similar  trend  and  show  less 
differences in volume than in heat demand. 

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Figure 39. Monthly electricity demand per sector in the Virtual community archetype in 2025 

Source: Own elaboration based on MODECO’s methodology and assumptions 

At  the  hourly  level  (Figure  40),  some  differences  are  observed  between  the  Virtual  community  and  Urban 
district load shapes, as the first has a more pronounced peak during the morning, looking more similar to the 
Business park archetype in this sense. Finally, the demand from EV charging remains more visible in this case 
for both studied regions, this might be due to the high presence of offices and banks in this case than in the 
Urban district. 

Figure 40. Mean electricity consumption reported in 2025 in the Virtual community archetype 

Source: Own elaboration based on MODECO’s methodology and assumptions 

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6  Energy price scenarios 

The marginal prices obtained from the first round execution of the UCED model are discussed in this section, 
as well as the energy tariffs formed from them by adding the taxes and Use-of-Network charges applicable 
to each scenario.  A  brief overview of the power system’s behaviour –  demand  and energy  dispatched 
per type of technology – leading to these prices is also presented, including the key indicators shown in Figure 
14: Energy Not Served, CO2 emissions and renewables curtailment.  

6.1  Power system indicators 

As  seen  in  Chapter  2,  the  considered  reference  scenario  for  the  evolution  of  the  European  power  system 
considers a gradual phase out of fossil-fuelled technologies and a considerable growth in variable renewable 
energies  (solar  and  wind)  and  energy  storage,  with  specific  technological  trends  for  each  geographical 
location.  As  shown  in  Figure  41,  which  summarizes  the  amount  of  energy  dispatched  per  technology  in 
Germany and Spain during the target years executed, the demand for the two countries analysed increments 
from 2025 to 2040. In Germany, the increase from 2025 to 2030 is similar to that observed from 2030 to 
2040,  which  means  that  in  the  latter  years,  demand  growth  happens  at  a  slower  rate.  On  the  contrary, 
demand in Spain remains fairly the same from 2025 to 2030, incrementing an average of just 2.3 TWh per 
year, whereas from 2030 to 2040 it grows at a faster pace, augmenting in average 7.0 TWh each year.  

Figure 41. Annual demand versus energy dispatched per technology and year in Germany and Spain 

BATS: Batteries; CCGT: Combined Cycle Gas Turbines; FCEL: Fuel Cell; GAST: Gas Turbines; HDAM: Hydro-reservoirs; HPHR: Open-loop hydro 
pumped storage; HPHS: Closed-loop hydro pumped storage; HRDT: Hard coal-fuelled generators; HROR: Hydro Run-of-River; LIGT: Lignite-
fuelled generators, OCGT: Open Cycle Gas Turbines; OILT: Oil-fuelled generators; ORES: Other Renewables; OTHT: Other non-renewables 
(combined heat and power); PHOT: solar photovoltaics; WTOF: wind offshore; WTON: wind onshore. 

Source: Own elaboration from the UCED’s model first executions 

As observed in the graph above, annual demand in Spain is always below the total generated energy, 
as  part  of  the  produced  energy  is  exported  to  neighbouring  countries.  Germany,  on  the  contrary,  relies  on 
energy  imports  to  cover  its  demand  in  the  three  analysed  years  as  the  total  national  production  is  below 
consumption requirements. In 2040, Germany’s demand gets significantly larger than the produced energy, 
complicating meeting demand at all hours. In fact, lost load events take place in this year and country 
during  19  hours  reported  in  four  particular  winter  days12;  meaning  that  the  system  is  not  able  to  meet 
demand with its own generation or with imported energy at that time. The volume of Energy Not Serve (ENS) 
in  2040  accounts  for  15.39  GWh.    No  other  year  in  Germany  and  Spain  presents  ENS  under  the  modelled 
conditions. 

12 The dates and times in which ENS is reported are: 22 January 2040 (18:00-23:00), 13 February (20:00-23:00), 16 February (19:00-
23:00), 18 December (20:00-23:00). 

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Wind  and  solar  technologies  have  a  prominent  role  in  both  analysed  countries as expected  due  to 
the  evolution  of  the  reference  power  system  scenario,  gaining  more  relevance  in  2040  when  these 
technologies  account  for  62%  and  70%  of  the  total  energy  generated  in  Germany  and  Spain,  respectively. 
Even by 2025, these generators already account for half the energy produced in both countries, which impact 
on  the  dynamics  of  the  obtained  marginal  prices  that  will  be  presented  in  the  next  section,  particularly  in 
hours  with  high  solar  irradiation.    This  is  particularly  important  in  Spain,  where  solar  technologies 
(concentrated solar power and photovoltaics) account for 19% of the total energy generated in 2025, but go 
up to 42% in 2040. Spanish wind farms represent the largest generation in 2025 (32%) but are relegated to 
a second place in the future years, when they are responsible for 29% of the total energy produced in the 
Mediterranean country.  

In  the  case  of  Germany,  wind  is  the  dominant  technology,  representing  40%  of  the  total  energy 
generated in 2025 and 45% in 20409, while solar photovoltaics account for just 13% and 17% of the energy 
produced  in  those  years.  It  is  also  relevant  to  point  out  the  intensive  usage  of  gas-fuelled  generators, 
particularly in the form of Combined Cycle Gas Turbines  (CCGT) and  combined  heat and power units, which 
are represented by the Other Non-Renewable (ONRT) category shown in Figure 41.  

The CO2 emissions associated with energy generation in each case are presented in Table 37. Germany has 
much higher carbon emissions than Spain due to a more intensive usage of combined cycle units. In 2025 and 
2030,  a  portion  of  the  emissions  is  also  related  to  the  utilization  of  lignite  (LIGT)  and  hard  carbon  (HRDT) 
plants. In 2030, Germany’s emissions decrease in comparison to 2025 even as gas generation grows, due to 
the almost phase out of carbon-based power plants, which pass from generating 5.2 TWh in 2025 to 1.7 TWh 
in  2030.  Their  usage  is  completely  eliminated  in  2040,  but  the  increment  in  gas  generation  is  more 
significant,  which  raises  total  emissions  in  2040  above  2025  levels.  In  Spain,  carbon  emissions  are  purely 
associated with combined cycle units. From 2025 to 2030 the energy generated from these plants decreases 
from 2.6 TWh to 0.6 TWh, which results in less carbon emissions. Nonetheless, it increases up to 20.8 TWh in 
2040 when nuclear facilities are no longer in operation, raising significantly the carbon emissions registered 
in Spain. 

Table 37 Annual volume of CO2 emissions associated to power generation in Germany and Spain 

Year 

2025 

2030 

2040 

CO2 emissions [kton] 

Germany 

Spain 

8,498.06 

7,889.67 

529.66 

113.08 

9778.93 

4,198.31 

Source: own elaboration with results from the UCED model execution. 

6.2  Marginal prices 

The first set of marginal prices used for the construction of the tariff scenarios described in Section  2.3 are 
obtained from adapting the  UCED  model to the  ESES reference scenario (see  Section 4.1.1). As observed in 
Table 38, the mean annual marginal prices obtained for Germany are overall higher than for Spain during the 
entire studied period. The largest difference between the two countries is observed in 2030, when the mean 
annual price in Germany is 157% higher than in Spain. In 2040, this gap narrows, as prices in Spain nearly 
tripled  from  2030  to  2040  whereas  in  Germany  2040  prices  increase  only  42%  in  comparison  to  2030, 
resulting  in  Germany’s  prices  being  just  17%  higher  than  Spain  at  2040.  In  summary,  for  the  modelled 
scenario,  it  is  observed  that  Germany  has  larger  prices  than  Spain  and  experiences  a  sustained  growth 
throughout the 16-year period, while Spain experiences a slight decrease (6%) in prices from 2025 to 2030 to 
later increase at a rapid pace till the end of the analysed timeframe. 

As observed  in  Figure  42,  rising  prices in  Germany  are  mostly  led  by  the  winter season,  which  maintains  a 
steady increasing trend for the whole analysed period. German prices in summer and transition seasons rise 
almost as fast as in winter from 2025 to 2030, but it then slows down. In Spain, winter prices also follow an 
increasing trend during the evaluated period, but it speeds up after 2030. For summer and transition seasons, 

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prices  actually  go  down  between  2025  and  2030,  but  then  rise  quickly,  reaching  a  mean  marginal  price 
similar to that reported for Germany during the same seasons, or in winter in Spain. 

Table 38 Mean annual marginal price registered in Germany and Spain for each target year 

Year 

2025 

2030 

2040 

Mean annual marginal price [EUR/MWh] 

Germany 

Spain 

35.62 

55.99 

79.69 

23.30 

21.82 

68.02 

Source: own elaboration with results from the UCED model execution. 

Figure 42. Mean marginal price per season and year registered in Spain and Germany 

Source: Own elaboration from the UCED’s model first executions 

When looking at the mean daily prices, it is identified that marginal prices in Spain do not follow an stablished 
pattern throughout the year, as there are certain periods in which daily prices remain low (< 20 EUR/MWh) for 
a sustained number of days in 2025 and 2030 (Figure 43). In the starting year, this happens from 07 April to 
14  May,  while  in  2030,  the  low-priced  period  extends  10  more  days  from  05  April  to  22  May  and  similar 
events are observed from 07 August to 17 September, 22 September to 17 October, and  20 October to 11 
November.  Such  low  daily  prices  are  reflected  in  the  mean  seasonal  prices  reported  for  the  summer  and 
transition periods in Spain at 2025 and 2030 (Figure 42). As observed in the graph below, the sustained low-
priced  periods  disappear  in  2040,  leading  to  an  increase  in  the  mean  price  reported  for  all  seasons  in  the 
years  between  2030  and  2040.  Nonetheless,  some  days  with  extremely  low  prices  (<  6  EUR/MWh)  are 
maintained around these same dates, accounting for the valley mean daily prices observed in 2040.  

In  Germany,  mean  daily  prices  raise  evenly  throughout  the  years,  except  for  valley  priced  days  (<  20 
EUR/MWh), concentrated mostly in summer and transition periods, in which prices actually tend to decrease 
from 2025 to 2040. (Figure 44) As noted, a particular set of days in which prices rise above 560 EUR/MWh 
are  registered  in  2040  (22  January,  13  and  16  February,  and  18  December).  These  correspond  to  days  in 
which lost load events take place and are the main cause between the high increase in the mean winter prices 
registered for Germany after 2031. Nonetheless, the rest of 2040 prices tend to go up in comparison to 2030 
values but maintain a similar daily trend to the former years, with valley prices going down or slightly up, but 
prices above the annual average mostly increasing significantly, thus raising the annual mean value expected 
for future years. 

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Figure 43. Mean daily marginal price registered in Spain in 2025, 2030 and 2040. 

Source: Own elaboration from the UCED’s model first executions 

Figure 44. Mean daily marginal price registered in Germany in 2025, 2030 and 2040. 

Source: Own elaboration from the UCED’s model first executions 

As  shown  in  the  next  figure,  hourly  peak  prices  for  both  regions  are  concentrated  in  late  night  and  early 
morning  hours.  However,  the  highest  prices  for  Germany  are  reported  at  night  whereas  in  Spain  these  are 
observed during early morning hours. During peak hours, prices increase for both countries towards the future. 
However, at low prices periods (8:00-15:00), marginal prices in Spain actually tend to decrease from 2024 to 
2040, while in Germany prices go up from 2025 to 2030 but decrease slightly from 2030 to the end of the 

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period. The low prices registered at this timeslot are linked to the high amount of solar energy generated13 in 
these  hours,  which  correspond  to  the  times  with  the  highest  solar  radiation  registered  in  both  regions  (see 
Figure 6). This low cost energy adds to the high volumes of wind energy also available at this time, bringing 
marginal prices down.  On the contrary peak prices are due to high demand requirements at times in which 
solar resources are not available and low cost technologies (renewables and fossil fuel-based) do not  have 
enough capacity to supply all of it, thus requiring the usage of expensive units. As explained before, for some 
hours in the German 2040 scenario, not even these are enough to meet peak demand in winter nights, which 
results in lost load events, valued at €3,000 in MODECO’s scenarios. 

Figure 45. Mean marginal price per hour and year registered in Spain and Germany 

Source: Own elaboration from the UCED’s model first executions 

Box 3.  Key trends from the modelled energy prices under a power system evolution led by distributed energy 

—  Marginal  prices  in  Germany  are  overall  higher  than  in  Spain  for  the  entire  period.  In  both  regions, 

prices tend to increase towards the future, but more significantly in Spain. 

—  Seasonally, summer and transition prices decrease in Spain from 2025 to 2030,  and increase after 
2030. Winter prices grow constantly but much faster after 2030. In Germany, summer and transition 
grow  mostly  from  2025  to  2030,  slightly  increasing  afterwards.  Winter  prices  maintain  a  linear 
increase during the 16-year period. 

—  For  both  countries,  winter  marginal  prices  are  the  highest.  However,  the  difference  between  this 

season and the rest is widest for Germany 2040. 

—  In Germany, four days in 2040 register extremely high prices due to lost load events. 

—  Peak  prices  occur  at  night  and  early  morning  hours  in  both  countries.  However,  in  Germany  the 

highest are registered at night and in Spain before dawn.  

—  A price increase is observed during peak price hours, whereas the rest of the day prices actually tend 

to decrease due to higher solar energy availability. 

6.3  Energy tariffs 

The applicable taxes and Use-of-Network charges are applied to the marginal prices obtained from the UCED 
model  to  form  the  energy  tariffs  used  in  the  scenarios  defined  in  Section  2.3.  The  prices  obtained  for  the 
scenarios with TOU charges are shown in Figure 46 for Germany and Figure 47 for Spain. As explained before, 
the charges applicable to low and medium voltage users are different (see Table 10 and Table 11) as the first 
imply  a  more  intensive  use  of  the  network  infrastructure.  Thus,  different  tariffs  are  obtained  for  low  and 

13 Solar energy is produced via solar PV in Germany, and via solar PV and concentrated solar power plants in the case of Spain. 

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medium voltage users in scenarios with dynamic and flat energy prices. As observed in the following figures, 
medium voltage tariffs are lower than their low voltage counterparts, which reflects each users’ usage from 
the network. The scenario with a PPA energy price (TOU_PPA) is only shown for medium voltage users as it is 
only evaluated within the industrial polygon archetype. Finally, the values for the scenario with no charges (No 
Charges) are also included for comparison.  

The energy costs obtained for the Peak power and Bandwidth models are not shown as they follow the same 
trend  as  the  No  Charges  case,  except  that  values  are  slightly  higher  due  to  the  inclusion  of  the  applicable 
electricity taxes. In these cases, the Use-of-Network charges are recovered through the capacity-based fees 
shown in Table 10 for the peak power-based model and in Table 11 for the bandwidth case. All archetypes 
except the industrial  polygon, which is interconnected to the  medium voltage  grid, are subjected to the low 
voltage fees. 

In 2025, the mean hourly values obtained for the dynamic (TOU [LV], and TOU [MV]) and flat rate (TOU_Flat 
[LV]  and  TOU_Flat  [MV])  scenarios  are  practically  the  same  for  both  countries  and  voltage  levels.  In  future 
years,  however,  the  mean  hourly  values  for  the  dynamic  tariff  scenarios  get  lower  than  for  the  flat  prices 
cases around midday, when marginal prices are at their lowest (see Figure 45). On the contrary, during night 
peak hours, the dynamic price tariffs get higher than in the flat rate scenario. This difference is particularly 
noticeable in 2040. For Spain, dynamic tariffs are also significantly higher than in the flat rate case before 
dawn, which is related to the marginal prices dynamic discussed in the previous section.  

Figure 46. TOU energy tariffs applicable to Energy communities in Germany 

Source: Own elaboration from the UCED’s model first executions 

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Figure 47. TOU energy tariffs applicable to Energy communities in Spain 

Source: Own elaboration from the UCED’s model first executions 

Following  the  methodology  defined  in  Section  2.3.2.1,  the  peak  and  off-peak  hours  are  defined  per  each 
season and year based on the residual load values identified according to the energy system characteristics 
defined  for  each  country.  The  final  classification  is  summarised  in  Table  39.  Then,  the  applicable  Use-of-
Network charges are applied to off-peak and peak hours, respectively. As the latter are higher, energy costs 
for  users are  always  more  expensive  at  peak  hours  in  the  TOU  scenarios,  although  the  difference  between 
peak and off-peak hours gets more significant in the future for the dynamic price cases as could be observed 
in the previous graphs. Such differences would influence investment decisions as will be explained in the next 
chapter. 

Table 39 Hours classified as peak in each country, year and season 

Year 

2025 

2030 

2040 

Germany 

Spain 

Summer 

Transition 

Winter 

Summer 

Transition 

Winter 

16:00-00:00 

16:00-00:00 

16:00-00:00 

00:00-2:00 

00:00-1:00 

00:00-2:00 

6:00-7:00 

7:00-8:00 

18:00-00:00 

19:00-00:00 

18:00-00:00 

00:00-1:00 

00:00-2:00 

00:00-2:00 

00:00-5:00 

00:00-3:00 

00:00-3:00 

17:00-00:00 

18:00-00:00 

18:00-00:00 

21:00-00:00 

19:00-00:00 

19:00-00:00 

00:00-2:00 

00:00-2:00 

00:00-2:00 

00:00-5:00 

00:00-3:00 

00:00-3:00 

18:00-00:00 

18:00-00:00 

18:00-00:00 

21:00-00:00 

19:00-00:00 

19:00-00:00 

Source: own elaboration with results from the UCED model execution. 

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7 

Investment model results 

The  use  of  different  tariff  structures  influences  the  investment  choices  of  Energy  communities  in  different 
manners.  However,  attention  must  also  be  paid  to  regional  differences  regarding  marginal  prices,  demand 
patterns,  resource  availability  and  climatic  conditions,  as  well  as  the  archetypes’  intrinsic  characteristics.  In 
Section 7.1, the results for the main Use-of-Network tariff structures – No charges, Time-of-Use, Bandwidth 
and Peak power – are discussed, highlighting the effect of this in the obtained results, as well as the influence 
of  other relevant  variables.  In  Section  7.2.1, the  key  findings from  using  different  energy  prices  –  dynamic, 
flat  and  PPA  (the  latter  only  in  the  Industrial  polygon)  –  under  a  TOU  structure  are  presented.  Finally,  a 
sensitivity analysis using different discount rates is done and discussed in Section 7.2.2. 

7.1  Tariff structures: TOU, Peak power, Bandwidth 

The  objective  function  values  obtained  for  the  base  tariff  scenarios  are  presented  in  the  table  below.  As 
observed,  all  values  are  positive,  which  indicate  that  the  costs  associated  with  the  assets  installation, 
operation and maintenance, as well as those related to demand response operation and electricity and fuel 
purchases  incurred  by  the  communities  in  the  16-year  period  are  in  aggregated  higher  than  the  benefits 
obtained  from  excess  electricity  selling  and  the  provision  of  smart  EV  charging  services.  The  largest  values 
are  reported  for  the  Industrial  polygon  archetype  as  its  large  electrical  demand  complicates  reaching  high 
self-consumption values through local generation, given the space and other constraints. In almost all cases 
the lowest value is reported for the No Charges scenario and the highest for the Bandwidth model. The only 
exceptions are the German Rural town, in which the TOU Scenario presents the lowest results, and the Spanish 
Virtual community, in which the highest value is reported for the TOU tariff. The reasons behind such results 
will  be  discussed  in  the  following  sections  in  which  each  archetype’s  investment  decisions  will  be  analysed 
individually. 

Table 40 Value of the objective function obtained for each case in million euros [M€] 

Archetype 

Germany 

Spain 

NC 

TOU 

BW 

PP 

NC 

TOU 

BW 

PP 

Business park 

4.32  

6.59 

14.05 

7.34 

3.71 

5.75 

8.73 

5.33 

Industrial polygon  161.86 

264.60 

367.14  294.36  109.07 

137.08 

210.04  143.21 

Rural town 

0.19 

0.09 

2.66 

0.66 

0.92 

1.25 

2.08 

1.21 

Urban district 

0.94 

1.53 

3.95 

1.62 

10.92 

11.47 

12.51 

11.34 

Virtual community 

2.22 

10.16 

11.36 

8.8 

2.22 

8.33 

6.95 

4.30 

Source: own elaboration with results from the UCED model execution. 

All the cases evaluated in this section obtained the defined gap value (<1%), except for the Rural town and 
Virtual community under the No Charges tariff, the Business park under the Bandwidth scenario, and the Rural 
town with a TOU tariff. The latter, however, was the only case with a gap value higher than 1%. The specific 
gap values obtained can be consulted in Annex 4. 

7.1.1  Business park 

The total investments made by the Business park communities in Germany and Spain are shown in Figure 48. 
In general terms, the Spanish Business park undergoes larger investments than the German community, but 
the differences are more significant in the No Charges and Bandwidth cases, whose results seem to be more 
sensitive to the regional variations. The Bandwidth scenario results in the largest total investments in Spain 
(7.8 M€) although just slightly below those reported under No Charges (7.55 M€). In Germany, both cases also 
result  in  similar  investments,  but  the  total  amount  is  2%  larger  in  the  No  Charges  than  in  the  Bandwidth 
scenario. The least total investments are found in the TOU and Peak-power tariff structures for both regions, 
with  investments  in  the  latter  being  slightly  below  (2-3%)  those  in  the  TOU  case.  In  all  tariff  structure 
scenarios, the Business park communities invest in gas-fuelled CHP, rooftop solar photovoltaics, V2G charging 
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stations  and  batteries.  This  archetype  was  assumed  to  have  no  land  space  available  for  ground-mounted 
solar and wind installations, so these options are not eligible investments. 

Figure 48. Investments performed in the Business park archetype under different Use-of-Network structures 

Source: Own elaboration with results from MODECO’s investment model 

The  results  for  the  German  Business  park  show  little  variation  between  the  No  Charges  and  Bandwidth 
cases. The installed CHP capacity is 1.86 MWe (3.38 MWt) in both cases, which is 25% above the mean 
thermal  demand  (2.70  MWt)  registered  for  this  archetype  in  winter  but  below  the  maximum  peak  demand 
(7.10 MWt), which suggest a correct sizing. The storage power considered is 14.12 MWh and 13.15 MWh 
in the No Charges case and Bandwidth models, respectively, and corresponds to energy-based batteries only. 
Additionally, 27 V2G chargers are installed when No Charges is considered, and 33 when using the 
Bandwidth restrictions.  As seen in  Figure 49, where the electrical balance for two  representative days in 
the Bandwidth scenario is shown, the installed batteries in the German Park are used to store excess CHP and 
solar production in low-priced windows and sell it back when prices get higher.  The PV solar rooftop installed 
in both scenarios corresponds to the maximum possible given the available area. As seen in the figure below, 
this results in some excess production during summer, which is used to charge batteries. 

In Spain, these two scenarios also lead to similar investment decisions. The installed CHP capacity is the 
same for the No Charges and Bandwidth tariffs (3.75 MWe, 6.83 MWt) and higher than in the German 
region  despite  that  the  Spanish  Business  park  has  a  thermal  demand  12%  lower.  Looking  at  the  annual 
investments made by the Spanish park under these scenarios, it is observed that the largest CHP capacities 
are installed in Spain in 2025 and 2040 (see the Bandwidth model example in  Figure 50). The cogeneration 
capacity installed in 2025 is pretty similar to that made in the German region. Moreover, the CHP operates at 
partial  load  practically  all  the  time,  which  is  why  the  new  CHP  power  installed  in  2040  does  not  make 
operational sense. It is just included to justify larger storage capacity without violating the model restrictions. 

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Figure 49. Electrical balance for the Business park communities under a Bandwidth tariff in two representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 11th (Ω: 24) and August 25th (Ω: 20) for Germany and January 31st (Ω: 27) and August 28th 
(Ω: 19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

Figure 50. Annual investments performed in the Business park archetype under the Bandwidth tariff case 

Source: Own elaboration with results from MODECO’s investment model. 

The storage power installed in the Spanish park under the No Charges and Bandwidth cases (3.75 
MWh)  doubles  that  considered  under  the  same  tariffs  in  the  German  region.  As  observed  in  the 
electrical  balance  for  the  Bandwidth  model  shown  in  Figure  49,  at  some  hours,  the  purchase  prices 

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considered in the Spanish Business park are close to zero, which permits charging batteries with grid 
electricity on top of excess energy and selling it later to obtain a profit. Given the considerable price spreads, 
these obtained revenues are high enough to justify installing excess CHP at the end of the period just to ‘trick’ 
the model into accepting larger investments in energy-based batteries.  

As  explained  before,  the  model  limits  the  storage  capacity  to  the  installed  power  capacity  to  avoid 
overinvestments in batteries solely for energy arbitrage purposes, which derives from the definition of energy 
communities  as  non-for-profit  entities.  However,  under  this  context,  revenues  associated  with  energy 
arbitrage  are  large  enough  to  support  the  installation  of  more  CHP  than  actually  needed  to  meet  the 
community’s  thermal  or  electrical  demand.  This  extra  CHP  capacity  is  acquired  at  the  end  of  the  period  to 
minimize the fixed operational and maintenance costs associated with this technology in the computation of 
the 16-year total operational costs. 

PV solar rooftop capacity is below the maximum permissible in both cases, but the installed capacity is lower 
in the No Charges (2.85 MW) than in the Bandwidth (2.97 MW), as marginal prices are lower in the first as 
taxes  are  not  considered,  and  no  opportunity  to  save  any  further  costs  are  present  as  no  Use-of-Network 
tariffs are considered. As explained in Section 6.2, marginal prices in Spain are low in high peak solar 
production  hours  (9:00  –  16:00)  and  get  even  lower  in  the  future,  which  makes  solar  a  less  attractive 
investment despite the lower LCOE offered by these technologies in Spain. In Germany, lower solar radiation 
increases  the  value  of  LCOE,  but  this  is  still  competitive  before  2030  due  to  the  larger  marginal  prices 
registered in this region (Figure 51. Solar LCOE in Germany and Spain versus mean marginal price during high 
solar  radiation  hours  (Figure  51).  For  this  reason,  when  looking  at  the  annual  investments  made  by  the 
communities, solar power is installed earlier in Germany than in Spain (see for instance the Bandwidth 
model results shown in Figure 50). Notably, no penalizations for bandwidth excess usage is reported for the 
German or Spanish Business park under the proposed investment strategy.      

Figure 51. Solar LCOE in Germany and Spain versus mean marginal price during high solar radiation hours 

Source: Own elaboration with results from MODECO’s investment model. 

The  Peak  power  scenario  results  in  slightly  larger  cogeneration  (1.93  MWe,  3.51  MWt)  capacity  being 
installed at the German Business park than under the rest of tariffs. However, the storage capacity considered 
is lower (5.98 MWh) as well as the number of V2G points (21). As in the other cases, PV solar rooftop is kept 
to the maximum possible. Although on most days, batteries are charged with excess local generation, at some 
hours, batteries need to use grid electricity as support (see the representative days shown in Figure 52 for the 
Peak  power  case).  Electricity  grid  charging  is  economically  penalized  under  the  Peak  power  tariff  when  it 

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contributes  to  increasing  demand  peaks,  reducing  the  times  in  which  it  can  be  done  up  to  a  certain  level 
without incurring in extra costs. For instance, on the August day shown in Figure 52, batteries stop charging at 
12:00 when the highest demand is presented. On the contrary, when using the No Charges scenario, batteries 
charge large energy volumes at low-priced periods. The lowest number of V2G points (21) are installed in the 
Business park under this tariff. 

Figure 52. Electrical balance for the Business park communities under a Peak power tariff in two representative days in 
February and August 2040 [Minimum Ω] 

The selected representative days are January 25th (Ω: 7) and August 11th (Ω: 11) for Germany and January 24th (Ω: 4) and August 16th (Ω: 
12) for Spain. In all cases, the days with the minimum weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

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Figure 53. Electrical balance for the Business park communities under a No Charges tariff in two representative days in 
February and August 2040 [Minimum Ω] 

The selected representative days are January 25th (Ω: 7) and August 11th (Ω: 11) for Germany and January 24th (Ω: 4) and August 16th (Ω: 
12) for Spain. In all cases, the days with the minimum weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

In Spain, the installed cogeneration capacity (1.90  MWe, 3.45 MWt) under the Peak power is larger than in 
the TOU but lower than in the No Charges and Bandwidth scenarios (where it was oversized). The  installed 
CHP size is aligned with the community’s thermal demand (demand peak of 6.3 MWt). Storage capacity 
is  also  lower  (14.09  MWh)  than  in  the  previous  cases  for  the  same  reasons  explained  for  the  German 
community. This is the only case in which the Business park installs power-based batteries (C-rate 2) instead 
of  just  energy-based  units  (C-rate  0.35).  The  storage  capacity,  however,  is  pretty  low  (30,2  kWh)  for  this 
battery  type.  As  happened  in  Germany,  the  Power  peak  tariff  results  in  the  least  number  of  V2G 
chargers (18) installed. 

Under the TOU tariff, the same CHP capacity as in the No Charges and Bandwidth models is installed in the 
German  community.  PV  solar  rooftop  is  also  kept  to  the  maximum  power  possible.  Storage  capacity  (7.01 
MWh), nonetheless, is lower than in these scenarios but higher than in the Peak power. In the TOU scenario, 
battery  grid  charging  is  also  costlier  than  in  the  Bandwidth  (up  to  a  certain  limit)  and  the  No 
Charges  model,  particularly  at  peak  hours,  which  makes  energy  arbitrage  less  profitable  for 
batteries, reducing its economic viability. The number of V2G stations (34) is similar to that installed in 
the Bandwidth case (33). However, it must be noted that the representative days are different for this tariff 
as the Use-of-Network tariffs result in a different price curve. 

In  Spain,  the  cogeneration  (1.63  MWe,  2.96  MWt)  and  storage  (13.45  MWh)  capacity  are  the lowest  in 
this scenario. The values, however, are not that far from those reported in the Peak power case even though 
different  representative  days  are  used.  As  in  most  cases,  only  energy-based  batteries  are  installed.  The 
number of V2G charging points installed are the highest (36) as in the German region.  

7.1.2 

Industrial polygon 

The  industrial  polygon  is  the  archetype  in  which  less  regional  differences  are  observed  regarding 
electrical  and  heat  demand  in  the  German  and  Spanish  cases,  as  energy  needs  are  more  process  than 
climate driven (see Section 3.1.2). Thus, investment choices in this archetype remain practically unaffected by 
this  variable.  As  shown  in  Figure  54,  the  results  from  the  investment  model  consider  installations  in  CHP, 
energy-based  storage,  V2G  charging  stations,  solar  PV  rooftop  and  low-capacity  wind  turbines.  The 

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investments  done  in  solar  PV  rooftop  and  low-capacity  wind  turbines  are  the  same  for  all  cases  and 
correspond to the maximum allowed given the available rooftop and land spaces.  

Figure 54. Investments performed in the Industrial polygon under different Use-of-Network structures 

Source: Own elaboration with results from MODECO’s investment model 

No  significant  differences  are  observed  in  the  total  amount  invested  by  the  German  or  Spanish 
communities under the TOU, No Charges and Bandwidth cases. The German community also results in 
the same investment decisions when considered the Peak power tariff. In all these scenarios, the same CHP 
capacity  is  installed  (37.52  MWe,  68.22  MWt),  which  corresponds  to  15%  above  the  thermal  demand  peak 
registered in the Industrial polygon. The average thermal demand in the Industrial polygon is 45.8 MWt, and 
values  are  above  that  threshold  just  50%of  hours  in  the  16-year  period,  which  means  that  the  CHP  unit 
operates  most  of  the  time  at  partial  load.  Still,  the  maximum  allowed  cogeneration  capacity  is  installed  to 
justify installing larger storage capacity to perform energy arbitrage. The storage capacity installed in all of 
these  cases  is  128.24  MWh,  and  corresponds  to  energy-based  batteries  (C-rate  0.35)  only.  The  number  of 
V2G points installed vary slightly among scenarios. The only exception is the German polygon under the Peak 
power tariff when only four stations are installed, while the average in the rest of cases is 38.  

In all these cases, the installed power of PV solar rooftop (6.63 MWe) and low-capacity wind turbines (0.74 
MWe) correspond to the maximum possible given the available land and rooftop space. Compared to the rest 
of  technologies  wind  influence  is  barely  noticeable  as  shown  in  the  electrical  balance  for  the  two 
representative days in the Bandwidth scenario (Figure 55). PV solar production is more significant in Spain as 
solar radiation is higher. As the representative days and price curves vary between regions, some difference in 
the asset’s operation can be observed. Still, these do not reflect in different investment decisions. 

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Figure 55. Electrical balance for the Industrial polygon communities under a Bandwidth tariff in selected representative 
days in January and August 2040 [Maximum Ω] 

The selected representative days are January 22nd (Ω: 22) and August 29th (Ω: 22) for Germany and January 23rd (Ω: 22) and August 29th 
(Ω: 23) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

The investment made in solar and low-capacity wind turbines are influenced by the technologies’ LCOE and 
the available area at the archetype.  The selected wind turbines have a higher LCOE than the high-capacity 
wind turbines or the ground-mounted PV solar, but they occupy the least area per installed Megawatt from all 
the renewable energies considered. As the available land is limited in this archetype, the model chooses the 
technology that permits installing the largest capacity. It must be noted that despite having larger LCOE than 
the other alternatives, it is still competitive against the electricity grid prices.  

As happens with solar, the year in which wind farms are installed varies across regions. In Germany, wind is 
installed  earlier  as  low-capacity  turbines  are  competitive  in  price  since  the  start  of  the  evaluation  period 
(Figure 56), while in Spain this equipment’s LCOE gets below the mean marginal prices until 2032. As seen in 
the annual investments reported under the Bandwidth scenario (Figure 57), the German polygon installs low-
capacity wind turbines in 2025 whereas the Spanish community does it until 2032.  

As PV solar rooftop does not compete against the rest of wind and solar technologies over land space, and its 
LCOE is competitive against marginal prices in both countries, the maximum possible is always installed. The 
investments  in  Germany  and  Spain  are  done  at  different  points  as  LCOE  becomes  competitive  against 
marginal prices after different years as explained in the previous archetype (see Figure 56). In general, these 
investments are done at earlier years in Germany than in Spain.  

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Figure 56. Wind LCOE in Germany and Spain versus mean marginal price 

Source: Own elaboration with results from MODECO’s investment model. 

Figure 57. Annual investments performed in the Industrial polygon archetype under the Bandwidth tariff case 

Source: Own elaboration with results from MODECO’s investment model 

It is relevant to note that in  this archetype,  the Spanish community  does incur in  some penalizations 
for excess energy withdrawal under the Bandwidth model. These start in 2034 and continue until the 
end of the period, representing average annual costs of 11,846 €. In the German community no penalizations 
are reported. As observed in the Bandwidth electrical balance for two representative days in 2040 (Figure 55), 
in both days, the Spanish polygon charges batteries around midday, when prices are low, to discharge at night 
and  dawn  when  selling  prices  reach  over  100  EUR/MWh.  However,  in  the  August  day,  it  surpasses  its 
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established limit  (52.44  MWe) as the low-priced window is narrower and the potential  economic 
benefits  to  sell  that  energy  back  later  permits  to  afford  such  penalties.  The  rest  of  the  time,  the 
model prefers to maintain demand up to the maximum possible without causing penalizations.  

The  Spanish  polygon  shows  some  difference  with  the  rest  of  scenarios when  using  the  Peak  Power  tariff.  
First, the installed CHP capacity is slightly below the other scenarios (32.47 MWe, 59.04 MWt), as is the wind 
power (0.65 MWe) and energy-based batteries installed (114.13 MWh). PV solar rooftop power is the same as 
in all other scenarios, but ground-mounted solar (0.19 MWe) is also installed in this particular case. Still, the 
installed amount is small given the limited land space considered for this archetype. As shown in  Figure 58, 
solar investments are encouraged in the Spanish polygon as its profile coincides with the community’s 
demand peaks, contributing to decrease costs associated with capacity-based network charges. In Germany, 
this is also the case, but the lower solar radiation available in this region makes this technology less attractive 
as  an  investment  even  under  a  Peak  power  tariff,  which  is  why  wind  is  preferred  on  land  and  PV  solar  is 
constrained to the rooftop area. 

Figure 58. Electrical balance for the Industrial polygon communities under a Peak power tariff in selected representative 
days in January and August 2040 [Maximum Ω] 

The selected representative days are January 22nd (Ω: 22) and August 29th (Ω: 22) for Germany and January 23rd (Ω: 22) and August 29th 
(Ω: 23) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

7.1.3  Rural town 

The  Rural  town  communities  invest  in  wind,  solar,  gas-fuelled  CHP,  batteries  and  V2G  charging 
points. In this case, however, a combination of  ground-mounted  solar, low and high-capacity wind turbines 
are  used  depending  on  the  tariff  case  evaluated.  In  this  archetype,  the  investments  done  by  the  Spanish 
community present less variations among tariff scenarios, whereas in Germany the  TOU case reports the 
largest investments, mostly related to CHP and storage installations (Figure 59).  

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Figure 59. Investments performed in the Rural town under different Use-of-Network structures 

Source: Own elaboration from the UCED’s model first executions 

The CHP capacities installed in the German Rural town under the No Charges, Bandwidth and Peak power are 
aligned  with  the  community’s  heat  requirements,  considering  that  in  Germany  an  average  thermal  power 
demand of  1.07  MWt is reported during the winter season. The  cogeneration power ranges from 0.68  MWe 
(1.24  MWt)  in  the  Bandwidth  to  0.75  MWe  (1.36  MWt)  in  the  No  Charges  case.  The  storage  capacity 
considered  are  also  pretty  similar  in  the  No  Charges  and  Bandwidth  tariffs  (4.33  MWh  and  4.43 
MWh).  Under  a  Peak  power  tariff,  significantly  higher  storage  is  installed  (4.88  MWh).  As  seen  in  the 
representative  day  show  for  August  2040  in  Figure  60,  in  Germany,  batteries  are  needed  to  reduce  the 
demand peaks reported at 8:00 and 9:00 hours for this archetype, as local generation at this time is limited. 
The number of V2G charging points is the same (14) for the No Charges and Bandwidth cases. In the Peak 
power scenario, two extra charging points are considered. 

In  all  these  tariffs,  low  and  high-capacity  wind  turbines  are  installed  in  similar  proportions  in  the 
German region. The largest wind capacity (0.77 MWe), nonetheless, is found at the No Charges scenario, 
in  which  no  solar  investments  –  rooftop  or  land  –  are  done.  In  the  Bandwidth  model,  slightly  less  wind 
capacity is installed (0.73 MWe), but solar PV rooftop (0.13 MWe) is also included in the local generation mix. 
Finally, in the Peak power scenario, part of potentially installed wind capacity is sacrificed (reaching 0.6 MWe) 
to instead include ground-mounted solar (0.22 MWe). As seen in the figure below, solar helps reducing peak 
demands  and,  therefore,  capacity-based  network  charges.  The  investment  decisions  over  wind  and  solar 
technologies  are  based  upon  the  technologies  costs,  the  curve  prices  and  the  land  available  as  discussed 
previously for the Industrial polygon.  

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Figure 60. Electrical balance for the Rural town communities under a Peak power tariff in selected representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 29th (Ω: 23) and August 19th (Ω: 21) for Germany and January 8th (Ω: 25) and August 6th (Ω: 
19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model. 

In  Spain,  the  installed  cogeneration  capacity  is  practically  the  same  (0.63  MWe,  1.15  MWt)  for  the  No 
Charges,  Bandwidth  and  Peak  Power  scenarios.  As  in  the  German  region,  this  capacity  is  adjusted  to  the 
community’s thermal demand. Wind installations are also pretty similar in the three cases,  with average 
high and low-capacity wind power of 0.49 MWeand 0.25 MWe, respectively. No solar is installed in any case. 
The installed storage capacity is the lowest in the No Charges case (0.25 MWh) and highest in the Peak power 
scenario (0.54 MWh). The latter is also the only case in which the Rural town installs power-based batteries 
(C-rate 2) and not only energy-base units (C-rate 0.35). However, as happened in the Business park archetype, 
the  installed  power-based  capacity  is  low  (13  kWe).  As  shown  above,  under  the  Peak  power  tariff, 
batteries are used in the Spanish town to store excess wind energy at times in which demand and 
prices are low to discharge at higher-priced hours (1:00 and 23:00) or when demand peaks occur 
(8:00). Still, in all cases, the storage capacity installed in Spain is significantly lower than in Germany as the 
wind  generation  profile  has  a  high  coincidence  to  high-priced  and  demand  periods,  which  makes  batteries 
usage less attractive.  

The  results  obtained  for  the  German  Rural  town  under  the  TOU  tariff  present  significantly  higher 
investments when compared with the rest of cases. The CHP capacity installed (1.91 MWe, 3.47 MWt) 
corresponds  to  the  maximum  allowed  investment  given  the  community’s  peak  demand  (3.18  MWt). 
The  CHP,  nonetheless,  was  already  utilized  at  partial  load  for  practically  all  hours  after  2025,  so  new 
investments in CHP are not justified in 2040 except for allowing higher storage instalments. As can be seen in 
Figure  61,  in  the  selected  days  for  the  German  Rural  town  there  are  higher  selling  prices  than  in  other 
archetypes,  reaching  over  100  EUR/MWh  in  several  days,  such  as  in  the  chosen  day  for  January  2040  at 
22:00 hours. This mix of conditions results in significantly larger storage capacity being added in the German 
town under the TOU tariff (9.38 MWh) than with the rest of tariffs in which the total storage capacity installed 
averages  4.55  MWh.  This,  in  turn,  leads  to  extra  CHP  capacity  installed  to  obey  the  model  rules.  Wind 
installations in this case (0.65 MWe) are similar to the Peak power case. Both, PV solar rooftop (0.05 MWe) 
and land (0.67 MWe) are also considered in this case, which represents the largest solar investments made in 
the German Rural town. The number of V2G points (18) are larger than for the rest of archetypes. 

On the  contrary, in Spain,  the lowest  CHP capacity  is installed under the  TOU tariff (0.56  MWe, 1.02 
MWt).  Storage  capacity  (0.57  MWh)  is  higher  than  in  the  rest  of  tariff  scenarios.  As  seen  in  Figure  61, 

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batteries in this case are used similarly to the other cases; their purpose is to store excess wind energy during 
low-priced periods to be later sold at a higher price. As the TOU uses different selected days than the rest of 
archetypes, the resulting price curves have a strong influence over the results obtained in this case. As can be 
seen in the figure below, the peak prices reported in the chosen representative day for August 2040 doubles 
the prices applicable to the Spanish town in the rest of scenarios, which reflects in more installed batteries as 
energy  arbitrage  becomes  more  profitable.  Still,  the  storage  capacity  installed  continues  being  significantly 
lower than  for Germany, as wind production in Spain  fits better the demand and price curves used,  making 
batteries less useful.   

Figure 61. Electrical balance for the Rural town communities under a TOU tariff in selected representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 29th (Ω: 23) and August 19th (Ω: 21) for Germany and January 8th (Ω: 25) and August 6th (Ω: 
19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model. 

Low  and  high  capacity  wind  turbines  are  also  considered  in  the  TOU  case.  High  capacity  installations  are 
favoured earlier as they offer a lower LCOE than the low-capacity types (see Figure 56). In the Spanish town, 
the  land-prices-technology  dynamics  imply  not  installing  any  PV  solar  on  land  as  prices  during  solar 
irradiation  hours  are  fairly  low,  and  self-consumption  is  already  covered  by  wind  production.  Despite  not 
competing over the same area availability, no PV solar rooftop is installed in the Spanish community under a 
TOU or any other tariff tested for the same reason that PV solar on land is disregarded: prices during solar 
radiation  hours  are  not  competitive.  As  in  the  Industrial  polygon,  for  land  installations,  the  model  finds  the 
technological  combination  that  permits  to  maximize  benefits,  considering  the  prices  curves,  generation 
profiles and technologies’ costs and features, such as land usage. 

7.1.4  Urban district 

In  the  Urban  district  archetype,  communities  invest  in  gas-fuelled  CHP,  batteries,  solar  PV  rooftop 
and V2G charging points (Figure 62). Ground mounted solar and wind farms are not possible investments 
due  to  land  usage  restrictions.  The  scenarios  that  prompt  the  largest  investments  are  the  No  charges  for 
Spain and the TOU for Germany, although just slightly above the No charges case. As happens in the previous 
archetypes, the major differences are mostly due to the decisions taken regarding investments in CHP 
and batteries. In this case, however, significant differences are observed regarding the amount of PV solar 
rooftop installed in each region, and among the tariff structures evaluated in the Spanish Urban district.  

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Figure 62. Investments performed in the Urban district under different Use-of-Network structures 

Source: Own elaboration from the UCED’s model first executions 

For the German district, the lowest amount invested (4.31  M€) is registered in the No Charges scenario. The 
difference, however, is narrow when compared to the rest of tariff analysed. The installed CHP capacity (1.58 
MWe, 2.87 MWt) is just below the community’s peak thermal demand (3.51 MWt). As in previous archetypes, 
this means  that  the  cogeneration  unit  operates at  partial  loads most  of  the  time.  The  installed  batteries 
(10.89  MWh)  are  the  lowest  considered  for  the  German  Urban  district,  but  are  large  enough  to 
need extra CHP installed to obey the model rules. PV solar rooftop capacity is also at its lowest in this 
scenario (2.24 MWe) as no  Use-of-Network  charges can be avoided as in other tariffs. The number of  V2G 
stations installed (5) is practically the same as for all other scenarios. 

In the Spanish region, the opposite trend is observed as the No Charges case is the one with the largest 
amount  of  money  invested  (2.09  M€).  While  the  PV  solar rooftop  installed  is  lower than  for other  cases 
(1.15  MWe), the  installed  CHP  capacity  is far  higher  (1.41  MWe,  6.44  MWt)  than  for  the  rest  of  the  tariffs, 
which result in cogeneration sizes of around 0.64 MWe (2.56 MWt) for the Spanish district. As happened with 
the  German  district,  an  oversized  CHP  is  installed  to  justify  investments  in  energy-based  batteries  (C-rate 
0.35).  The  storage  capacity  considered  in  this  scenario  (7.29  MWh)  is  below  that  installed  for  the  German 
district, but it is significantly higher than that installed in the Bandwidth and Peak power models, which use 
the same representative days as the No Charges case.  

The CHP capacity installed in the German district under the Bandwidth and Peak power cases is equal to that 
installed in the No Charges case. Storage capacities, nonetheless, are higher under these tariffs, and in both 
cases round 11.3 MWh. As shown in Figure 63, batteries under the Peak power tariff are used to store excess 
solar  and  CHP  electricity  in  low-priced  periods  to  be  consume  later  when  purchase  price  are  higher.  The 
installed solar PV rooftop is also larger as the Bandwidth and Peak power offer some further opportunities to 
reduce costs by avoiding Use-of-Network tariffs through self-consumption. The solar power in the Bandwidth 
(2.36 MWe) is below that considered in the Peak power case (2.41 MWe), which corresponds to the maximum 
allowed  given  area  restrictions.  This  as  in  the  latter  cost  saving  opportunities  through  peak  shaving  offer 
higher benefits; for instance, see the electrical balance for the representative day in January 2040 shown in 
Figure 63. 

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Figure 63. Electrical balance for the Urban district communities under a Peak power tariff in selected representative days 
in January and August 2040 

The selected representative days are January 18th (Ω: 23) and August 25th (Ω: 24) for Germany and January 27th (Ω: 23) and August 28th 
(Ω: 19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

In the Spanish district, the installed cogeneration capacity is at a similar level for both the Bandwidth (0.67 
MWe,  1.22  MWt)  and  Peak  power  (0.62  MWe,  1.13  MWt)  tariffs.  This  is  sized  to  the  community’s  thermal 
requirements  (mean  winter  thermal  demand  of  0.77  MWt).  However, the  storage  capacity  installed  is more 
significant in the Bandwidth (5.62 MWh) than in the Peak power (3.53 MWh). As seen in  Figure 63, under a 
Peak power structure, batteries are mostly charged with excess solar that is discharge at night, when no solar 
is produced, to supply demand and avoid electricity purchases at high-priced hours. In the Bandwidth scenario, 
however, batteries are  also  charged  through  the  grid  (Figure  64).  Notably,  in  any  case the  maximum  PV 
solar rooftop capacity (2.41 MWe) is installed in the Spanish district, the energy prices are so low 
during high solar production hours that is more convenient to consume directly from the grid.  In 
the Bandwidth scenario the PV solar rooftop considered is 1.29 MWe while in the Peak power this is slightly 
larger. V2G stations installed are 4 and 5, respectively.  

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Figure 64. Electrical balance for the Urban district communities under a Bandwidth tariff in selected representative days 
in January and August 2040 

The selected representative days are January 18th (Ω: 23) and August 25th (Ω: 24) for Germany and January 27th (Ω: 23) and August 28th 
(Ω: 19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

The results obtained for the TOU scenario show similar dynamics to those described for other archetypes. In 
Germany,  investments  in  batteries  (12.26  MWh)  are  larger  than  in  Spain  (3.81  MWh)  as  price 
spreads are  not  as  pronounced  in  the  latter (see  Figure  65).  For  Germany, this  encourages installing  extra 
CHP capacity in 2040 (totalling 1.88 MWe, 3.42 MWt) to allow further batteries instalments, even when the 
equipment’s  full  load  operation  is  not  required  most  of  the  time.  In  Spain,  a  CHP  size  (0.6  MWe,  1.1  MWt) 
more  aligned  to  the  district  heat  demand  (mean  winter  thermal  demand  equal  to  0.8  MWt  per  hour)  is 
installed. In this case, the German Urban district installs the maximum PV solar rooftop capacity possible due 
to  space  restrictions  (2.41  MWe).  This  is  decided  based  upon  the  regional  electricity  prices  and  the 
technology’s  LCOE  (See  Figure  51).  However,  the  Spanish  district  only  installs  62%  of  this  capacity  as 
marginal  prices  during  solar  radiation  hours  are  low,  and  get  even  lower  in  future  years.  The  installed  V2G 
charging points are similar for both regions (5 in Germany and 6 in Spain.  

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Figure 65. Electrical balance for the Urban district communities under a TOU tariff in selected representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 18th (Ω: 23) and August 18th (Ω: 21) for Germany and January 22th (Ω: 25) and August 18th 
(Ω: 17) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

7.1.5  Virtual community 

The  total  investments  made  in  the  Virtual  community  cases  are  shown  in  Figure  66.  As  in  this  case  the 
community  members  are  not  within  the  same  location,  CHP  installation  is  not  considered  feasible. 
Moreover,  this  is  the  only  case  in  which  energy-based  Use-of-Network  tariffs  are  associated  with  self-
consumption. The Virtual community members still save money as self-consumption avoids paying the entire 
tariff costs, and just a fraction is charged. In this archetype, the communities invest in batteries (mostly 
energy-based),  solar  PV,  low  and  high-capacity  wind  turbines,  and  V2G  charging  points.  Overall, 
investments  in  Germany  are  higher  than  in  Spain.  The largest  investments  are  reported  for  the  Peak 
power case (6 M€) followed by the TOU tariff (5 M€), while in the two other scenarios the amount of money 
invested is 4.2 M€. In Spain, there are less differences among scenarios regarding the total amount invested, 
going from 3.53 M€ in the Bandwidth model to 3.40 M€ in the Peak power case. 

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Figure 66. Investments performed in the Virtual community under different Use-of-Network structures 

Source: Own elaboration from the UCED’s model first executions 

In Germany, the No Charges scenario results in similar investments to the Bandwidth model. In Germany, the 
available land space is filled with high and low-capacity turbines, with equal installed power for both tariffs 
(1.36  MWe  and  1.05  MWe  of  high  and  low-capacity, respectively).  High  capacity  is  preferred  over  low-
capacity as there is wide land space available and the first wind turbine type offers the lowest LCOE. PV land 
is not considered even though it offers a lower LCOE than low-capacity wind as it occupies more space and 
would  reduce  total  renewable  production,  particularly  as  solar  resources  in  Germany  are  less  abundant.  PV 
solar rooftop  is installed,  as  it  does  not  compete  over  land  space,  with  smaller capacity  in  the  No  Charges 
(0.35 MWe) than Bandwidth model (0.44 MWe). A larger solar capacity is installed in the Bandwidth model as 
the  taxes  considered  in  this  scenario  make  self-consumption  more  beneficial  by  avoiding  these  costs  even 
below the penalization limit. Batteries investments are 3% larger for the German Virtual community under a 
Bandwidth  model,  but  the  No  Charges  case  results  in  more  V2G  charging  points  (89  versus  56  in  the 
Bandwidth model), which can also be used as storage as done in the representative days shown in Figure Y 
for the Bandwidth scenario. The high number of V2G points installed in this archetype are due to the larger 
influence area considered, which results in a higher number of electric vehicles circulation. 

In Spain, practically the same investment decisions are taken under the No Charges and the Bandwidth model. 
The only relevant difference is that in the No Charges case, some power-based storage (C-rate 2) is installed, 
although the capacity is small (0.08 MWe). As seen in Figure 66, the total amount invested in these scenarios 
is  lower  in  Spain  than  in  Germany  (on  average,  17%  less).  The  main  difference  is  the  storage  capacity,  as 
wind, solar and  V2G are installed at similar levels. As happened in the Rural town, the Spanish wind profile 
results  in  more  wind  production  during  high  price  periods.  This  makes  batteries  less  attractive.  For 
instance, in the representative days shown in  Figure 67, no batteries are used in Spain as during low-priced 
periods wind excess is used to charge electric vehicles, which represent a fixed income for the community. The 
rest of the time, excess production is injected to the grid. 

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Figure 67. Electrical balance for the Virtual communities under a Bandwidth tariff in selected representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 2th (Ω: 25) and August 28th (Ω: 23) for Germany and January 26th (Ω: 27) and August 28th 
(Ω: 19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

Under the Peak power tariff, the German community results in the  largest investments from all Virtual 
community cases. The main differences are related to  battery investments as the wind power installed is 
actually  lower  than  in  the  previous  cases  (-27%),  and  the  solar  capacity  is  above  the  No  Charges  and 
Bandwidth,  but  below  the  TOU  scenario.  This is the  only  case  in  which  the  German  community  installs  PV 
solar on land (2.38 MWe). The latter as solar production coincides with the community peak demands, which 
is why a larger capacity of PV solar rooftop is installed (0.54 MWe) compared to the previous tariff scenarios 
(0.44  MWe  and  0.35  MWe  are  installed  in  the  Bandwidth  and  No  Charges  cases,  respectively).  The  total 
storage capacity installed in the German Virtual Community is 13.36 MWe, 70% and 60% more than in the 
No  Charges  and  Bandwidth  cases.  As  observed  in  the  electrical  balance  shown  in  Figure  68,  batteries  are 
mostly used by the German community to lower summer demand peaks as wind load factor is lower 
during  this  season  (see  Figure  7).  Batteries  are  charged  at  dawn  when  prices  are  low  and  discharge 
between  8:00  and  15:00  when  peak  demand  take  place.  In  the  Bandwidth  and  No  Charges  scenarios,  less 
storage is installed as less benefits are obtained from using batteries. As seen in the figure above, batteries 
are discharged at night when prices are higher, still the price spread is not as high as the costs avoided 
through peak shaving. The amount of energy-based storage in this case disincentives the installation of V2G 
points, which is the lowest in the four scenarios tested. 

In the Spanish region, the installed wind capacity is also lower (-17%) than in the No Charges and Bandwidth 
cases.  As in the German  community, ground-mounted PV solar (1.14  MWe) is also considered under a Peak 
power tariff, but no PV solar rooftop is installed. According to MODECO assumptions, solar on land offers a 
lower LCOE than on rooftop, which is why it is prioritized to supply demand peaks. As happened in the German 
region,  the  Peak  power  tariff  results  in  the  least  number  of  V2G  charging  stations  installed.  In  this  case, 
however,  the  energy-based  batteries  capacity  is  the  lowest  (2.29  MWh)  from  the  four  tariffs  analysed.  As 
seen in the representative days shown in  Figure  68, during  peak demand times there is plenty of  wind and 
solar energy available, which makes less beneficial to install and operate batteries (as shown in Figure 6 and 
Figure  7,  wind  resources  and  solar  resources  are  more  stable  throughout  the  year  than  in  Germany). 
Moreover, excess renewable production during low-priced windows is mostly used for electric vehicle charging.  

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Figure 68. Electrical balance for the Virtual communities under a Peak power tariff in selected representative days in 
January and August 2040 [Maximum Ω] 

The selected representative days are January 2nd (Ω: 25) and August 28th (Ω: 24) for Germany and January 26th (Ω: 27) and August 28th 
(Ω: 19) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

For the German  community, the TOU tariff results in the second largest total investments. The total 
wind capacity (2.26 MWe) is higher than in the Peak power tariff but lower than in the rest. In this case, the 
solar  PV  rooftop  capacity  installed  is  the  highest  (1.37  MWe),  but  contrary  to  the  Peak  power,  no  ground-
mounted solar is considered. Under a TOU tariff, solar represents higher potential economic benefits than the 
No Charges and Bandwidth cases as it avoids paying full Use-of-Network charges for consumption at those 
hours. These  potential savings, however, are below those  achieved through  peak shaving in the Peak  power 
case. The total energy-based batteries installed is 22% lower than in the previous tariff scenario. In this case, 
the largest number of V2G points are registered.  As the representative days selected are different for 
this case, the electrical balance for the TOU tariff is shown in  Figure 69. As observed, in both of the shown 
days, no batteries are operated in the German community, while V2G points are actively charging during 
low-priced  windows  in  August.  In  this  context,  batteries  are  mostly  relegated  to  performing  energy 
arbitrage  in  days  with  wide  price  spreads,  which  mostly  take  place  towards  the  end  of  the  16-year  period, 
when  the  energy-based  storage  is  implemented  (Figure  70).    In  the  rest  of  tariff  scenarios,  batteries  are 
installed  earlier  in  Germany,  although  the  largest  capacity  is  always  installed  at  the  end  evaluation  period 
(2040). 

As  happened  in  Germany,  the  TOU  tariff  results  in  the  Spanish  community  investing  in  higher  wind 
capacity (2.12  MWe) than in the Peak power but lower than in the rest.  Solar is also favoured  under this 
tariff, as it is the only case aside from the Peak power in which  ground-mounted solar is installed (0.91 
MWe) in Spain. No solar PV rooftop is installed in the Spanish community under any tariff, as it has a higher 
LCOE  than  solar  on  land,  resulting  even  less  competitive  given  the  low  energy  prices  registered  at  solar 
radiation  hours  in  Spain.  As  prices  during  solar  production  hours  are  low,  solar  production  is  used  as  a 
complement energy source to charge electric  vehicles or  batteries that  will be  discharged later when  prices 
get  considerably  higher  (see  the  January  representative  day  shown  Figure  69).  The  amount  of  storage 
installed for this case (3.29 MWh) is lower than in the Bandwidth and No Charges cases, but higher than in 
the  Peak  Power.  The  results,  nonetheless,  seem  to  be  more  impacted  by  the  representative  days  selected, 
which contain wider price spreads than the rest of scenarios as shown in the January day in Figure 69. 

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Figure 69. Electrical balance for the Virtual communities under a TOU tariff in selected representative days in January 
and August 2040 [Maximum Ω] 

The selected representative days are January 2nd (Ω: 25) and August 25th (Ω: 22) for Germany and January 18th (Ω: 26) and August 4th (Ω: 
17) for Spain. In all cases, the days with the highest weight (Ω) per month were selected. 
Source: Own elaboration with results from MODECO’s investment model 

Figure 70. Annual investments performed in the Virtual community archetype under the TOU case 

Source: Own elaboration with results from MODECO’s investment model 

7.2  Sensitivity tests 

In  the  TOU  tariff  scenario,  further  tests  were  run  using  a  flat  rate  for  the  energy  purchase  price 
instead of the dynamic price. The Use-of-Network tariffs are maintained the same as in the base case. For 
the  Industrial  polygon  an  additional  scenario  was  analysed  using  a  fixed  price  for  the  entire  16-year 
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period,  simulating  a  PPA/bilateral  contract  scenario.  As  explained  in  Section  2.3.1,  this  price  was  set 
based on the costs from the generators considered in the power system model for each region.  

Using  a  flat  rate  with  narrower  differences  between  high  and  low  priced  hours  complicates  finding  the 
optimal solution for some cases. Although the model reaches a solution within the established maximum time 
(6  hours)  for  all  scenarios,  this  is  far  from  the  optimal  for  some  of  the  archetype-region  combinations.  As 
explained in Chapter 4, this is indicated by the gap value reported by the GAMS software. This situation was 
more often observed in the Spanish region, in which all archetypes except the Virtual community (gap: 6.2%) 
finalized  the  optimization  process  with  gap  values  greater  than  9.6%,  even  when  extra  restrictions  were 
added14.  For  Germany,  most  of  the  archetypes  managed  to  get  a  gap  value  below  6,0%  but  only  after 
integrating  the  additional  positive  value  constraint.  The  only  exception  was  the  Business  archetype  (gap: 
37,0%), which was also the case with the highest gap for the Spanish region (gap: 51,0%).  

For  these  reasons  only  the  results  for  the  Industrial  polygon  (gap:  1.25%),  Rural  town  (gap:  5.7%),  Urban 
district (1.9%) and Virtual community (gap: 0.5%) are discussed in this section, although one of them got gaps 
below  the  maximum  threshold  used  for  the  base  case  scenarios (<0.1%).  For these  reasons, the  sensitivity 
test results must be interpreted with caution considering that the proposed investment path is not as close to 
the  optimal  solution  as  those  shown  in  the  previous  section.  A  similar  situation  was  encountered  for  the 
Industrial polygon when using the 16-year fixed price (TOU_PPA). When the extra positive value constraint, the 
case  in  Germany  managed  to  reach  a  gap  value  of  5,0%  but  the  Spanish  community  only  decrease  up  to 
14%, which is why the Spanish archetypes results are not discussed. 

7.2.1  Sensitivity to different price rates 

As  part  of  the  sensitivity  tests  run  in  this  study,  a  flat  rate  price  was  tested  for  the  German  community 
archetypes under a TOU tariff. The results obtained for the German archetypes with gap values below 6% are 
shown  in  Figure  71.  As  expected,  the  resulting  investments  in  energy  storage  were  significantly 
reduced  as  price  spreads  narrowed  down  significantly  when  a  mean  annual  price  is  used  as  the  base 
electricity costs. For 2040, when high selling prices are present, the mean average also rises (see Figure 53 in 
Section 6.2), making it  costlier to charge batteries with grid energy and decreasing  potential revenues from 
energy  arbitrage  activities.  For  the  archetypes  with  large  energy  demands  (Industrial  polygon  and  Virtual 
community), using a flat rate resulted in zero storage investments, as local energy production can be mostly 
consumed directly.  

Notably,  changing  to  a  flat  rate  also  results  in  the  installation  of  power-based  storage  in  the  Virtual 
community, a type of investment previously identified only under Peak power scenarios, but the invested sum 
is barely noticeable as the installed capacity is minimum. The largest reduction in volume storage when using 
a flat rate are observed in the Industrial polygon in which zero storage capacity is installed. This is followed 
by  the  Virtual  community  (-98%)  and  Rural  town  (-96%)  archetypes.  The  least  reduction  for  the  flat  rate 
cases is observed in the Urban district (-72%).  

For the Industrial polygon, using the 16-year fixed price (TOU_PPA) results in 11% reduction in the storage 
capacity installed compared to the dynamic price case. As could be seen in Figure 53 (Section 6.3), the fixed 
prices used in 2025 in the TOU_PPA case result in energy tariffs with peak prices slightly above those of the 
dynamic price scenario (TOU). However, in future years, dynamic prices increase at peak hours and decrease 
at valley times. These price differences result in batteries being installed in 2033 and 2034 in the dynamic 
case, while in the PPA scenario, investments are done until the end of the evaluation period (2038 and 2040) 
when  energy-based  batteries’  costs  are  low  enough  to  offer  some  profit.  In  the  flat  rate  scenario,  no 
investments in batteries are reported despite offering higher prices and a similar trend to the PPA case. It is 
therefore assumed that the storage investment reported for the PPA scenario might be overestimated given 
the larger gap value obtained for this scenario. 

Investments  in  CHP  are  also  reduced  (around  60%  reduction)  particularly  in  those  archetypes  in  which 
unrequired additional CHP was installed by the end of the period to allow further battery installations (Rural 
town and Urban district). In the Industrial polygon, CHP installed capacity remains the same for all TOU cases 
despite the energy price structure. As explained in Section 7.2, the CHP installed in the German polygon under 

14 As explained in Section 4.2, those cases that using the standard configuration reached gap values above the desired target (0.1%) were 
repeated adding a new constraint that limited the objective function to positive values: positive value constraint.  

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these conditions is sized to its thermal demand. It must be noted that CHP investments are not considered an 
option for the Virtual community archetype. 

Regarding the amount of PV solar installed, no changes among tariff scenarios are observed in the Industrial 
polygon and Urban district. Similarly, in the Industrial polygon, wind investments are maintained equal. In the 
Rural town, however, ground mounted PV solar capacity (0.3 MWe) is reduced in comparison to the base case 
(0.6 MWe) as well as low-capacity turbines, which are also decreased but to a lower extent (from 0.29 MWe 
to  0.25  MWe).  On  the  contrary,  high-capacity  turbines  capacity  increased  to  0.43  MWe  from the  0.36  MWe 
reported in the dynamic price case. PV solar rooftop, which does not compete over land space, increases in 
this and the  Virtual community archetypes.  As new representative days were  selected for this scenario, the 
results are also affected by  the  behaviour of the energy  selling prices, which  remain linked to the dynamic 
prices.  Although  these  were  already  low  on  the  base  case,  it  gets  even  lower  for  the  representative  days 
selected  for  the  flat  rate  scenario,  which  discourages  selling  energy,  particularly  at  solar  radiation  hours. 
Moreover, the reduced storage investments shifting excess energy to hours with higher prices as done in the 
dynamic price case, in which high price peaks were profited. 

In  the  Virtual  community,  the  capacity  of  PV  solar  on  land  is  increased  from  zero  to  0.5  MWe,  while  low-
capacity wind turbines’  capacity is reduced  considerably (from 0.81 MWe to 0.55  MWe).  High-capacity  wind 
units  are  just  slightly  increased  (+1%).  Overall,  the  flat  price  resulted  in  larger  renewable  capacity  being 
installed  in  the  Virtual  community  and  lower  in  the  Rural  town.  For  this  particular  archetype  the  flat  rate 
means that solar is able to obtain higher benefits during radiation hours as tariffs are in average larger in this 
timeframe,  but  it  also  means  paying  larger  Use-of-Network  tariff  than  in  the  dynamic  case.  The  extra 
benefits, however outweighs the burdens. Wind power, on the contrary, loses some of the evening peak prices 
registered in Germany at evening and night  under the TOU  with dynamic prices, obtaining in average lower 
benefits, which are not compensated by the decreased Use-of-Network payments.  

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Figure 71. Investments performed in German archetypes under a TOU tariff with dynamic, flat and PPA prices 

Results for the PPA energy price are deliberately omitted for the Rural town, Urban district and Virtual Community archetypes as this 
scenario is only considered for the Industrial polygon. 
Source: Own elaboration from the UCED’s model first executions 

7.2.2  Sensitivity to different discount rates 

The tariff base cases – TOU, Bandwidth and Peak Power  – were repeated using the maximum discount rate 
for  Germany  (2.5%)  instead  of  the  minimum  (1.3%)  listed  in  Table  2.  For  most  scenarios,  using  the  higher 
discount  rate  results  in  lower  sums  being  invested  in  energy  assets,  which  is  expected  as  future  money 
revenues are reduced when considering the present value of future cash flows. In most cases, however, the 
differences between using the minimum and maximum discount rate are below 1%. As observed in Figure 72, 
the  case  in  which  the  difference  between  discount  rates  is  more  visible  is  the  Business  park  under  the 
Bandwidth  tariff.  Using  the  1.3%  discount  rate  results  in  9.6%  more  money  invested  in  energy  assets  than 
when  considering  the  2.5%  rate.  In  this  case,  the  largest  increment  is  observed  in  the  investments  done  in 
energy-based storage.  

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Figure 72. Investments performed in German archetypes under the base tariff scenarios considering different discount 
rates 

The minimum discount rate considered is 1.3%, and the maximum 2.5%. 
Source: Own elaboration with results from MODECO’s investment model 

As shown in Figure  49, during the representative  days in  the summer season, batteries are  mostly  charged 
using excess solar production for the German Business park under a Bandwidth model. For both discount rate 
scenarios, the solar installed capacity is maintained the same (the maximum permissible given the available 
rooftop  area).  Given  that  storage  investments  are  done  towards  the  end  of  the  evaluation  period;  these 
investments  are  more  sensible  to  decrements  in  the  value  of  future  expected  revenues.  The  exceptional 
scenarios in which the total sum invested is higher when considering the 2.5% discount rate, are the Industrial 
polygon  and  Rural  town  under  the  Bandwidth  model,  and  the  Virtual  community  under  a  TOU  tariff.  In  the 
Virtual community and Industrial polygon cases, the differences obtained for the different discount rates are 
quite  low  (<  0.5%).  In  the  Rural  town,  however,  the  investments  done  when  using  the  2.5%  rate  are  3.3% 
higher  than  with  the  lower  rate.  Contrary  to  the  Business  park,  the  Rural  town  under  a  Bandwidth  model 
results in much higher investments in energy storage when using the maximum discount rate. Although these 

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investments are also done towards the end of the evaluation period, they are affected differently given that 
the investments in variable renewable energy assets (solar, wind) also increment in this case, which was not 
the case in the Business park archetype.  

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8  Operational model results 

The operational model follows a similar formulation to the investment model, but allowing for further details 
in  some  assets  and  the  possibility  to  optimize  the  entire  year  (8760  time  steps)  instead  of  selecting 
representative  days.  This  is  possible  as  the  installed  capacities  are  known  and  each  year  is  optimized 
individually, which reduces the number of variables and computational time (see Chapter 4). From the  case 
studies  discussed  in  Chapter  7,  the  optimal  operation  of  the  assets  installed  by  the  German  and  Spanish 
archetypes under the TOU, Bandwidth and Peak power tariffs is analysed for each target year (2025, 2030, 
2040), looking at the key indicators evolution following the installation of the energy assets dictated by the 
investment model. As shown in Figure 14, those key indicators are: the volume of energy dispatched per type 
of technology and its associated CO2 emissions, the percentage of demand covered by self-consumption, the 
amount  of  energy  purchased  from  the  grid,  energy  costs  disaggregated  by  payment  concept,  and  the 
revenues associated to energy sales. 

8.1  Local generation mix 

The annual demand and generation per type of technology is presented in (Figure 80) for German archetypes 
and (Figure  81)  for  the  Spanish.  The  technological  categories have  been  narrowed  down  to:  Solar PV, Wind 
turbines,  and  Gas-fuelled  CHP.  Biomass  CHP  is  not  included  as  it  is  not  installed  in  any  region.  The  annual 
electricity purchased is also shown as its volume gives hints about the level of energy arbitrage performed in 
certain scenarios.  

In  Germany,  it  is  observed  that  local  generation  (wind,  solar,  CHP)  surpasses  demand  in  most 
archetypes, except  for the Industrial polygon (where baseload demand is  particularly high) and the Virtual 
Community  (in  which  Use-of-Network  charges  are  also  applied  to  self-consumption).  This  indicates  that  a 
fraction of the energy generated by the community in these cases (Business park, Rural town, Urban district) 
is being sold back to the grid at some point. In all German scenarios, the amount of local energy generated 
grows  in  2040,  when  marginal  prices  are  considerably  higher  (Figure  45).  The  highest  local  generation 
increases in 2040 are observed in the Rural town and Urban district archetypes under a TOU tariff and in the 
Urban district  when a Peak power is considered. In all cases, the  major increase is due to a more intensive 
CHP usage. 

In  the  German  Business  park,  Rural  town  and  Urban  district  archetypes,  it  is  observed  that  the  power 
production from CHP is equal or larger than the communities’ electrical demand (with the exception 
of the Business park 2025 under a Bandwidth tariff). However, as shown in Figure 73, boilers are required 
in all of scenarios to cover the thermal demand of the German communities, even in those cases in 
which  CHP  power  generation  increases  considerably  in  2040.  The  Industrial  polygon  is  the  only  German 
archetype in which practically all thermal demand (low and medium heat) is supplied by CHP in 2040, while in 
previous years it already covers a large percentage of it (> 93% in all tariffs). For this case, producing all heat 
through  CHP  does  not  translate  into  higher electricity  exports  as  it  is  consumed  locally  given  the  polygon’s 
large electrical demand. 

In  the  case  of  Spain,  which  has  a  lower  thermal  demand  and  lower  marginal  prices,  the  local  power 
generation only surpasses electrical demand in 2025 and 2030 in specific cases, which indicates that 
lower surplus electricity is sold than in Germany in these years. In 2040, nonetheless, a similar trend to the 
German  archetypes  is  observed,  with  local  generation  being  higher  than  demand  in  all  archetypes  and 
tariffs except the Industrial polygon and Virtual community; and with the largest increase from 2030 to 2040 
in  the  Rural  town  and  Urban  district  under  TOU  tariffs  and  the  Urban  district  under  Peak  power,  being  the 
result  of  a  higher  CHP  usage.  In  this  region,  boilers  play  a  more  significant  role  in  covering  the 
community’s  thermal  demand.  In  fact,  the  only  case  in  which  CHP  covers  all  thermal  requirements  is  the 
Industrial polygon in 2040 under a TOU tariff.  

The effect of the tariff structure on the final generation mix is similar for both regions.  The use of a TOU 
tariff  structure  reflects  in  higher  local  production,  particularly  in  2040.  This  is  more  evident  in  those 
scenarios in  which representative days with  pronounced  peak prices were selected (Urban  district and Rural 
town).  The  only  exceptions  are  the  Industrial  polygon,  in  which  the  tariff  structure  seems  to  have  a  subtler 
effect  on  the  community’s  generation  mix,  and  the  Virtual  community,  where  chargers  are  also  applied  to 
self-consumption. This tariff also reflects on a lower boiler usage, particularly in 2040. This is especially 
visible in the Spanish cases as in the German, the Peak  power scenarios results in  similar shares  regarding 
CHP and boiler usage. 

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Figure 73. Annual demand, purchased electricity and local generation per type of technology in German cases 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 74. Annual demand, purchased electricity and local generation per type of technology in Spanish cases 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 75. Annual thermal demand and heat generation per type of technology in German cases. 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 76. Annual thermal demand and heat generation per type of technology in Spanish archetypes. 

Source: Own elaboration with results from MODECO’s operational model 

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The Bandwidth scenario, on the contrary, tends to result in lower local generation and disincentives 
the usage of solar PV technologies compared to the other tariffs, especially in the Spanish region. Even in 
those scenarios in which representative days with high electricity prices are chosen for 2040, resulting in high 
electricity  surpluses  being  generated,  the  results  for  the  Bandwidth  model  show  a  slight  increase  when 
compared  to  2030  values.  In  some  cases,  however,  the  Bandwidth  model  results  in  larger  electricity 
purchases, even beyond the community’s need. In Spain, the Bandwidth model also reflects in a significant 
increase in boiler usage in 2030  as CHP  power production is lower even  when similar capacities have been 
installed.  

The usage of a Peak power tariff results in larger solar investments, particularly in the German cases. As 
explained  before,  wind  power  matches  better  with  peak  demands  in  the  Spanish  archetypes,  which  makes 
solar PV usage less attractive for peak shaving purposes under this tariff. In the  archetypes with low and 
medium demand (Business park, Rural town, Urban district), this tariff leads to a significant decrease in 
the amount of electricity purchased from the grid, being practically zero in the German region. The share 
of heat supplied by CHP and boilers is similar to TOU in the German archetypes while in Spain it leads to a 
lower boiler usage than in the Bandwidth but higher than in the TOU scenarios. 

The  Industrial  polygon  is  the  archetype  with  the  largest  heat  and  electrical  demand,  and  the  only  in  which 
self-generation  does  not  surpasses  consumption  at  any  case  (Figure  73  and  Figure  74),  requiring  external 
sourced electricity to cover the community’s demand during the entire evaluated period. Contrary to the other 
archetypes in which CHP production to supply heat demand translates in electricity surpluses, in the Industrial 
polygon,  the  CHP  power  generation  (for  low  and  medium  heat)  only  covers  a  share  of  the  total  electrical 
demand even when the maximum possible capacity is installed. 

8.1.1  Emitted and avoided CO2 emissions 

The total community emissions after the installation of the selected energy assessment is shown in Figure 81 
and  Figure  82.  Similarly, the  baseline  emissions  from the  alternative  case  (only  boilers and grid  purchases) 
are shown with the purpose to identify those scenarios in which the installed energy assets result in lower CO 2 
emissions (marked with an orange arrow). As noted in the following figures,  a larger number of cases in 
which  CO2  emissions  are  offset  through  the  installation  of  local  power  and  heat  generation 
assets  are  reported  in  Spain  that  in  Germany.  The  latter  as  the  main  source  of  emissions  at  the 
community’s  level  are  the  boilers  and  CHP  units,  whose  size  and  usage  is  strongly  related  to  the 
communities’  thermal  demand,  which  is  considerably  higher  in  Germany  than  Spain.  The  second  source  of 
emissions is grid electricity, which has a different emissions factor (tonCO2/MWh) depending on the available 
generation technologies at each hour, and is significantly higher for Germany than for Spain (see Chapter 6). 

Within  the  evaluated  scenarios.  the  Bandwidth  tariff  seems  to  favoured  CO2  emissions  reduction, 
especially in earlier years as all archetypes report some savings in 2025 and 2030  – and some even in 
2040 – under this tariff in the Spanish region, as well as most of the German archetypes (the only exception 
is the Urban district that does not report emissions reductions in Germany at any of the evaluated years). As 
previously  discussed,  this  model  results  in  lower  local  generation  than  other  tariffs  as  the  model  tends  to 
avoid incurring in penalizations for excess electricity injections and, below that limit, self-generation presents 
less opportunities per cost reduction due to the existence of a fixed charge. Thus, the amount of local energy 
and heat generated by the communities in this scenario tends to be slightly below that of the Peak Power or 
TOU  cases;  such  differences  are  more  noticeable  in  Spain  (see  for  instance  the  heat  volume  produced  by 
boilers under this tariff and region in Figure 76. 

The  Peak  power  and  TOU  tariff  results  varies  from  a  case-to-case  basis.  In  the  TOU  tariff  a  pair  of  cases 
result surprising due to the considerable increment in the community’s’ CO2 emissions in 2040: The German 
Urban  district  and  Rural  town.  As observed  in  Figure  73,  these  are  related  to  a  high  increase  in  CHP  power 
production,  which  is  used  for  meeting  the  community’s  demand  and  charge  batteries  to  sold  or  consume 
energy  at  later  times  when  prices  are  higher.  In  Spain,  less  differences  are  observed  between  the  TOU 
scenario and the other tariff cases. 

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Figure 77. CO2 emissions from the operation of installed assets versus base case in the German archetypes 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 78. CO2 emissions from the operation of installed assets versus base case in the Spanish archetypes 

Source: Own elaboration with results from MODECO’s operational model 

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As  explained,  CHP  power  production  increases  considerably  in  2040  in  the  German  Rural  town  and  Urban 
district archetypes under a TOU tariff. However, the CHP’s thermal production decreases for these archetypes 
in  these  same  years.  Within  MODECO,  it  is  assumed  that  CHP  units  can  shift  their  production  modes  to 
prioritised  electrical  instead  of  heat  production  as  happens  in  real  operation.  These  functional  modes  are 
represented in the optimization model through the polygon area described in Section 4.3.3 while the assumed 
values  can  be  consulted  in  Annex  3.  However,  the  results  obtained  for  these  cases  indicate  that  some 
adjustments  might  be  needed  for  the  assumed  values  delimiting  the  polygon  or  in  the  selection  of  a 
polygonal  shape  that  better  represents  the  type  of  CHP  units  modelled  in  this  project.  Relevantly,  this 
operational  mode  also  increases  CHP’s  carbon  intensity  as it  only  offsets  grid  power  consumption,  which  is 
low carbon at many hours due to the power mix considered in the reference ESES (see Section 6.1) and do not 
displaces boiler usage. 

The Virtual community is the only case that reports emissions savings across all years and tariff 
scenarios  in  both  regions.  This,  however,  is  expected  as,  under  MODECO  assumptions,  the  Virtual 
community  can  only  invest  in  renewable  or  storage  assets  given  the  lack  of  physical  proximity  among  its 
members,  which  complicates the installation of CHP  units for shared  heating systems. For this reason, this 
archetype  is  the  only  in  which  a  decreasing  trend  is  observed  for  CO2  emissions  from  2025  to 
2040,  as  the  electricity  produced  by  the  communities  are  mostly  carbon  free.  In  the  rest  of 
archetypes,  a  slight  increase  is  observed  in  the  emissions  registered  from  2025  to  2030,  but  they  tend  to 
peak until 2040.  

The Industrial polygon is the only in which externally sourced green hydrogen is considered as an available 
fuel. As green hydrogen is assumed to have no carbon emissions associated to its combustion, its 
usage  in  CHP  and  boilers  reduces  the  carbon  footprint  of  these  assets.  In  the  TOU  and  Bandwidth 
scenarios,  the  investments  done  result  in  lower  carbon  emissions  for  the  German  and  Spanish 
polygons. This as thermal production is all or mostly cover through Hydrogen combustion and a significant 
share of the consumed electricity is locally generated with renewable energies,  resulting in lower emissions 
that the grid alternative. 

In  the  Peak  power,  nonetheless,  an  increase  in  emissions  is  reported.  As  seen  in  the  graphics  showing  the 
community’s heat and electricity generation per technology (Figure 73 and Figure 75 for Germany, and Figure 
74  and  Figure  76  for  Spain),  there  are  no  major  differences  between  the  volume  of  heat  or  electricity 
generated by the CHP or purchase from the grid. However, the need to reduce peak demands – which result in 
significant capacity-based payments – forces the community to generate larger energy at different days and 
times than in the Bandwidth and TOU tariffs. In some of these days, Natural gas results to be cheaper than 
Hydrogen,  resulting  in  a  larger  consumption  of  this  fuel  in  this  tariff  (Figure  79).  This  happens  in  both 
Germany and Spain, as although the considered prices are different, the same daily trend is considered. 

Moreover,  when  looking  at  the  hourly  electricity  purchase  trends  (Figure  80),  it  is  observed  that  the  peak 
shaving hours, when the polygon reduces demand to avoid power-based costs, coincide with the hours with 
lower  carbon  emissions.  While  at  night,  when  the  polygon  consumes  more  to  make  up  for  the  reduction 
imposed around midday, it buys energy that has more associated emissions. This not the case for the other 
archetypes as its demand peaks tend to coincide with high emissions hours, which also tend to be the more 
expensive  as  they  are  produced  by  fossil-fuel  generator,  which  are  costlier  than  clean  energies  under 
MODECO future scenario assumptions.  

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Figure 79. Mean annual fuel cost and total fuel consumption in the Industrial polygon 

Source: Own elaboration with results from MODECO’s operational model 

Figure 80. CO2 emissions from the operation of installed assets versus base case in the German archetypes 

Source: Own elaboration with results from MODECO’s operational model 

8.2  Economic benefits 

The communities’ annual electrical balance is presented in the following figures, considering the total amount 
of  electricity  purchased,  generated  (disaggregated  by  self-consumed  and  surplus  electricity15),  stored16  and 

15 Electricity that is locally generated by the community and not use for self-consumption. 

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sold.  The  community’s  demand  is  also  presented,  as  well  as  the  economic  benefits  obtained  from  surplus 
electricity sales and avoided purchase costs due to self-consumption.  

As already mentioned, the electrical balance for the German (Figure 81) and Spanish (Figure 82) archetypes 
show  that  the  amount  of  electricity  purchased  tends  to  be  lower  in  the  Peak  power  scenario.  Moreover,  it 
results in zero purchased electricity for the German Business park, Rural town and Urban district, which cover 
their demand with local generation since 2025. In most of the evaluated scenarios, the Peak power tariff tend 
to  result  in  similar  economic  benefits  as  those  obtained  for  a  Bandwidth  model  for  the  high-demand 
communities (Industrial polygon and Virtual community).  

In both regions, the Peak power scheme results in higher economic benefits when compared to the 
Bandwidth  model,  but  lower  than  in  the  TOU  cases,  which  in  general  results  in  the  largest 
economic benefits. For some cases those benefits are due to higher costs avoided while in others they are 
the  result  of  higher  surplus  electricity  sales,  or  both.  As  explained  the  Bandwidth  model  seems  to  lead  to 
larger  electricity  purchases,  although  in  the  German  region  the  differences  are  narrower  than  in  Spain. 
Particularly in the latter, the Rural town and Urban district show larger electricity purchases when considering 
the Bandwidth tariff rather than the Peak Power or TOU, 

In Germany, it is also observed that the Peak power tariff leads to lower storage usage, particularly as 
no  grid  battery  charging  is carried  out.  In  Spain,  the  used  tariff  does not  seem  to  have  a  strong  impact  on 
storage  usage.  Furthermore,  in  both  regions,  energy  storage  tends  to  be  utilized  at  the  end  of  the 
evaluation period regardless of the tariff  scenario,  as there is a more  pronounced  difference  between 
valley and peak-priced hours.  

In  most  of  the  scenarios,  the  major  economic  benefit  for  the  communities  is  the  electricity  costs 
avoided  through  self-consumption.  In  fact,  electricity  sales  revenues  are  irrelevant  in  2025,  and  low  in 
2030, and just get significant up to 2040. Moreover, the exceptional cases in which electricity sales are the 
main economic benefit take place only in 2040 – when the annual mean marginal price rises and  difference 
between  seasonal  and  hourly  prices  widens  (see  Chapter  6)  –  in  low  and  medium  demand  archetypes.  The 
latter also happens with more frequency in Bandwidth and Peak power scenarios. Only the German Rural town 
and  Urban  district  present  larger  benefits  associated  to  electricity  sales  than  costs  avoided  under  a  TOU 
scheme, which is explained by the high electricity costs from the representative days selected for these cases. 

8.2.1  Avoided energy costs 

As seen in the previous chapter, the major economic benefit to the communities is avoiding electricity costs 
through self-consumption; the values reported for each case re shown in  Figure 83 and Figure 84.In Spain, 
the major avoided costs are registered in the TOU scenario, being Use-of-Network charges the most 
significant costs for 2025  and 2030. In  2040, the price of  energy becomes the  largest cost avoided 
through  the  investments  made  by  the  Spanish  communities.  In  the  Peak  power  tariff,  a  similar  trend  is 
observed for this region, although the total costs avoided are always lower than in the TOU case.  

The  Bandwidth  tariff  represents  the  lowest  costs  avoided  as  no  Use-of-Charges  costs  are  saved  through 
electricity self-generation and storage. Still, this scenario is not the exception, and in 2040 it results in large 
economic savings due to the high energy prices avoided through self-consumption. It is important to highlight 
that the current investment model does not include the contracted bandwidth value as a variable 
which  could  be  an  interesting  feature  to  add  in  a  future  version.  Nonetheless,  within  this  tariff, 
communities can reduce charges costs by avoiding penalizations for exceeding the amount of energy injected 
or withdraw from the grid. 

In Germany, the tariff scenario that represents the largest savings is the Peak power. In general Use-of-
Network charges are higher in Germany than in Spain for all scenarios. It seems, however, that the regional 
difference  between the  network costs places on the power-based  charge applied in the Peak power  case is 
more significant than the higher peak and off-peak charges applied in the TOU case. In the Bandwidth model, 
nonetheless,  the  same  trend  as  in  Spain  are  observed,  no  Use-of-Network  charges  are  avoided  by  the 
installation  of  the  selected  energy  assets,  still  the  avoided  energy  prices  represent  significant  economic 
benefits to the German archetypes in 2040. 

16 Refers to the amount of energy that is stored at the community’s energy assets (batteries or EV) at the close of the annual balance. 
This energy could come from surplus generation or purchased electricity. 
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 Contrary to Use-of-Network charges, taxes represent the lowest cost share in all tariffs and regions, but are 
particularly small in the Spanish cases. As explained in Section 2.3.3, Spain uses and ad valorem tax, assumed 
as 5.11% of the brut energy costs based on the electricity tax currently applied in the country. Nonetheless, 
the  used  percentage  probably  results  in  an  underestimation  of  taxes  impact  on  energy  costs  in 
Spain, as in reality the country also applies taxes on contracted and used power. Thus, to better reflect the 
fiscal burden on electricity consumption, using a higher percentage might be recommendable to account for 
those network costs that are recover through power consumption taxes and are not part of the 5.11% tax. 

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Figure 81. Annual electrical balance, energy sales income and electrical cost avoided in German scenarios 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 82. Annual electrical balance, energy sales income and electrical cost avoided in Spanish scenarios 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 83. Avoided energy costs in the Spanish scenarios disaggregated by cost component 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 84. Avoided energy costs in the German scenarios disaggregated by cost component 

Source: Own elaboration with results from MODECO’s operational model 

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8.3  Energy costs 

8.3.1  Disaggregated energy payments 

The total annual costs associated with the purchase of electricity are shown in  Figure 85 (Spain) and Figure 
86 (Germany) disaggregated by component: Use-of Network charges, taxes and energy costs (marginal 
electricity  prices).  For  the  Bandwidth  scenario,  the  applicable  Penalizations  for  exceeding  the  contracted 
Bandwidth are represented in a particular category, as they are also part of the Use-of-Network charges, but 
its  visibility  provides  useful  information  about  the  community’s  behaviour,  particularly  considering  that  in 
most  cases,  the  community’s  energy  operations  tend  to  avoid  incurring  in  penalizations  for  both, 
energy injections and withdrawal (see Chapter 7).  

As observed in Figure 85 and Figure 86, Use-of-Network charges have a high relevance in the total purchased 
costs bored by the communities, representing the largest share for all scenarios. Under a  Bandwidth model, 
charges  costs  are  particularly  high  in  both  regions,  which  is  explained  by  the  consideration  of  a  fixed 
subscription  cost  per  contracted  kilowatt  (Table  41)  –  calculated  monthly  –  that  cannot  be  offset 
through  self-generation  under  MODECO  assumptions.  As  explained  in  Section  2.3.2.3,  the  contracted 
bandwidth  assumed  for each  community  corresponds  to  90%  of  the  community’s  peak  demand  in  the  16-
year period which would lead to penalizations in a certain number of hours. The contracted value considered 
in each case can be seen in the following table. 

Table 41 Use-of-Network charges applied in the Bandwidth scenarios by region and voltage level 

Country 

Archetype 

Contracted 
bandwidth [kWe] 

Subscription  
price [€/kWh] 

Annual subscription 
costs [k€] 

Business park 

3060.24 

Industrial polygon 

52435.85 

Spain 

Rural town 

Urban district 

Virtual community 

Business park 

Industrial polygon 

Germany 

Rural town 

Urban district 

723.75 

944.15 

2705.06 

2879.95 

52561.8 

692.61 

888.28 

Virtual community 

2574.41 

Source: own elaboration with methodology from Section 2.3.2.3. 

10.12 

10.11 

10.12 

10.12 

10.12 

18.50 

18.49 

18.50 

18.50 

18.50 

371 

6361 

87 

114 

328 

639 

11662 

153 

197 

571 

From the tested scenarios, the only cases in which penalizations cost are significant are the German 
Rural town and Urban district archetypes. In both cases the large majority of the penalizations are related 
to excess energy injections as in these archetypes (which have the lowest demands from all archetypes), the 
relations  among  energy  prices,  and  demand  and  generation  profiles,  justify  exceeding  the  contracted 
bandwidth as the obtained revenues greatly surpassed this cost. In the rest of  scenarios, energy assets are 
operated in a way that avoids exceeding the bandwidth at almost all hours. 

The  charges  applied  in  the  Time-Of-Use  scenario  following  the  methodology  described  in  Section  2.3.2.1 
are shown in Table 42.  As previously explained, the Medium Voltage costs are used for the Industrial polygon 
archetype, whereas the Low Voltage costs are applied to the rest. By analysing the data, it can be seen that in 
the  mean  value  for  the  full  year,  the  charges  price  account  for  a  lower  proportion  to  the  electricity 

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price than the energy price. On the other hand, when one looks at Figure 85 and Figure 86, it can clearly 
be  seen  how  the  charges  have  in  most  cases  a  greater  impact  in  the  final  electricity  purchase  cost.  This 
happens because the optimization model tries to buy energy when it is cheaper. This happens when the 
energy  cost  is  in  its  lowest  values,  and  as  a  consequence,  the  charges  end  up  having  a  greater 
impact than the energy cost in most cases. Similarly, the taxes are computed as a fixed proportion of the 
electricity  price  in  Spain,  and  as  a  constant  value  in  Germany,  being  these  values  always  smaller  than  the 
charges and the energy cost. 

Table 42 Use-of-Network charges (€/MWh) applicable in the TOU scenario by year, user and voltage level.  

Year 

Price 
category 

2025 

2030 

2040 

Off-peak 

Peak 

Off-peak 

Peak 

Off-peak 

Peak 

Spain 

Germany 

LV* Charges 
[€/MWh] 

MV* Charges 
[€/MWh] 

LV Charges 
[€/MWh] 

MV Charges 
[€/MWh] 

36.22 

91.60 

36.53 

91.91 

35.57 

90.95 

17.24 

48.27 

43.61 

122.40 

17.39 

48.52 

43.76 

122.65 

16.93 

47.48 

43.30 

121.61 

27.97 

70.92 

28.11 

71.06 

27.51 

70.46 

*LV: Low Voltage; MV: Medium Voltage. 
Source: own elaboration with methodology from Section 2.3 

From  the  archetype-specific  behaviours,  two  interesting  cases  are  Urban  district  and  Rural  town  in 
Germany. In the TOU scenario, both cases buy practically zero energy in 2025 and 2030, which explains the 
extremely low energy cost shown in Figure 84. However, they experience a dramatic increase in the amount of 
energy bought, reflecting in a significant rise in the energy costs bored by the community. However, as shown 
in Figure 81, both archetypes also significantly increase their amount of surplus local generation, sold power, 
and stored electricity. This is an indication of intense energy arbitrage and selling activities, which reflect in 
significant revenues – particularly related to energy sales - for the community. As explained before, there is 
not clarity of whether or not these level of energy trading could be still classified as economic benefits and 
not financial profit generation. This does not happen in the Bandwidth and Peak power model. 

In  the  Peak  power  scenario,  the  yearly  charges  are  computed  based  on  the  considered  power  cost  (7.88 
€/kWh  and  33.04  €/kWh  in  Spain  and  Germany,  respectively)  which  is  applied  over  the  community’s 
maximum  demanded  power  registered  each  month.  This  price  is  high  enough  to  encourage  the 
communities to invest in assets allowing them to reduce its peak demand as much as possible to minimize 
charges costs. In fact, this tariff is the only one resulting in zero or nearly zero electricity purchases reported 
in the three target years (German Business park, Urban district, Rural town) and a substantial decrease in the 
Spanish low and medium demand archetypes. 

As explained in previous chapters, the Bandwidth model results in the largest energy purchases and thus in 
the higher buying expenses. Only in the industrial polygon (and less significantly in the Virtual community), the 
energy  costs  reported  in  the  Peak  power tariff  are  at  the  same  level  as those  reported  under  a  Bandwidth 
tariff. In these archetypes, the energy costs contribution  to total purchase expenses get closer to the share 
reported  by  Use-of-Network  charges.  This  can  be  explained  by  the  fact  that  demand  peaks,  which  are 
associated  to  a  power-based  charge,  happens  during  low-priced  hours.  Still,  reducing  the  power  costs 
represents  a  larger  benefit  for  the  community  so  it  still  reduces  demand  at  these  hours  to  increase  it  at 
higher  priced  periods,  increasing  energy  charges  but  minimizing  power-based  costs.  This  strategy  results  in 
costlier electricity as shown by the weighted average energy price paid by this archetype and marked with 
blue dots in Figure 85. 

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Figure 85. Disaggregated energy payments (price, taxes, Use-of-Network chargers) in German scenarios 

Source: Own elaboration with results from MODECO’s operational model 

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Figure 86. Disaggregated energy payments (price, taxes, Use-of-Network chargers) in Spanish scenarios 

Source: Own elaboration with results from MODECO’s operational model 

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In some cases such as the Business park and Rural town in the Bandwidth model, the Rural Town and Urban 
district  in  the  Peak  power,  or  the  Virtual  community  under a  Time-Of-Use  tariff,  an  annual  decrease  in  the 
weighted average energy costs is observed despite the rising annual marginal prices observed in both regions 
(Figure 45). This, however, is explained by  the growing energy storage and self-generation capacity that takes 
place in these scenarios towards the end of the evaluation period (see for instance the investment planning 
laid out for the German Virtual community under a TOU tariff shown in Figure 70). The communities do not 
only have more local generation available but can also make smart purchasing through the use of 
batteries and EV smart charging points. 

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9  Conclusions 

Energy communities are new players in the European energy market whose participation is expected to take a 
more  prominent  role  in  the  upcoming  years  as  the  regulatory  framework  supporting  their  participation  in 
market  activities  matures  across  member  countries.  Under  this  context,  understanding  how  economic  and 
regulatory  conditions  might  impact  on  Energy  communities  becomes  a  relevant  topic  for  policy  makers 
looking  to  advance  the  energy  transition.    MODECO  contributes  to  this  discussion  by  providing  optimization 
tools and analysis that permit to find the optimal investment and operational decisions expected from Energy 
communities under future energy prices and different tariff structures.  In particular, this study analysed the 
investment decisions made by five Energy communities archetypes over a 16-year period and considering two 
regions (Germany, Spain) and three tariff structures (TOU, Peak Power and Bandwidth). An additional scenario 
considering no charges or taxes at all is also evaluated for comparison purposes. 

Under the considered assumptions, all evaluated tariffs result in similar invested sums for the 16-year period 
except when representative days with considerably higher peak-priced hours are used. Under these conditions, 
the TOU  model leads to significantly higher investments  from Energy Communities, particularly in batteries, 
as  these  obtain  significant  revenues  from  performing  energy  arbitrage  by  charging  at  low-cost  hours  and 
selling the electricity back at these particular high-priced hours. Under the Peak power and Bandwidth model, 
batteries investments also increase but to a moderate level as increasing energy consumption leads to higher 
power-based  costs  in  the  first,  and  consumption  and  injections  get  penalized  above  a  certain  limit  in  the 
second. 

In other words, communities’ storage investments have a higher responsiveness to market price signals under 
a TOU tariff model. This leads to overinvestments in pricing conditions such as those considered in this study: 
low prices at high renewable production hours – commonly reaching zero - and extremely high prices at hours 
in which  peak demands coincide  with null renewable production. Although higher storage investments seem 
like a desirable outcome, our results show that a large  portion of the  batteries installed under a TOU tariff 
have  low  utilizations,  remaining  mostly  unused,  except  when  extreme  prices  are  registered,  which  only 
happens  during  a  few  hours  annually.  Notably,  storage  overinvestments  take  place  even  when  additional 
restrictions have been added to prevent excessive surplus generation or energy arbitrage given communities’ 
objective  to  prioritize  social,  environmental,  and  economic  benefits  over  financial  profit.  Still,  we  obtained 
these  results  considering  perfect  forecasting,  where  in  reality  a  margin  of  error  would  exist.  Moreover,  this 
type of investments represents a level of risk that communities are unlikely to assume. 

The rest of evaluated technologies  – wind turbines, solar PV, CHP, electrolyzer, hydrogen storage tank  – are 
only  slightly  affected  when  considering  different  tariff  structures  or  even,  price  curves.  In  particular,  the 
communities’ solar and wind investments are led by other factors: investment and operational costs, demand 
curves, and available area. In particular, we highlight the available area as an important characteristic shaping 
the  modelled  communities’  investment  paths.  Moreover,  for  renewables (wind,  solar),  using  the  Peak  power 
tariff tends to favour the technology whose generation profile matches the community’s consumption curves 
even  when  batteries are  also  installed.  Still, the  volume  of  surplus  generation  registered  by  the  community 
does not change significantly; only happens at different times.  

In  general,  communities tend  to  invest  in  self-generation  assets  as long  as the  investment  and operational 
costs  are  competitive  against  average  market  prices.  This  becomes  clearer  when  looking  at  the  obtained 
results for the sensibility analysis using a flat rate instead of the dynamic prices in the TOU tariff scenario. In 
this  case,  investments  in  batteries  are  significantly  reduced  whereas  investments  in  other  assets  remain 
practically  the  same  as  when  using  the  dynamic  prices.  We  suggest  running  further  sensibility  tests 
considering  the  two  other  tariffs  and  varying  the  investment  and  operational  costs  to  corroborate  these 
findings,  particularly  for  the  electrolyzer  and  hydrogen  storage  tank  as  the  assumed  costs  resulted  in  zero 
installed units for all scenarios.  

Under future system scenarios with a majority share of renewables, local generation might not always result 
in  carbon  offsets  if  CHP  units  fuelled  by  natural  gas  are  installed,  even  if  these  displace  boiler  usage. 
Nowadays,  this is  not  an  issue  as  grid  electricity  is  still  carbon  intensive  so  the  operation  of  CHP  results  in 
emissions savings not only when compared to boiler combustion but also to grid electricity consumption. In a 
future power system like the reference Energy System Evolution Scenario used in MODECO in which most of 
the time the available electricity is carbon free, the installation of CHP units leads to higher carbon emissions 
if natural gas is used as combustion fuel. Using hydrogen-fuelled technologies is an interesting alternative in 
this regard as demonstrated by the Industrial polygon case. In this study, no carbon tax was imposed on CHP 
electrical generation, but we recommend to consider its inclusion in future studies. 

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From  the  communities’  gains  perspective,  the  TOU  tariff  results  in  the  highest  economic  benefits  for  the 
German community archetypes followed closely by the Peak power tariff. In Spain, the Peak power leads to 
the  highest  benefits  followed  by  the  TOU  tariff,  with  similar values  for  both  tariffs.  In  the  two  regions,  the 
Bandwidth  model  resulted  in  the  lowest  benefits  even  when  similar investments  as  in  the  other  tariffs  are 
made.  However,  this  outcome  is  likely  more  favourable  if  the  contracted  bandwidth  is  a  variable  to  be 
optimized and not a fixed  value as assumed in this analysis. We recommend to include this case in further 
analysis  considering  some  restrictions  regarding  the  maximum  number  of  times  that  the  community  can 
change their selected bandwidth within the 16-year evaluation period. 

On the other side, the use of the Bandwidth model results in the most Use-of-Network charges paid by the 
user  due  to  the  existence  of  a  fixed  cost  per  contracted  power  unit,  while  in  the  TOU  and  Peak  power 
schemes,  communities  can  reduce  significantly  or  even  avoid  the  payment  of  Use-of-Network  charges 
through self-consumption. Although this feature results in economic gains for the communities, reduces the 
amount collected for grid cost recovery even when communities make use of grid infrastructure to supply part 
of their base demand, charge batteries and inject their surplus electricity for other consumers to use. This is 
important as we found that energy arbitrage and electricity sales could become relevant economic activities 
for future Energy communities. 

Regardless of the tariff or archetype, self-consumption represents the largest economic benefit in 2025 and 
2030  for  all  cases,  even  when  considering  the  Virtual  Community  archetype  or  the  Bandwidth  tariff  cases. 
Nonetheless, electricity sales take place during the entire evaluated period, meaning that surplus energy sales 
result in an economically attractive activity up to different levels. The only exception is the Industrial polygon, 
due to its large electricity demand all local generation is addressed to self-consumption. In 2040 when peak 
prices  rise  considerably  but  off-peak  actually  fall,  energy  arbitrage  becomes  a  more  significant  revenue 
source for all communities. 

From the three analysed tariffs – TOU, Bandwidth and Peak power – only the Subscription Bandwidth model 
considers  a  cost  beyond  energy  injections,  first  implicit  in  the  cost  paid  for  the  contracted  bandwidth,  and 
second, in the form of penalizations for excess energy injections above the contracted limit. This is a feature 
that  makes  this  tariff  scheme  an  interesting  option  for  scenarios  in  which  Energy  communities  actively 
engaged  in  energy  arbitrage  and  electricity  surplus  selling,  such  as  those  considered  in  this  study. 
Nonetheless, we advise to complement this analysis with a study on grid impacts from Energy communities’ 
operation under a Subscription Bandwidth tariff, analysing their imposed cost on the system versus the costs 
recovered via Use-of-Network charges. 

As  study  follows  a  cost  minimization  approach, the  modelled  communities operate  their energy  assets in  a 
way  that  avoids  the  penalizations  associated  with  excess  energy  injections  and  withdrawals  beyond  the 
established bandwidth limits. Still, in the  scenarios in which days with wide price spreads are used (German 
Rural town and Business park), the communities choose to bear the penalizations costs in the hours that the 
selling price is so high that this cost is easily offset. This happens only a few hours, but the volume of injected 
energy  is  considerably  higher  than  at  other  times.  In  this  sense,  regulators  could  consider  a  scalable 
penalization fee as the network impact of exceeding the contracted bandwidth by a large percentage does not 
have the same impact as just for a few kilowatts, even if it is just for a few hours per year.  

In  the  Virtual  community  archetype,  the  consideration  of  partial  Use-of-Network  charges  applied  to  self-
consumption also results in higher grid costs recovery. Nonetheless, the total charges paid by communities in 
this case are lower than for the Bandwidth model, whose charges remain fixed as the contracted bandwidth 
does not  change.  However,  our  results  indicate  that  the  Portuguese  regulation,  in  which  partial  charges  are 
applied to virtual self-consumption depending on the load and generation location, is an interesting proposal 
recognizing the benefits of Energy communities with geographically spread members, while also considering 
their network impacts. Further analysis on these rules impacts on energy communities and grid cost recovery 
would be advisable. 

Overall,  the  study  indicates  that  none  of  the  evaluated  tariff  structures  poses  significant  barriers  to  future 
expansion  of  energy  communities.  As  long  as  investment  and  operational  costs  are  competitive  against 
energy  prices,  the  installation  of  self-generation  assets  (solar  PV,  wind,  CHP)  will  translate  into  significant 
economic benefits for the communities. In all cases, storage installations will be also encouraged to promote 
energy injections and withdrawals in convenient times for the communities and the power system, maximizing 
savings  and  sales  revenues.  Purely  energy-based  tariffs  (TOU),  however,  could  lead  to  overinvestments  in 
storage units that would be only used at specific times when prices surpass a given price threshold.  

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The introduction of power-based charges, e.g. in the Bandwidth and Peak power models, seems to avoid this 
pitfall even in future power scenarios in which wide price differences are present. In particular, the Bandwidth 
tariff  presents  an  opportunity  to  adapt  Use-of-Network  charges  to  a  future  system  in  which  prosumers 
become more active, reshaping the grid’s demand and generation nodes. This becomes especially relevant as 
the  study  shows  that  not  only  self-consumption,  but  also  energy  arbitrage  and  electricity  sales  will  be 
relevant activities for future Energy communities. However, we recommend testing additional features when 
considering this novel tariff such as optimizing the contracted bandwidth, considering scalable penalizations 
fees, and setting a restriction on the number of times communities can update their contracted bandwidth.  

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Definitions  

ACER  

Agency for the Cooperation of Energy Regulators 

ASHP 

Air Sourced Heat Pumps 

BATS 

Batteries 

BDEW 

German Association of Energy and Water Industries 

BGW 

German Federation of the Gas and Water Industry 

BW 

Bandwidth 

CAPEX 

Capital Expenses 

CCGT 

Combined Cycle Gas Turbines 

CDD 

CHP 

COP 

DAI 

DE 

Cooling Degree Days 

Combined Heat and Power 

Coefficient of Performance 

Distributed Artificial Intelligence 

Germany 

DHW 

Domestic Heat Water 

DSR 

DSO 

EB 

EC 

ED 

Demand Side Response 

Distributor System Operator 

Energy based 

Energy Community 

Electrical Demand 

ENS 

Energy Not Served 

ELVIS 

Electric Vehicle Charging Infrastructure Simulator 

ERAA 

European Resources Adequacy Assessment 

ES 

Spain 

ESES 

Energy System Evolution Scenario 

EP 

EU 

EUA 

EUI 

EV 

Electrical Power 

European Union 

European Union Allowances 

Energy Use Intensity 

Electric Vehicle 

FCEL  

Fuel cell 

GAMS 

General Algebraic Modelling Language 

GAST 

Gas Turbines 

GHG 

Greenhouse Gas 

GR 

Greece 

GSHP 

Ground Sourced Heat Pumps 

HDD 

Heating Degree Days 

HDAM 

Hydro-reservoirs 

HP 

Heat Pump 

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HPHR 

Open-loop Hydro Pumped Storage 

HPHS 

Closed-loop Hydro Pumped Storage 

HRDT 

Hard coal-fuelled Generators 

HRE4 

Heat Roadmap Europe 

HRQR 

Hydro Run-of-River 

HV 

ICCT 

IEA 

High Voltage 

International Council on Clean Transportation 

International Energy Agency 

IREC  

Catalonia Institute for Energy Research 

IRENA 

International Renewable Energy Agency 

ISLP 

Industrial Standard Load Profiles 

ITC 

JRC 

kWe 

kWh 

kWt 

Information and Communication Technology 

Joint Research Centre 

Kilowatt Electrical 

Kilowatt-hour 

Kilowatt Thermal 

LCOE 

Levelized Cost of Electricity 

LIGT 

Lignite-fuelled generator 

LV 

MFB 

MILP 

Low Voltage 

Multi Family Buildings 

Mixed Integer Linear Programming problem 

MODECO  Modelling of Energy Communities 

MV 

MWe 

MWh 

MWt 

Medium Voltage 

Megawatt Electrical 

Megawatt-hour 

Megawatt Thermal 

NACE 

Nomenclature of Economic Activities 

NAICS 

North American Industrial Classification System 

NREL 

National Renewable Energy Laboratory 

NPV 

Net Present Value 

OCGT 

Open Cycle Gas Turbine 

OECD 

Economic Cooperation and Development 

OILT 

Oi-fuelled generators 

ORES 

Other Renewables 

OPEX 

Operational Expenses 

OTHT 

Other non-renewables 

PEM 

Proton Exchange Membrane 

PHOT 

Solar photovoltaics 

PPA 

Power Purchase Agreement 

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PV 

RAC 

R2M 

SC 

SFB 

SME 

SOC 

TD 

TOU 

TP 

Photovoltaic 

Regulamento do Autoconsumo 

Research to Market solution 

Space Cooling 

Single Family Building 

Small and Medium Enterprises 

State-of-Charge 

Thermal Demand 

Time-of-Use 

Thermal Power 

TYNDP 

Ten Year National Development Plan 

UCED 

Unit Commitment and Economic Dispatch 

VOM 

Variable Operational and Maintenance costs 

VOLL 

Value of Lost Load 

V2G 

Vehicle-to-Grid 

WACC  Weighted Average Cost of Capital 

WD 

WK 

Working days 

Weekend 

WSHP  Water Sourced Heat Pumps 

WTOF  Wind Offshore 

WTON  Wind Onshore 

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List of boxes  

Box 1.  Defining “close enough” optimal solutions under limited testing times .................................................................... 52 

Box 2 Drawing the line between economic benefits and purely financial profit generation ......................................... 55 

Box 3.  Key trends from the modelled energy prices under a power system evolution led by distributed energy
 .................................................................................................................................................................................................................................................... 88 

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List of figures  

Figure 1. Power production and services by energy citizens per member state expected in 2050 .............................9 

Figure 2. Installed power by technology in Germany in 2025, 2030 and 2030 for selected reference scenario
 .................................................................................................................................................................................................................................................... 13 

Figure 3. Installed power by technology in Spain in 2025, 2030 and 2030 for selected reference scenario .. 13 

Figure 4. Monthly mean, maximum and minimum air temperature values registered in each target region ... 14 

Figure 5. Mean air temperature per hour registered each season in the analysed regions .......................................... 15 

Figure 6. Mean solar load factor per hour registered each season in the analysed regions ........................................ 15 

Figure 7. Mean wind load factor per hour registered each season in the analysed regions ........................................ 15 

Figure 8. Community-energy market interaction considered for all archetypes except the Virtual community
 .................................................................................................................................................................................................................................................... 17 

Figure 9. Annual energy consumption in MWh/year per household (Single-family and Multi-Family buildings) 
and region disaggregated by end usage .......................................................................................................................................................... 34 

Figure 10. Distribution of companies per working day cluster in each economic sector ................................................ 36 

Figure 11. Hourly curves showing total energy demand (heat and electricity) for selected industrial standard 
load profiles from the JERICHO-E database [data adjusted to 1000 MWh/day] .................................................................... 38 

Figure 12. EV share in total passenger cars fleet per year ............................................................................................................... 41 

Figure 13. Economic assumptions considered for smart and non-smart EV charging stations ................................. 43 

Figure 14. Schematic diagram of the optimization models used within MODECO project ............................................ 49 

Figure 15. Feasible operational region for a CHP unit given four operational points ....................................................... 61 

Figure 16. Monthly heat demand per sector in the Business park archetype in 2025 .................................................... 64 

Figure 17. Mean heat consumption reported in 2025 in the Business park archetype in Germany and Spain 65 

Figure 18. Daily electricity demand per sector in the Business park archetype in Spain [2025] ............................... 65 

Figure 19. Daily electricity demand per sector in the Business park archetype in Germany [2025]....................... 66 

Figure 20. Mean electricity consumption reported in 2025 in the Business park archetype in Germany and 
Spain ........................................................................................................................................................................................................................................ 66 

Figure 21. Mean heat consumption reported in 2025 in the Industrial polygon archetype .......................................... 68 

Figure 23. Monthly heat demand by temperature level in the Industrial polygon in 2025 .......................................... 69 

Figure 24. Mean electricity consumption reported in 2025 in the Industrial polygon archetype (Others include 
EV and heat pump electrical consumption) .................................................................................................................................................... 70 

Figure 25. Monthly heat demand per sector in the Rural town archetype in 2025 ........................................................... 72 

Figure 26. Mean heat consumption reported in 2025 in the Rural town communities in Germany and Spain 72 

Figure 27. Daily electricity demand per sector in the Rural town archetype in Germany [2025] ............................. 73 

Figure 28. Daily electricity demand per sector in the Rural town archetype in Spain [2025] ..................................... 73 

Figure 29. Mean electricity consumption reported in 2025 in the Rural town communities in Germany and 
Spain ........................................................................................................................................................................................................................................ 74 

Figure 30. Monthly heat demand per sector in the Urban district archetype in 2025 ..................................................... 76 

Figure 31. Mean heat consumption reported in 2025 in the Urban district communities in Germany and Spain
 .................................................................................................................................................................................................................................................... 76 

Figure 32. Annual heat consumption and associated CO2 emissions for the Urban district archetype ............... 77 

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Figure 33. Daily electricity demand per sector in the Urban district archetype in Germany [2025] ....................... 77 

Figure 34. Daily electricity demand per sector in the Urban district archetype in Spain [2025] ............................... 78 

Figure 35. Mean electricity consumption reported in 2025 in the Urban district communities ................................. 78 

Figure 36. Annual electricity consumption and associated CO2 emissions for the Urban district archetype ..... 79 

Figure 37. Monthly heat demand per sector in the Virtual community archetype in 2025 .......................................... 81 

Figure 38. Mean heat consumption reported in 2025 in the virtual community archetype in Germany and 
Spain ........................................................................................................................................................................................................................................ 81 

Figure 39. Monthly electricity demand per sector in the Virtual community archetype in 2025 .............................. 82 

Figure 40. Mean electricity consumption reported in 2025 in the Virtual community archetype ............................. 82 

Figure 41. Annual demand versus energy dispatched per technology and year in Germany and Spain .............. 84 

Figure 42. Mean marginal price per season and year registered in Spain and Germany ............................................... 86 

Figure 43. Mean daily marginal price registered in Spain in 2025, 2030 and 2040. ....................................................... 87 

Figure 44. Mean daily marginal price registered in Germany in 2025, 2030 and 2040. ............................................... 87 

Figure 45. Mean marginal price per hour and year registered in Spain and Germany .................................................... 88 

Figure 46. TOU energy tariffs applicable to Energy communities in Germany ..................................................................... 89 

Figure 47. TOU energy tariffs applicable to Energy communities in Spain ............................................................................. 90 

Figure 48. Investments performed in the Business park archetype under different Use-of-Network structures
 .................................................................................................................................................................................................................................................... 92 

Figure 49. Electrical balance for the Business park communities under a Bandwidth tariff in two 
representative days in January and August 2040 [Maximum Ω] ..................................................................................................... 93 

Figure 50. Annual investments performed in the Business park archetype under the Bandwidth tariff case . 93 

Figure 51. Solar LCOE in Germany and Spain versus mean marginal price during high solar radiation hours 94 

Figure 52. Electrical balance for the Business park communities under a Peak power tariff in two 
representative days in February and August 2040 [Minimum Ω] .................................................................................................... 95 

Figure 53. Electrical balance for the Business park communities under a No Charges tariff in two 
representative days in February and August 2040 [Minimum Ω] .................................................................................................... 96 

Figure 54. Investments performed in the Industrial polygon under different Use-of-Network structures ......... 97 

Figure 55. Electrical balance for the Industrial polygon communities under a Bandwidth tariff in selected 
representative days in January and August 2040 [Maximum Ω] ..................................................................................................... 98 

Figure 56. Wind LCOE in Germany and Spain versus mean marginal price ............................................................................ 99 

Figure 57. Annual investments performed in the Industrial polygon archetype under the Bandwidth tariff 
case .......................................................................................................................................................................................................................................... 99 

Figure 58. Electrical balance for the Industrial polygon communities under a Peak power tariff in selected 
representative days in January and August 2040 [Maximum Ω] .................................................................................................. 100 

Figure 59. Investments performed in the Rural town under different Use-of-Network structures ...................... 101 

Figure 60. Electrical balance for the Rural town communities under a Peak power tariff in selected 
representative days in January and August 2040 [Maximum Ω] .................................................................................................. 102 

Figure 61. Electrical balance for the Rural town communities under a TOU tariff in selected representative 
days in January and August 2040 [Maximum Ω] .................................................................................................................................... 103 

Figure 62. Investments performed in the Urban district under different Use-of-Network structures ................ 104 

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Figure 63. Electrical balance for the Urban district communities under a Peak power tariff in selected 
representative days in January and August 2040 .................................................................................................................................. 105 

Figure 64. Electrical balance for the Urban district communities under a Bandwidth tariff in selected 
representative days in January and August 2040 .................................................................................................................................. 106 

Figure 65. Electrical balance for the Urban district communities under a TOU tariff in selected representative 
days in January and August 2040 [Maximum Ω] .................................................................................................................................... 107 

Figure 66. Investments performed in the Virtual community under different Use-of-Network structures ..... 108 

Figure 67. Electrical balance for the Virtual communities under a Bandwidth tariff in selected representative 
days in January and August 2040 [Maximum Ω] .................................................................................................................................... 109 

Figure 68. Electrical balance for the Virtual communities under a Peak power tariff in selected representative 
days in January and August 2040 [Maximum Ω] .................................................................................................................................... 110 

Figure 69. Electrical balance for the Virtual communities under a TOU tariff in selected representative days 
in January and August 2040 [Maximum Ω] ................................................................................................................................................ 111 

Figure 70. Annual investments performed in the Virtual community archetype under the TOU case ................ 111 

Figure 71. Investments performed in German archetypes under a TOU tariff with dynamic, flat and PPA 
prices .................................................................................................................................................................................................................................... 114 

Figure 72. Investments performed in German archetypes under the base tariff scenarios considering 
different discount rates............................................................................................................................................................................................ 115 

Figure 73. Annual demand, purchased electricity and local generation per type of technology in German 
cases .................................................................................................................................................................................................................................... 118 

Figure 74. Annual demand, purchased electricity and local generation per type of technology in Spanish 
cases .................................................................................................................................................................................................................................... 119 

Figure 75. Annual thermal demand and heat generation per type of technology in German cases. .................. 120 

Figure 76. Annual thermal demand and heat generation per type of technology in Spanish archetypes. ...... 121 

Figure 77. CO2 emissions from the operation of installed assets versus base case in the German archetypes
 ................................................................................................................................................................................................................................................. 123 

Figure 78. CO2 emissions from the operation of installed assets versus base case in the Spanish archetypes
 ................................................................................................................................................................................................................................................. 124 

Figure 79. Mean annual fuel cost and total fuel consumption in the Industrial polygon ............................................ 126 

Figure 80. CO2 emissions from the operation of installed assets versus base case in the German archetypes
 ................................................................................................................................................................................................................................................. 126 

Figure 81. Annual electrical balance, energy sales income and electrical cost avoided in German scenarios
 ................................................................................................................................................................................................................................................. 129 

Figure 82. Annual electrical balance, energy sales income and electrical cost avoided in Spanish scenarios
 ................................................................................................................................................................................................................................................. 130 

Figure 83. Avoided energy costs in the Spanish scenarios disaggregated by cost component............................... 131 

Figure 84. Avoided energy costs in the German scenarios disaggregated by cost component .............................. 132 

Figure 85. Disaggregated energy payments (price, taxes, Use-of-Network chargers) in German scenarios .. 135 

Figure 86. Disaggregated energy payments (price, taxes, Use-of-Network chargers) in Spanish scenarios .. 136 

Figure 87. CHP assumed configuration considered for small natural gas-fuelled units. ............................................ 201 

Figure 88. CHP assumed configuration for small biomass-fuelled units. ............................................................................. 201 

Figure 89. Simplified feasible operational region considered for units (operating points in green) .................... 202 

Figure 90. Reference hydrogen tank dimensions and occupied surface area .................................................................... 204 

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List of tables  

Table 1. Definition of Renewable and Citizen energy community in the European legislation .......................................8 

Table 2.  Minimum and maximum WACC values considered for each target region ......................................................... 16 

Table 3.  Summary of the rules applied to self-consumption under the Portuguese normative ............................... 18 

Table 4.  Number and type of building in each archetype for year 2025 ................................................................................. 19 

Table 5 Biomass prices considered for Germany and Spain in the target years [EUR/MWh] ........................................ 19 

Table 6 Green hydrogen prices for Germany and Spain in the target years [EUR/MWh] ................................................. 20 

Table 7 Technologies considered in each Energy community archetype as potential investment options ......... 21 

Table 8 Comparison of CAPEX and OPEX values proposed by MODECO against ESES’ assumptions for 
available technologies ................................................................................................................................................................................................. 22 

Table 9 Regional data used to calculate the applicable Unit Distribution Tariff per voltage level ........................... 24 

Table 10 Applicable capacity-based charges per country and voltage level. ......................................................................... 26 

Table 11 Applicable contracted bandwidth cost and penalization fees per country and voltage level. ................ 27 

Table 12 Per unit taxes applicable to energy carriers of interest according to OECD data. .......................................... 28 

Table 13 Type of customer represented in the electrical standard load profiles developed by BDEW ................. 30 

Table 14 Annual electricity demand from Single-family and Multi-family units without considering space 
cooling .................................................................................................................................................................................................................................... 31 

Table 15 Building types considered in the gas standard load profiles methodology ........................................................ 33 

Table 16 Sink and source temperature applicable to considered heat pump technologies .......................................... 39 

Table 17 CAPEX, OPEX and useful life considered for heat pumps and boilers used in residential users ........... 39 

Table 18 Installation and operation costs of equipment for heat pump’s participation in DSR programs .......... 40 

Table 19 Number of non-smart charging stations considered in each archetype by year and owner category.
 .................................................................................................................................................................................................................................................... 42 

Table 20 Assumptions considered for charging stations for domestic and business use .............................................. 42 

Table 21 Assumptions for standard EV models considered .............................................................................................................. 43 

Table 22 Number of EV circulating in the energy communities per year disaggregated by owner type .............. 44 

Table 23 GHG emission factors for natural gas combustion in the residential sector ..................................................... 46 

Table 24 Indicators associated with solar PV and Energy communities. .................................................................................. 50 

Table 25 Definition of the cost terms used in the investment model’s objective function ........................................... 53 

Table 26 CO2 emission factors associated to natural gas, hydrogen and biomass combustion................................ 62 

Table 27 Business park indicators ...................................................................................................................................................................... 63 

Table 28 CO2 emissions associated with energy usage in the Business park archetype ................................................ 64 

Table 29 Industrial polygon indicators ............................................................................................................................................................ 67 

Table 30 CO2 emissions associated with energy usage in the Industrial polygon archetype ....................................... 67 

Table 31 Rural town indicators ............................................................................................................................................................................. 70 

Table 32 CO2 emissions associated with energy usage in the Rural town archetype ....................................................... 71 

Table 33 Urban district indicators ...................................................................................................................................................................... 74 

Table 34 CO2 emissions associated with energy usage in the Urban district archetype ................................................. 75 

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Table 35 Virtual community indicators ........................................................................................................................................................... 79 

Table 36 CO2 emissions associated with energy usage in the Virtual community archetype ..................................... 80 

Table 37 Annual volume of CO2 emissions associated to power generation in Germany and Spain .................... 85 

Table 38 Mean annual marginal price registered in Germany and Spain for each target year .................................. 86 

Table 39 Hours classified as peak in each country, year and season ......................................................................................... 90 

Table 40 Value of the objective function obtained for each case in million euros [M€].................................................. 91 

Table 41 Use-of-Network charges applied in the Bandwidth scenarios by region and voltage level .................. 133 

Table 42 Use-of-Network charges (€/MWh) applicable in the TOU scenario by year, user and voltage level.134 

Table 44. Nomenclature for parameters in the Investment model ........................................................................................... 161 

Table 45. Variables for the Investment model ........................................................................................................................................ 163 

Table 46. Objective function for the Investment model.................................................................................................................... 165 

Table 48. Available roof and land equations for the Investment model ................................................................................ 169 

Table 49. Wind generation parameters for the Investment model ............................................................................................ 170 

Table 50. Wind generation equations for the Investment model ................................................................................................ 170 

Table 51. Solar generation parameters for the Investment model ........................................................................................... 171 

Table 52. Solar generation equations for the Investment model ............................................................................................... 171 

Table 53. Electrical Storage parameters for the Investment model ......................................................................................... 171 

Table 54. Electrical Storage equations for the Investment model ............................................................................................. 171 

Table 55. Hydrogen Storage parameters for the Investment model ........................................................................................ 172 

Table 56. Hydrogen Storage equations for the Investment model ............................................................................................ 173 

Table 57. Electrolyzer parameters for the Investment model....................................................................................................... 174 

Table 58. Electrolyzer equations for the Investment model .......................................................................................................... 174 

Table 59. CHP parameters for the Investment model ........................................................................................................................ 174 

Table 61. V2G parameters for the Investment model ....................................................................................................................... 176 

Table 63. Demand response parameters for the Investment model ........................................................................................ 178 

Table 64. Demand response equations for the Investment model ............................................................................................ 178 

Table 65. Boiler parameters for the Investment model .................................................................................................................... 178 

Table 66. Boiler equations for the Investment model ........................................................................................................................ 179 

Table 67. Sets for the Operational model .................................................................................................................................................. 180 

Table 68. Parameters for the Operational model ................................................................................................................................. 180 

Table 69. Variables for the operational Model ........................................................................................................................................ 185 

Table 72. Peak power constraints for the Operational model ....................................................................................................... 189 

Table 73. Time of Use constraints for the Operational model ...................................................................................................... 189 

Table 78. Demand response constraints for the Operational model ........................................................................................ 192 

Table 80. Hydrogen Storage constraints for the Operational model ........................................................................................ 194 

Table 81. Boilers constraints for the Operational model .................................................................................................................. 195 

Table 82. Scalar parameters for PV solar technologies .................................................................................................................... 196 

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Table 83. Scalar parameters for Wind turbine technologies .......................................................................................................... 197 

Table 84. Scalar parameters for EV smart chargers ........................................................................................................................... 198 

Table 85. Scalar parameters for biomass-fuelled CHP ..................................................................................................................... 199 

Table 87 Efficiency and fuel characteristics considered for each CHP configuration .................................................... 202 

Table 88 Scalar parameters for the PEM electrolyzer ........................................................................................................................ 203 

Table 89 Scalar parameters for the Hydrogen storage tank ......................................................................................................... 204 

Table 90 Scalar parameters for energy and power based batteries (0.35 C-rate) .......................................................... 205 

Table 91 Scalar parameters for boilers ....................................................................................................................................................... 206 

Table 92 Scalar parameters for demand response .............................................................................................................................. 207 

Table 93. Gap values reported by the EC investment model for the base case tariff scenarios............................ 208 

Table 94. Gap values reported by the EC investment model for the price rate sensitivity cases .......................... 208 

Table 95. Gap values reported by the EC investment model for the discount rate sensitivity cases .................. 209 

Table 96. Gap values reported by the EC operational model for the base case tariff scenarios ........................... 210 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

159 

 
 
 
Annexes 

Annex 1. Mathematical Formulation for MODECO’s Investment Model  

Nomenclature 

Table 43. Nomenclature for the Investment model 

Set 

Description 

Elements 

𝐹 

Set of all considered fuels. 

𝐾𝐺𝐸𝑁 

𝐾𝐻2 

𝐾𝐸𝐿 

𝐾𝐸𝐺𝐸𝑁 

𝐾𝐸𝑆 

𝐾 𝑆𝑇 

generator 

Different 
technologies 
considered. PV accounts for Photovoltaic 
Panels,  WT  for  Wind  Turbine,  CHP  for 
Combined  Heat  &  Power,  and  EL  for 
Electrolyser.  𝑆𝐶𝐻𝑃𝑓1,3
  consumes  fuel  of 
type  𝑓1  and  𝑓3, while  𝑆𝐶𝐻𝑃𝑓2
consume fuels type 𝑓2.  

only 

Set of hydrogen storages considered. 

Set of all Electrolysers considered. 

Different 
generator 
electrical 
technologies considered. PV accounts for 
Photovoltaic  Panels,  WT 
for  Wind 
Turbine,  CHP  for  Combined  Heat  & 
Power. 

Different  electrical  storage  technologies 
considered.  ES  accounts  for  Electrical 
Storage. 

of 

all 

Set 
technologies 
storage 
considered.  𝑆𝐻2accounts  for  hydrogen 
storage. 

𝐹 ={Natural  gas,  biomass,  hydrogen},  where 
𝑓1 = Natural Gas, 𝑓2 =Biomass, 𝑓3 =Hydrogen. 

𝐾𝐺𝐸𝑁
= {𝑆𝑃𝑉1, 𝑆𝑃𝑉2, 𝑆𝑊𝑇1, 𝑆𝑊𝑇2, 𝑆𝐶𝐻𝑃𝑓1,3

, 𝑆𝐶𝐻𝑃𝑓2

, 𝑆𝐸𝐿} 

𝐾𝐻2 = { 𝑆𝐻2} 

𝐾𝐸𝐿 = {𝑆𝐸𝐿} 

𝐾𝐸𝐺𝐸𝑁 = 𝐾𝐺𝐸𝑁\𝐾𝐸𝐿 

𝐾𝐸𝑆 = {𝑆𝐸𝑆1, 𝑆𝐸𝑆2} 

𝐾 𝑆𝑇 = 𝐾𝐸𝑆 ∪ 𝐾𝐻2 

𝐾𝑉2𝐺 

Set of V2G chargers considered. 

𝐾𝐵 

Set of Boilers considered. 

𝐾 

𝑇 

𝐷 

Set  of  all 
generators, 
chargers (V2G) and electrolyzer. 

technologies  considered: 
vehicle-to-grid 
storages, 

Set of time steps in a day. See that 𝑁𝑇 is 
used  as  the  number  of  time  steps 
considered. 

Set  of  representative  days.  See  that  𝑁𝐷 
is used  as  the  number  of  representative 
days considered. 

𝐾𝑉2𝐺 = {𝑣2𝑔}, *only  one  type  of  V2G  can  be 
considered in our modelisation. 

𝐾𝐵 = {𝑆𝐵1, 𝑆𝐵2}, *only a second type of boiler 
is considered in Industrial Polygon Archetype 

𝐾 = 𝐾𝐸𝐺𝐸𝑁 ∪ 𝐾 𝑆𝑡 ∪ 𝐾𝑉2𝐺 ∪ 𝐾𝐸𝐿 ∪ 𝐾𝐵 

𝑇 = {0,1,2, … , 𝑁𝑇 = 23} 

𝐷 = {0,1,2, … , 𝑁𝐷} 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

160 

 
 
Set 

𝑀 

𝑌 

𝑊 

𝑊𝑦 

Description 

Set of indexed months. 

Set  of  years  considered  in  investment 
planning.  See  that  𝑁𝑦  is  used  as  the 
number of years considered 

Elements 

𝑀 = {1,2, … ,12} 

𝑌 = {1,2, … , 𝑁𝑦 = 15} 

Set  of  all  coordinates  where  investment 
is allowed. 

𝑊 =   {(𝑦, 1,0,0), 𝑦 ∈ 𝑌} 

Coordinates where investment is allowed 
in year 𝑦. 

𝑊𝑦 = {(𝑦, 1,0,0)} 

Source: own elaboration. 

Table 44. Nomenclature for parameters in the Investment model 

Parameter 

Description 

Units 

Prices 

𝑏𝑢𝑦
𝜆𝑦,𝑚,𝑑,𝑡

𝑓𝑢𝑒𝑙,𝑓𝑖 
𝜆𝑦,𝑚,𝑑,𝑡

𝑒𝑣
𝜆𝑦,𝑚,𝑑,𝑡

𝑠𝑒𝑙𝑙
𝜆𝑦,𝑚,𝑑,𝑡

𝑝𝑒𝑎𝑘 
𝜆𝑦,𝑚

𝑓𝑖𝑥  
𝜆𝑦,𝑚

𝑒𝑥𝑐𝑒𝑒𝑑 
𝜆𝑦,𝑚

𝜆𝑑𝑟 

𝑖𝑛𝑣,𝐺𝐸𝑁 
𝐶𝑆𝑘,𝑦

𝑜𝑝,𝐺𝐸𝑁 
𝐶𝑆𝑘,𝑦

𝑖𝑛𝑣,𝐸𝑆 
𝐶𝑆𝑘,𝑦

𝑜𝑝,𝐸𝑆 
𝐶𝑆𝑘,𝑦

𝑖𝑛𝑣,𝐻2 
𝐶𝑆𝑘,𝑦

𝑜𝑝,𝐻2 
𝐶𝑆𝑘,𝑦

Purchase price of 𝑘𝑊ℎ. 

Purchase prices of fuel 𝑓𝑖𝜖𝐹. 

Price for the user of the V2G charge.  

Sell price of 𝑘𝑊ℎ. 

Peak power price in month m and year 𝑦. 

Fix power price in month m and year 𝑦. 

Price of exceeded power in month m and year 𝑦. 

Cost of the activation of demand response. 

Investment  cost  for  kWe  of  𝑠𝑘  installed  in  year  y,  for 
𝑠𝑘 ∈ 𝐾𝐺𝐸𝑁 ∪ 𝐾𝐵.  

Operational  cost  for  kWe  of  𝑠𝑘  installed  in  year  y,  for 
𝑠𝑘 ∈ 𝐾𝐺𝐸𝑁 ∪ 𝐾𝐵. 

Investment  cost  for  kWh  of  𝑠𝑘  installed  in  year  y,  for 
𝑠𝑘 ∈ 𝐾𝐸𝑆. 

Operational  cost  for  kWh  of  𝑠𝑘  installed  in  year  y,  for 
𝑠𝑘 ∈ 𝐾𝐸𝑆. 

Investment cost for 𝑚3 of 𝑠𝑘 installed in year y, for 𝑠𝑘 ∈
𝐾𝐻2. 

Operational cost for 𝑚3 of 𝑠𝑘 installed in year y, for 𝑠𝑘 ∈
𝐾𝐻2. 

161 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

€/𝑘𝑊ℎ 

€/𝑚𝑜𝑙𝑓𝑖 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊 

€/𝑘𝑊 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑚3 

€/𝑚3 

 
 
 
 
 
𝑖𝑛𝑣,𝐸𝐿 
𝐶𝑆𝑘,𝑦

𝑠𝑣,𝐸𝐿 

𝐶𝑆𝑘

𝑜𝑝,𝐸𝐿 
𝐶𝑆𝑘,𝑦

𝑖𝑛𝑣,𝑉2𝐺 

𝐶𝑦

𝐶𝑠𝑣,𝑣2𝑔 

𝑜𝑝,𝑣2𝑔 

𝐶𝑦

𝐶𝑔𝑒𝑛 

Loads 

𝑒𝑙
𝐿𝑦,𝑚,𝑑,𝑡

𝑡ℎ
𝐿𝑦,𝑚,𝑑,𝑡

𝑒𝑣
𝐿𝑦,𝑚,𝑑,𝑡

𝐻𝑃
𝐿𝑦,𝑚,𝑑,𝑡

𝑡ℎ,ℎ
𝐿𝑦,𝑚,𝑑,𝑡

EVs 

𝑖𝑛
𝐸𝑉𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡
𝐸𝑉𝑦,𝑚,𝑑,𝑡

Parameter 

Description 

Investment cost for kW of 𝑠𝑘 installed in year y, for 𝑠𝑘 ∈
𝐾𝐸𝐿.  

Salvage value for a kW of 𝑠𝑘 installed, for 𝑠𝑘 ∈ 𝐾𝐸𝐿. 

Operational cost for kW of 𝑠𝑘 installed in year y, for 𝑠𝑘 ∈
𝐾𝐺𝐸𝑁. 

Units 

€/𝑘𝑊 

€/𝑘𝑊 

€/𝑘𝑊 

Investment cost for V2G charger installed in year 𝑦. 

€/𝑐ℎ𝑎𝑟𝑔𝑒𝑟 

Salvage value for V2G charger installed. 

Operational cost for V2G charger installed in year. 

€/𝑐ℎ𝑎𝑟𝑔𝑒𝑟 

€/𝑐ℎ𝑎𝑟𝑔𝑒𝑟 

Cost for generated 𝑘𝑊ℎ, only in Virtual Community. 

€/𝑘𝑊ℎ 

Electrical load curve. 

Thermal load curve. 

Private household EV load curve. 

HP electrical load curve. 

High temperature thermal load curve (only for industrial 
archetype). 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

Number  of  EV  that  come  in  at  public  V2G  charging 
station. 

Positive integer vector 

Number  of  EV  that  leave  in  at  public  V2G  charging 
station. 

Positive integer vector 

Renewable Generation 

𝑊𝑇
𝐿𝐹𝑦,𝑚,𝑑,𝑡

  Wind  power 
installed. 

𝑃𝑉
𝐿𝐹𝑦,𝑚,𝑑,𝑡

Solar  power 
installed. 

load  factor.  kWe  generated  per  𝑘𝑊 

𝑘𝑊/𝑘𝑊installed 

load  factor.  kWe  generated  per  𝑘𝑊 

𝑘𝑊/𝑘𝑊installed 

Other 

Δ𝑡 

𝜔𝑦,𝑚,𝑑 

𝐺𝐸𝑁 
𝐴𝑠𝑘

Time interval between time steps, in hours. 

(0,1] 

Weight of representative day 𝑑 in month 𝑚 and year 𝑦. 

Positive integer 

Surface occupied by kWe of generator 𝑠𝑘 installed. 

𝑚2/𝑘𝑊 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

162 

 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

𝐸𝑆 
𝐴𝑠𝑘

𝐻2 
𝐴𝑠𝑘

Surface occupied by kWh of storage 𝑠𝑘 installed. 

Surface  occupied  by  𝑚3  of  hydrogen  storage  𝑠𝑘 
installed. 

Units 

𝑚2/𝑘𝑊ℎ 

𝑚2/𝑚3 

𝐴𝑉2𝐺 

Surface occupied by charger installed. 

𝑚2/𝑐ℎ𝑎𝑟𝑔𝑒𝑟 

𝑟𝑜𝑜𝑓  
𝐴𝑦,𝑚,𝑑,𝑡

𝑙𝑎𝑛𝑑  
𝐴𝑦,𝑚,𝑑,𝑡

Total  available 
technologies in roof. 

surface  available 

for 

installing 

Total  available 
technologies in land. 

surface  available 

for 

installing 

𝑚2 

𝑚2 

𝐿𝑆𝑠𝑘 

Life stamp of sub technology 𝑠𝑘. 

Positive integer value 

Source: own elaboration. 

Table 45. Variables for the Investment model 

Variables 

Description 

Domain 

Units 

𝑔𝑒𝑛,𝑒𝑙
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑔𝑒𝑛,𝑡ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑠𝑒𝑙𝑙
𝑝𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦
𝑝𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦
𝑓𝑖𝑦,𝑚,𝑑,𝑡

𝑐ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

Generated electrical power by technology 𝑠𝑘. 

Generated thermal power by 𝐶𝐻𝑃 type 𝑠𝑘. 

Power injected to the grid. 

Electrical power bought from the grid. 

Fuel 𝑓𝑖 bought externally. 

Charged power to electrical storage 𝑠𝑘𝜖𝐾𝐸𝑆. 

Discharged power from electrical storage 𝑠𝑘𝜖𝐾𝐸𝑆. 

𝑐ℎ
𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

Charged power to electrical storage 𝑠𝑘𝜖𝐾𝑉2𝐺. 

𝑑𝑐ℎ
𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

Discharged power from  𝑠𝑘𝜖𝐾𝑉2𝐺. 

𝐸𝑆
𝑠𝑜𝑐𝑠𝑘,𝑦,𝑚,𝑑,𝑡

Energy stored in storage 𝑠𝑘𝜖𝐾𝐸𝑆. 

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡

Energy stored in storage 𝑠𝑘𝜖𝐾𝑉2𝐺. 

𝑖𝑛𝑠𝑡,𝑎

𝑒𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

Installed  energy  capacity  for  technology  𝑠𝑘𝜖𝐾𝐸𝑆 
in area a={land, roof}. 

𝑖𝑛𝑠𝑡
𝑣𝑠𝐾, 𝑦̂ ,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡
𝑛𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑐𝑜𝑛𝑠,𝐸𝐿  
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

Installed volume for technology 𝑠𝐾 ∈ 𝐾𝐻2. 

Installed number of V2G chargers. 

Power consumed by electrolyser 𝑠𝑘 ∈ 𝐾𝐸𝐿. 

163 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑁 

𝑅+ 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑚𝑜𝑙/ℎ 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊ℎ 

𝑘𝑊ℎ 

𝑘𝑊ℎ 

𝑚3 

𝑖𝑛𝑡 

𝑘𝑊 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Description 

Domain 

Units 

Variables 

𝑔𝑒𝑛,𝐸𝐿

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

𝑓3𝑆𝐶𝐻𝑃𝑓1,3

,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

𝑓1𝑆𝐶𝐻𝑃𝑓1,3

,𝑦,𝑚,𝑑,𝑡

Hydrogen generated by electrolyzer 𝑠𝑘 ∈ 𝐾𝐸𝐿. 

  Hydrogen (fuel 𝑓3) consumed by CHP type 𝑆𝐶𝐻𝑃𝑓1,3

(only for industrial archetype). 

  Natural  gas  (fuel    𝑓1  )  consumed  by  CHP  type  

𝑆𝐶𝐻𝑃𝑓1,3

  (gas). 

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

𝑓2𝑆𝐶𝐻𝑃𝑓2

,𝑦,𝑚,𝑑,𝑡

𝐻2

𝑚𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐻2
𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑖𝑛
𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡
𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛
𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑐
𝑥𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐
𝑥𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑐
𝑢𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐
𝑢𝑦,𝑚,𝑑,𝑡

𝑠𝑢
𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑠𝑑
𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐶𝐻𝑃
𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡

  Biomass  𝑓2  consumed  by  CHP  type  𝑆𝐶𝐻𝑃𝑓2

(biomass). 

Quantity of hydrogen inside the hydrogen storage 
𝑠𝑘 ∈ 𝐾𝐻2. 

Hydrogen rate inflow to 𝑠𝑘 ∈ 𝐾𝐻2. 

Hydrogen rate outflow from 𝑠𝑘 ∈ 𝐾𝐻2. 

Binary indicator charge/discharge in 𝑠𝑘 ∈ 𝐾𝐻2. 

Number of captured number of EV’s that come in. 

Number of captured number of EV’s that go out. 

Number  of  captured  number  of  EV’s  that  are 
plugged in. 

Binary indicator for the increment of demand. 

Binary indicator for the decrement of demand. 

Increased power demand. 

Decreased power demand. 

Binary indicator for start-up ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃 . 

Binary indicator for shut-down ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃 . 

Binary indicator for CHP state ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃. 

𝑁 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑅+ 

𝑁 

𝑁 

𝑁 

𝑁 

𝑁 

𝑁 

𝑅+ 

𝑅+ 

𝑁 

𝑁 

𝑁 

𝑚𝑜𝑙𝐻2/ℎ 

𝑚𝑜𝑙𝐻2
ℎ

𝑚𝑜𝑙𝑔𝑎𝑠
ℎ

𝑚𝑜𝑙𝑏𝑖𝑜𝑚𝑎𝑠𝑠
ℎ

𝑚𝑜𝑙𝐻2 

𝑚𝑜𝑙𝐻2/ℎ 

𝑚𝑜𝑙𝐻2/ℎ 

[0,1] 

Positive integer 

Positive integer 

Positive integer 

[0,1] 

[0,1] 

𝑘𝑊 

𝑘𝑊 

[0,1] 

[0,1] 

[0,1] 

Source: own elaboration. 

Objective Function 

The  investment  model  can  be  configured  with  three  different  objective  functions  depending  on  the  tariff 
applied to the cost of electricity, Time of Use (TOU) – applicable to all cases with pure energy-based charges - 
Peak  Power  (PP),  or  Bandwidth  (BW)  scenarios.  And  so,  the  objective  function  defined  for  the  investment 
model is the Eq. 18 that was described in Section 4.2.2, which is repeated below. 

𝐹 = −𝐵𝑒𝑛 + (𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑡𝑎𝑟𝑖𝑓𝑓 + 𝐶𝑜𝑠𝑡𝑖𝑛𝑣 + 𝐶𝑜𝑠𝑡𝑜𝑝 + 𝐶𝑜𝑠𝑡𝑑𝑟 + 𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 + 𝐶𝑜𝑠𝑡𝐶𝐻𝑃 + 𝐶𝑜𝑠𝑡𝑔𝑒𝑛), 𝑡𝑎𝑟𝑖𝑓𝑓 ∈ {𝑇𝑂𝑈, 𝑃𝑃, 𝐵𝑊} 

164 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The different terms defining the objective functions are described below, 

Table 46. Objective function for the Investment model 

Term 

𝐵𝑒𝑛 

Equation 

The first term accounts for all the benefits obtained from selling energy to the electrical 
market; 

𝑁𝑦

𝐵𝑒𝑛 =   ∑ ( ∑

𝑦=1

𝑚∈𝑀,𝑑∈𝐷

𝜔𝑦,𝑚,𝑑 · ∆𝑡
(1 + 𝑅)𝑦−1

𝑠𝑒𝑙𝑙

· ∑(𝑝𝑦,𝑚,𝑑,𝑡
𝑡∈𝑇

· 𝜆𝑦,𝑚,𝑑,𝑡

𝑠𝑒𝑙𝑙,𝑒𝑙 + 𝜆𝑦,𝑚,𝑑,𝑡

𝑒𝑣

𝑖𝑛
· 𝑒𝑣𝑦,𝑚,𝑑,𝑡

)
)

𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 

This term adds together all the cost related to the buy of the different fuels considered, 

𝑁𝑦

𝐶𝑜𝑠𝑡𝑓𝑢𝑒𝑙 =   ∑ ( ∑
𝑦=1

𝑚∈𝑀,𝑑∈𝐷,𝑡∈𝑇

𝜔𝑦,𝑚,𝑑 · ∆𝑡
(1 + 𝑅)𝑦−1

· (∑ 𝑓𝑖𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦

𝑓𝑢𝑒𝑙,𝑓𝑖 
· 𝜆𝑦,𝑚,𝑑,𝑡

))

𝑓𝑖𝜖𝐹

𝐶𝑜𝑠𝑡𝑖𝑛𝑣 

The third term 𝐶𝑜𝑠𝑡𝑖𝑛𝑣  accounts for the investment costs from all years.  

𝐶𝑜𝑠𝑡𝑖𝑛𝑣 = 𝐶𝑜𝑠𝑡𝑖𝑛𝑣,𝐴   + 𝐶𝑜𝑠𝑡𝑖𝑛𝑣,𝐵 

For the technologies with life stamp equal or greater than the investment period, then the 
first sum is the investment cost multiplied by the capacity installed. 

𝑁𝑦

𝐶𝑜𝑠𝑡𝑖𝑛𝑣,𝐴 = ∑ ∑ (

𝑠𝑘𝜖 𝐾𝐸𝐺𝐸𝑁

𝑦=1

𝑖𝑛𝑣,𝐺𝐸𝑁 · (𝑁𝑦 − 𝑦 + 1)
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1 · 𝐿𝑆𝑠𝑘 

) · ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

)

𝑖𝑛𝑠𝑡

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑁𝑦

+   ∑ ∑ (

𝑠𝑘𝜖𝐾𝐸𝑆

𝑦=1
𝑁𝑦

+   ∑ ∑ (

𝑠𝑘∈𝐾𝐻2

𝑦=1

𝑖𝑛𝑣,𝐸𝑆 · (𝑁𝑦 − 𝑦 + 1)
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1 · 𝐿𝑆𝑠𝑘

) · ( ∑ 𝑒𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑣,𝐻2 · (𝑁𝑦 − 𝑦 + 1)
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1 · 𝐿𝑆𝑠𝑘

) · ( ∑ 𝑣𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

In the case of the technologies that have a life stamp lower than the investment period, 
then the computation is a little bit different. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

165 

 
 
 
 
 
 
 
 
Term 

Equation 

𝐿𝑆𝑣2𝑔

𝐶𝑜𝑠𝑡𝑖𝑛𝑣,𝐵 = ∑
𝑦=1

𝑖𝑛𝑣,𝑉2𝐺

𝐶 𝑦
(1 + 𝑅)𝑦−1 · ( ∑ 𝑛𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑁𝑦 − 𝑦 + 1
𝐿𝑆𝑣2𝑔

·

𝑖𝑛𝑣,𝑉2𝐺

𝐶𝑦
(1 + 𝑅)𝑦−1) · ( ∑ 𝑛𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑠𝑣,𝑉2𝐺

𝑖𝑛𝑣,𝑉2𝐺 · 𝐶𝑦
𝐶𝑦
(1 + 𝑅)𝑁𝑦−1

𝑖𝑛𝑣,𝑉2𝐺

𝐶𝑦
(1 + 𝑅)𝑦−1 ·
𝐿𝑆𝑠𝑘

𝑖𝑛𝑣,𝐸𝐿

𝐶𝑠𝑘,𝑦

· ( ∑ 𝑛𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑁𝑦 − 𝑦
𝐿𝑆𝑣2𝑔

) · ( ∑ 𝑛𝑦̂,𝑚̂ ,𝑑̂,𝑡̂
𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑠𝑡

)

(1 + 𝑅)𝑦−1 · ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

)

𝑖𝑛𝑠𝑡,𝐸𝐿

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑣,𝐸𝐿

𝐶𝑠𝑘,𝑦

𝑁𝑦 − 𝑦 + 1
𝐿𝑆𝑠𝑘

·  

(1 + 𝑅)𝑦−1) · ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

)

𝑖𝑛𝑠𝑡,𝐸𝐿

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑁𝑦

+ ∑ (

𝑦=𝐿𝑆𝑣2𝑔+1
𝐿𝑆𝑣2𝑔

−   ∑

𝑦=1
𝑁𝑌

+ ∑ (

𝑦=𝐿𝑆𝑣2𝑔

+ ∑ (∑

𝑠𝑘∈𝐾𝐸𝐿
𝑁𝑦

𝑦=1

+ ∑ (

+1

𝑦=𝐿𝑆𝑠𝑘
𝐿𝑆𝑠𝑘

−   ∑

𝑦=1
𝑁𝑌

𝑠𝑣,𝐸𝐿

𝑖𝑛𝑣,𝐸𝐿 · 𝐶𝑠𝑘,𝑦
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑁𝑦−1 · ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡,𝐸𝐿

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

+ ∑ (

𝑦=𝐿𝑆𝑠𝑘

𝑖𝑛𝑣,𝐸𝐿

𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1 ·

𝑁𝑦 − 𝑦 
𝐿𝑆𝑠𝑘

) · ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡,𝐸𝐿

)

)  

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝐶𝑜𝑠𝑡𝑜𝑝 

The fourth term 𝐶𝑜𝑠𝑡𝑜𝑝  accounts for the operational costs from all years. At each year, it 
is  considered  the  total  kWh  or  capacity  installed  for  each  technology  and  multiply  this 
term by the base 

𝑜𝑝 ; 
operational cost 𝐶𝑘,𝑦

𝑁𝑦

𝐶𝑜𝑠𝑡𝑜𝑝 = ∑ ∑
𝑦=1

𝑠𝑘𝜖𝐾𝐺𝐸𝑁

𝑜𝑝,𝐺𝐸𝑁

𝑖𝑛𝑣,𝐺𝐸𝑁 · 𝐶𝑠𝑘
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1

· ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑁𝑦

+ ∑ ∑
𝑠𝑘𝜖𝐾𝐸𝑆

𝑦=1
𝑁𝑦

+ ∑ ∑
𝑠𝑘𝜖𝐾𝐻2

𝑦=1
𝑁𝑦

+ ∑ ∑
𝑠𝑘𝜖𝐾𝐻2

𝑦=1
𝑁𝑦

+ ∑ ∑
𝑠𝑘∈𝐾𝐵

𝑦=1

𝑜𝑝,𝐸𝑆

𝑖𝑛𝑣,𝐸𝑆 · 𝐶𝑠𝑘
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1

𝑜𝑝,𝐻2

𝑖𝑛𝑣,𝐻2 · 𝐶𝑠𝑘
𝐶𝑠𝑘,𝑦
(1 + 𝑅)𝑦−1

· ( ∑ 𝑒𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

· ( ∑ 𝑣𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝐶𝑠𝑘,𝑦

𝑖𝑛𝑣,𝑉2𝐺 · 𝐶𝑜𝑝,𝑉2𝐺
(1 + 𝑅)𝑦−1

· ( ∑ 𝑛𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

)

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑜𝑝,𝐵,

𝑖𝑛𝑣,𝐵 · 𝐶𝑠𝑘
𝐶𝑠𝑘,𝑦 
(1 + 𝑅)𝑦−1 · ( ∑ 𝑃𝑠𝑘,𝑖𝑛𝑖 

𝐵

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑠𝑡,𝐵

+ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

)

𝐶𝑜𝑠𝑡𝑑𝑟 

Cost  depending  on  the  power  amount  increased  or  decreased  for  demand  respond 

166 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
  
 
 
Term 

services 

Equation 

𝑁𝑦

∑ ( ∑

𝑦=1

𝑚∈𝑀,𝑑∈𝐷,𝑡𝜖𝑇

𝜔𝑦,𝑚,𝑑

(1 + 𝑅)𝑦−1 · 𝜆𝑑𝑟 ·

𝑖𝑛𝑐
(𝑥𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐
+ 𝑥𝑦,𝑚,𝑑,𝑡

))

𝐶𝑜𝑠𝑡𝑔𝑒𝑛  

Cost  associated  to  the  generation  of  electrical  energy.  Only  applies  in  the  Virtual 
Community archetype. 

𝑁𝑦

𝐶𝑜𝑠𝑡𝑔𝑒𝑛 =   ∑ ∑

𝑦=1

𝑚∈𝑀,𝑑∈𝐷

𝜔𝑦,𝑚,𝑑 · ∆𝑡
(1 + 𝑅)𝑦−1

·

𝐶𝑔𝑒𝑛

· (∑

𝑡∈𝑇

∑
𝑠𝑘∈{𝑆𝑃𝑉1,𝑆𝑃𝑉2,𝑆𝑊𝑇1,𝑆𝑊𝑇2}

𝑔𝑒𝑛
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

+ ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ

𝑑𝑐ℎ
+ 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

) 

𝑠𝑘∈𝐾𝐸𝑆

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑇𝑂𝑈 

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝑃𝑃 

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑒𝑙,𝐵𝑊 

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑁𝑦
𝑒𝑙,𝑇𝑂𝑈 = ∑ ( ∑
𝑦=1

𝑚∈𝑀,𝑑∈𝐷

𝜔𝑦,𝑚,𝑑 · ∆𝑡
(1 + 𝑅)𝑦−1

𝑏𝑢𝑦

· ∑ 𝑝𝑦,𝑚,𝑑,𝑡
𝑡∈𝑇

𝑏𝑢𝑦,𝑒𝑙
· 𝜆𝑦,𝑚,𝑑,𝑡

)

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑁𝑦
𝑒𝑙,𝑃𝑃 = ∑ ( ∑
𝑦=1

𝑚∈𝑀,𝑑∈𝐷

𝜔𝑦,𝑚,𝑑 · ∆𝑡
(1 + 𝑅)𝑦−1

· (𝑝𝑦,𝑚

𝑝𝑒𝑎𝑘 · 𝜆𝑦,𝑚

𝑝𝑒𝑎𝑘) · ∑ 𝑝𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦

𝑏𝑢𝑦,𝑒𝑙
· 𝜆𝑦,𝑚,𝑑,𝑡

)

𝑡∈𝑇

𝐶𝑜𝑠𝑡𝑏𝑢𝑦

𝑁𝑦
𝑒𝑙,𝑃𝑃 = ∑ ( ∑
𝑦=1
𝑚∈𝑀

𝑓𝑖𝑥 · 𝑃BW · ∆𝑡
𝜆𝑦,𝑚
(1 + 𝑅)𝑦−1

· ∑ 𝜔𝑦,𝑚,𝑑 · ((𝑝𝑦,𝑚,𝑑,𝑡
𝑑∈𝐷,𝑡∈𝑇

𝑜𝑢𝑡,𝑖𝑛𝑓 + 𝑝𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡,𝑠𝑢𝑝) · 𝜆𝑦,𝑚

𝑒𝑥𝑐𝑒𝑒𝑑 +   𝑝𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦

𝑏𝑢𝑦,𝑒𝑙 )
· 𝜆𝑦,𝑚,𝑑,𝑡

) 

Source: own elaboration. 

The objective is to minimize F in the domain D given by all the constraints defined in this document. Consider 
the following: 

  𝝎𝒚,𝒎,𝒅 is the coefficient weighting the selected representative days. 
 

The objective function is considered from a Net Present Value point of view, and so, we are bringing 
to the  present all the  benefits and costs.  All monetary  quantities  𝒒𝒏 from year y are  multiplied for 
the term: 

𝟏

(𝟏+𝑹)𝒚−𝟏. 

 = 𝒑𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂

𝒊𝒏𝒔𝒕,𝒍𝒂𝒏𝒅 + 𝒑𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂

𝒊𝒏𝒔𝒕,𝒓𝒐𝒐𝒇  and 

 

In order to simplify the objective function, it is assumed that  𝒑𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂
𝒊𝒏𝒔𝒕
𝒆𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂

𝒊𝒏𝒔𝒕,𝒓𝒐𝒐𝒇  
𝒊𝒏𝒔𝒕,𝒍𝒂𝒏𝒅 + 𝒆𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂

=   𝒆𝒔𝒌,𝒚̂,𝒎̂ ,𝒅̂,𝒕̂

𝒊𝒏𝒔𝒕

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

167 

 
 
 
 
 
 
 
 
 
 
 
 
 
Balance equations 

 Table 47. Balance equations for the Investment model 

Term 

Eq. 29 

Electrical 
balance 

Equation 

The sum of loads is equal to the total generation ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑒𝑙
𝐿𝑦,𝑚,𝑑,𝑡

𝑒𝑣
+ 𝐿𝑦,𝑚,𝑑,𝑡

𝐻𝑃
+ 𝐿𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑐
+ 𝑢𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐸𝐿
+   ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

+ ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

𝑐ℎ
+   𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

𝑠𝑒𝑙𝑙
+ 𝑝𝑦,𝑚,𝑑,𝑡

  =  𝑝𝑦,𝑚,𝑑,𝑡

𝑠𝑘∈𝐾𝐸𝐿
𝑏𝑢𝑦 + 𝑢𝑦,𝑚,𝑑,𝑡

𝑠𝑘𝜖𝐾𝐸𝑆
𝑑𝑒𝑐 ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝐾𝑔𝑒𝑛

𝑔𝑒𝑛,𝑒𝑙

𝑑𝑐ℎ
+   𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

+ ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ

𝑠𝑘𝜖𝐾𝐸𝑆

30 

Eq. 
Thermal 
balance  

Thermal load is equal to the sum of thermal power generated by CHP and boiler type B1 
generation  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑀,  and  depending  on  the  archetype,  for  the 
corresponding 𝑓𝑖 ∈ 𝐹 

𝑡ℎ
𝐿𝑦,𝑚,𝑑,𝑡

=  

∑
𝑠𝑘∈{𝑆𝐶𝐻𝑃𝑓1,3

,𝑆𝐶𝐻𝑃𝑓2

}

𝑔𝑒𝑛,𝑡ℎ,𝐶𝐻𝑃
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑔𝑒𝑛,𝑡ℎ,𝐵
+ ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑠𝑘∈{𝑆𝐵1}

High  thermal  load  is  equal  to  thermal  power  generated  by  high  boiler  generation,  type  
𝐵2, ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑀, and depending on the archetype, for the corresponding 
𝑓𝑖 ∈ 𝐹 

ℎ𝑖𝑔ℎ,𝑡ℎ =   ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝐿𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈{𝑆𝐵2}

𝑔𝑒𝑛,𝑡ℎ,𝐵

Eq. 31  

High thermal 
balance 
(only 
Industrial 
Polygon) 

in 

Eq. 32 

Hydrogen 
balance 

The  sum  of  hydrogen  (fuel  𝑓3) generated  by  the  electrolyser,  the  hydrogen  discharged 
from  the  hydrogen  storages  and  the  hydrogen  bought,  is  equal  to  the  sum  of  the 
hydrogen  consumed  by  the  CHP, the  boilers  and  the  hydrogen  charged  to  the  hydrogen 
storage ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌;  

𝑓3𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦 + ∑ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝐾𝐸𝐿

𝑔𝑒𝑛,𝐸𝐿

+   ∑ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ

𝑠𝑘∈𝐾𝐻𝑆
=   ∑ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐵

+ ∑ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

+ ∑ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

Eq. 33 

Natural  gas 
balance 

Eq. 34 

Biomass 
balance 

𝑠𝑘∈ 𝐾𝐵

𝑠𝑘∈{𝑆𝐶𝐻𝑃𝑓1,3

}

𝑠𝑘∈𝐾𝐻2

The natural gas (fuel 𝑓1)  bought is equal to the gas consumed by boilers and CHP  ∀ 𝑡 ∈
𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌;  

𝑓1𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦 =   𝑓1𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐵1 + 𝑓1𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐵2 + ∑ 𝑓1𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝑆𝐶𝐻𝑃𝑓1,3

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

The  biomass  (fuel  𝑓2) bought  is  equal  to  the  biomass  consumed  𝐶𝐻𝑃𝑓2,  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈
𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌;  

𝑓2𝑦,𝑚,𝑑,𝑡

𝑏𝑢𝑦 =   ∑ 𝑓2𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈{𝑆𝐶𝐻𝑃𝑓2

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

}

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

168 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Eq. 35 

Avoid 
oversizing 

Eq. 36 

Avoid 
oversizing 

Eq. 37 

Avoid 
oversizing 

The total amount of power generation installed has to be lower or equal total amount of 
electrical demand ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

∑ (𝜔𝑦,𝑚,𝑑 · ( ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

𝑔𝑒𝑛,𝑒𝑙 + ∑ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝐾𝐸𝑆

𝑠𝑘∈𝐾𝐺𝐸𝑁

𝑑𝑐ℎ

))

≤ ∑ 𝜔𝑦,𝑚,𝑑 · (𝐿𝑦,𝑚,𝑑,𝑡

𝑒𝑙

𝐻𝑃
+ 𝐿𝑦,𝑚,𝑑,𝑡

𝑒𝑣
+ 𝐿𝑦,𝑚,𝑑,𝑡

)

𝑌,𝑀,𝐷,𝑇

The  total  capacity  of  electrical  storage  installed  has  to  be  lower  than  the  available 
maximum electrical generation at  ∀ (𝑦, 𝑚, 𝑑, 𝑡) ∈ 𝑊; 

∑ (𝑒𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓 + 𝑒𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓)

𝑠𝑘∈{𝑆𝐸𝑆1,𝑆𝐸𝑆2}

· 𝐶𝑠𝑘

𝑖𝑛𝑠𝑡,𝑠𝑘
𝑟𝑎𝑡𝑒,𝐸𝑆 ≤ ∑ 𝑝𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝐾𝐺𝐸𝑁

The total installed power of CHP has to be lower than the peak power of thermal demand 
per a security range: 

𝑦

𝑖𝑛𝑠𝑡
∑ 𝑝𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑖=1

∗  

1
𝐶𝐻𝑃 ≤ 𝐿 
𝜂𝑠𝑘

𝑡ℎ̅̅̅̅ 

Source: own elaboration. 

Available roof and land 

Table 48. Available roof and land equations for the Investment model 

Term 

Eq. 38 

Roof area 

The investment in roof area is limited by 𝐴𝑟𝑜𝑜𝑓; 

Equation 

∑ ∑  𝑒𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓 · 𝐴𝑠𝑘

𝑠𝑘∈{𝑆𝐸𝑆1,𝑆𝐸𝑆2}

+ ∑ ∑  𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

𝑠𝑘∈{𝑆𝑃𝑉2}

𝑖𝑛𝑠𝑡

· 𝐴𝑠𝑘

≤   𝐴𝑟𝑜𝑜𝑓 

Eq. 
Land area 

39   

The investment in roof area is limited by 𝐴𝑙𝑎𝑛𝑑; 

𝑖𝑛𝑠𝑡
∑  𝑛𝑣2𝑔,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

· 𝐴𝑣2𝑔

+ ∑ ∑  𝑣𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

𝑠𝑘∈𝐾𝐻2

𝑖𝑛𝑠𝑡

· 𝐴𝑠𝑘

+ ∑ ∑  𝑒𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑠𝑡,𝑙𝑎𝑛𝑑 · 𝐴𝑠𝑘

𝑠𝑘∈{𝑆𝐸𝑆1,𝑆𝐸𝑆2}

𝑌,𝑀,𝐷,𝑇

+ ∑

𝑠𝑘∈𝐾𝐺𝐸𝑁\ {𝑆𝑃𝑉2}

𝑖𝑛𝑠𝑡
∑  𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑌,𝑀,𝐷,𝑇

· 𝐴𝑠𝑘

≤   𝐴𝑙𝑎𝑛𝑑 

Eq. 40 

  First 
per year 

day 

Eq. 41 

  Peak 
power 

The  installation  of  technologies  is  allowed  only  the  first  day  of  each  year,  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈
𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑀, ∀𝑠𝑘 ∈ 𝐾, and ∀ 𝑎 ∈ {𝑙𝑎𝑛𝑑, 𝑟𝑜𝑜𝑓}; 

𝑖𝑛𝑠𝑡,𝑎
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≥ 0, if (y, m, d, t) ∈ 𝑊, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑠𝑡,𝑎

= 0. 

Purchasing power has to be lower than its monthly peak power, ∀ 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑝𝑒𝑎𝑘 ≥ 𝑝𝑦,𝑚,𝑑,𝑡
𝑝𝑦,𝑚

𝑏𝑢𝑦

169 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
constraints 

 Eq. 42  

 Bandwidth 
constraints 

Purchasing  power  and  selling  power  have  to  be  bounded  by  the  bandwidth  power.  The 
power required outside the band is accounted for monthly in the corresponding variables. 
∀ 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑏𝑢𝑦 − 𝑝𝑦,𝑚
𝑝𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡,𝑖𝑛𝑓 ≤ 𝑃BW  

𝑠𝑒𝑙𝑙 − 𝑝𝑦,𝑚
𝑝𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡,𝑠𝑢𝑝 ≤ 𝑃BW 

Eq. 43 

Purchasing power and selling power cannot be happening at the same time. 

  Bounds  for 
bought 
power 

𝑏𝑢𝑦 ≤ 𝑀 · (1 − 𝑥𝑒𝑙) 
𝑝𝑦,𝑚,𝑑,𝑡

Eq. 44 

Purchasing power and selling power cannot be happening at the same time. 

  Bounds  for 
sold power  

Source: own elaboration. 

Wind generation 

𝑠𝑒𝑙𝑙 ≤ 𝑥𝑒𝑙 · 𝑀 

𝑝𝑦,𝑚,𝑑,𝑡

Table 49. Wind generation parameters for the Investment model 

Parameter 

Description 

Units/Domain 

𝐾𝑊𝑇 

𝑊𝑇  
𝑃𝑠𝑘,𝑖𝑛𝑖

𝑊𝑇  
𝜂𝑠𝑘,𝑦

Set of wind turbine types. 

𝐾𝑊𝑇 = {𝑆𝑊𝑇1, 𝑆𝑊𝑇2} 

Initial power of 𝑠𝑘 installed, ∀𝑠𝑘 ∈ 𝐾𝑊𝑇. 

Efficiency of 𝑠𝑤𝑡 in year y. 

𝑘𝑊 + 

[0,1] 

Source: own elaboration. 

Term 

Eq. 45 

  Wind 
generation 

Equation 

Wind  generation  depending  on  the  power  installed  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and 
 ∀𝑠𝑘 ∈ {𝑆𝑊𝑇1, 𝑆𝑊𝑇2}; 

𝑁𝑦

𝑔𝑒𝑛,𝑒𝑙 =   𝜂𝑠𝑘,𝑦
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑊𝑇 · 𝐿𝐹𝑦,𝑚,𝑑,𝑡

𝑊𝑇

· (𝑃𝑠𝑘,𝑖𝑛𝑖

𝑊𝑇 + ∑ ( ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂
𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑦=1

𝑖𝑛𝑠𝑡

)

) 

Table 50. Wind generation equations for the Investment model 

Source: own elaboration. 

Solar Generation 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

170 

 
 
 
 
 
 
Table 51. Solar generation parameters for the Investment model 

Parameter 

Description 

Units/Domain 

𝐾𝑃𝑉 

Set of PV panel types. The first type of PV is installed in 
land, whereas the second one is installed in roof. 

𝐾𝑃𝑉 =   {𝑆𝑃𝑉1, 𝑆𝑃𝑉2} 

𝑃𝑠𝑘,𝑖𝑛𝑖 

Initial power of 𝑠𝑝𝑣 . 

𝑃𝑉  
𝜂𝑠𝑘,𝑦

Efficiency of 𝑠𝑘 in year y. 

Source: own elaboration. 

𝑘𝑊 + 

[0,1] 

Table 52. Solar generation equations for the Investment model 

Term 

Eq. 46  

  Solar 
generation 

Total solar power generated ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌, for 𝑠𝑘 ∈ {𝑆𝑃𝑉1, 𝑆𝑃𝑉2}; 

Equation 

𝑔𝑒𝑛,𝑒𝑙 =   𝜂𝑠𝑘,𝑦
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑃𝑉 · 𝐿𝐹𝑦,𝑚,𝑑,𝑡

𝑃𝑉

𝑁𝑦

· (𝑃𝑠𝑘,𝑖𝑛𝑖 + ∑ ∑ 𝑝𝑠𝑘,𝑦̂,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡

) 

𝑦=1

𝑦̂,𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

Source: own elaboration. 

Electrical Storage 

Table 53. Electrical Storage parameters for the Investment model 

Parameter 

Description 

𝐾𝐸𝑆 

Set of storage types.  

Units/Domain 

𝐾𝐸𝑆 = {𝑆𝐸𝑆1, 𝑆𝐸𝑆2} 

𝑑𝑐ℎ,𝐸𝑆 
𝜂𝑠𝑘,𝑦

𝑐ℎ,𝐸𝑆 
𝜂𝑠𝑘,𝑦

𝑆𝑂𝐶𝑠𝑘

𝑚𝑎𝑥 

𝑆𝑂𝐶𝑠𝑘

𝑚𝑖𝑛 

𝑆𝑂𝐶𝑠𝑘

𝑖𝑛𝑖 

Discharging Efficiency of 𝑠𝑘 in year y. 

Charging Efficiency of 𝑠𝑘 in year y. 

Max. SOC allowed. 

Min. SOC allowed. 

Initial daily SOC. 

𝑆𝑂𝐶𝑠𝑘

𝑓𝑖𝑛𝑎𝑙  Min. final daily SOC. 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

𝑟𝑎𝑡𝑒,𝐸𝑆 

𝐶𝑠𝑘

Power rate as compared to the capacity of the battery. 

𝑅+, ℎ−1 

Source: own elaboration. 

Table 54. Electrical Storage equations for the Investment model 

 Term 

Equation 

Eq. 47 

Energy balance into the storage ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌; 𝑎𝑛𝑑 ∀𝑠𝑘 ∈ 𝐾𝐸𝑆; 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

171 

 
 
 
 
           
Energy 
balance 

𝐸𝑆
𝑠𝑜𝑐𝑠𝑘,𝑦,𝑚,𝑑,𝑡

=

𝑦

𝑆𝑂𝐶𝑠𝑘

𝑖𝑛𝑖 · ∑ ∑ (𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑖

𝑖=1

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓)
𝑖𝑛𝑠𝑡,𝑙𝑎𝑛𝑑 + 𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

+ 𝜂𝑠𝑘,𝑦

𝑐ℎ,𝐸𝑆 · ∆𝑡 · 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

𝐸𝑆

𝑠𝑜𝑐𝑠𝑘,𝑦,𝑚,𝑑,𝑡−1

+ 𝜂𝑠𝑘,𝑦

𝑐ℎ,𝐸𝑆 · ∆𝑡 · 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

−

𝑑𝑐ℎ
∆𝑡 · 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑑,𝐸𝑆
𝜂𝑠𝑘,𝑦

=  

{

     𝑖𝑓 𝑡 = 1 

−

𝑑𝑐ℎ
∆𝑡 · 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑑,𝐸𝑆
𝜂𝑠𝑘,𝑦

            ∀𝑡 > 1

Eq. 48 

 Only 
charge/disch
arge  mode 
allowed 

Eq. 49   

of 

 Bound 
power 
through  C-
rate relation 

Eq. 50  

 SOC bounds 

Eq. 51  

 Final  daily 
SOC bound 

The  technology  𝑠𝑘 ∈ 𝐾𝐸𝑆   can  only  be  in  charge  mode,  or  discharge  mode  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈
𝐷, 𝑚 ∈ 𝑀 and 𝑦 ∈ 𝑌; 

𝑐ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐸𝑆
≤ 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

· 𝑀 

𝑑𝑐ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤ (1 − 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐸𝑆

) · 𝑀 

Power Upper bound ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 and  𝑦 ∈ 𝑌, and  𝑠𝑘 ∈ 𝐾𝐸𝑆; 
𝑦

𝑐ℎ
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑𝑐ℎ
+ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤ ∑ ∑ (𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓)
𝑖𝑛𝑠𝑡,𝑙𝑎𝑛𝑑 + 𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

𝑖=1

𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑖

𝑟𝑎𝑡𝑒,𝐸𝑆 

· 𝐶𝑠𝑘

Maximum and minimum energy amount of energy allowed into the storage  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈
𝐷, 𝑚 ∈ 𝑀 , 𝑦 ∈ 𝑌; 𝑎𝑛𝑑 𝑠𝑘 ∈ 𝐾𝐸𝑆; 

𝑦

𝑆𝑂𝐶𝑠𝑘

𝑚𝑖𝑛 · 𝑒𝑠𝑘,𝑦

𝑖𝑛𝑠𝑡,𝑡𝑜𝑡 ≤ 𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡

𝑠𝑘

≤ 𝑆𝑂𝐶𝑠𝑘

𝑚𝑎𝑥 · ∑ ∑ (𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑖

𝑖=1

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓)
𝑖𝑛𝑠𝑡,𝑙𝑎𝑛𝑑 + 𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

Minimum final state of charge of the storage at the end of each day  𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈
𝑌; 𝑎𝑛𝑑 𝑠𝑘 ∈ 𝐾𝐸𝑆; 

𝑦

𝑠𝑘
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡𝑓

≥ 𝑆𝑂𝐶𝑠𝑘

𝑓𝑖𝑛𝑎𝑙 · ∑ ∑ (𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑖

𝑖=1

𝑖𝑛𝑠𝑡,𝑟𝑜𝑜𝑓)
𝑖𝑛𝑠𝑡,𝑙𝑎𝑛𝑑 + 𝑒𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

Source: Modification of the model from Igualada González et al. (2013)  

Hydrogen Storage 

Table 55. Hydrogen Storage parameters for the Investment model 

Parameter 

Description 

𝐾𝐻2 

Set of types of Hydrogen Storages considered. 

𝑅 

Gas constant.   

Mean temperature inside the tank 𝑠𝑘. 

Discharging Efficiency of ℎ𝑠 in year 𝑦. 

Charging Efficiency of 𝑠𝑘 in year 𝑦. 

𝑚𝑒𝑎𝑛 

𝑇𝑠𝑘

𝑑𝑐ℎ  
𝜂𝑠𝑘,𝑦

𝑐ℎ  
𝜂𝑠𝑘,𝑦

𝐻2 
𝐶𝑅𝑠𝑘

Units/Domain 

𝐾𝐻2 = {𝑆𝐻2} 

8.31446 

𝑚3 · 𝑃𝑎
𝐾 · 𝑚𝑜𝑙

𝐾 

[0,1] 

[0,1] 

Maximum mols per hour that can get out/in the tank per 
𝑚3 of tank. 

𝑚𝑜𝑙/(𝑚3 · ℎ) 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

172 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

Units/Domain 

𝑚𝑎𝑥 

𝑄𝑠𝑘

𝑚𝑖𝑛 

𝑄𝑠𝑘

𝑖𝑛𝑖 
𝑄𝑠𝑘

𝑓𝑖𝑛𝑎𝑙 

𝑄𝑠𝑘

Maximum pressure allowed. 

Minimum pressure allowed. 

𝑃𝑎 

𝑃𝑎 

Initial daily quantity of hydrogen per 𝑚3. 

                        𝑚𝑜𝑙𝐻2 /𝑚3   

Final daily pressure. 

𝑃𝑎 

Source: own elaboration. 

Table 56. Hydrogen Storage equations for the Investment model 

Term 

Eq. 52 

Hydrogen 
balance 

Eq. 53 

Bi-directionality 
relation 

Eq. 54 

Charge/ 
discharge bounds  

Mol of 𝐻2 equation in the storage ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 and 𝑦 ∈ 𝑀, and ∀𝑠𝑘 ∈ 𝐾𝐻2; 

Equation 

𝐻2

𝑚𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑖𝑛𝑖
  𝑄𝑠𝑘
𝑚𝑒𝑎𝑛 · ∑ ∑ 𝑣𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑅 · 𝑇𝑠𝑘
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑠𝑡

𝑖=1

𝑦

=  

+ 𝜂𝑠𝑘,𝑦

𝑐ℎ · ∆𝑡 · 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

−

𝑑

∆𝑡 · 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑑
𝜂𝑠𝑘,𝑦

 , 𝑡 = 1

{

𝐻2

𝑚𝑠𝑘,𝑦,𝑚,𝑑,𝑡−1

+ 𝜂𝑠𝑘,𝑦

𝑐ℎ · ∆𝑡 · 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐ℎ

−

𝑑
∆𝑡 · 𝑓3𝑦,𝑚,𝑑,𝑡
𝑑
𝜂𝑠𝑘,𝑦

 , 𝑡 > 1

The  hydrogen  tank  cannot  charge  and  discharge  hydrogen  at  the  same  time  step 
∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and ∀𝑠𝑘 ∈ 𝐾𝐻2; 

𝑐ℎ

0 ≤ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐻2
≤   𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

· 𝑀 

𝑑

0 ≤ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤ (1 − 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐻2

) · 𝑀 

The hydrogen charge and discharge is bound by the volume installed and the C-rate 
considered ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and ∀𝑠𝑘 ∈ 𝐾𝐻2; 

𝑦

𝑐ℎ

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑑

+ 𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤  ∑ ∑ 𝑣𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝑖𝑛𝑠𝑡

𝐻2 
  · 𝐶𝑅𝑠𝑘

Eq. 55  

SOC bounds 

Limits for the pressure inside the tank step ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and ∀𝑠𝑘 ∈
𝐾𝐻2; 

𝑦

𝑦

𝑚𝑖𝑛 · ∑ ∑ 𝑣𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑄𝑠𝑘
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝑖𝑛𝑠𝑡

  ≤ 𝑅 · 𝑇𝑠𝑘

𝐻2
𝑚𝑒𝑎𝑛 · 𝑚𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤ 𝑄𝑠𝑘

𝑚𝑎𝑥 · ∑ ∑ 𝑣𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝑖𝑛𝑠𝑡

Eq. 56  

Final 
pressure bound 

daily 

Minimum quantity  of  hydrogen  stored  at  the  end of  each  day  𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌, 
and ∀𝑠𝑘 ∈ 𝐾𝐻2; 

𝑦

𝑅 · 𝑇𝑠𝑘

𝐻2
𝑚𝑒𝑎𝑛 · 𝑚𝑠𝑘,𝑦,𝑚,𝑑,𝑡𝑓

≥ 𝑄𝑠𝑘

𝑓𝑖𝑛𝑎𝑙 · ∑ ∑ 𝑣𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖𝑛𝑠𝑡

𝑖=1

Source: own elaboration. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

173 

 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
  
Electrolyzer 

Table 57. Electrolyzer parameters for the Investment model 

Parameter 

Description 

𝐾𝐸𝐿 

Set of electrolysers considered. 

𝐿𝐻𝑉𝐻2 

Lower heating value of hydrogen at 1º C.  

𝐸𝐿 
𝜂𝑠𝑘

Electrolyser 𝑠𝑘 efficiency. 

Source: own elaboration. 

Table 58. Electrolyzer equations for the Investment model 

Units/Domain 

𝐾𝐸𝐿 = {𝑆𝐸𝐿} 

6.9222 · 10−5 𝑘𝑊ℎ
𝑚𝑜𝑙

[0,1] 

Term 

1. 
Eq. 57 

Power 
consumed 
bounds 

Equation 

The  power  consumed  by  electrolyser  depends  on  the  total  power  installed  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈
𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌, and ∀𝑠𝑘 ∈ 𝐾𝐸𝐿; 

𝑦

0 ≤ 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐸𝐿 ≤ ∑ ∑ 𝑝𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂

𝑖𝑛𝑠𝑡,𝐸𝐿

𝑖=1

𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

2. 
58 

Eq. 

Relation between power consumed and hydrogen generated   ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈
𝑌, and , ∀𝑠𝑘 ∈ 𝐾𝐸𝐿; 

Hydrogen 
generation 

𝑔𝑒𝑛,𝐸𝐿 =  

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐸𝐿

𝐸𝐿 ·   𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝜂𝑠𝑘
𝐿𝐻𝑉𝐻2

Source:  (Nojavan et al., 2017) 

Combined Heat and Power 

Table 59. CHP parameters for the Investment model 

Parameter 

Description 

Units/Domain 

𝐾𝐶𝐻𝑃 

Set of types of CHP depending on fuel type. 

, 𝑆𝐶𝐻𝑃𝑓2

𝐾𝐶𝐻𝑃 = {𝑆𝐶𝐻𝑃𝑓1,3
}. The 
first  type  can  consume  gas 
the 
and  hydrogen  while 
second 
consumes 
biomass. 

type 

𝐶𝐻𝑃 
𝜂𝑠𝑘

𝑓2

𝜂𝑆𝐶𝐻𝑃𝑓2

𝑓1

𝜂𝑆𝐶𝐻𝑃𝑓1,3

Heat and electricity power ratio of 𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃. 

Conversion factor from fuel 𝑓2 (biomass) to electricity by 
𝑆𝐶𝐻𝑃𝑓2

. 

Conversion factor from fuel 𝑓1 (natural gas) to electricity 
by 𝑆𝐶𝐻𝑃𝑓1,3

. 

[0,1] 

[0,1] 

[0,1] 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

174 

 
 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

Units/Domain 

𝑓3

𝜂𝑆𝐶𝐻𝑃𝑓1,3

Conversion  factor  from  fuel  𝑓3  (hydrogen)  to  electricity 
by 𝑆𝐶𝐻𝑃𝑓1,3

. 

𝑖𝑛𝑖 

𝑈𝑠𝑘

𝑠𝑢 
𝑇𝑠𝑘

𝑠𝑑 
𝑇𝑠𝑘

Initial daily state of 𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃.  

Minimum uptime of 𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃. 

Minimum shutdown time of 𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃. 

[0,1] 

{0,1} 

ℎ𝑜𝑢𝑟𝑠 

ℎ𝑜𝑢𝑟𝑠 

𝑆𝑈𝑠𝑘

𝑚𝑎𝑥 

Maximum  number  of  times  that  a  𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃   can  be 
opened. 

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 

Source: own elaboration. 

Table 60. CHP equations for the Investment model 

Term 

Eq. 59 

Power 
consumed 
bound 

Eq. 60 

Power 
consumed 
bound 

Eq. 61 

Power 
consumed 
bound 

Eq. 62 

Heat 
generation 

Eq. 63 

Initial state 

Equation 

Lower bound for power installed in ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌, ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃; 

𝑦

𝑔𝑒𝑛,𝑒𝑙

0 ≤   𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

  ≤ ∑ ∑ 𝑝𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝑖𝑛𝑠𝑡

Bound  of  power  generated  by  state  of  CHP,  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌, ∀𝑠𝑘 ∈
𝐾𝐶𝐻𝑃; 

𝑔𝑒𝑛,𝑒𝑙

0 ≤   𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐶𝐻𝑃
  ≤ 𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡

· 𝑀 

Generated power equals the fuel consumed by the conversion factor to electrical power, 
∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌. For the natural gas CHP, 

𝑔𝑒𝑛,𝑒𝑙

𝑝𝑆𝐶𝐻𝑃𝑓1,3
For the biomass CHP, 

,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

  =   𝑓1𝑆𝐶𝐻𝑃𝑓1,3

,𝑦,𝑚,𝑑,𝑡

𝑓1

· 𝜂𝑆𝐶𝐻𝑃𝑓1,3

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

+ 𝑓3𝑆𝐶𝐻𝑃𝑓1,3

,𝑦,𝑚,𝑑,𝑡

𝑓3

· 𝜂𝑆𝐶𝐻𝑃𝑓1,3

𝑔𝑒𝑛,𝑒𝑙

𝑝𝑆𝐶𝐻𝑃𝑓2

,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛𝑠,𝐶𝐻𝑃

  =   𝑓2𝑆𝐶𝐻𝑃𝑓2

,𝑦,𝑚,𝑑,𝑡

𝑓2

· 𝜂𝑆𝐶𝐻𝑃𝑓2

Relation  between  thermal  power  and  electrical  power  ∀ 𝒕 ∈ 𝑻, 𝒅 ∈ 𝑫, 𝒎 ∈ 𝑴 𝒂𝒏𝒅 𝒚 ∈
𝒀, ∀𝒔𝒌 ∈ 𝑲𝑪𝑯𝑷; 

𝑔𝑒𝑛,𝑡ℎ,𝐶𝐻𝑃 =  
𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡

1
𝐶𝐻𝑃 · 𝑝𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝜂𝑠𝑘

𝑔𝑒𝑛,𝑒𝑙

Initial daily state operation ∀ 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌, and  ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃; 

𝐶𝐻𝑃
𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡0

= 𝑈𝑠𝑘

𝑖𝑛𝑖,𝐶𝐻𝑃 

175 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
A constraint to know if CHP changes the state on to off or off to on ∀𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈
𝑀, 𝑦 ∈ 𝑌, and  ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃; 

𝐶𝐻𝑃
𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐶𝐻𝑃
− 𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡−1

𝑠𝑢
= 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝑠𝑑
− 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

A minimum uptime for the CHP plant ∀𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌, and  ∀𝑠𝑘 ∈ 𝐾𝐶𝐻𝑃; 

𝑡
∑

𝑖=𝑡−𝑇𝑠𝑘

𝑠𝑢+1

𝑠𝑢
𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤

𝐶𝐻𝑃
𝑢𝑠𝑘,𝑦,𝑚,𝑑,𝑡

A  minimum  shutdown  time  for  the  CHP  plant  ∀𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and   ∀𝑠𝑘 ∈
𝐾𝐶𝐻𝑃; 

𝑡
∑

𝑖=𝑡−𝑇𝑠𝑘

𝑠𝑑+1

𝑠𝑑
𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡

≤

𝐶𝐻𝑃
𝑢𝑦,𝑚,𝑑,𝑡

A  minimum  shutdown  time  for  the  CHP  plant  ∀𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌,  and   ∀𝑠𝑘 ∈
𝐾𝐶𝐻𝑃; 

𝑠𝑢
∑ 𝑥𝑠𝑘,𝑦,𝑚,𝑑,𝑡
𝑡∈𝑇

≤ 𝑆𝑈𝑠𝑘

𝑚𝑎𝑥  

Eq. 64 

Change 
state 

of 

Eq. 65 

Time limit 

Eq. 66 

Time 
limit 
switch down 

Eq. 67 

Maximum 
of 
number 
times 
that 
CHP  can  be 
opened  per 
day 

Source: own elaboration. 

Vehicle-to-Grid 

Table 61. V2G parameters for the Investment model 

Parameter 

Description 

Units/Domain 

𝑑
𝜂𝑣2𝑔𝑠,𝑦

𝑐ℎ
𝜂𝑣2𝑔,𝑦

𝑆𝑂𝐶𝑒𝑣

𝑚𝑖𝑛 

𝑆𝑂𝐶𝑒𝑣

𝑚𝑎𝑥 

𝑖𝑛𝑖 
𝑆𝑂𝐶𝑒𝑣 

𝑆𝑂𝐶𝑒𝑣

𝑒𝑛𝑑 

𝑏
𝐸𝑒𝑣,𝑦

𝑚𝑎𝑥 
𝑃𝑠𝑣2𝑔

𝐸𝑉𝑖𝑛𝑖

𝑐𝑜𝑛 

Discharging Efficiency in year 𝑦. 

Charging Efficiency in year 𝑦. 

Minimum SOC allowed. 

Maximum SOC allowed. 

Initial state of charge per EV. 

Final state of charge at the departure time. 

EV battery capacity. 

Maximum  charging  &  discharging  power  from  V2G 
charger. 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

𝑘𝑊ℎ 

𝑘𝑊 

Number  of  EV  that  are  connected  at  first  time  step  of 
the day. 

𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑣𝑎𝑙𝑢𝑒 

Source: own elaboration. 

176 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
Table 62. V2G equations for the Investment model 

Term 

Eq. 68 

Number 
of 
EVs that come 
in 

Equation 

Let 𝐸𝑉𝑐𝑜𝑛 be the number of vehicles that would ideally try to be connected at each time 
step, 

𝐸𝑉𝑦,𝑚,𝑑,1

𝑐𝑜𝑛 = 𝐸𝑉𝑖𝑛𝑖
𝑐𝑜𝑛
𝑐𝑜𝑛 = 𝐸𝑉𝑦,𝑚,𝑑,𝑡−1

𝐸𝑉𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛 + 𝐸𝑉𝑦,𝑚,𝑑,1

𝑖𝑛

𝑜𝑢𝑡

− 𝐸𝑉𝑦,𝑚,𝑑,1

, ∀𝑦, 𝑚, 𝑑, 

𝑖𝑛
+ 𝐸𝑉𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡

− 𝐸𝑉𝑦,𝑚,𝑑,𝑡

, ∀𝑦, 𝑚, 𝑑, 𝑡 > 1 

Then, the number of EVs that can go in is; 

𝑖𝑛
𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑖𝑛
≤ 𝐸𝑉𝑦,𝑚,𝑑,𝑡

 ∀𝑦, 𝑚, 𝑑, 

Then, the number of connected EVs is bounded as follows; 

Eq.69                    
EVs connected 
bounds 

𝑐𝑜𝑛 ≤ 𝐸𝑉𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛

𝑒𝑣𝑦,𝑚,𝑑,𝑡
𝑦

 ∀𝑦, 𝑚, 𝑑, 𝑡 

𝑒𝑣𝑦,𝑚,𝑑,1

𝑐𝑜𝑛 ≤ ∑ ∑ 𝑛𝑣2𝑔,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝑖𝑛𝑠𝑡

 ∀𝑦, 𝑚, 𝑑 

The number of connected EVs is; 

Eq.70                    
EVs connected 
balance 

𝑒𝑣𝑦,𝑚,𝑑,1

𝑐𝑜𝑛 = 𝐸𝑉𝑖𝑛𝑖 
𝑐𝑜𝑛
𝑐𝑜𝑛 = 𝑒𝑣𝑦,𝑚,𝑑,𝑡−1 

𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛 + 𝑒𝑣𝑦,𝑚,𝑑,1

𝑖𝑛

− 𝑒𝑣𝑦,𝑚,𝑑,1

𝑜𝑢𝑡 ∀𝑦, 𝑚, 𝑑 

𝑖𝑛
+ 𝑒𝑣𝑦,𝑚,𝑑,𝑡

− 𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑜𝑢𝑡 ∀𝑦, 𝑚, 𝑑, ∀𝑡 > 1 

upper 

Eq.71  

SOC 
bound 

Eq.72  

     SOC  lower 
bound 

Maximum energy stored allowed ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌; 

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡

≤ 𝑆𝑂𝐶𝑒𝑣

𝑚𝑎𝑥 · 𝑒𝑣𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛

𝑏
· 𝐸𝑒𝑣,𝑦

The minimum SOC allowed  ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀 𝑎𝑛𝑑 𝑦 ∈ 𝑌 depends on the number of 
EVs plugged in, the final expected SOC for the EVS that will go out in the next time step, 
and the initial SOC of the EVs that come in; 

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡

≥ {

𝑐𝑜𝑛
𝑒𝑣𝑦,𝑚,𝑑,𝑡 
𝑐𝑜𝑛
𝑒𝑣𝑦,𝑚,𝑑,𝑡 

· 𝑆𝑂𝐶𝑒𝑣

𝑜𝑢𝑡

𝑚𝑖𝑛 · 𝐸𝑒𝑣𝑦
𝑖𝑛𝑖 · 𝐸𝑒𝑣𝑦

𝑏 + 𝑒𝑣𝑦,𝑚,𝑑,𝑡+1
𝑜𝑢𝑡

𝑏 + 𝑒𝑣𝑦,𝑚,𝑑,𝑡+1

· 𝑆𝑂𝐶𝑒𝑣

· (𝑆𝑂𝐶𝑒𝑣

𝑒𝑛𝑑 − 𝑆𝑂𝐶𝑒𝑣

; ∀𝑡 > 1 𝑑, 𝑚, 𝑦

𝑏

𝑚𝑖𝑛) · 𝐸𝑒𝑣,𝑦
𝑏

· (𝑆𝑂𝐶𝑒𝑣

𝑒𝑛𝑑 − 𝑆𝑂𝐶𝑒𝑣

𝑖𝑛𝑖) · 𝐸𝑒𝑣,𝑦

;           𝑡 = 1, ∀𝑑, 𝑚, 𝑦

Eq.73      SOC 
balance 

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡

 𝑒𝑣𝑦,𝑚,𝑑,𝑖𝑛𝑖 

𝑐𝑜𝑛

· 𝑆𝑂𝐶𝑒𝑣

𝑖𝑛𝑖 · 𝐸𝑒𝑣𝑦

𝑏 + 𝜂𝑣2𝑔,𝑦

𝑐ℎ

𝑐ℎ
· ∆𝑡 · 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,1

−

𝑐ℎ
∆𝑡 · 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,1
𝑑
𝜂𝑣2𝑔,𝑦

; ∀ 𝑑, 𝑚, 𝑦

=  

{

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡−1

+ 𝜂𝑣2𝑔,𝑦

𝑐ℎ
𝑐ℎ ∆𝑡 · 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

−

𝑐ℎ
∆𝑡 · 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡
𝑑
𝜂𝑣2𝑔,𝑦

;                   ∀𝑡 > 1, 𝑑, 𝑚, 𝑦

Eq.74  
Charge 
discharge 
bounds 

Maximum charge and discharge power given by the chargers, ∀ 𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈
𝑌; 

and 

𝑐ℎ
𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

𝑑

+ 𝑝𝑣2𝑔,𝑦,𝑚,𝑑,𝑡

𝑐𝑜𝑛
≤ 𝑒𝑣𝑦,𝑚,𝑑,𝑡 

· 𝑃𝑣2𝑔

𝑚𝑎𝑥 

Eq.75    Final 
daily SOC 

Minimum final SOC per day ∀𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑒𝑣
𝑠𝑜𝑐𝑦,𝑚,𝑑,𝑡𝑓

𝑐𝑜𝑛
≥ 𝑒𝑣𝑦,𝑚,𝑑,𝑡𝑓

177 

· 𝑆𝑂𝐶𝑣2𝑔

𝑒𝑛𝑑 · 𝐸𝑒𝑣,𝑦

𝑏

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Source: Modification of the model from  Meenakumar et al. (2020). 

Demand Response 

Table 63. Demand response parameters for the Investment model 

Parameter 

Description 

Units/Domain 

𝑖𝑛𝑐 
𝑆𝑑𝑟

𝑑𝑒𝑐 
𝑆𝑑𝑟

𝑓𝑙𝑒𝑥 
𝑆𝑑𝑟

𝑈𝑖𝑛𝑐 

𝑈𝑑𝑒𝑐 

𝑇𝑑𝑟 

𝑁𝑑𝑟 

Load increase share. 

Load decrease share. 

Load increase share.  

Initial state of increment at first time step of every day.  

Initial state of decrement at first time step of every day. 

Maximum time of demand response. 

Number of activations per day. 

Source: own elaboration. 

Table 64. Demand response equations for the Investment model 

Term 

Equation 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

hours 

N 

Eq.76                
Initial state 

Initial state of demand response, ∀𝑦 ∈ 𝑌, 𝑚 ∈ 𝑀, 𝑑 ∈ 𝐷; 

𝑖𝑛𝑐
𝑢𝑦,𝑚,𝑑,𝑡0
𝑑𝑒𝑐
𝑢𝑦,𝑚,𝑑,𝑡0

= 𝑈𝑖𝑛𝑐 

= 𝑈𝑑𝑒𝑐 

Eq.77        
Decrease 
demand 

Eq.78          
Increase 
demand 

Upper bound of decreased amount of power demand ∀𝑡  ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

0 ≤ 𝑥𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐 ≤ 𝑢𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐

· 𝐷ℎ𝑝,𝑡 · 𝑆𝑑𝑟

𝑓𝑙𝑒𝑥 · 𝑆𝑑𝑟

𝑑𝑒𝑐 

Upper bound of increased amount of power demand ∀𝑡 ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

0 ≤ 𝑥𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑐

𝑖𝑛𝑐
≤ 𝑢𝑦,𝑚,𝑑,𝑡

· 𝐷ℎ𝑝,𝑡 · 𝑆𝑑𝑟

𝑓𝑙𝑒𝑥 · 𝑆𝑑𝑟
𝑖𝑛𝑐 

Eq.79                  
Time limit 

Consecutive time step of demand response activation ∀𝑡  ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑡+1
∑ (𝑥𝑦,𝑚,𝑑,𝑡

𝑑𝑒𝑐 + 𝑥𝑦,𝑚,𝑑,𝑡

𝑖𝑛𝑐

Source: Modification of the model from Heitkoetter et al. (2021).  

𝑖=𝑡−𝑇𝑑𝑟+1

Boiler 

Table 65. Boiler parameters for the Investment model 

Parameter 

Description 

𝐾𝐵 

Set of Boilers considered 

) ≤   𝑇𝑑𝑟

Units/Domain 

𝐾𝐵 = {𝑆𝐵1, 𝑆𝐵2} 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

178 

 
 
 
 
 
 
 
Parameter 

Description 

Units/Domain 

𝐵
𝑃𝑠𝑘,𝑦,𝑖𝑛𝑖 

𝐵 
𝜂𝑆𝑘,𝑓𝑖

𝑓𝑙𝑒𝑥 
𝑆𝑑𝑟

𝑈𝑖𝑛𝑐 

𝑈𝑑𝑒𝑐 

𝑇𝑑𝑟 

𝑁𝑑𝑟 

Installed power of boilers in year 𝑦, ∀𝑠𝑘 ∈   𝐾𝐵. 

Conversion from fuel 𝑓𝑖, 𝑖 = 1,3, to thermal power  

Load increase share.  

Initial state of increment at first time step of every day.  

Initial state of decrement at first time step of every day. 

Maximum time of demand response. 

Number of activations per day. 

Source: own elaboration. 

Table 66. Boiler equations for the Investment model 

𝑘𝑊𝑡 

𝑘𝑊𝑡
𝑚𝑜𝑙𝑓𝑖

[0,1] 

[0,1] 

[0,1] 

hours 

N 

Term 

Eq.80          
Relation 
between 
power 
consumption 

and 

Eq.81  Power 
generation 
bound 

Eq.82 
Installed 
power  bound 
boiler 

Eq.83  Decide 
gas 
or 
hydrogen 

Equation 

𝑔𝑒𝑛,𝑡ℎ,𝐵 = ∑ ∑ 𝜂𝑆𝑘,𝑓𝑖
𝑝𝑆𝑘,𝑦,𝑚,𝑑,𝑡
𝑠𝑘∈𝐾𝐵

𝑓∈{𝑓1,𝑓3}

𝐵 

𝑐𝑜𝑛𝑠,𝐵

· 𝑓𝑖𝑆𝑘,𝑦,𝑚,𝑑,𝑡

Upper bound of decreased amount of power demand ∀𝑡, ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈ 𝑀, 𝑦 ∈ 𝑌; 

𝑦

𝑔𝑒𝑛,𝑡ℎ,𝐵 ≤ 𝑃𝑠𝑘,𝑦,𝑖𝑛𝑖 
𝑝𝑆𝑘,𝑦,𝑚,𝑑,𝑡

𝐵

𝑖𝑛𝑠𝑡,𝐵

+ ∑ ∑ 𝑝𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

Limit power installed by the initial power installed at first timestep, ∀ 𝑦 ∈  𝑌; 

𝑦

𝐵
𝑃𝑠𝑘,𝑦,𝑖𝑛𝑖 

𝑖𝑛𝑠𝑡,𝐵

+ ∑ ∑ 𝑝𝑠𝑘,𝑖,𝑚̂ ,𝑑̂,𝑡̂
𝑚̂ ,𝑑̂,𝑡̂𝜖𝑊𝑦

𝑖=1

𝐵
≤ 𝑃𝑠𝑘,1,𝑖𝑛𝑖 

At  each  time  step  only  gas  or  hydrogen  consumption  is  allowed  ∀𝑡, ∈ 𝑇, 𝑑 ∈ 𝐷, 𝑚 ∈
𝑀, 𝑦 ∈ 𝑌,  and  ∀𝑠𝑘 ∈ 𝐾𝐵; 

𝑐𝑜𝑛𝑠,𝐵 ≤ (1 − 𝑢𝑠𝑘.𝑦,𝑚,𝑑,𝑡

𝑓3𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐵

) · 𝑀 

𝑐𝑜𝑛𝑠,𝐵 ≤ 𝑢𝑠𝑘.𝑦,𝑚,𝑑,𝑡

𝑓1𝑠𝑘,𝑦,𝑚,𝑑,𝑡

𝐵

· 𝑀 

Source: own elaboration. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

179 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Annex 2. Mathematical Formulation for MODECO’s Operational Model  

Sets and parameters 

Table 67. Sets for the Operational model 

Set 

Description 

𝑇  

Set of time intervals. 

𝒩𝑒𝑠 

Set of numbers of Electrical Storage. 

𝒩𝑐ℎ𝑝 

Set of numbers of CHP. 

𝐷  

𝑀  

𝐽 

𝐿 

Set of days. 

Set of months. 

Discount rate scenarios 

Price scenarios 

Source: own elaboration. 

Table 68. Parameters for the Operational model  

Elements 

𝑡 ∈ 𝑇 

𝓃𝑒𝑠 ∈ 𝒩𝑒𝑠 

𝓃𝑐ℎ𝑝 ∈ 𝒩𝑐ℎ𝑝 

𝑑  ∈  𝐷  

𝑚  ∈ 𝑀  

𝑗 ∈ 𝐽 

𝑙 ∈ 𝐿 

Parameter 

Description 

Units 

Source 

Curves 

𝐻𝑡𝑏𝑙,𝑡 

𝐻
𝐻𝑡𝑏𝑙,𝑡 

𝐷ℎ𝑝,𝑡 

𝐷𝑒𝑏𝑙,𝑡 

Thermal base load at time 𝑡. 

High thermal base load at time t 

Heat pumps demand at time t 

Electrical base load demand at time t 

180 

𝑘𝑊ℎ𝑡ℎ 

𝑘𝑊ℎ𝑡ℎ 

𝑘𝑊 

𝑘𝑊 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

Units 

Source 

𝑃𝑝𝑣,𝑡 

Power given to the net from PV at time t 

𝑃𝑤𝑡,𝑡 

Power given to the net from WT at time t 

𝑐
𝑁𝐸𝑉,𝑡

𝑑
𝑁𝐸𝑉,𝑡

Number  of  EV  connecting  to  a  charger  station  at 
the beginning of time 𝑡. 

Number  of  EV  disconnecting  to  a  charging  station 
at the beginning of time t 

𝐶𝑜𝑛 
𝑁𝐸𝑉,𝑡

Number of EV plugged in 

𝑘𝑊 

𝑘𝑊 

𝑁 

𝑁 

𝑁 

on 

on 

on 

on 

on 

Based 
Investment 
outputs 

Based 
Investment 
outputs 

Based 
Investment 
outputs 

Based 
Investment 
outputs 

Based 
Investment 
outputs 

Cost for energy bought at time 𝑡. 

€/𝑘𝑊ℎ 

UCED output 

Price for energy sold at time 𝑡. 

€/𝑘𝑊ℎ 

UCED output 

Costs 

𝑏𝑢𝑦 
𝜆𝑡

𝑠𝑒𝑙𝑙 
𝜆𝑡

𝑛𝑒𝑡𝑔𝑒𝑛 
𝜆𝑡

𝑝𝑒𝑎𝑘 
𝜆𝑚 

𝜆𝑓𝑖𝑥 

Network cost for energy generation at time t 

Peak power cost. 

Fix cost for using the red. 

𝜆𝑒𝑥𝑐𝑒𝑒𝑑 

Cost for exceeding the power band. 

ℎ2 
𝜆𝑡

𝑏 
𝜆𝑡

𝑔 
𝜆𝑡

𝑐ℎ  
𝜆𝐸𝑉,𝑡

𝑠𝑑
𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
𝜆𝑛𝑐ℎ𝑝,𝑡

𝜆𝑑𝑟 

Cost for hydrogen consumption at time t 

Cost for biomass consumption at time t 

Cost for gas consumption at time t 

Cost  for  the  EV  entering  the  charging  station  at 
time t 

Cost for closing the CHP at time 𝑡. 

Cost for opening the CHP at time 𝑡. 

Demand response cost. 

Parameter per technology 

€/𝑘𝑊 

€/𝑘𝑊 

€/𝑘𝑊 

€/𝑘𝑊 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€ 

€/𝑘𝑊ℎ 

€/𝑘𝑊ℎ 

€/𝑘𝑊 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

181 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
𝑘𝑊ℎ
𝑚𝑜𝑙

[0,1] 

𝑃𝑎 

𝑃𝑎 

𝑃𝑎 

𝑚3 · 𝑃𝑎 
𝐾 · 𝑚𝑜𝑙 

𝐾 

𝑚3 

𝑁 

Parameter 

Description 

Units 

Source 

𝑃𝐸𝐿 

𝑃𝑏𝑎𝑛𝑑 

𝑃𝐸𝐿 

𝐻2 
𝑁𝐸𝐿

Maximum power consumed by the electrolyser. 

Maximum selling/buying power of the band. 

Lower limit of power in electrolyser. 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

Maximum rate of hydrogen molar in electrolyser. 

𝑁𝑚3/ℎ 

Investment 
output 

Investment 
output 

Investment 
output 

𝐿𝐻𝑉𝐻2 

Lower heating value of hydrogen. 

𝜂𝐸𝐿 

𝐻2 

𝑄0

𝑄𝐻2 

𝑄𝐻2 

Electrolyser efficiency. 

Hydrogen tank pressure in the first time. 

Upper limit of hydrogen tank pressure. 

Lower limit of hydrogen tank pressure. 

𝑅 

Gas constant. 

Investment 
output 

Investment 
output 

Investment 
output 

Mean temperature inside the vessel. 

Overall tank volume. 

Number of demand response activations per day. 

𝑚𝑒𝑎𝑛 

𝑇𝐻2

𝑉𝐻2 

𝑑𝑎𝑦 

𝑁𝑑𝑟

𝑇𝑑𝑟 

Maximum  consecutive  time  steps  allowed  of 
demand response. 

ℎ𝑜𝑢𝑟𝑠 

𝑡𝑜𝑡𝑎𝑙
𝑁𝑐ℎ𝑎𝑟𝑔𝑒𝑟𝑠

Total number of chargers available. 

𝑏  
𝐸𝑒𝑣

𝑚𝑎𝑥 

𝑃𝑣2𝑔

𝐸𝑉𝑖𝑛𝑖

𝑐𝑜𝑛 

𝐸𝑒𝑣,0 

𝑐ℎ 
𝜂𝑒𝑣

𝑑𝑐ℎ 
𝜂𝑒𝑣

Energy capacity of an individual EV Battery. 

Maximum charging power of a V2G charging node. 

Initial  number  of  EV  plugged  in  the  charging 
station. 

Initial state of charge of battery Pool.  

Charging efficiency of the EV. 

Discharging efficiency of the EV. 

𝑆𝑂𝐶𝐸𝑉,0 

Initial  state  of  charge  of  individual  EV  arriving  at 
the charging station 

𝑁 

𝑘𝑊ℎ 

𝑘𝑊 

𝑁 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

182 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

𝑆𝑂𝐶𝐸𝑉,𝑓 

Final  state  of  charge  of  individual  EV  departing  at 
the charging station 

Maximum state of charge for Individual EV Battery. 

Minimum state of charge for Individual EV Battery. 

Initial  State  of  charge  (SOC)  of  an  individual  EV 
Battery. 

Source 

Units 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

Final expected SOC of an individual EV Battery.  

[0,1] 

Minimum power for each type of Electrical Storage 

𝑘𝑊 

Maximum power for each type of Electrical Storage 

𝑘𝑊 

Investment 
output 

Investment 
output 

𝑆𝑂𝐶𝑒𝑣

𝑚𝑎𝑥 

𝑆𝑂𝐶𝑒𝑣

𝑚𝑖𝑛 

𝑆𝑂𝐶𝑒𝑣

𝑖𝑛𝑖 

𝑆𝑂𝐶𝑒𝑣

𝑓𝑖𝑛 

𝑃𝑛𝑒𝑠 

𝑃𝑛𝑒𝑠 

𝑆𝑂𝐶𝑛𝑒𝑠,0 

Initial state of charge for each Electrical Storage at 
time initial 

𝑑𝑐ℎ 
𝜂𝑛𝑒𝑠

𝑐ℎ  
𝜂𝑛𝑒𝑠 

𝑆𝑂𝐶𝑛𝑒𝑠 

𝑆𝑂𝐶𝑛𝑒𝑠 

Discharge  Efficiency  of  the  Electrical  Storage  for 
each type of battery 

Charge Efficiency of the Electrical Storage for each 
type of Battery.  

Maximum state of charge for Electrical Storage for 
each Electrical Storage. 

Minimum state of charge for Electrical Storage for 
each Electrical Storage. 

𝐸𝑛𝑒𝑠 

Electrical  Storage  capacity  for  each  type  of 
Electrical Storage. 

HRCHP

𝑏 

Heat rate of biomass to power in CHP. 

𝐺𝑒𝑙  
𝐶𝐶𝐻𝑃

𝐻𝑒𝑙  
𝐶𝐶𝐻𝑃

𝐺𝑡ℎ  
𝐶𝐶𝐻𝑃

𝐻𝑡ℎ  
𝐶𝐶𝐻𝑃

𝑃𝑛𝑐ℎ𝑝 

𝑃𝑛𝑐ℎ𝑝 

Conversion factor from gas to electrical power 

Conversion  factor  from  hydrogen  to  electrical 
power 

Conversion factor from gas to thermal power 

Conversion factor from hydrogen to thermal power 

Maximum Electrical power for each CHP. 

Minimum Electrical power for each CHP. 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

𝑘𝑊ℎ 

Investment 
output 

𝑘𝑊  

𝑘𝑊  

Investment 
output 

Investment 
output 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

183 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
𝐻𝑛𝑐ℎ𝑝 

𝑈𝑛𝑐ℎ𝑝,0 

𝑠𝑑  
𝑇𝑛𝑐ℎ𝑝

𝑠𝑢  
𝑇𝑛𝑐ℎ𝑝

𝐵
𝑃𝑛𝑐ℎ𝑝

𝐷
𝑃𝑛𝑐ℎ𝑝

𝐶
𝐻𝑛𝑐ℎ𝑝

𝑃ℎ𝑠 

𝑖𝑛𝑐 
𝑆𝑑𝑟

𝑑𝑒𝑐 
𝑆𝑑𝑟

𝑓𝑙𝑒𝑥 
𝑆𝑑𝑟

𝑖𝑛𝑐  
𝑈𝑑𝑟,0

𝑑𝑒𝑐  
𝑈𝑑𝑟,0

𝑑𝑎𝑖𝑙𝑦 

𝑁𝑑𝑟

𝑁𝑑𝑟 

Parameter 

Description 

Units 

Source 

Maximum Thermal power for each CHP. 

𝑘𝑊ℎ𝑡ℎ  

Investment 
output 

Initial state of the CHP for each CHP at initial time. 

[0,1] 

Minimum off time for each CHP. 

Minimum uptime for each CHP. 

Theoretical Electrical power B for each CHP. 

Theoretical Electrical power D for each CHP. 

ℎ𝑜𝑢𝑟𝑠  

ℎ𝑜𝑢𝑟𝑠 

𝑘𝑊 

𝑘𝑊 

Investment output 

Investment output 

Theoretical thermal power C for each CHP. 

𝑘𝑊ℎ𝑡  

Investment output 

Investment output 

Investment output 

Investment output 

Investment output 

Investment output 

Investment output 

Maximum power for Electrical Storage. 

Load increase share. 

Load decrease share. 

Flexible Share. 

Initial state of increment at time initial. 

Initial state of descend at time initial. 

𝑘𝑊 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

Number of demand response activations per day 

ℎ𝑜𝑢𝑟𝑠 

Maximum time of demand response 

𝐻2𝑎𝑙𝑙𝑜𝑤𝑒𝑑 

If hydrogen is allowed in the archetype 

𝑏
𝑃𝑖𝑛𝑠𝑡

𝑃𝐻2 

𝑃𝑃𝑉𝑟 

𝑃𝑃𝑉𝑙 

𝑃𝑊𝑇𝑙 

𝐻2 

𝐻𝑏

𝐺 
𝐻𝑏

𝑙𝑎𝑛𝑑 
𝜂𝑃𝑉

𝑟𝑜𝑜𝑓 
𝜂𝑃𝑉

Installed power for boilers 

Maximum power for hydrogen tank 

Installed power of PV on roof 

Installed power of PV on land 

Installed power of low wind turbine 

Conversion hydrogen to heat in the boiler 

Conversion gas to heat in the boiler 

Efficiency of PV land in year 

Efficiency of PV roof in year 

184 

ℎ𝑜𝑢𝑟𝑠 

[0,1] 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

[0,1] 

[0,1] 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Parameter 

Description 

Units 

Source 

𝑙𝑜𝑤 
𝜂𝑊𝑇

ℎ𝑖𝑔ℎ 
𝜂𝑊𝑇

Efficiency of WT low in year 

Efficiency of WT high in year 

[0,1] 

[0,1] 

Source: own elaboration. 

Variables 

Table 69. Variables for the operational Model 

Description 

Units/Domain 

Variable 

𝑣2𝑔𝑡

𝑖𝑛 

𝑣2𝑔𝑡

𝑜𝑢𝑡 

𝑒𝑒𝑣,𝑡 

𝑐ℎ  
𝑝𝑒𝑣,𝑡

𝑑𝑐ℎ 
𝑝𝑒𝑣,𝑡

𝑢𝑛𝑒𝑠,𝑡 

𝑐ℎ  
𝑝𝑛𝑒𝑠,𝑡

𝑑𝑐ℎ  
𝑝𝑛𝑒𝑠,𝑡

V2G vehicles entering the charging station at time t. 

V2G vehicles departing the charging station at time t 

Energy level of EVs Battery Pool at time 𝑡. 

Charging power of EVs Battery Pool at time 𝑡. 

Discharging power of EVs Battery Pool at time 𝑡. 

State  of  the  EVs  Battery  Pool  {1  is  charging,  0 
otherwise} at time 𝑡. 

Charging  power  for  each  type  of  Electrical  Storage  at 
time 𝑡. 

Discharging power for each type of Electrical Storage at 
time 𝑡. 

𝑠𝑜𝑐𝑛𝑒𝑠,𝑡 

State  of  charge  for  each  type  of  Electrical  Storage  at 
time 𝑡. 

𝑢𝑛𝑐ℎ𝑝,𝑡 

𝑠𝑢
𝑥𝑛𝑐ℎ𝑝,𝑡

𝑠𝑑
𝑥𝑛𝑐ℎ𝑝,𝑡

𝑝𝑛𝑐ℎ𝑝,𝑡 

ℎ𝑛𝑐ℎ𝑝,𝑡 

𝑖𝑛𝑐  
𝑢𝑑𝑟,𝑡

𝑑𝑒𝑐  
𝑢𝑑𝑟,𝑡

𝑖𝑛𝑐  
𝑥𝑑𝑟,𝑡

State of the CHP {1 is open, 0 closed} at time 𝑡. 

Change off to on for each CHP at time 𝑡. 

Change on to off for each CHP at time 𝑡.  

Electrical power for each CHP at time 𝑡. 

Thermal power for each CHP at time 𝑡. 

State  of  increment  {1  is  incrementing,  0  otherwise}  at 
time 𝑡. 

State of descend {1 is descending, 0 otherwise} at time 
𝑡. 

Increased power at time 𝑡. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

185 

𝑁 

𝑁 

𝑘𝑊ℎ 

𝑘𝑊 

𝑘𝑊 

[0,1] 

𝑘𝑊 

𝑘𝑊 

[0,1] 

[0,1] 

[0,1] 

[0,1] 

𝑘𝑊 

𝑘𝑊𝑡ℎ 

[0,1] 

[0,1] 

𝑘𝑊 

 
 
 
 
 
 
 
 
Variable 

Description 

Units/Domain 

𝑑𝑒𝑐  
𝑥𝑑𝑟,𝑡

𝑏𝑢𝑦 
𝑝𝑡

𝑠𝑒𝑙𝑙 

𝑝𝑡

𝑏𝑢𝑦 
𝑢𝑡

𝑝𝑒𝑎𝑘 
𝑝𝑚

𝑏𝑢𝑦
𝑧𝑏𝑎𝑛𝑑,𝑡

𝑠𝑒𝑙𝑙
𝑧𝑏𝑎𝑛𝑑,𝑡

𝑝𝑒𝑙,𝑡

𝐻2 

𝑢𝑡

𝐻2  
𝑛𝑒𝑙,𝑡

𝐻2 
𝑞𝑡

𝐻2
𝑛𝑛𝐶𝐻𝑃,𝑡

𝑐ℎ   
𝑝ℎ𝑠,𝑡

𝑑𝑐ℎ  
𝑝ℎ𝑠,𝑡

𝑡𝑜𝑡𝑎𝑙 

𝑛𝐸𝑉,𝑡

𝑝𝑤𝑡,𝑡 

𝑝𝑝𝑣,𝑡 

ℎ𝑏,𝑡 

ℎ2𝑏,𝑡 

Decreased power at time 𝑡. 

Buying power at time 𝑡 from the grid. 

Selling power at time 𝑡 to the grid. 

State of direction in the grid tie {1 buy, 0 sell} at time 𝑡. 

Peak power per month. 

Buying exceed power of the band at time 𝑡. 

Selling exceed power of the band at time 𝑡. 

Electrical power consumed by electrolyze at time 𝑡. 

Electrolyser  and  CHP  cannot  produce  or  consume 
hydrogen from the storage at the same time. 

Produced hydrogen mol/H by electrolyze at time  . 

Pressure level of the tank. 

Consumed hydrogen molar/H by CHP. 

Power charged in the hydrogen Storage. 

Power Discharged in the hydrogen Storage. 

Total number of EV in the charging Station at time t 

Electrical power for wind turbine at time t 

Electrical power for photovoltaic at time t 

Thermal power produced by the boilers at time t 

Hydrogen consumed by the boilers at time t 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

[0,1] 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊 

[0,1] 

𝑚𝑜𝑙
𝐻

𝑃𝑎 

𝑚𝑜𝑙
𝐻

𝑘𝑊 

𝑘𝑊 

𝑁 

𝑘𝑊 

𝑘𝑊 

𝑘𝑊𝑡ℎ 

ℎ2𝐶𝐻𝑃,𝑡 

Hydrogen consumed by the CHP at time t 

𝑔𝑏,𝑡 

𝑥𝑏,𝑡 

Gas consumed by the boilers at time t 

The boiler is consuming gas or hydrogen 

[0,1] 

𝑏𝑜𝑢𝑔ℎ𝑡  Gas bought for the boiler or the CHP 
𝑔𝑡

𝑏𝑜𝑢𝑔ℎ𝑡  Hydrogen bought 

ℎ2𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 
𝑏𝑡

Biomass bought 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

186 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Variable 

Description 

Units/Domain 

𝑔𝑐ℎ𝑝,𝑡 

𝑏𝐶𝐻𝑃,𝑡 

ℎ𝑖𝑔ℎ 

ℎ2𝑏,𝑡

ℎ𝑖𝑔ℎ 
𝑔𝑏,𝑡

Gas consumed by the CHP at time t 

Biomass consumed by the CHP at time t 

Hydrogen  consumed by boilers for  high temperature at 
time t 

Natural  gas  consumed  by  boilers  for  high  temperature 
at time t 

𝑥𝑒𝑙,𝑡 

Electrolyzer is active or not 

Source: own elaboration. 

[0,1] 

Objective Function                                                                                                                                                                                                

Table 70. Objective function for the Operational model 

Objective 
function 

Equation 

Peak Power  Min (Peak power cost) + (buy/sell energy from the grid) + (demand responds activations 

cost) + (CHP operation costs). 

𝑀𝑖𝑛  ∑ (𝐶𝑝𝑒𝑎𝑘 · 𝑝𝑚

𝑝𝑒𝑎𝑘) +

𝑚∈𝑀

𝑑𝑐ℎ + ∑

𝑝𝑒𝑣,𝑡

𝑛𝑒𝑠∈𝒩𝑒𝑠

 ℎ2𝑡
𝑔 ∗ 𝑔𝑡
𝜆𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 + 𝜆𝑡

𝑏 ∗ 𝑏𝑡
𝑏𝑜𝑢𝑔ℎ𝑡 − 𝜆𝐸𝑉,𝑡

𝑐ℎ

+   𝜆𝑡
𝑑𝑐ℎ )) + 
𝑏𝑜𝑢𝑔ℎ𝑡 +  

(𝑝𝑛𝑒𝑠,𝑡

· 𝑣2𝑔𝑡

𝑖𝑛)   

𝑏𝑢𝑦 · 𝑝𝑡

𝑏𝑢𝑦 − 𝜆𝑡

𝑠𝑒𝑙𝑙 · 𝑝𝑡

𝑠𝑒𝑙𝑙 + 𝜆𝑑𝑟(𝑥𝑑𝑟,𝑡

𝑑𝑒𝑐 )
𝑖𝑛𝑐 + 𝑥𝑑𝑟,𝑡

∆𝑡   ∑ ( 𝜆𝑡
𝑡∈𝒯  

𝑛𝑒𝑡𝑔𝑒𝑛 · (𝑝𝑝𝑣,𝑡 + 𝑝𝑤𝑡,𝑡 + 

∑

(𝑛𝑐ℎ𝑝∈𝒩𝑐ℎ𝑝)

𝑠𝑑
(𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑑
· 𝑥𝑛𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
+ 𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
· 𝑥𝑛𝑐ℎ𝑝,𝑡

)

+ 𝜆𝑡

ℎ2 ·

Bandwidth  Min (buy/sell energy from the grid) + (fixed and variable band costs) + (demand responds 

activations cost) + (CHP operation costs)  

𝑀𝑖𝑛 ∆𝑡   ∑ ( 𝜆𝑡

𝑏𝑢𝑦 · 𝑝𝑡

𝑏𝑢𝑦 − 𝜆𝑡

𝑠𝑒𝑙𝑙 · 𝑝𝑡

𝑠𝑒𝑙𝑙 + 𝜆𝑓𝑖𝑥 · 𝑃𝑏𝑎𝑛𝑑 + 𝜆𝑒𝑥𝑐𝑒𝑒𝑑 ∗ (𝑧𝑏𝑎𝑛𝑑,𝑡

𝑏𝑢𝑦 + 𝑧𝑏𝑎𝑛𝑑,𝑡

𝑠𝑒𝑙𝑙

)

𝑡∈𝒯  

+   𝜆𝑑𝑟(𝑥𝑑𝑟,𝑡

𝑖𝑛𝑐 + 𝑥𝑑𝑟,𝑡

𝑑𝑒𝑐 ) + 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

187 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
𝑛𝑒𝑡𝑔𝑒𝑛 · (𝑝𝑝𝑣,𝑡 + 𝑝𝑤𝑡,𝑡 + 𝑝𝑒𝑣,𝑡
 𝜆𝑡

𝑑𝑐ℎ

+ ∑ (𝑝𝑛𝑒𝑠,𝑡

𝑑𝑐ℎ )) + 

∑ (𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑑

𝑠𝑑
· 𝑥𝑛𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
+ 𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
· 𝑥𝑛𝑐ℎ𝑝,𝑡

)

+ 

𝑛𝑒𝑠∈𝒩𝑒𝑠

(𝑛𝑐ℎ𝑝∈𝒩𝑐ℎ𝑝)

ℎ2 ·  ℎ2𝑡
𝜆𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 + 𝜆𝑡

𝑏 ∗ 𝑏𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 + 𝜆𝑡

𝑔 ∗ 𝑔𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 − 𝜆𝐸𝑉,𝑡

𝑐ℎ

· 𝑣2𝑔𝑡

𝑖𝑛)    

Time 
Use 

of 

Min (buy/sell energy from the grid) + (demand responds activations cost) +(CHP operation 
costs); 

𝑀𝑖𝑛 ∆𝑡  ∑

𝑡∈𝒯  

( 𝜆𝑡

𝑏𝑢𝑦 · 𝑝𝑡

𝑏𝑢𝑦 − 𝜆𝑡

𝑠𝑒𝑙𝑙 · 𝑝𝑡

𝑠𝑒𝑙𝑙 + 𝜆𝑑𝑟(𝑥𝑑𝑟,𝑡

𝑖𝑛𝑐 + 𝑥𝑑𝑟,𝑡

𝑑𝑒𝑐 ) +   𝜆𝑡

𝑛𝑒𝑡𝑔𝑒𝑛 · (𝑝𝑝𝑣,𝑡 + 𝑝𝑤𝑡,𝑡 +

𝑑𝑐ℎ + ∑

𝑝𝑒𝑣,𝑡

𝑛𝑒𝑠∈𝒩𝑒𝑠

∑

(𝑛𝑐ℎ𝑝∈𝒩𝑐ℎ𝑝)

𝑠𝑑
(𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑑
· 𝑥𝑛𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
+ 𝜆𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢
· 𝑥𝑛𝑐ℎ𝑝,𝑡

)

+ 𝜆𝑡

ℎ2 ·

 ℎ2𝑡
𝑔 ∗ 𝑔𝑡
𝜆𝑡
Source: own elaboration. 

𝑏𝑜𝑢𝑔ℎ𝑡 + 𝜆𝑡

𝑏 ∗ 𝑏𝑡
𝑏𝑜𝑢𝑔ℎ𝑡 − 𝜆𝐸𝑉,𝑡

𝑐ℎ

(𝑝𝑛𝑒𝑠,𝑡

𝑑𝑐ℎ )) + 
𝑏𝑜𝑢𝑔ℎ𝑡 +  

· 𝑣2𝑔𝑡

𝑖𝑛)   

Balance Equations                                                                                                                                                                              

Table 71. Balance constraints for the Operational model 

Term 

Eq.84 Power 
balance 

Eq.85  
Thermal 
power 
balance 

Eq.86 
Hydrogen 
Balance 

The electrical power balance must be satisfied ∀𝑡 ∈ 𝑇; 

Equation 

𝑏𝑢𝑦 + 𝑃𝑝𝑣,𝑡 + 𝑃𝑤𝑡,𝑡 + ∑ (𝑝𝑛𝑐ℎ𝑝,𝑡) + 𝑝𝑒𝑣,𝑡
𝑝𝑡

+ 𝑥𝑑𝑟,𝑡

𝑑𝑒𝑐 =

 𝑝𝑡

𝑖𝑛𝑐
𝑠𝑒𝑙𝑙 + 𝐷𝑒𝑙,𝑡 + 𝑥𝑑𝑟,𝑡

𝑑𝑐ℎ
𝑑𝑐ℎ   + ∑ 𝑝𝑛𝑒𝑠,𝑡
𝒩𝑒𝑠

𝒩𝑐ℎ𝑝
𝑐ℎ + 

+ 𝑝𝑒𝑣,𝑡  

𝑐ℎ ) + 𝑝𝑒𝑙,𝑡

∑(𝑝𝑛𝑒𝑠,𝑡
𝒩𝑒𝑠

The thermal power balance must be satisfied ∀𝑡 ∈ 𝑇; 

∑ ℎ𝑛𝑐ℎ𝑝,𝑡 + ℎ𝑏,𝑡   ≥ 𝐻𝑡𝑏𝑙,𝑡
𝒩𝑐ℎ𝑝

Hydrogen balance must be satisfied ∀𝑡 ∈ 𝑇; 

𝐻2 + 𝑝ℎ𝑠,𝑡
𝑛𝑒𝑙,𝑡

𝑑𝑐ℎ  +  ℎ2𝑡

𝑏𝑜𝑢𝑔ℎ𝑡 =  ℎ2𝑏,𝑡 +  ℎ2𝑏,𝑡

ℎ𝑖𝑔ℎ +   𝑝ℎ𝑠,𝑡

𝑐ℎ  +  ℎ2𝐶𝐻𝑃,𝑡 

Source: own elaboration. 

188 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
 
 
 
 
  
 
  
 
 
Peak Power 

Table 72. Peak power constraints for the Operational model 

Term 

Eq.87 
Monthly 
peak power 

Equation 

The  Peak  power  is  computed  monthly  and  it’s  the  maximum  power  bought  for  each 
month ∀𝒕 ∈   𝑻𝒎; 

𝑏𝑢𝑦  ≤  𝑝𝑚
𝑝𝑡 

𝑝𝑒𝑎𝑘 

Source: own elaboration. 

Time-of-use 

Table 73. Time of Use constraints for the Operational model 

Term 

Eq.88 
Bought 
power 

Equation 

With the help of Eq.96 Time of Use tariff is only allowed to sell or buy power at the same 
time. This equation determines the bought power ∀𝒕 ∈  𝑻; 

𝑏𝑢𝑦 ≤ 𝑢𝑡
𝑝𝑡

𝑏𝑢𝑦 · 𝑀 

Eq.89     
Sold power 

With the help of Eq.95 Time of Use tariff is only allowed to sell or buy power at the same 
time. This equation determines the sold power ∀𝒕 ∈  𝑻; 

𝑠𝑒𝑙𝑙 ≤ (1 − 𝑢𝑡
𝑝𝑡

𝑏𝑢𝑦) · 𝑀 

Source: own elaboration. 

Bandwidth 

Table 74. Bandwidth constraints for the Operational model 

Term 

Eq.90 
Bought 
power 

Equation 

With the help of eq.92 Bandwidth tariff is only allowed to sell or buy power at the same 
time. This equation determines the bought power ∀𝒕 ∈  𝑻;  

𝑏𝑢𝑦 ≤ 𝑢𝑡
𝑝𝑡

𝑏𝑢𝑦 · 𝑀 

Eq.91     
Sold power 

With the help of eq.91 Bandwidth tariff is only allowed to sell or buy power at the same 
time. This equation determines the sold power ∀𝒕 ∈  𝑻; 

𝑠𝑒𝑙𝑙 ≤ (1 − 𝑢𝑡
𝑝𝑡

𝑏𝑢𝑦) · 𝑀 

A constraint that tells how much we are beyond the buying limit of the band ∀𝒕 ∈ 𝑻; 
𝑏𝑢𝑦 − 𝑧𝑏𝑎𝑛𝑑,𝑡
𝑝𝑡

𝑏𝑢𝑦 ≤ 𝑃𝑏𝑎𝑛𝑑 

Eq.92 
Exceeded 
bought 
power  over 
the band 

Eq.93 

A constraint that tells how much we are beyond the selling limit of the band ∀𝒕 ∈ 𝑻;  

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

189 

 
 
 
 
 
 
 
                                                                                                                                                                                           
 
𝑠𝑒𝑙𝑙 − 𝑧𝑏𝑎𝑛𝑑,𝑡
𝑝𝑡

𝑠𝑒𝑙𝑙 ≤ 𝑃𝑏𝑎𝑛𝑑 

Exceeded 
sold  power 
over 
the 
band 

Source: own elaboration. 

Vehicle-to-Grid 

Table 75. V2G constraints for the Operational model 

Term 

Eq.94         
EV in 

Eq.95         
EV out 

Eq.96         
EV definition 

Eq.97       
EV 
limit 

upper 

 EVs 

Eq.98 
plugged in 

Eq.99 
Energy 
balance 

Eq.100    
SOC bounds 

Eq.101    
SOC 
limit 

upper 

Eq.102  
Limit energy 

Eq.103  
Final SOC 

Electrical vehicles entering the charging station ∀𝑡 ∈ 𝑇. 

Constraints 

𝑣2𝑔𝑡

𝑖𝑛 ≤   𝑁𝐸𝑉,𝑡

𝑐

Electricals vehicles exciting the charging station ∀𝑡 ∈ 𝑇. 

𝑣2𝑔𝑡

𝑜𝑢𝑡 ≤ 𝑀 

Defining how many EV are available ∀𝑡 ∈ 𝑇. 

𝐶𝑜𝑛 
𝑡𝑜𝑡𝑎𝑙 =   𝑁𝐸𝑉,𝑡
𝑛𝑒𝑣,𝑡

An upper limit for how many EV available ∀𝑡 ∈ 𝑇. 

𝑡𝑜𝑡𝑎𝑙 ≤ 𝑁𝑐ℎ𝑎𝑟𝑔𝑒𝑟𝑠
𝑛𝑒𝑣,𝑡

𝑡𝑜𝑡𝑎𝑙

The balance of EV available at the charging station. 

𝑡𝑜𝑡𝑎𝑙 = {

𝑛𝑒𝑣,𝑡

𝑡𝑜𝑡𝑎𝑙 + 𝑣2𝑔𝑡
𝑛𝑒𝑣,0
𝑡𝑜𝑡𝑎𝑙 + 𝑣2𝑔𝑡
𝑛𝑒𝑣,𝑡−1

𝑖𝑛 − 𝑣2𝑔𝑡
𝑖𝑛 − 𝑣2𝑔𝑡

𝑜𝑢𝑡  ;            𝑡 = 1
𝑜𝑢𝑡 ;   ∀𝑡 ∈ [2, 𝑇]

The balance for the energy available having in to account the loss efficiency for charging 
and discharging  ∀𝑡 ∈  𝑇 ; 

· (𝑝𝑒𝑣,𝑡

𝑐ℎ ⋅ 𝜂𝑒𝑣 

𝑐ℎ −

𝑒𝑒𝑣,𝑡   =  𝑒𝑒𝑣,𝑡−1  +  ∆𝑡
𝑑𝑐ℎ
𝑝𝑒𝑣,𝑡
𝑑𝑐ℎ − 𝑣2𝑔𝑡
𝜂𝑒𝑣

𝑜𝑢𝑡 · 𝑆𝑂𝐶𝐸𝑉 ,𝑓   · 𝐸𝑒𝑣

𝑏   + 𝑣2𝑔𝑡

𝑖𝑛 · 𝑆𝑂𝐶𝐸𝑉 ,0  

· 𝐸𝑒𝑣

𝑏 )    

A lower limit for the SOC of EV ∀𝑡 ∈ 𝑇 ; 

𝑒𝑒𝑣,𝑡 ≥ 𝑛𝑒𝑣,𝑡

𝑡𝑜𝑡𝑎𝑙 · 𝑆𝑂𝐶𝑒𝑣

𝑚𝑖𝑛 · 𝐸𝑒𝑣

𝑏 + 𝑣2𝑔𝑒𝑣,𝑡+1

𝑜𝑢𝑡

· (𝑆𝑂𝐶𝐸𝑉𝑓 − 𝑆𝑂𝐶𝑒𝑣

𝑏  
𝑚𝑖𝑛) · 𝐸𝑒𝑣

An upper limit for the SOC of EV  ∀𝑡 ∈  𝑇 ; 

𝑒𝑒𝑣,𝑡 ≤ 𝑆𝑂𝐶𝑒𝑣

𝑚𝑎𝑥 · 𝑛𝑒𝑣,𝑡

𝑡𝑜𝑡𝑎𝑙 · 𝐸𝑒𝑣
𝑏  

A lower limit for the energy available  ∀𝑡 ∈  𝑇 ; 

𝑐ℎ +   𝑝𝑒𝑣,𝑡
𝑝𝑒𝑣,𝑡

𝑑𝑐ℎ ≤ nev,t

𝑡𝑜𝑡𝑎𝑙 ·   𝑃𝑣2𝑔

𝑚𝑎𝑥 

A lower bound for the final SOC. 

190 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
                                                                                                                                                                                                
 
 
 
  
 
𝑒𝑒𝑣,𝑓 ≥ 𝐸𝑒𝑣,0 · 𝐸𝑒𝑣

𝑏 · 𝑛𝑒𝑣,𝑓

𝑡𝑜𝑡𝑎𝑙 

Source: Modification of the model from  Meenakumar et al. (2020). 

Electrical Storage    

Table 76. Electrical Storage constraints for the Operational model 

Term 

Eq.104 
Charging 
bounds 

Eq.105 
Discharging 
bounds 

Constraints 

An upper and lower limit for charging that cannot be surpassed  ∀𝑡 ∈  𝑇 , ∀𝑛𝑒𝑠 ∈ 𝑁𝐸𝑆; 

𝑢𝑛𝑒𝑠,𝑡 · 𝑃𝑛𝑒𝑠 ≤ 𝑝𝑛𝑒𝑠,𝑡

𝑐

≤ 𝑢𝑛𝑒𝑠,𝑡 · 𝑃𝑛𝑒𝑠 

An upper and lower limit for discharging that cannot be surpassed  ∀𝑡 ∈  𝑇 , ∀𝑛𝑒𝑠 ∈ 𝑁𝐸𝑆; 

(1 − 𝑢𝑛𝑒𝑠,𝑡) · 𝑃𝑛𝑒𝑠 ≤ 𝑝 𝑛𝑒𝑠,𝑡 

𝑑

≤ (1 − 𝑢𝑛𝑒𝑠,𝑡) · 𝑃𝑛𝑒𝑠 

Eq.106 
Initial 
balance 

An  initial  balance  of  the  energy  available  before  the  loss  of  energy  for  charging  or 
discharging the electrical storage   ∀𝑛𝑒𝑠 ∈ 𝑁𝐸𝑆; 

SOC 

𝑠𝑜𝑐 𝑛𝑒𝑠,1 · 𝐸𝑛𝑒𝑠 =   𝑆𝑂𝐶𝑛𝑒𝑠,0 · 𝐸𝑛𝑒𝑠   + 𝜂𝑛𝑒𝑠

𝑐ℎ · 𝑝𝑛𝑒𝑠,1

𝑐

−

𝑑
𝑝𝑛𝑒𝑠,1
𝑑𝑐ℎ  
𝜂𝑛𝑒𝑠

Eq.107     
SOC bounds 

An upper and lower limit for the SOC  ∀𝑡 ∈  𝑇 , ∀𝑛𝑒𝑠 ∈ 𝑁𝐸𝑆; 

𝑆𝑂𝐶𝑛𝑒𝑠

𝑚𝑖𝑛 ≤ 𝑠𝑜𝑐𝑛𝑒𝑠,𝑡 ≤ 𝑆𝑂𝐶𝑛𝑒𝑠

𝑚𝑎𝑥 

Eq.108      
SOC balance 

A  balance of the energy available before the loss of energy for charging or discharging 
the electrical storage  ∀𝑡 ∈  𝑇 , ∀𝑛𝑒𝑠 ∈ 𝑁𝐸𝑆; 

𝐸𝑛𝑒𝑠 · 𝑠𝑜𝑐𝑛𝑒𝑠,𝑡 = 𝐸𝑛𝑒𝑠 · 𝑠𝑜𝑐 𝑛𝑒𝑠,𝑡−1 + Δ𝑡 · (𝜂𝑛𝑒𝑠

𝑐ℎ · 𝑝𝐸𝑆,𝑛𝑒𝑠,𝑡

𝑐

−

𝑑
𝑝𝐸𝑆,𝑛𝑒𝑠,𝑡
𝑑𝑐ℎ ) 
𝜂𝑛𝑒𝑠

Eq.109     
SOC Final 

A constraint to impose the final state of charge is at least the same as the initial state of 
charge. 

𝑡 = 𝑐𝑎𝑟𝑑(𝑇)  

Source: Modification of the model from Igualada González et al. (2013). 

𝐸𝑛𝑒𝑠 · 𝑠𝑜𝑐𝑛𝑒𝑠,𝑡 ≤ 𝑆𝑂𝐶𝑛𝑒𝑠,0 · 𝐸𝑛𝑒𝑠 

Combined Heat and Power 

Table 77. CHP constraints for the Operational model 

Term 

Eq.110 
Power 
bounds 

Equation 

An upper and lower limit for power production that cannot be surpassed  ∀𝑡 ∈  𝑇 , 
∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

𝑢𝑛𝑐ℎ𝑝,𝑡 ·   𝑃𝑛𝑐ℎ𝑝 ≤ 𝑝 𝑛𝑐ℎ𝑝,𝑡 ≤ 𝑢𝑛𝑐ℎ𝑝,𝑡 · 𝑃 𝑛𝑐ℎ𝑝 

Eq.111 

An upper and lower limit for heat production that cannot be surpassed  ∀𝑡 ∈  𝑇 , ∀𝑛𝑐ℎ𝑝 ∈

191 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
                                                                                                                                                                                     
 
 
 
 
Thermal 
power 
generation 
bound 

Eq.112    
Initial state 

Eq.113 
Change of 
state 

Eq.114      
Time limit 

Eq.115      
Time limits 
switch down 

Eq.116 
Polygon 
model of 
CHP A 

Eq.117 
Polygon 
model of 
CHP B 

Eq.118 
Polygon 
mode 
CHP C 

of 

𝑁𝐶𝐻𝑃; 

0 ≤ ℎ𝑛𝑐ℎ𝑝,𝑡 ≤ 𝑢𝑛𝑐ℎ𝑝,𝑡 · 𝐻 𝑛𝑐ℎ𝑝 

Defining if the plant is open or closed at time initial  ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

𝑈𝑛𝑐ℎ𝑝,0 = 𝑢𝑛𝑐ℎ𝑝,0 

A constraint to know if the plant changes the state on to off or off to on  ∀𝑡 ∈  𝑇 , 
∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

𝑢𝑛𝑐ℎ𝑝,𝑡 − 𝑢𝑛𝑐ℎ𝑝,𝑡−1 = 𝑥𝑛𝑐ℎ𝑝,𝑡

𝑠𝑢

𝑠𝑑
− 𝑥𝑛𝑐ℎ𝑝,𝑡

A minimum uptime for the CHP plant  ∀𝑡 ∈ [𝑇 𝑛𝑐ℎ𝑝

𝑠𝑢  , 𝑇] , ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

𝑡
∑

𝑖=𝑡−𝑇

𝑠𝑢 +1
𝑛𝑐ℎ𝑝

𝑠𝑢
𝑥𝑛𝑐ℎ𝑝,𝑡

≤

𝑢𝑛𝑐ℎ𝑝,𝑡 

A minimum shutdown time for the CHP plant ∀𝑡 ∈ [𝑇𝐶𝐻𝑃,𝑛𝑐ℎ𝑝

𝑠𝐷

 , 𝑇] , ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

𝑡
∑

𝑖=𝑡−𝑇

𝑠𝑑 +1
𝑛𝑐ℎ𝑝

𝑠𝑑
𝑥𝑛𝑐ℎ𝑝,𝑡

≤

𝑢𝑛𝑐ℎ𝑝,𝑡 

Limits the Feasible Operating Region of the CHP below the line AB of the trapezoid ∀𝑡 ∈
 𝑇 , ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

0 ≤ (𝑃𝑛𝑐ℎ𝑝

𝐵 − 𝑃𝑛𝑐ℎ𝑝) · (ℎ𝑛𝑐ℎ𝑝,𝑡) + (𝑃𝑛𝑐ℎ𝑝 − 𝑝𝑛𝑐ℎ𝑝,𝑡) · 𝐻𝑛𝑐ℎ𝑝 

Limits the Feasible Operating Region of the CHP above the line BC of the trapezoid  ∀𝑡 ∈
 𝑇 , ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

(𝑝𝑛𝑐ℎ𝑝,𝑡 − 𝑃𝑛𝑐ℎ𝑝

𝐷

) · 𝐻𝑛𝑐ℎ𝑝

𝐶 − (𝑃𝑛𝑐ℎ𝑝 − 𝑃𝑛𝑐ℎ𝑝

𝐷

)ℎ𝑛𝑐ℎ𝑝,𝑡 ≥   −(1 − 𝑢𝑛𝑐ℎ𝑝,𝑡 · 𝑀) 

Limits the Feasible Operating Region of the CHP above the line CD of the trapezoid ∀𝑡 ∈
 𝑇 , ∀𝑛𝑐ℎ𝑝 ∈ 𝑁𝐶𝐻𝑃; 

(𝑝𝑛𝑐ℎ𝑝,𝑡 − 𝑃𝑛𝑐ℎ𝑝) · (𝐻𝑛𝑐ℎ𝑝 − 𝐻𝑛𝑐ℎ𝑝

𝐶

𝐵
) − (𝑃𝐶𝐻𝑃,𝑛𝑐ℎ𝑝

− 𝑃𝑛𝑐ℎ𝑝) · (ℎ𝑛𝑐ℎ𝑝,𝑡 − 𝐻𝑛𝑐ℎ𝑝

𝐶

)  

≤ −(1 − 𝑢𝑛𝑐ℎ𝑝,𝑡) · 𝑀 

Source: (Mansouri et al., 2020). 

Demand Response 

Table 78. Demand response constraints for the Operational model 

Term 

Equations 

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192 

 
 
 
 
  
 
Term 

Eq.119 
Initial state 

Eq.120 
Decrease 
demand 

Eq.121 
Increase 
demand 

Eq.122   
Time limit 

Eq.123 
Activations 
per day 

Equations 

Defining the initial State of increment and decrease for demand response; 

𝑈𝑑𝑟,0

𝑖𝑛𝑐  
𝑖𝑛𝑐 = 𝑢𝑑𝑟,0

𝑈𝑑𝑟,0

𝑑𝑒𝑐  
𝑑𝑒𝑐 = 𝑢𝑑𝑟,0

An upper and lower limit for decrease demand response ∀𝒕 ∈ 𝑻; 

0 ≤ 𝑥𝑑𝑟,𝑡

𝑑𝑒𝑐 ≤ 𝑢𝑑𝑟,𝑡

𝑑𝑒𝑐 · 𝐷ℎ𝑝,𝑡 · 𝑠𝑑𝑟

𝑓𝑙𝑒𝑥 · 𝑆𝑑𝑟

𝑑𝑒𝑐 

An upper and lower limit for increase demand response ∀𝒕 ∈ 𝑻; 

0 ≤ 𝑥𝑑𝑟,𝑡

𝑖𝑛𝑐 ≤ 𝑢𝑑𝑟,𝑡

𝑖𝑛𝑐 · 𝐷ℎ𝑝,𝑡 · 𝑠𝑑𝑟

𝑓𝑙𝑒𝑥 · 𝑆𝑑𝑟
𝑖𝑛𝑐 

The demand response is not allowed to be performed consecutive for more than an 
upper limit ∀𝒕 ∈ [𝑻𝒅𝒓 − 𝟏, 𝑻 − 𝟏]; 

𝑡+1
∑ (𝑢𝑑𝑟,𝑡

𝑖𝑛𝑐 + 𝑢𝑑𝑟,𝑡

𝑑𝑒𝑐 ) ≤   𝑇𝑑𝑟

𝑖=𝑡−𝑇𝑑𝑟+1

The demand response is not allowed to be performed daily for more than an upper 
limit ∀𝒅 ∈ 𝑫; 

𝑑⋅𝑑ℎ
∑ (𝑢𝑑𝑟,𝑡

𝑑𝑒𝑐 )
𝑖𝑛𝑐   +  𝑢𝑑𝑟,𝑡

  ≤ 𝑁𝑑𝑟

𝑑𝑎𝑦 · 𝑇𝑑𝑟 

𝑡=(𝑑−1)⋅𝑑ℎ+1

Source: Modification of the model from Heitkoetter et al. (2021).  

Electrolyser 

Table 79. Electrolyzer constraints for the Operational model 

Term 

Constraints 

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193 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Term 

Eq.125 
Power 
bounds 

Eq.126 
Hydrogen 
bound 

Eq.127 
Hydrogen 
generation 

Constraints 

An upper and lower limit for the electrolyze power ∀𝒕 ∈ 𝑻; 

𝑃𝐸𝐿   ≤ 𝑝𝑒𝑙,𝑡 ≤   𝑃𝐸𝐿 

The produced hydrogen molar is not allowed to surpass an upper limit ∀𝒕 ∈ 𝑻; 

𝐻2 ≤ 𝑁𝐸𝐿
𝐻2 
𝑛𝑒𝑙 ,𝑡

A loss of efficiency for producing hydrogen molar ∀𝒕 ∈ 𝑻; 

𝐻2 =  

𝑛𝑒𝑙,𝑡

𝜂𝐸𝐿 · 𝑝𝑒𝑙,𝑡
𝐿𝐻𝑉𝐻2

Source: Modification of the model from Nojavan and Zare (2018). 

Hydrogen Storage 

Table 80. Hydrogen Storage constraints for the Operational model 

Term 

Eq.127 
Initial state 

Eq.128 
Pressure 
bounds 

Eq.129 
Storage 
balance 

Eq.130 
Charge 
Bound 

Eq.131 
Discharge 
Bound 

Constraints 

The initial pressure of the tank is defined 

𝐻2 = 𝑄0
𝑞0

𝐻2 

An upper and lower limit for the pressure of the tank ∀𝑡 ∈ 𝑇; 

𝑄𝐻2 ≤ 𝑞𝑡

𝐻2 ≤ 𝑄𝐻2 

A provision of the dynamic model for the hydrogen storage pressure ∀𝑡 ∈ 𝑇; 
𝑚𝑒𝑎𝑛 

𝐻2 = 𝑞𝑡−1
𝑞𝑡

𝐻2 +  

(𝑛𝑒𝑙,𝑡

𝐻2 − (𝐻𝑅𝐻2 · 𝑝𝑐ℎ𝑝,𝑛𝑐ℎ𝑝,𝑡)) · 𝛥𝑡 

𝑅 · 𝑇𝐻2
𝑉𝐻2

An upper and lower limit for the power charged in the hydrogen storage ∀𝑡 ∈ 𝑇; 

0  ≤ 𝑝ℎ𝑠,𝑡

𝑐ℎ    ≤ 𝑢𝑒𝑙,𝑡

𝐻2   ⋅ 𝑃ℎ𝑠 

An upper and lower limit for the power discharged in the hydrogen storage ∀𝑡 ∈ 𝑇; 

0  ≤ 𝑝ℎ𝑠,𝑡

𝑑𝑐ℎ   ≤ (1 − 𝑢𝑒𝑙,𝑡

𝐻2 )  ⋅ 𝑃ℎ𝑠 

Source: Modification of the model from Nojavan and Zare (2018). 

Boilers 

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Table 81. Boilers constraints for the Operational model 

Term 

Eq.132   
High thermal 
balance 

Eq.133 
Thermal 
balance 

Eq.134 
Bounds h2 

Eq.135 
Bounds gas 

Eq.136 
Boiler bound 

Constraints 

High thermal balance ∀𝒕 ∈ 𝑻: 

ℎ𝑖𝑔ℎ · 𝐻𝑏
𝑔𝑏,𝑡

𝐺 + ℎ2𝑏,𝑡

ℎ𝑖𝑔ℎ · 𝐻𝑏

ℎ2+ =   𝐻𝑡𝑏𝑙,𝑡 

𝐻

Thermal balance ∀𝒕 ∈ 𝑻: 

ℎ𝑏,𝑡 = ℎ2𝑏,𝑡 · 𝐻𝑏

𝐺 
ℎ2 + 𝑔𝑏,𝑡 · 𝐻𝑏

An upper and lower limit for the hydrogen ∀𝒕 ∈ 𝑻. 

0 ≤ ℎ2𝑏,𝑡 ≤   𝑃𝑖𝑛𝑠𝑡

𝑏

· 𝑀 · 𝑥𝑏,𝑡 

An upper and lower limit for the ga ∀𝒕 ∈ 𝑻 s. 

0 ≤ 𝑔𝑏,𝑡 ≤ 𝑃𝑖𝑛𝑠𝑡

𝑏

· 𝑀 · (1 − 𝑥𝑏,𝑡) 

An upper and lower limit for the thermal power of the boiler ∀𝒕 ∈ 𝑻; 

0 ≤ ℎ𝑏,𝑡 ≤ 𝑃𝑖𝑛𝑠𝑡

𝑏

Source: own elaboration. 

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195 

 
 
 
   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Annex 3. Technical parameters for energy assets in the investment and operational models  

The  parameters  used  for  each  energy  asset  category  are  presented  below,  highlighting  in  yellow  those 
included  in  the  investment  model  and  in  green  those  used  in  the  operational  one.  The  parameters  without 
colour are used in both models. 

Only investment. 

Only operational. 

Both models. 

In addition to the presented parameters, the operational model requires as inputs the installed capacity per 
technology and year decided by the investment model. This is not always indicated in the presented tables but 
it must be considered as a required input. Moreover, there are some yearly, daily or hourly vectors that are 
also  inputted  to  the  model  and  are  not  discussed  in  this  document  as  the  assumptions  behind  these  data 
have been already discussed the main document body and are available at the Annex database. 

For the investment model, all technologies have a parameter indicating the area occupied per unit of capacity 
installed. However, this area is only considered relevant when dealing with ground-mounted solar PV and wind 
turbines as they  compete for the same available surface. Furthermore, rooftop solar PV is restricted by the 
available rooftop space. In the industrial archetype, the area occupied by the hydrogen storage is also added 
as a constraint related to the available land space. For all other technologies, a negligible area value is used 
(1E-20) to make their space usage insignificant to the decision-making process. 

Solar Photovoltaics 

Solar PV technologies are  distinguished by the equipment location, using different parameters  whether it is 
installed on rooftop or on the ground, as the investment model decides the installed capacity considering the 
available  surface  for  each  case.  Weather  data  and  other  parameters  needed  to  calculate  generated  power 
from  solar  irradiation  are  not  given  as  the  solar  production  is  calculated  based  on  the  Load  Factor  Curves 
available at the Annex database. 

Table 82. Scalar parameters for PV solar technologies 

Parameter 

Description 

Value 

Units 

ETA_PV_ROOF  Efficiency of PV solar systems in rooftop. 

ETA_PV_LAND  Efficiency of PV solar systems ground mounted. 

100% 

100% 

% 

% 

A_PV_ROOF 

Area per capacity unit of PV solar rooftop. 

5.10 

m2/kWe 

A_PV_LAND 

Area per capacity unit of ground-mounted PV solar. 

29.4 

m2/kWe 

Source: Own elaboration with data from Drücke et al. (2021); Urbina (2014); Müller et al. (2021); and Cagle et al. (2022). 

As observed in Table 82, efficiency values are set at 100% as the Load factor curve already incorporates the 
typical  PV  solar  panels  efficiency.  Using  the  provided  hourly  load  factors  for  solar  PV,  an  annual  capacity 
factor  of  10.9%  is  calculated  for  the  German  case  and  18.3%  for  Spain.  These  values  are  close  to  the 
average  capacity  factors  reported  for  both  countries,  which  varies  between  10%  and  14%  for  Germany 
(Drücke  et  al.,  2021)  and  is  estimated  above  20%  for  Spain(Urbina,  2014).  The  values  used  for  MODECO 
correspond  to  a  specific  region  within  the  country  and  not  an  average  national  value,  which  explains  the 
discrepancies. 

Regarding  the  surface  used  per  type  of  solar  PV  installation,  a  value  of  5.052  m2/kWe  is  established  for 
rooftop systems based on the value defined by Müller et al. (2021) for glass-back sheet modules. For ground 
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mounted  systems,  Cagle  et  al.  (2022)  proposed  a  value  of  34  We/m2  (equivalent  to  29.4  m2/kWe).  It  is 
assumed  that  PV  systems  on  the  ground  require  a  larger  surface  considering  the  needed  space  between 
module lines. 

Wind turbines 

Onshore  wind turbine  investments  are  possible  in  the  Industrial  polygon,  Rural  town  and Virtual  community 
archetypes,  where  two  types  of  turbines  can  be  installed  based  on  their  specific  capacity  which  in  turn  is 
related to the turbine’s rotor diameter17.  The LOW specific capacity is considered to have a hub height of 200 
m, and the HIGH specific capacity a hub height of 50 m following the criteria used by the authors of the wind 
investment and operational costs (Ioannis Tsiropoulos,  Dalius Tarvydas, and Andreas Zucker 2018).  The two 
models  differ  in  the  required  investment  per  technology,  but  also  in  their  power  generation  and  land  use 
efficiencies. 

Table 83. Scalar parameters for Wind turbine technologies 

Parameter 

Description 

Value 

Units 

ETA_WT_LOW  Efficiency of wind turbines with LOW specific capacity. 

ETA_WT_HIGH  Efficiency of wind turbines with HIGH specific capacity 

A_WT_LOW 

Area per capacity unit of wind turbines LOW. 

A_WT_HIGH 

Area per capacity unit of wind turbines HIGH. 

100% 

100% 

% 

% 

160 

m2/kWe 

67.5 

m2/kWe 

Source: Own elaboration with data from Ioannis Tsiropoulos, Dalius Tarvydas, and Andreas Zucker (2018); Dalla Longa et al. (2018); Sun, 
Yang, and Gao (2019); Obane, Nagai, and Asano (2020). 

As done with solar, a 100% value is used for the wind turbines efficiencies (ETA_WT_LOW and ETA_WT_HIGH) 
given  that  the  actual  efficiency  is  already  incorporated  in  the  load  factor  values.  The  area  occupied  per 
installed capacity unit is established using a reference rotor diameter (RD) defined for each wind turbine type. 
The  HIGH  specific  capacity  turbine  is assumed  to  have  a  rotor diameter of  90  meters based  on  the  Vestas 
V90 model used as a reference for large turbines (base capacity of 3 MW) in a JRC study on wind potential in 
Europe (Dalla Longa et al., 2018). The LOW specific capacity model is assumed to have a rotor diameter of 40 
meters as defined for small-sized turbines (base capacity of 250 kWe) in the aforementioned JRC’s study. The 
land surface needed per each turbine unit is calculated as 25RD2 based  on the optimal value suggested by 
Sun,  Yang,  and  Gao  (2019)  A  similar  relation  (30RD2)  is  suggested  by  Obane,  Nagai,  and  Asano  (2020).To 
obtained  the  area  per  capacity  unit,  the  obtained  surface  is  divided  by  the  applicable  reference  capacity, 
obtaining the values described in Table 83. 

Smart V2G Chargers 

Most of the scalar parameters required for the V2G chargers modelling are presented in Section 3.3.2, except 
for the State of Charge (SOC) operational range for the individual EV units (SOC_MAX_EV and SOC_MIN_EV), 
which is set as 95%-5% a suggested by Wang et al. (2020) and Fan et al. (2019). The SOC level of the EV 
arriving  (SOC_INI_EV)  and  departing  (SOC_FIN_EV)  from  the  charging  station  is  set  based  on  the  findings 
from  Corchero  García  (2015)  as  explained  in  this  document.  The  maximum  charging/discharging  power  at 
individual  charger  correspond  to  the  charging  stations  capacity  (11  kWe)  assumed  for  V2G  chargers.  The 
charging and discharging efficiencies are considered 95%. 

Additionally, the models require to establish the initial number of EV at the start of the day (EV_CON_INI) as 
well as the associated aggregated energy capacity to that number of vehicles. The first is set as zero for the 
investment model as the definitive number of installed chargers is unknown prior to the optimization process. 
For the operational model, in which the number of installed chargers is a given input, it is assumed that at the 
start of the day (00:00), 25% of the installed chargers are occupied. 

17 A wind turbine’s specific capacity or specific power is a parameter that relates the swept area of its rotor to the installed power (watts). 
It is measure in watts per square meter (W/m2) (Bolinger et al., 2021). 

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Table 84. Scalar parameters for EV smart chargers 

Parameter 

Description 

Value 

Units 

ETA_CH_V2G 

Charging efficiency of EV batteries. 

ETA_DCH_V2G 

Discharging efficiency of EV batteries. 

A_V2G 

Surface occupied by an individual charger 
(disregarded in the final scenarios) 

95% 

95% 

% 

% 

1E-20  m2/unit 

E_B_V2G 

Energy capacity of individual EV batteries. 

Calculated based on 
average fleet capacity. 

kWe 

P_MAX_CH_V2G 

Maximum charging/discharging at individual 
charger 

EV_CON_INI 

Initial number of EV (previous to optimization) at 
the start of the day (00:00). 

11 

kWe 

0 

EV 
number 

EV_POOL_INI 

Aggregated energy capacity of battery pool at the 
start of the day (00:00). 

EV_CON_INI *E_B_V2G 

kWe 

SOC_MAX_EV 

Maximum SOC for individual EV. 

SOC_MIN_EV 

Minimum SOC for individual EV. 

SOC_INI_EV 

SOC level of individual EV arriving at the charging 
station. 

SOC_FIN_EV 

SOC level of individual EV departing at the 
charging station. 

Source: Own elaboration with data from Wang et al. (2020); Fan et al. (2019); and Corchero García (2015). 

95% 

5% 

% 

% 

58% 

% 

84% 

% 

Combined Heat and Power 

In all archetypes, two configurations – small and large units – of Combined Heat and Power (CHP) fuelled by 
gaseous  fuels  (natural  gas  or  hydrogen)  were  initially  considered  as  a  potential  investment  option  for  all 
archetypes  except  the  Virtual  community.  However,  after  modelling  the  archetype’s  electrical  and  heat 
demand,  only  the  small-sized  configuration  (<  20  MWe)  is  kept.  The  same  is  done  for  the  biomass-fuelled 
CHP units, which are considered an investment option only in the Rural town archetype. 

 Given the complexities of the investment decision model, a simplified mathematical model is used for both 
CHP  types,  assuming  a  linear  relationship  between  heat  and  electrical  production,  and  varying  mainly  the 
thermal and electrical efficiencies depending on the CHP’s assumed configuration per type of fuel used. For 
the  operational  model, in  which  the  installed  capacity  is  already  known, a  more  complex  model  is selected, 
using  a  trapezoid  with  four  theoretical  operating  points  representing  the  unit’s  Feasible  Operational  Region 
(FOR). As noted in Table 85, the higher complexity of the approach used in the operational model translates 
into a higher number of inputs than in the investment model. 

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198 

 
 
 
 
 
 
Table 85. Scalar parameters for biomass-fuelled CHP 

Type 

Parameter 

Description 

Value 

Units 

CHP_R_POWER_B 

Installed 
fuelled CHP 

capacity 

for  biomass-

Result from investment 
model 

kWe 

MIN_EL_B 

Minimum operational power output 

CHP_R_POWER_B * 0.4 

kWe 

MAX_EL_B 

Maximum operational power output 

CHP_R_POWER_B * 1 

kWe 

MAX_TH_B 

Maximum useful heat output 

CHP_R_POWER_B * 0.85 * 
[1/CHP_CONV_B] 

kWt 

B_POINT_B 

Theoretical operating point B 

MAX_TH_B 

kWt 

C_POINT_B 

Theoretical operating point C 

D_POINT_B * 
[1/CHP_CONV_B] 

kWt 

D_POINT_B 

Theoretical operating point D 

MIN_EL_B 

kWe 

U_INI_B 

Initial  state  of  CHP  biomass  at 
optimization start (on/off) 

1 

[1,0] 

B_CONV_EL 

Fuel to electricity ratio (biomass 

0.1927 

kWe/mol 

B_CHP_CONV 

Heat to power ratio (CHP -biomass) 

2.2222 

kWt/kWe 

ETA_EL_CHP_B 

HP  electrical  efficiency 
biomass) 

(CHP 

- 

ETA_H_CHP_B 

CHP heat efficiency (CHP - biomass) 

0.35 

0.78 

% 

% 

C_OFF_B 

CHP shutdown cost (CHP -biomass) 

0 

Euros 

C_ON_B 

CHP start-up cost (CHP - biomass) 

See Eq. 138 

Euros 

)
e
W
M
0
2

<
(

L
L
A
M
S

T_SD_B 

Minimum off time (CHP biomass) 

T_SU_B 

Minimum on time ( CHP - biomass) 

MAX_ON_B 

Maximum  amount  of  times  per  day 
that the CHP unit can be turn off and 
turn on again 

3 

4 

h 

h 

1 

Units 

Source:  Own  elaboration  with  data  from  Algie  and  Wong  (2002);  Alipour,  Zare,  and  Mohammadi-Ivatloo  (2014);  Nazari-Heris, 
Mohammadi-ivatloo,  and  Nazarpour  (2019);  Eurostat  (2017);  Sims  et  al.  (2007);  Forest  Research  (2022);  Pettersen  (1984);  Dimoulkas 
and Amelin (2015); Yu, Zhang, and Guan (2022); Gambarotta et al. (2015); Facci, Andreassi, and Ubertini (2014); U.S. Energy Information 
Agency (2020); and Ghaffarpour et al. (2018). 

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Table 86 Scalar parameters for gas-fuelled CHP 

Type 

Parameter 

Description 

Value 

Units 

CHP_R_POWER_G 

Installed  capacity  for  gas-fuelled 
CHP 

Result from investment 
model 

kWe 

MIN_EL_G 

Minimum operational power output 

CHP_R_POWER_G * 0.4 

kWe 

MAX_EL_G 

Maximum operational power output 

CHP_R_POWER_G * 1 

kWe 

MAX_TH_G 

Maximum useful heat output 

CHP_R_POWER_G * 0.85 * 
[1/CHP_CONV_B] 

kWt 

B_POINT_G 

Theoretical operating point B 

MAX_TH_G 

kWt 

C_POINT_G 

Theoretical operating point C 

D_POINT_G * 
[1/CHP_CONV_G] 

kWt 

D_POINT_G 

Theoretical operating point D 

MIN_EL_G 

kWe 

U_INI_G 

Initial 
optimization start (on/off) 

state  of  CHP  gas  at 

[1,0] 

1 

G_CONV_EL 

Fuel to electricity ratio (natural gas) 

0.09832 

kWe/mol 

H_CONV_EL 

Fuel to electricity ratio (hydrogen) 

0.03033 

kWe/mol 

G_CHP_CONV 

Heat to power ratio (CHP -gas) 

1.81818 

kWt/kWe 

ETA_EL_CHP_G 

HP  electrical  efficiency 
biomass) 

(CHP 

- 

ETA_H_CHP_G 

CHP heat efficiency (CHP - biomass) 

C_OFF_G 

CHP shutdown cost (CHP -biomass) 

0.42 

0.76 

% 

% 

0 

Euros 

C_ON_G 

CHP start-up cost (CHP - biomass) 

See Eq. 138 

Euros 

)
e
W
M
0
2

<
(

L
L
A
M
S

T_SD_G 

Minimum off time (CHP gas) 

T_SU_G 

Minimum on time ( CHP – gas) 

MAX_ON_G 

Maximum  amount  of  times  per  day 
that the CHP unit can be turn off and 
turn on again 

3 

4 

h 

h 

1 

Units 

Source:  Own  elaboration  with  data  from  Algie  and  Wong  (2002);  Alipour,  Zare,  and  Mohammadi-Ivatloo  (2014);  Nazari-Heris, 
Mohammadi-ivatloo,  and  Nazarpour  (2019);  Eurostat  (2017);  Sims  et  al.  (2007);  EUROGAS  (2011);  Dimoulkas  and  Amelin  (2015);  Yu, 
Zhang, and Guan  (2022); Gambarotta et al.  (2015);  Facci,  Andreassi,  and  Ubertini  (2014);  U.S.  Energy  Information  Agency  (2020);  and 
Ghaffarpour et al. (2018). 

The technical parameters applicable per fuel differ as they represent different CHP configurations. In the case 
of natural gas CHP, the small-sized equipment is assumed to be a gas turbine associated to a Heat Recovery 
Steam Generator (HRSG) from which heat is transferred to the district heating network (Figure 87). In the case 
of the biomass units considered for the Rural town archetype, a regular steam turbine cycle coupled with a 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

200 

 
 
 
 
 
 
 
HRSG unit (Figure 88) is considered. As small-sized biomass units are now the only option, pellets are used as 
the default biomass fuel type. 

Figure 87. CHP assumed configuration considered for small natural gas-fuelled units. 

Source: Own elaboration. 

Figure 88. CHP assumed configuration for small biomass-fuelled units. 

Source: Own elaboration. 

The parameters referring to the theoretical operational points are based on the simplified feasible operational 
region  defined  for  both  CHP.  The  required  operating  points  (B_POINT,  C_POINT,  D_POINT)  are  based  on  the 
simplified  model  proposed  by  Algie  and  Wong  (2002);  Alipour,  Zare,  and  Mohammadi-Ivatloo  (2014);  and 
Nazari-Heris, Mohammadi-ivatloo, and Nazarpour (2019).The trapezoid FOR and the required operating points 
are  indicated  in  Figure  89.  As  observed,  these  can  be  calculated  as  a  percentage  of  the  equipment’s  rated 
power under normal conditions; which is the value obtained by the investment model. Point A represents the 
upper limit of the active  power output of the CHP  unit,  defined as 115% the  rated  power, based on typical 
requirements for rotating units as explained by (Algie and Wong, 2002). In the parameters listed in Table 85 
and Table 86, Point A can be considered the unit’s maximum electrical output (MAX_EL_G and MAX_EL_B) and 
Point  B  is  the  amount  of  heat  produced  at  the  rated  power  under  normal  conditions.  This  is  calculated 
considering  the  electricity  to  useful  heat  ratio  (CHP_CONV)  defined  for  each  case.  Finally,  Point  D  is  set  as 
50% the rated power, and Point C, the corresponding heat production at that point. 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

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Figure 89. Simplified feasible operational region considered for units (operating points in green) 

Source: Own elaboration based on the model proposed by Algie and Wong (2002). 

The  fuel  to  electricity  (B_CONV_EL,  G_CONV_EL,  H_CONV_EL)  and  power  to  heat  (CHP_CONV_B, 
CHP_CONV_G)  ratios  are  calculated  for  each  CHP  configuration  considered  in  MODECO,  based  on  the 
applicable efficiency values. For the fuel to electricity ratio, the system’s electrical efficiency (ƞ) is considered 
as well as the  fuel’s Low Heating Value (LHV),  density (ρ) and molar mass (M) as indicated in Eq. 137. The 
fuel to heat ratio is defined based on the default power-to-heat values established in the reporting template 
for heat and power generation aligned with Directive 2012/27/EU of the European Parliament and the Council 
of  25  October  2012  on  energy  efficiency  (Eurostat,  2017).  The  considered  efficiency  values  and  fuel 
characteristics used to calculate the fuel-to-electricity ratio are listed in Table 87. 

E1. 137 Fuel to electricity ratio for fuel X (biomass, natural gas or hydrogen) 

𝑋_𝐶𝑂𝑁𝑉_𝐸𝐿 = 𝐿𝐻𝑉  [

𝑘𝑊ℎ

𝑚3 ] ∗  

1

𝜌

[

𝑚3
𝑘𝑔

] ∗ 𝑀 [

𝑘𝑔

𝑚𝑜𝑙

] ∗   ƞ𝑒𝑙  

Table 87 Efficiency and fuel characteristics considered for each CHP configuration 

CHP 
size 

Fuel 

Configuration 

Ƞel [%] 

LHV 
[kWh/m3] 

ρ [kg/m3] 

M [kg/mol] 

Small 

Natural gas 

Fig. 1 

Large 

Natural gas 

Fig. 2 

Small 

Hydrogen 

Fig.1 

Large 

Hydrogen 

Fig. 2 

Small 

Pellets 

Fig. 3 

Large 

Woodchips 

Fig. 3 

42% 

55% 

42% 

55% 

35% 

35% 

9.749 

9.749 

2.997 

2.997 

875 

3,120 

0.668 

0.01604 

0.668 

0.01604 

0.084 

0.00202 

0.084 

0.00202 

250 

650 

0.15731 

0.15731 

Source:  efficiency values correspond to the upper limits per technology stated by Sims et al. (2007); LHV for natural gas is taken from 
EUROGAS  (2011),  and  density  at  Normal  Temperature  and  Pressure  (NTP)  and  molar  mass  correspond  to  the  values  applicable  to 
methane  (CH4);  LHV  and  density  for  biomass  is  taken  from    Forest  Research  (2022)  and  the  molar  mass  from  biomass  is  roughly 
approximated  by  considering  the  molar  mass  of  cellulose  (C6H10O5,  162,139  g/mol),  hemicellulose  (C5H8O4,  132.114  g/mol)  and  lignin 
(C9H7.92O2.40(OCH3)0.92,  183.03  g/mol)  –  the  latter  defined  based  on  the  composition  found  in  spruce  (Picea  abies)  samples  reported  by 
Pettersen (1984) -considering a distribution of 50%, 30%, and 20%, respectively, based on the typical shares for dry wood presented by 
Pettersen (1984). 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

202 

 
 
 
The equipment minimum up and down times are set as 4 and 3 hours, respectively, as done in Dimoulkas and 
Amelin  (2015).  U_INI_G  and  U_INI_B  are  binary  variables  indicated  the  state  of  the  CHP  unit  prior  to  the 
optimization [1 = on, 0 = off]. Shutdown costs are assumed as zero for all cases, whereas start-up costs are 
considered  as a  value  dependent  on  the  system’s installed  capacity, which  is why  different  approaches are 
taken  for  the  investment  and  operational  models.  In  the  first  case,  no  costs  are  considered  and  instead  a 
restriction  is  imposed  over  the  number  of  times  per  day  that  the  unit  can  be  turn  off  and  turn  on.  This  is 
assumed  as  one  per  day  given  that  generators  do  not  usually  start  up  more  than  twice  per  day  (Yu  et  al., 
2022), and this is a common assumption made in similar optimization problems. 

Finally,  the  start-up  costs  considered  for  the  operational  model  are  calculated  considering  the  extra  fuel 
required to warm-up the engines –assumed as the required fuel to operate the  machine for 10 minutes at 
nominal power as done by Gambarotta et al. (2015) – plus the additional equipment wear costs. In the work 
done by Facci, Andreassi, and Ubertini (2014), the latter costs are hypothesized as equivalent to the value of 
one hour of maintenance. A similar approach is done in MODECO assuming that maintenance costs for this 
type of technology represent around 50% of the total operational expenses (U.S. Energy Information Agency, 
2020)–  without  considering  fuel  costs  –  and  a  maintenance  period  of  48  hours  per  year  as  done  by 
Ghaffarpour et al. (2018)As the operational expenses (OPEX) are defined as a percentage of the investment 
cost (CAPEX), and the CAPEX depends on the final rated power installed (MAX_EL_B), the Eq. 138 is applied to 
calculate the start-up cost for each case using the applicable parameters to each CHP type (gas or biomass). 

Eq. 138 CHP start-up cost calculation 

𝑆𝑡𝑎𝑟𝑡𝑢𝑝 𝑐𝑜𝑠𝑡  =  

1 [ℎ]
6

∗ 𝐶𝐻𝑃_𝑅_𝑃𝑂𝑊𝐸𝑅[𝑘𝑊𝑒𝑙]   ∗

1

𝐶𝑂𝑁𝑉_𝐸𝐿 [

𝑘𝑊ℎ𝑒𝑙
𝑚𝑜𝑙

]

∗  𝐹𝑈𝐸𝐿_𝐶𝑂𝑆𝑇 [

𝐸𝑈𝑅
𝑚𝑜𝑙

] + 

                                                          𝐶𝐴𝑃𝐸𝑋 [

𝐸𝑈𝑅
𝑘𝑊𝑒𝑙

] ∗ 𝐶𝐻𝑃_𝑅_𝑃𝑂𝑊𝐸𝑅[𝑘𝑊𝑒𝑙]   ∗ %𝑂𝑃𝐸𝑋 ∗  

0.5

48

Electrolyzer 

The  electrolyzer  efficiency  is  set  as  67.5%  considering  that  the  power-to-hydrogen  efficiency  for  PEM 
electrolyzer ranges between 65% and 70% for PEM technologies (Hu et al., 2022). The same authors report 
that the minimum operating load for PEM electrolyzers can be defined between 0-10%, so the upper limit is 
used as an assumption for the P_MIN_PCTG_EL parameter. For the Low Heating Value (LHV) of hydrogen gas, 
the value reported by Rau, Willauer, and Ren (2018) is used. For the operational model, the upper power limit 
considered is the installed rated power defined by the investment model, and the lower limit is based on the 
defined minimum operating load. 

Table 88 Scalar parameters for the PEM electrolyzer 

Parameter 

Description 

Value 

Units 

EL_R_POWER 

Rated power 

Result from investment 

kWe 

ETA_EL 

A_EL 

Power-to-hydrogen efficiency. 

Area per unit capacity installed. 

MAX_P_EL 

Maximum power. 

MIN_P_EL 

Minimum power. 

67.5% 

% 

1E-20  m2/kWe 

EL_R_POWER 

kWe 

EL_R_POWER * 
P_MIN_PCTG_EL 

kWe 

P_MIN_PCTG_EL 

Minimum operating load. 

0.1 

% 

LHV_H2 

Lower heating value of hydrogen (H2) 

0.067 

kWh/mol 

Source: Own elaboration with data from Hu et al. (2022); and Rau, Willauer, and Ren (2018). 

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203 

 
 
 
   
 
Hydrogen tank 

The tank’s technical characteristics are defined based on the information presented by (Nojavan et al., 2017). 
The maximum and minimum pressure inside the vessel are defined as 1,380,000 Pa and 200,000 Pa, and the 
mean temperature is set at 313 K. The initial daily pressure and minimum daily pressure are both stated as 
1,000,000  Pa.  The  area  occupied  per  unit  of  volume  storage  is  (A_HS)  is  defined  considering  a  vertical 
orientation  and  the  diameter  and  nominal  volume  of  a  commercial  hydrogen  storage  tank  for  industrial 
applications (Figure 90). It is assumed that the tank requires a square surface whose sides’ lengths are equal 
to the tank diameter. 

Figure 90. Reference hydrogen tank dimensions and occupied surface area 

Source: Own elaboration based on the technical sheet from Lapesa Grupo Empresarial (n.d.) 

Finally,  the  ratio  between  tank  volume  and  the  maximum  hydrogen  hourly  flow  (C_RATE_HS)  is  calculated 
considering  the  density  of  hydrogen  at  13.8  bar  and  313  K  (1.16600  kg/m3)  and  the  gas  molar  mass 
(0.00202 kg/mol). The density value is calculated using the data reported in the Hydrogen Tools published by 
the U.S. Pacific Northwest National Laboratory (n.d.). A discharge duration of 24 hours is considered. No losses 
from the storage unit are considered so efficiencies are set as 100% (ETA_CH_HS, ETA_DCH_HS). 

Table 89 Scalar parameters for the Hydrogen storage tank 

Parameter 

Description 

Value 

Units 

ETA_CH_HS 

Charging efficiency 

ETA_DCH_HS 

Discharging efficiency 

A_HS 

Area  per  volumetric  unit  (m3)  of 
hydrogen storage installed 

1 

1 

% 

% 

0.09 

m2/m3 

Q_MAX_HS 

Maximum pressure inside the tank 

1380000 

Pa 

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204 

 
 
 
 
 
Parameter 

Description 

Value 

Units 

Q_MIN_HS 

Minimum pressure inside the tank 

200000 

Pa 

R_GAS_CONSTANT  R gas constant. 

8.3145 

m3 Pa/K mol 

TA_MEAN 

Mean temperature inside the vessel 

313 

K 

P_MAX_CH_HS 

Maximum hydrogen rate inflow 

Result from investment 

mol/h 

P_MAX_DCH_HS 

Maximum hydrogen rate outflow 

Result from investment 

mol/h 

Q_INI_HS 

Initial daily pressure 

Q_FIN_HS 

Minimum final daily pressure 

C_RATE_HS 

Ratio  between 
maximum  hydrogen  hourly 
(in/out) 

tank  volume  and 
flow 

1000000 

1000000 

Pa 

Pa 

24.07499 

mol/ m3·h 

Source: Own elaboration with data from Nojavan, Zare, and Mohammadi-Ivatloo (2017); Lapesa Grupo Empresarial (n.d.); and U.S. Pacific 
Northwest National Laboratory (n.d.). 

Batteries 

The technical parameters for Li.-ion batteries are listed in Table 90, as observed, all parameters are equal for 
energy  and  power-based  equipment  except  for  the  C-rate,  which  is  based  considering  the  applications 
described  by  Tsiropoulos,  Tarvydas,  and  Lebedeva  (2018).  The  charging  and  discharging  efficiencies 
(ETA_DCH_ES, ETA_CH_ES), and the maximum and minimum State of Charge (SOC) are based on the values 
projected for 2030 by (Nastasi et al., 2021). The initial (SOC_INI_ES) and final (SOC_FIN_ES) are defined as 
50% within MODECO. 

Table 90 Scalar parameters for energy and power based batteries (0.35 C-rate) 

Parameter 

Description 

Value 

Units 

ETA_DCH_ES_ENERGY  Discharging efficiency for energy-based batteries. 

ETA_CH_ES_ENERGY 

Charging efficiency for energy-based batteries. 

97.5% 

97.5% 

% 

% 

MIN_CH_ENERGY 

Minimum charging power for energy-based batteries. 

0 

kWh 

MAX_CH_ENERGY 

Maximum charging power for energy-based batteries. 

kWh 

MIN_DCH_ENERGY 

Minimum discharging power for energy-based batteries. 

0 

kWh 

MAX_DCH_ENERGY 

Maximum discharging power for energy-based batteries. 

kWh 

SOC_INI_ES_ENERGY 

Initial State of Charge (SOC) at the start of the day. 

SOC_FIN_ES_ENERGY 

Final State of Charge (SOC) at the end of the day. 

C_RATE_ES_ENERGY 

C-rate for energy-based batteries 

SOC_MAX_ES_ENERGY 

Maximum  State  of  Charge 
batteries. 

(SOC)  for  energy-based 

205 

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50% 

50% 

0.35 

95% 

% 

% 

- 

% 

 
 
 
  
  
Parameter 

Description 

Value 

Units 

SOC_MIN_ES_ENERGY  Minimum State of Charge (SOC) for energy-based batteries. 

5% 

ETA_DCH_ES_POWER 

Discharging efficiency for power-based batteries. 

ETA_CH_ES_POWER 

Charging efficiency for power-based batteries. 

97.5% 

97.5% 

% 

% 

% 

MIN_CH_POWER 

Minimum charging power for power-based batteries. 

0 

kWh 

MAX_CH_POWER 

Maximum charging power for power-based batteries. 

kWh 

MIN_DCH_POWER 

Minimum discharging power for power-based batteries. 

0 

kWh 

MAX_DCH_POWER 

Maximum discharging power for power-based batteries. 

kWh 

SOC_INI_ES_POWER 

Initial State of Charge (SOC) at the start of the day. 

SOC_FIN_ES_POWER 

Final State of Charge (SOC) at the end of the day. 

C_RATE_ES_POWER 

C-rate for power-based batteries. 

50% 

50% 

0.35 

SOC_MAX_ES_POWER  Maximum State of Charge (SOC) for power-based batteries. 

95% 

SOC_MIN_ES_POWER  Minimum State of Charge (SOC) for power-based batteries. 

5% 

Source: Own elaboration with data from Nastasi et al. (2021); Tsiropoulos, Tarvydas, and Lebedeva (2018) 

% 

% 

- 

% 

% 

Boilers 

The  fuel-to-heat  ratios  shown  in  Table  91  are  calculated  for  natural  gas  and  hydrogen  considering  the 
physical properties of both fuels at NTP conditions, as well as the combustion efficiency (ƞcomb) – assumed as 
85% for residential (Vakkilainen, 2017) and industrial (Vanwortswinkel and Wouter, 2010) boilers – as shown 
in Eq. 139. The data for natural gas can be consulted in Table 87. In the case of Hydrogen, a LHV of 2.997 
kWh/m3, density (ρ) of 0.090 and molar mass (M) of 0.00202 kg/mol are considered. Finally, the model also 
requires a limit on the maximum thermal capacity from boilers installed in the community. This is set equal to 
the capacity available in the starting year  (2025), as afterwards the heat generated from boilers decreases 
due  to  the  assumed  growth  in  other  technologies  (heat  pumps  and  solar  thermal),  which  is  defined 
exogenously. 

Table 91 Scalar parameters for boilers 

Parameter 

Description 

Value 

Units 

G_CONV_B 

(natural  gas)  mol  to  heat  ratio 

Fuel 
residential and commercial boilers. 

in 

H_CONV_B 

Fuel (hydrogen) mol to  heat  ratio in residential 
and commercial boilers. 

G_CONV_IB 

Fuel (natural gas) mol to heat ratio in industrial 
boilers. 

H_CONV_IB 

Fuel  (hydrogen)  mol  to  heat  ratio  in  industrial 
boilers. 

0.22388 

kWt/mol 

0.068604 

kWt/mol 

0.201320 

kWt/mol 

0.062104 

kWt/mol 

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206 

 
 
  
  
 
P_INST_B_INI  Boilers thermal capacity installed each year. 

P_MAX_B 

Maximum boiler capacity installed. 

Defined each year based 
on demand. 

Equal to installed in 
2025. 

kWt 

kWt 

Source: Own elaboration with data from Vakkilainen (2017); Vanwortswinkel and Wouter (2010). 

Eq. 139 Fuel to electricity ratio per fuel (biomass, natural gas or hydrogen) 

𝐹𝑈𝐸𝐿_𝐶𝑂𝑁𝑉_𝐵 =

𝐿𝐻𝑉𝑓𝑢𝑒𝑙 [

𝑘𝑊ℎ
𝑚3 ]∗𝑀𝑓𝑢𝑒𝑙 [
𝑘𝑔
𝑚3]

𝜌𝑓𝑢𝑒𝑙 [

𝑘𝑔
𝑚𝑜𝑙

]

∗ ƞ𝑐𝑜𝑚𝑏   

As the considered residential boiler costs are given per unit basis in the used database, these are converted to 
euros per kilowatt thermal to be used in the investment model. To do so, it is assumed a thermal load of 25 
kWt per single-family household (Schiro et al., 2020).For flats, a smaller number is assumed (20 kWt) given 
their smaller surface. In the  case of the boilers in  multifamily buildings, the boiler unit in which costs were 
based are scaled to serve all dwellings in the building. Thus, an average number of 12 dwellings per building 
unit  is  assumed  considering  the  available  data  reported  in  the  Entranze  database  for  European  countries 
(Entranze  Project,  2008).  Furthermore,  it  must  be  considered  than  in  the  original  database  costs  are 
differentiated  per multifamily  and single-family  units, but  in  MODECO’s investment  model  only  one  type  of 
boiler is considered so the average cost between these two boiler types is assumed. For industrial boilers, the 
costs are already given per kilowatt thermal basis, so no conversion is needed. 

Demand response 

Finally, the parameters used to model the demand response program are listed below. The only value, which 
was  not  mentioned  in  that  document  is  the  maximum  number  of  activations  per  day  that  is  set  as  3 
activations per day. This value is in line with the range (1-12 activations per day) analysed by Prüggler (2013) 
and  is  aligned  with  the  upper  value  proposed  by  Zimmermann  et  al.  (2016)  for  the  maximum  number  of 
activations expected for shiftable loads (1,100 per year or 3.014 per day). 

Table 92 Scalar parameters for demand response 

Parameter 

Description 

Value 

Units 

C_DR 

Variable cost for demand response. 

.010 

€/kWh 

S_INC 

Available load increase share. 

S_DEC 

Available load decrease share. 

S_FLEX 

Share  from  demand  that  participates 
response. 

in  demand 

U_INC_INI 

Initial state of increment at start of the day. 

U_DEC_INI 

Initial state of decrement at first time of the day. 

T_DR 

Maximum time of demand response activation. 

D_DR 

Maximum  number  of  demand  response  activations  per 
day. 

Source: Own elaboration with data from Prüggler (2013); and Zimmermann et al. (2016). 

75% 

0% 

40% 

0 

0 

3 

3 

% 

% 

% 

[1,0] 

[1,0] 

h 

--- 

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Annex 4. Gap values obtained for the scenarios executed in the EC investment model  

Table 93. Gap values reported by the EC investment model for the base case tariff scenarios 

Country 

Discount 
rate 

Archetype 

No Charges 

TOU 

Bandwidth 

Peak 
Power 

Business park 

< 0,01% 

< 0,01% 

0.17%  < 0,01% 

Industrial polygon 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Germany 

1.3% 

Urban district 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Rural town 

0.65% 

4% 

< 0,01%  < 0,01% 

Virtual community 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Business park 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Industrial polygon 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Spain 

3.0% 

Urban district 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Rural town 

< 0,01% 

< 0,01% 

< 0,01%  < 0,01% 

Virtual community 

0.58% 

< 0,01% 

< 0,01%  < 0,01% 

Source: own elaboration with data from MODECO investment model 

Table 94. Gap values reported by the EC investment model for the price rate sensitivity cases  

Country 

Discount rate 

Archetype 

TOU_Flat  TOU_PPA 

Business park 

< 0,01% 

Industrial polygon 

1.25% 

5% 

Germany 

1.3% 

Urban district 

Rural town 

1.94% 

5.70% 

Source: own elaboration with data from MODECO investment model 

Virtual community 

0.54% 

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208 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 95. Gap values reported by the EC investment model for the discount rate sensitivity cases  

Country 

Discount rate 

Archetype 

TOU 

Bandwidth  Peak power 

Business park 

< 0,01% 

0.13% 

< 0,01% 

Industrial polygon 

< 0,01% 

0.04% 

0.04% 

Germany 

2.5% 

Urban district 

< 0,01% 

< 0,01% 

< 0,01% 

Rural town 

2.2% 

< 0,01% 

0.11% 

Virtual community 

< 0,01% 

< 0,01% 

0.02% 

Source: own elaboration with data from MODECO investment model 

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209 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Annex 5. Gap values obtained for the scenarios executed in the EC operational model  

Table 96. Gap values reported by the EC operational model for the base case tariff scenarios 

Country  Discount rate 

Archetype 

Year 

TOU 

Bandwidth  Peak Power 

Business park 

Industrial polygon 

Urban district 

Rural town 

Virtual community 

2025 

< 
0,01% 

< 
0,01% 

< 
0,01% 

< 0,01% 

0.03% 

< 0,01% 

< 0,01% 

< 0,01% 

< 0,01% 

1.99% 

< 0,01% 

< 0,01% 

< 
0,01% 

< 0,01% 

< 0,01% 

Business park 

0.29% 

< 0,01% 

0.08% 

Germany 

1.3% 

Industrial polygon 

< 
0,01% 

< 0,01% 

< 0,01% 

Urban district 

2030 

0.03% 

< 0,01% 

< 0,01% 

Rural town 

1.72% 

< 0,01% 

0.11% 

Virtual community 

< 
0,01% 

< 0,01% 

< 0,01% 

Business park 

1.05% 

< 0,01% 

0.23% 

Industrial polygon 

< 
0,01% 

< 0,01% 

< 0,01% 

Urban district 

2040 

0.37% 

< 0,01% 

Rural town 

0.49% 

< 0,01% 

0.46% 

0.45% 

Virtual community 

Business park 

Industrial polygon 

Spain 

3.0% 

2025 

Urban district 

Rural town 

Virtual community 

210 

< 
0,01% 

< 
0,01% 

< 
0,01% 

< 
0,01% 

< 0,01% 

< 0,01% 

< 0,01% 

0.58% 

< 0,01% 

< 0,01% 

< 0,01% 

0.08% 

< 0,01% 

0.61% 

0.87% 

< 
0,01% 

< 0,01% 

< 0,01% 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

 
 
 
 
 
 
 
 
Business park 

0.29% 

< 0,01% 

2.42% 

Industrial polygon 

< 
0,01% 

< 0,01% 

< 0,01% 

Urban district 

2030 

1.46% 

< 0,01% 

Rural town 

0.15% 

< 0,01% 

1.99% 

4.04% 

Virtual community 

< 
0,01% 

< 0,01% 

< 0,01% 

Business park 

0.05% 

< 0,01% 

0.44% 

Industrial polygon 

< 
0,01% 

< 0,01% 

< 0,01% 

Urban district 

2040 

0.87% 

< 0,01% 

Rural town 

0.44% 

< 0,01% 

2.26% 

4.78% 

Virtual community 

< 
0,01% 

< 0,01% 

< 0,01% 

Source: own elaboration with data from MODECO operational model 

Study by IREC and R2M Solution under Service Contract no. 942132-IPR-2021 

211 

 
 
 
 
 
 
GETTING IN TOUCH WITH THE EU 

In person 

All over the European Union there are hundreds of Europe Direct centres. You can find the address of the centre nearest you online 
(european-union.europa.eu/contact-eu/meet-us_en). 

On the phone or in writing 

Europe Direct is a service that answers your questions about the European Union. You can contact this service: 

— by freephone: 00 800 6 7 8 9 10 11 (certain operators may charge for these calls), 

— at the following standard number: +32 22999696, 

— via the following form: european-union.europa.eu/contact-eu/write-us_en. 

FINDING INFORMATION ABOUT THE EU 

Online 

Information  about  the  European  Union  in  all  the  official  languages  of  the  EU  is  available  on  the  Europa  website  (european-
union.europa.eu). 

EU publications 

You  can  view  or  order  EU  publications  at  op.europa.eu/en/publications.  Multiple  copies  of  free  publications  can  be  obtained  by 
contacting Europe Direct or your local documentation centre (european-union.europa.eu/contact-eu/meet-us_en). 

EU law and related documents 

For access to legal information from the EU, including all EU law since 1951 in all the official language versions, go to EUR-Lex 
(eur-lex.europa.eu). 

Open data from the EU 

The  portal  data.europa.eu  provides  access  to  open  datasets  from  the  EU  institutions,  bodies  and  agencies.  These  can  be 
downloaded and reused for free, for both commercial and non-commercial purposes. The portal also provides access to a wealth 
of datasets from European countries.