AC/DC hybrid grid modelling enabling a high share of renewables : final report.
Date: 2023-02-06
Institutions: Directorate-General for Energy
Subjects: electrical energy, energy grid, energy research, renewable energy, solar energy, wind energy

AC/DC hybrid grid modelling 
enabling a high share of 
Renewables 

Final report 

1 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AC/DC hybrid grid modelling 
enabling a high share of 
Renewables 

Final Report 

4 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
EUROPEAN COMMISSION 

Prepared for the European Commission, DG ENER,  
under service contract N° ENER/2021/OP/0008-B5/SER/2020-563/SI2.864123 

EUROPEAN COMMISSION 

Directorate-General for Energy 
Directorate B - Just Transition, Consumers, Energy Efficiency and Innovation 
Unit ENER.B5 - Innovation, Research, Digitalisation, Competitiveness 

Contact: Eric Lecomte 

E-mail: eric.lecomte@ec.europa.eu  

European Commission 
B-1049 Brussels 

Authors:  

O. Antoine, L. Papangelis, P. Tielens, K. Karoui (Engie Impact)  
H. Ergun, G. Bastianel, A. Agbemuko, J. Beerten, W. Leterme, D. Van Hertem (KU Leuven/EnergyVille) 

Manuscript completed: November 2022 

First edition: February 2023 

LEGAL NOTICE 

This document has been prepared for the European Commission however it reflects the views only of the authors, and do 
not necessarily reflect the official opinion of the Commission. The Commission does not guarantee the accuracy of the data 
included  in  this  assessment.  Neither  the  Commission  nor  any  person  acting  on  the  Commission’s  behalf  may  be  held 
responsible for the use which may be made of the information contained therein. More information on the European Union is 
available on the Internet (http://www.europa.eu). 

EN PDF    

  ISBN  978-92-76-60277-4      

  doi:10.2833/627100   

  MJ-05-22-426-EN-N 

Luxembourg: Publications Office of the European Union, 2023 

© European Union, 2023  

The  reuse  policy  of  European  Commission  documents  is  implemented  by  the  Commission  Decision  2011/833/EU  of  12 
December 2011 on the reuse of Commission documents (OJ L 330, 14.12.2011, p. 39). Except otherwise noted, the reuse 
of 
is  authorised  under  a  Creative  Commons  Attribution  4.0  International  (CC-BY  4.0)  licence 
(https://creativecommons.org/licenses/by/4.0/).  This  means  that  reuse  is  allowed  provided  appropriate  credit  is  given  and 
any changes are indicated. 

this  document 

For any use or reproduction of elements that are not owned by the European Union, permission may need to be sought 
directly from the respective rightsholders. 

5 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

1.  Executive summary (English) 

Disclaimer 

The  information  and  views  set  out  in  this  report  are  those  of  the  authors  and  do  not 
necessarily  reflect  the  official  opinion  of  the  Commission.  The  Commission  does  not 
guarantee  the  accuracy  of  the  data  included  in  this  study.  Neither  the  Commission    nor  
any  person  acting  on  the  Commission’s  behalf  may  be  held responsible for the use 
which may be made of the information contained therein. 

Context 

The  following  years  will  see  a  massive  increase  in  the  penetration  of  renewable  energy 
sources (RES) in Europe. This is valid for wind (onshore and offshore), solar photovoltaics 
but also other types of renewable resources (e.g. tidal). Most of these renewable energy 
sources  are  interfaced  via  power  electronic  devices  called  inverters  to  the  electrical  grid 
and are generally named Inverter Based Resources (IBRs).  

The  first  main  impact  of  the  increasing  penetration  of  renewable  energy  is  that  the 
electrical  power  is  transmitted  over  longer  distance  (i.e.  from  RES  locations  to  the  load 
centres) and with a higher variability compared to the existing system with large (thermal) 
power plants close to load centres. 

The  second  main  impact  is  that  the  increased  penetration  of  Inverter  Based  Resources 
replaces synchronous machines connected to the network. Firstly, this implies a reduction 
of  the  directly  coupled  energy  stored  in  the  rotating  masses  and  in  the  windings  of  the 
synchronous  generators.  The  fact  to  have  less  mechanical  and  electromagnetic  energy 
temporarily stored in the grid makes the power system more sensitive to disturbances and 
therefore potentially more unstable. The second consequence is that the operation of the 
power  system  is  now  governed  by  the  controls  of  the  power  electronic  inverters,  rather 
than  by  the  natural  response  of  traditional  generators.  This  causes  a  new  paradigm  in 
power system operations and at this moment, there is still no consensus on how to plan 
and  operate  a  large  power  system  with  almost  100%  penetration  of  Inverter  Based 
Resources. There are indeed some mitigation options that could help to improve stability 
of such  systems,  such  as  advanced  controls  of  inverters  or  HVDC1  converters (i.e. “Grid 
Forming”), or installation of additional assets (e.g. synchronous condensers, e-STATCOM, 
Battery  Energy  Storage  System  (BESS),  etc.).  However,  there  is  still  ongoing  research 
and development on the implementation of advanced control loops and on the technology 
itself, and as such there is to date no universal solution to improve this issue. 

These  two  main  impacts  reinforce  the  link  between  generation  and  transmission 
expansion  planning,  and  also  outline  the  necessity  to  consider  transmission  grid 
constraints when integrating more renewable energy sources into the energy mix. For the 
above-mentioned  reasons,  it  is  expected  that  HVDC  technology  will  be  increasingly 
installed in the European electrical grid and the network will evolve to a hybrid AC/DC 
grid. 

Scope of work 

Considering  that  traditional  cost-benefit  analyses  at  the  European  level  are  mainly 
focused  on  energy  needs  rather  than  on  power  grid  needs,  this  work  analyses  HVDC 
technology and its potential to provide additional benefits for integrating more Renewable 

1 The study considers  exclusively Voltage Source Converter (VSC) HVDC. Therefore, the wording HVDC always refers to 
VSC-HVDC. 

5 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Energy  Sources  in  the  network.  These  additional  benefits  could  be  provided  by  the 
following range of functionalities: 

•  Power flow control capability 
•  Voltage support 
•  Frequency and inertia support 
•  Grid forming 
•  Blackstart capability 

This  work  aims  at  providing  modelling  requirements  of  AC/DC  grids  and  in  particular  to 
propose  clear  guidelines  to  evaluate,  at  the  planning  stage,  all  benefits  that  can  be 
provided by the HVDC technology in a system with high share of RES. The ultimate goal 
is to allow decision makers to make better informed decisions.  

Therefore, we focus on the long-term planning stage when the evaluation of the costs and 
benefits of a project candidate takes place. Commonly used CBA methods do not capture 
all  the  technical  risks  related  to  operation  of  a  system  with  high  penetration  of  Inverter 
Based Resources. Therefore, operating conditions might not be stable and would require 
system  services,  additional  investment  or  redispatch  to  be  viable.  For  the  sake  of 
illustration,  an  overview  of  the  HVDC  functionalities  and  their  contribution  to  mitigate 
technical challenges can be found in Figure 1. 

Figure 1 - HVDC functionalities vs technical challenges in grid with high penetration of renewable energy sources. 

Summary of the work 

This  study  identifies  limitations  of  the  classical  CBA  methodologies  and  proposes 
improvements that can be summarized by the three following priorities: 

•  More detailed power system representation, towards a nodal network model 
• 

Integration  of  power  flow  control  and  stability  constraints  in  the  optimization 
problem 

•  Addition  of  qualitative  KPIs  regarding  system  stability  (in  particular  for 

frequency and converter-driven stability) 

These  improvements  are  to  be  added  to  the  existing  ENTSO-E  CBA  approach  which 
forms  the  basis  of  the  proposed  incremental  approach  (illustrated  in  Figure  2).  These 
incremental levels of complexity are proposed to better quantify some KPIs and also risks 
in systems with high penetration of Inverter Based Resources. The main point is that the 
zonal  approach  may  provide  optimistic  benefits,  in  the  sense  that  some  costs  can  be 
“hidden”  because  of  security  and  operational  challenges.  Therefore,  it  is  highly 
recommended to perform a CBA using the nodal network model and considering stability 
metrics. Both inertia and converter-driven stability metrics can be translated into KPIs by 
assessing how many operating conditions per year are at risk of frequency or converter-

6 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

driven instability. These quantitative KPIs should be used as an indicator of the need for 
future  investment  or  for  operational  measures.  Regarding  frequency  stability,  a  cost  is 
also evaluated based on redispatch methodology (similar to current B.10 KPI of ENTSO-
E). Regarding the converter-driven stability KPI, it must be seen as a risk indicator, which 
can lead to more detailed simulations in the next stage of the project or even to additional 
investments. 

Figure 2 – Overview of proposed CBA approach 

The  work  performed  can  be  summarized  into  the  three  following  parts  (which  are  more 
detailed in sections 5, 6 and 7). 

1.  “Enhanced” CBA methodology 

The  proposed  CBA  approach  quantifies  additional  benefits  and  identifies  potential 
risks  for  system  stability.  It  is  important  to  note  that  some  of  these  additional  benefits 
such  as  through  power  flow  control  can  only  be  seen  when  performing  the  CBA  on  a 
detailed  nodal  grid  model  (instead  of  a  zonal  model  often  used)  and/or  by  including 
stability (inertia) constraints in the analysis.  

Firstly,  an  existing  open-source  AC/DC  grid  optimal  power  flow  (OPF)  model  has  been 
used in order to determine the social welfare benefits considering internal congestion 
in  the  network,  as  opposed  to  using  zonal  models  neglecting  intrazonal  constraints. 
Further, the OPF model has been modified to determine the additional benefits provided 
by the power flow control provided by HVDC links during contingency situations. Using the 
modified  OPF  formulation,  the  redispatch  costs  are  minimized  for  a  number  of 
selected critical contingencies. The modified OPF tool has been made available as 
an open-source tool as well2. By performing two separate calculations with disabled and 
enabled  power  flow  control,  the  additional  benefits  through  power  flow  control  are 
determined.  The  results  show  that  security  related  redispatch  costs  can  be  significantly 
decreased by making use of such controllability. 

2 The tool can be accessed via https://github.com/Electa-Git/CBAOPF.jl  

7 

 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Moreover, the developed OPF implementation allows to include additional constraints. An 
inertia constraint has been tested for two study cases and it was clearly observed that the 
HVDC technology could considerably reduce the minimum inertia constraint, which 
by  consequence  increases  the  number  of  stable operating conditions.  This  effect  is  also 
quantified  by  means  of  redispatch  cost  reduction  as  a  proxy  of  required  reserves  to 
ensure frequency stability. 

An extremely important aspect is power system stability in a system with high penetration 
of inverter-based RES. While it is generally agreed that detailed time-domain simulations 
are  needed  in  order  to  assess  stability  in  a  weak  grid,  models  with the  required  level  of 
detail and accuracy of the control parameters are typically not available for the considered 
planning horizon. For this reason, it is recommended to evaluate risk of instabilities (at 
specific locations of the grid and/or at specific operating conditions) via calculation 
of simplified indicators. 

2.  Modelling and implementation guidelines 

One  part  of  the  work  (summarized  in  section  6.1)  specifically  focuses  on  the  modelling 
requirements  for  the  HVDC  technology.  A  comprehensive  review  of  the  type  of  models 
and the adequate level of detail for all observed phenomena in presence of inverter based 
resources was presented. For each functionality/technical aspects of HVDC systems, the 
modelling requirements have been specified.  

Section  6.2  and  section  6.3  detail  the  modelling  requirements  for  implementing  the 
proposed CBA approach. These sections provide to the interested reader all the required 
information for implementing the proposed approach.  

3.  Illustration on realistic use cases 

The  use  cases  provided  us  not  only  with  quantitative  results  but  also  with  a  return  of 
experience  on  the  proposed  implementation.  The  zonal  approach  has  been  easily 
implemented, however it is clear that the nodal approach has led to significant challenges, 
mainly  attributed  to  available  data.  It  has  been  shown  that  our  approach  could  be 
implemented on multi-country systems with several thousands of generators.  

Main findings and recommendations for future improvements 

(i) 

Main Findings 

(1)  Use of nodal network is necessary: Although zonal models can determine the 
socio-economic  benefits  of  new  interconnectors  in  a  computationally  efficient 
manner, they tend to underestimate these benefits as the internal congestion in 
the  network  is  not  considered.  The  reason  therefore  is  the  zonal  approach 
underestimates  the  curtailment  of  renewable  energy  due  to  internal  network 
congestion in high RES scenarios, where the added value of interconnection is 
even more  significant.  Our  study  shows  that  more complex  nodal models 
can  be  feasibly  used  within  of  CBA  methodologies  despite  higher 
computational  complexity  (24  hours  vs.  30  min  for  yearlong  calculations)  and 
higher data requirements. 

(2)  Power flow control provides significant benefits: The study shows that HVDC 
technology  provides  significant  benefits  through  power  flow  control  in 
case  of  contingencies  by  reducing  the  required  redispatch  cost. 
Especially embedded HVDC links can reduce redispatch costs in the order of 
several tens of millions of Euros per year in case of severe contingencies in the 
system. To analyse such benefits, the use of nodal models is unavoidable. 

(3)  Stability  constraints  are  necessary:  It  is  essential  to consider  stability  /  inertia 
constraints  in  long  term  planning  models  to  estimate  the  additional  risk  of 

8 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

deteriorating system inertia for determining the best mitigation options. Further, 
our  study  shows  that  inertia  provision  through  HVDC  decreases  the 
necessary  cost  for  ensuring  system  stability  in  the  order  of  several  ten 
million Euros per year.  

(4)  Stability indicator can be used to identify operational risks: Our study shows 
that  simplified  models  with  stability  and  inertia  constraints  can  provide 
acceptable  high-level  results  for  CBA  analysis.  In  terms  of  dynamic  data 
and control parameters, it is clear that the most accurate data allow to be more 
confident in the results of advanced tools. However, with currently available 
models  and  datasets,  it  is  not  always  adequate  to  perform  intensive 
detailed  simulations  for  long-term  planning  studies.  We  conclude  that 
detailed  dynamic  simulations  should  only  be  used  in  cases  where  detailed 
network and equipment models are available. As such, potential risks and de-
risking  actions  have  to  be  identified  but  can  be  done  later  in  the  planning 
process when detailed models are available.  

(5)  Harmonized  models  are  needed:  Our  study  shows  the  need  to  harmonize 
the network models used in the context of CBAs. Especially, to quantify the 
effects  of  congestion  and  benefits  through  power  flow  control  as  well  as  to 
better  approximate  dynamic  stability  constraints,  harmonized  models  are 
essential. 

(ii) 

Recommendations for future improvements 

(1)  Dataset  Improvement:  As  the  network  data  are  mandatory  in  our  proposed 
approach,  it  is  extremely  important  to  have  a  reliable  European  network 
model  (static).  To  that  end,  different  datasets  used  for  long  term  generation 
and  transmission  expansion  planning  versus  detailed  grid  models  used  to 
perform  power  flow  studies should  be  harmonized  in  order to  obtain  accurate 
results  capturing  all  benefits.  The  modelling  section  provides  clear 
requirements  in  terms  of  the  tools  and  model  details  for  studying  each 
phenomenon.  It  has  been  shown  in  this  study  (and  also  in the  literature)  that 
control  parameters  have  a  huge  influence  on  IBR  stability.  Therefore,  in  the 
near future it is extremely important to have a European grid model with 
representative  control  parameters  for  existing  IBRs.  This  will  allow  to 
perform a better screening of the instabilities that might occur 

(2)  Need  for  high-performance  computer  infrastructure:  Although  detailed  nodal 
models  are  computationally  more  expensive,  parallelization  of  calculations, 
application  of  artificial  intelligence  methods  for  contingency  filtering,  improved 
clustering techniques for selecting a subset of representative operating points 
(both for steady state and dynamic analysis) and the use of dedicated high-
performance computer infrastructure can allow the implementation of the 
demonstrated  mathematical  models  within  state-of-the  art  tools.  Further, 
the  development  of  dedicated  open-source  tools  can  help  to  provide 
transparent results in the context of the CBA. 

(3)  Defining power system stability in the future grid: Our study shows a particular 
approach for including stability indicators within CBA methodologies. However, 
there  are  a  variety  of  stability  indicators,  which  all  can  be  quantified  using 
different  types  of  optimisation  /  simulation  models.  As  such,  in  the  long  run  it 
will  be  important  to  define  stability  indicators  in  a  harmonized  way. 
Especially,  in  the  context  of  grid  forming  and  black  start  capabilities,  clear 
definitions  are  needed,  based  on  which  indicators  can  be  defined,  and 
subsequently models can be developed to quantify these indicators. We 
believe  that  fundamental  research  and  a  broad  stakeholder  involvement  are 
necessary to achieve this goal. 

9 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

2.  Résumé exécutif (Français) 

Disclaimer 

Les  informations  et  points  de  vue  exposés  dans  ce  rapport  sont  ceux  des  auteurs  
et    ne    reflètent    pas    nécessairement    l’opinion  officielle    de    la    Commission.    La  
Commission  ne  garantit  pas  l'exactitude  des  données incluses dans cette étude. Ni la 
Commission,  ni  aucune  personne  agissant  au  nom  de  la  Commission  ne  peuvent    être  
tenues  responsables  de  l’utilisation  qui  pourrait  être  faite  des  informations  qui  y  sont 
contenues. 

Contexte 

Les  années  futures  verront  une  intégration  massive  d’énergie  renouvelable  en  Europe. 
Cette  énergie  renouvelable  proviendra  de  l’éolien  (onshore  et  offshore);  du  solaire 
photovoltaïque  mais  également  d’autres  sources  d’énergies  (p.ex.  via  les  marées).  Ces 
sources  d’énergie  sont  interfacées  via  de  l’électronique  de  puissance  vers  le  réseau 
électrique  et  sont  communément  appelées  dans  la  littérature  Inverter  Based  Resources 
(IBRs).  

Un  des  impacts  majeurs  de  cette  pénétration  croissante  d’énergie  renouvelable  est  que 
l’électricité doit être transmise sur de grandes distances (depuis la source d’énergie vers 
les centres de consommation) et avec plus de variabilités qu’avec des sources d’énergie 
conventionnelles (comme des centrales thermiques). 

Le second impact est que les sources d’énergie renouvelables (machines non tournantes 
et  sans  inertie)  remplacent  les  machines  synchrones  connectées  au  réseau  électrique. 
Cela  implique  une  réduction  de  l’énergie  stockée  dans  les  masses  tournantes  des 
turbines  et  dans  les  enroulements  des  générateurs  synchrones.  Le  fait  d’avoir  moins 
d’énergie  mécanique  et  électromagnétique  disponible  temporairement  rend  le  système 
plus sensible aux perturbations et par conséquent potentiellement plus instable. De plus, 
la  stabilité  du  réseau  est  alors  gouvernée  par  les  lois  de  régulation  des  onduleurs 
d’électronique de puissance, plutôt que par la réponse naturelle des machines tournantes. 
Cela cause un nouveau paradigme dans l’exploitation des réseaux électriques et, au jour 
d’aujourd’hui, il n’y a pas de consensus sur la manière  de planifier et exploiter un grand 
réseau  électrique  avec  presque  100%  d’Inverter  Based  Resources.  Il  y  a  bien 
évidemment  des  solutions  qui  existent  pour  améliorer  la  stabilité  du  système,  comme 
l'utilisation  de  régulation  avancée  sur  les  onduleurs  des  HVDC  (p.ex.  « Grid  Forming »), 
ou  l’installation  d’assets  supplémentaires  (p.ex.  compensateur  synchrone,  e-STATCOM, 
batteries, etc.). Cependant, l’implémentation de boucles de régulation avancées ainsi que 
la technologie même ne sont pas encore totalement matures et il n’y a à ce jour pas de 
solution universelle pour améliorer cela. 

Ces  deux  impacts  majeurs  renforcent  le  lien  nécessaire  entre  la  planification  de  la 
génération et du réseau de transport, et soulignent également le besoin de considérer les 
contraintes du réseau électrique lorsqu’on veut intégrer plus d’énergie renouvelable dans 
le  mix  énergétique.  Pour  ces  réseaux,  il  est  attendu  que  la  technologie  HVDC  soit 
installée de manière croissante dans le réseau européen qui va évoluer vers un réseau 
hybride AC/DC. 

Cadre du projet 

En considérant que les analyses couts-bénéfices traditionnelles, au niveau européen, se 
concentrent  essentiellement  sur  les  besoins  énergétiques  plutôt  que  sur  les  besoins  du 
réseau  électrique,  ce travail  analyse  en  particulier  la  technologie  HVDC  et  son  potentiel 
pour 
intégrer  plus  d’énergie 
renouvelable.  Ces  bénéfices  additionnels  peuvent  être  fournis  par  les  fonctionnalités 
suivantes: 

fournir  de  services  réseaux  additionnelles  et  ainsi 

10 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

•  Contrôle de l’écoulement de puissance 
•  Support en tension 
•  Support en fréquence et inertiel 
•  Grid forming 
•  Capacité blackstart 

Ce  projet  vise  à  fournir  des  exigences  de  modélisation  pour  les  réseaux  AC/DC  et  en 
particulier  à  proposer  des  lignes  directrices  claires  pour  évaluer,  lors  de  la  planification, 
les bénéfices qui peuvent être fournis par la technologie HVDC dans un système à forte 
pénétration  de  renouvelable.  L’objectif  final  étant  d’avoir  des  informations  claires  pour 
faciliter la prise de décisions d’investissements. 

Par conséquent, nous nous sommes concentrés sur la planification long-terme, quand est 
effectuée  l’évaluation  des  couts  et  bénéfices  d’un  projet  candidat.  Généralement,  les 
études couts-bénéfices ne capturent pas tous les aspects techniques liées à l’exploitation 
d’un système à haute pénétration de renouvelable. Par conséquent, certaines conditions 
d’exploitation pourraient être instables et ainsi nécessiter des couts supplémentaires pour 
être  viable  (p.ex.  via  services  réseaux,  investissements  additionnels  ou  redispatch).  La 
Figure  3  illustre  les  challenges  opérationnels  ainsi  que  les  services  qui  peuvent  être 
fournis par la technologie HVDC. 

Figure 3 - challenges opérationnels ainsi que les services qui peuvent être fournis par la technologie HVDC. 

Résumé du travail effectué 

L’étude  a  permis  d’identifier  les  limitations  des  études  couts-bénéfices  classiques  et 
propose des améliorations qui peuvent être résumées par les trois points suivants : 

•  Représentation plus détaillée du réseau électrique, jusqu’à un modèle nodal 
• 

Intégration  des  régulations  d’écoulement  de  puissance  et  des  contraintes  de 
stabilité dans le problème d’optimisation 

•  Ajout  d’indicateurs  évaluant  le  risque  de  problèmes  de  stabilité  (notamment 

pour la stabilité en fréquence et stabilité des onduleurs). 

Ces améliorations doivent être ajoutées à l’approche existante utilisée par ENTSO-E, qui 
forme la base de l’approche incrémentale proposée (illustrée à la Figure 6). Ces niveaux 
de  complexité  croissants  sont  proposés  pour  mieux  quantifier  certains  indicateurs  mais 
également  les  risques  liés  aux  systèmes  à  forte  pénétration  de  renouvelable.  Un  point 
important à souligner est que l’approche zonale pourrait montrer des bénéfices optimistes, 
dans le sens où certains couts peuvent être « cachés » à cause de contraintes de sécurité 
ou  de  challenges  opérationnels.  Par  conséquent,  il  est  hautement  recommandé 
d’exécuter  l’étude  coûts-bénéfices  en  utilisant  un  modèle  nodal  du  réseau  et  en 
considérant des indicateurs de stabilité. Les métriques liées à l’inertie et à la stabilité des 
onduleurs peuvent être traduites en indicateurs de performance en évaluant le nombre de 

11 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

points  de  fonctionnement  par  an  qui  sont  à  risque.  Cela  mène  donc  à  des  indicateurs 
quantitatifs  qui  peuvent  être  utilisés  pour  évaluer  la  nécessité  d’investissements 
supplémentaires ou de mesures opérationnelles. Concernant la stabilité en fréquence, un 
cout est également évalué, basé sur la méthodologie de redispatch (similaire à l’indicateur 
B.10  actuellement  utilisé  par  ENTSO-E).  Pour  la  stabilité  liée  aux  onduleurs,  l’indicateur 
doit  être  vu  comme  une  quantification  de  risque  et  des  simulations  supplémentaires 
devront  être  effectuées  à  un  stade  ultérieur  d’avancement  du  projet  pour  déterminer  les 
potentiels couts additionnels. 

Le travail effectué peut être résumé en trois parties distinctes, comme suit : 

Figure 4 – Overview de l’approche proposée 

1. Méthodologie couts-bénéfices “améliorée“ 

L’approche  couts-bénéfices  proposée  quantifie  les  bénéfices  additionnels  et  identifie  les 
risques  potentiels  pour  la  stabilité  du  système.  Il  est  important  de  noter  que  certains  de 
ces bénéfices (comme le contrôle de l’écoulement de puissance) ne peuvent être évalués 
qu’en utilisant un modèle réseau détaillé (plutôt qu’un modèle zonal) et/ou en incluant des 
contraintes de stabilité (p.ex. inertie).  

Premièrement,  un  modèle  open-source  existant  d’écoulement  de  charge  optimal  d’un 
réseau AC/DC a été utilisé. Ce modèle permet de déterminer les bénéfices pour le bien-
être  social,  en  considérant 
le  réseau  électrique, 
contrairement  au  modèle  zonal  qui  néglige  les  contraintes  internes.  De  plus,  le  modèle 
d’optimisation  d’écoulement  de  charge  a  été  modifié  de  manière  à  déterminer  les 
bénéfices  additionnels  fournis  par  la  capacité  de  contrôle  d’écoulement  de  charge  des 
liens HVDC.  

les  congestions 

internes  dans 

En  utilisant  cette  formulation  modifiée3,  les  couts  de  redispatch  sont  minimisés  pour  un 
nombre de contingences sélectionnées. En exécutant deux calculs séparés, avec et sans 
la fonctionnalité de contrôle d’écoulement de charge, les bénéfices de cette fonctionnalité 

3 L’outil est accessible via https://github.com/Electa-Git/CBAOPF.jl  

12 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

peuvent  être  déterminés.  Les  résultats  confirment  que  les  couts  de  redispatch  peuvent 
effectivement être grandement diminués en utilisant cette fonctionnalité. 

De  plus,  l’implémentation  de  l’outil  d’optimisation  permet  d’inclure  des  contraintes 
additionnelles. L’ajout d’une contrainte d’inertie a été testée pour deux cas d’étude et il a 
été clairement démontré que la technologie HVDC permettait de réduire l’inertie minimum 
pour  garantir  la  stabilité  du  système.  Ce  qui  par  conséquent,  augmente  le  nombre  de 
conditions  d’exploitations  satisfaisant  la  stabilité  en  fréquence.  Ceci  a  également  été 
quantifié via un calcul de redispatch. 

Un  dernier  important  aspect  est  la  stabilité  des  réseaux  électriques  à  haute  pénétration 
d’énergie renouvelable (interfacée via de l’électronique de puissance). Il est généralement 
recommandé  de  faire  des  études  très  détaillées  et  des  simulations  temporelles  pour 
vérifier  la  stabilité  de  ce  type  de  réseaux.  Cependant,  les modèles  adéquats,  et  avec  le 
niveau  suffisant  de  détails,  ne  sont  pas  disponibles  actuellement  pour  des  études  de 
planification.  Pour  cette  raison,  il  est  recommandé  d’évaluer  le  risque  d’instabilité  via 
l’utilisation d’indicateurs dédiés. 

2. Modélisation et lignes directrices pour l’implémentation 

Une  partie  du  travail  (décrite  en  section  6.1),  s’est  spécifiquement  concentrée  sur  les 
exigences de modélisation pour la technologie HVDC. Une revue complète des types de 
modèles ainsi que du niveau de détail adéquat, en fonction du phénomène étudié, a été 
présenté.  Pour  chaque  fonctionnalité  de  la  technologie  HVDC,  les  exigences  de 
modélisation sont spécifiées. 

Les  sections  6.2  et  6.3  détaillent  les  exigences  de  modélisation  pour  implémenter  la 
méthode  couts-bénéfices  proposée.  Ces  sections  contiennent  toutes  les  informations 
nécessaires pour implémenter cette approche.  

3. Illustration sur des cas d’études réalistes 

Les cas d’études fournissent non seulement des résultats quantitatifs mais aussi un retour 
d’expérience  sur  l’implémentation  proposée.  L’approche  zonale  a  été  implémentée  sans 
problème alors que l’approche utilisant les modèles réseaux plus détaillés (nodal) nous a 
mené à de nombreux challenges (notamment au niveau des données disponibles). Il a été 
démontré  que  notre  approche  pouvait  être  utilisée  dans  un  large  système  comptant 
plusieurs milliers de générateurs.  

Enseignements principaux et recommandations pour le futur 

(i) 

Enseignements principaux 

(1)  L’utilisation  d’un  modèle  nodal  du  réseau  est  nécessaire:  Bien  que  le modèle 
zonal permette de déterminer les bénéfices socio-économiques des projets de 
transmission,  les  résultats  peuvent  être  optimistes  en  sous-estimant  l’impact 
des  congestions  internes.  Cela  a  pour  effet  de  sous-estimer  les  bénéfices 
d’assets  permettant  de  contrôler  l’écoulement  de  puissance  et  il  est  dès  lors 
important d’utiliser un modèle nodal du réseau. Notre étude a montré qu’il était 
faisable  d’utiliser  les  modèles  nodaux  dans  une  étude  couts-bénéfices 
européenne, malgré un temps de calcul largement supérieur (24 heures vs. 30 
min  pour  le  calcul  d’une  année  cible)  et  des  exigences  plus  élevées  sur  les 
données. 

(2)  Le  contrôle  de  l’écoulement  de  puissance  fournit  des  bénéfices  importants: 
L’étude  a  montré  que  la  technologie  HVDC  fournit  des  bénéfices 
important  via  sa  capacité  à  contrôler  l’écoulement  de  puissance, 
notamment  en  cas  de  contingence.  En  particulier,  les  liaisons  HVDC 

13 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

intégrées dans le réseau AC permettent de réduire les couts de redispatch de 
plusieurs dizaines de millions par an. 

(3)  Les  contraintes  de  stabilité  sont  nécessaires:  Il  est  nécessaire  de  considérer 
des  contraintes  de  stabilité  (p.ex.  inertie)  dans  les  modèles  de  planification 
long-terme.  Cela  permet  d’estimer  le  risque  lié  à  la  diminution  de  l’inertie  du 
système  et  ainsi  de  déterminer  quelles  sont  les  meilleures  solutions  pour  y 
faire  face.  De  plus,  notre  étude  a  montré  que  la  provision  d’inertie  via  la 
liaison  HVDC  réduit  le  coût  de  redispatch  pour  garantir  la  stabilité  du 
système de plusieurs dizaines de millions par an.  

(4)  Des  indicateurs  de  stabilité  sont  recommandés  pour  identifier  les  risques 
opérationnels: L’étude a montré que l’utilisation d’indicateurs de stabilité donne 
des  résultats  acceptables  pour  des  études  couts-bénéfices.  Il  est  bien 
évidemment  plus  précis  d’utiliser  des  modèles  détaillés,  mais  lorsque 
ceux-ci  ne  sont  pas  disponibles,  l’utilisation  des  indicateurs  proposés 
est  pertinente,  de  manière  à  identifier  les  risques  de  potentiels  coûts 
supplémentaires.  Il  est  dès  lors  recommandé  de  faire  des  simulations 
avancées  uniquement  lorsque  les  modèles  nécessaires  sont  disponibles.  Par 
exemple, dans un stade ultérieur de développement du projet.  

(5)  Des  modèles  harmonisés  sont  nécessaires:  En  particulier,  l’harmonisation 
des  modèles  réseaux  est 
l’impact  des 
congestions  internes  et  les  bénéfices  via  contrôle  de  l’écoulement  de 
puissance.  De  plus,  des  modèles  harmonisés  sont  nécessaires  pour  mieux 
approximer les limites de stabilité. 

importante  pour  quantifier 

(ii) 

Recommandations pour améliorations futures 

(1)  Amélioration de la base de donnée: Les données réseaux étant indispensables 
dans  notre  approche,  il  est  extrêmement  important  d’avoir  un  modèle  fiable 
du  réseau  européen.  Pour  cela,  les  bases  de  données  utilisées  pour  la 
planification  de  la  génération,  de  la  transmission  et  pour  les  études 
d’écoulement  de  charge  doivent  être  harmonisées.  Par  ailleurs,  un  travail 
important  est  nécessaire  pour  modéliser  de  manière  adéquate  les  assets 
interfacés via de l’électronique de puissance. Cela permettra une meilleure 
évaluation des risques d’instabilité. 

(2)  Besoin  d’infrastructures  de  calcul  performantes:  Bien  que  les  calculs  utilisant 
des  modèles  détaillés  du  réseau  électriques  sont  plus  gourmands  en 
puissance de calcul, des techniques existent pour améliorer le temps de calcul. 
Il  est  possible  de  paralléliser  les  simulations,  d’utiliser  des  algorithmes 
les  points  de 
filtrer 
d’intelligence  artificielle,  de 
fonctionnement.  De  plus, 
l’utilisation  d’infrastructures  hautement 
performantes  permettraient  d’implémenter  la  méthode  proposée  dans 
des outils de pointe. D’autre part, l’utilisation d’outils open-source permet de 
garantir la transparence envers les parties prenantes. 

les  contingences  et 

(3)  Définition  d’un  indicateur  de  stabilité  pour  le réseau  électrique  du  futur:  Deux 
indicateurs  de  stabilité  ont  été  utilisés  dans  cette  étude.  D’autres  indicateurs 
existent dans la littérature et certains sont assez prometteurs pour déterminer 
notamment l’impact de boucles de contrôle avancées sur la stabilité du réseau. 
Il  est  dès  lors  important  de  définir  un  indicateur  de  stabilité  de  manière 
harmonisée  et  qui  puisse  être utilisé  dans  des études couts-bénéfices. Il  est 
cependant attendu que cela nécessite l’implication des parties prenantes ainsi 
qu’un effort de recherche fondamentale. 

14 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Table of Contents 

1.  Executive summary (English) ...................................................................... 5 

2.  Résumé exécutif (Français) ....................................................................... 10 

3.  Glossary .................................................................................................... 16 

4. 

5. 

Introduction ................................................................................................ 18 

“Enhanced” CBA methodology .................................................................. 21 

5.1. Description of the existing ENTSO-E CBA approach .........................................21 
5.2. Drivers for an “enhanced” CBA approach ..........................................................26 
5.3. Overview of “enhanced” CBA approach ............................................................30 
5.4. Data for determining CBA-KPIs of the selected use cases ................................34 
5.5. Interface between steady-state optimization and power system simulations .....35 

6.  Modelling and implementation guidelines .................................................. 39 

6.1. Technical Aspects of HVDC and Modelling Requirements .................................39 
6.2. Steady-state Optimization:  Modelling Requirements to determine Techno-
economic KPIs .........................................................................................................60 
6.3. Modelling Requirements to determine proposed stability KPIs ..........................75 

7. 

Illustration on use cases ............................................................................ 80 

7.1. Use case selection .............................................................................................80 
7.2. Navarra Landes .................................................................................................92 
7.3. Celtic interconnector ..........................................................................................95 
7.4. Ultranet + A-North ........................................................................................... 107 
7.5. EuroAsia.......................................................................................................... 112 
7.6. 2050 MTDC ..................................................................................................... 117 
7.7. Main challenges encountered during analysis of the use cases ....................... 118 

8.  Main findings and recommendations ....................................................... 119 

9.  Appendix I: stakeholder interaction .......................................................... 123 

9.1. Stakeholder feedback on use case selection ................................................... 123 
9.2. Modelling requirements and cost-benefit analysis ........................................... 123 

10. 

11. 

Appendix II: use case selection ............................................................ 126 

Appendix III: Data sources for the zonal economic dispatch model ..... 127 

12.  References ........................................................................................... 129 

15 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

3.  Glossary 

AVM 

BESS 

BW  

CBA 

CCS 

CCT 

CCGT 

DSR 

ED 

EMT 

ENS 

FRR 

IBR 

IGBT 

KPI 

LCC 

MMC 

MTDC 

MS 

OCGT 

P2G 

PE 

PLL 

PTDF 

PtP 

POC 

Average Value Model 

Battery Energy Storage System 

Bandwidth 

Cost-Benefits Analysis 

Carbon capture and storage 

Critical Clearing Time 

Combined-cycle gas turbine 

Demand side response 

Economic dispatch 

Electromagnetic transient 

Energy Not Served 

Frequency Restoration Reserve 

Inverter-Based Resource 

Insulated Gate Bipolar Transistors 

Key Performance Indicator 

Line Commutated Converter 

Modular Multilevel Converters 

Multi-terminal HVDC 

Member state 

Open-cycle gas turbine 

Power to grid 

Power Electronic 

Phase-locked loop 

Power Transfer Distribution Factor 

Point-to-Point 

Point-Of-Connection 

16 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

RES 

RMS 

RR 

SCR 

SPWM 

TNEP 

TYNDP 

VOLL 

VSC 

Z/Y 

Renewable Energy Source 

Root-Mean Square 

Replacement Reserve 

Short-circuit ratio 

Sinusoidal Pulse Width Modulation 

Transmission Network Expansion Plan 

Ten Year Network Development Plan 

Value of Lost Load 

Voltage Source converter 

Impedance /admittance 

17 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

4. 

Introduction 

The  transition  towards  a  carbon  neutral  economy  by  2050  will  require  a  large-scale 
electrification of the energy system, with an almost fully decarbonized power system. To 
this  end  and  following  the  European  Green  Deal,  the  Commission  proposed  in  March 
2020  the  European  Climate  Law  to  provide  the  necessary  legal  framework.  The  2050 
climate-neutrality objective will also impact the trajectory for achieving this goal. By 2030, 
for  instance,  about  50  percent  of  electricity  generation  in  Europe  will  be  based  on  wind 
and solar energy [1]. In particular, the European Commission has high ambitions in terms 
of further offshore renewable energy development (wind, but also wave and tidal) and this 
led  to the  definition  of  an  EU  Strategy  on  Offshore  Renewable  Energy  published  end  of 
2020 [2]. 

In order to reach these ambitious targets (for offshore but also for other renewable energy 
sources  and  the  transmission  of  their  power  output  to  the  consumption  locations),  the 
electrical  grid  has  to  be  planned  in  a  cost-economic  way  that  allows  transmission  of 
energy  over  long  distances  while  keeping  a  high  security  of  supply.  This  is  a  real 
challenge  in  a  future  power  system  integrating  more  intermittent  and  power  electronic 
interfaced  generation.  Therefore,  the  current  power  system  planning  methodologies  will 
need  to  evolve  to  adapt  to  the  high  renewable energy  sources  landscape.  For  example, 
more coordinated grid planning approaches could be envisaged. These approaches could 
mean  sector  coupling,  more  coordination  between  onshore  and  offshore  planning,  or 
coordinated  spatial  planning  (especially  offshore  for  allocation  of  areas  for  offshore 
plants).  For  instance,  in  its  proposal  for  a  revision  of  the  TEN-E  Regulation  (December 
2020), the Commission emphasized the need to define offshore renewable generation to 
be deployed in each sea basin by 2030, 2040 and 2050 and to define integrated offshore 
network development plans. 

Looking  at  the  European  network,  HVDC  is  seen  as  one  of  the  key  technologies  of  the 
future with several HVDC connections considered in the TYNDP 2020, as shown in Figure 
5. It has been generally used for interconnection between the different synchronous areas 
(e.g. HVDC connections between the Nordic countries, Continental Europe, Great Britain 
and Ireland), but also to increase the transfer capacity between countries (e.g. Spain and 
France).  Currently,  more  complex  HVDC  connections  are  investigated  in  order  to  take 
advantage  of  remotely  located  renewable  sources  of  energy,  mainly  the  vast  offshore 
wind  potential  in  the  surrounding  seas.  In  particular,  the  PROMOTioN  project  estimated 
the wind potential in the North Sea to 205 GW. ENTSO-E expects that by 2030 59% of the 
transmission network investments in Europe will be in HVDC technology. The majority of 
these new investments is expected to use the VSC technology. 

18 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 5 - Subset of HVDC connections in TYNDP 2020 of ENTSO-E 

Up to now, the vast majority of HVDC connections in the world consists of point-to-point 
links, sparsely spread in the power systems. However, with the expected development of 
HVDC  connections,  the  penetration  of  HVDC  connections  will  increase  with  multiple 
HVDC  connections  in close  proximity  and between  the  same systems. In addition, more 
complex  technologies  such  as  Multi-Terminal  DC  (MTDC)  grids  or  offshore  hubs  might 
become more attractive and be realized.  

This  transition  and  integration  of  HVDC  systems  is  not  without  its  challenges.  Technical 
barriers still have to be surpassed in terms of the protection of such systems – there is still 
low availability and experience from HVDC circuit breakers – as well as in terms of multi-
vendor  interoperability  –  as  intellectual  property  rights  between  different  vendors  should 
be  protected.  Other  important  challenges  involve  the  control,  operation  and  planning  of 
such hybrid AC/DC systems, especially when they are combined with high penetration of 
renewable  energy  sources.  The  need  for  coordination  between  the  TSOs  in  the  above 
challenges  is  expected  to  further  increase  and  be  of  crucial  importance.  Operating 
guidelines,  system  planning  methodologies  and  market  procedures  should  be  revisited 
and adapted in order to cope with this shift in the power system paradigm.  

Regardless  of  the  shape  of  the  future  grid  topologies,  HVDC  connections  will  provide 
several benefits to the power systems due to their special characteristics such as voltage 
support, improving stability or providing system services (blackstart, frequency, etc.).  

It  is  however  challenging  to  fully  integrate  these  risks  and  benefits  of  new  technologies 
such  as  HVDC  in  the  planning  studies  as  part  of  an  integrated  cost-benefit  analysis 
(CBA),  as  the  initial  focus  of  the  European  CBA  is  mainly  on  energy  exchange  and  on 
conventional technologies, and less on power system technical aspects and stability. The 
rapid evolution of the grid and of the technology caused significant changes and therefore 
more  details  must  be  included  in  the  CBA  studies  to  compare  appropriately  different 
technological  options.  This  is  especially  true  for  meshed  HVDC  grids,  multi-terminal 
HVDC or for HVDC links embedded within the AC grid. 

In  order  to  address  these  challenges  and  to  allow  decision  makers  to  make  better 
informed  decisions,  this  study  aims  at  providing  modelling  requirements  of  AC/DC  grids 
and in particular to propose clear guidelines to evaluate, at the planning stage, all benefits 
that can be provided by HVDC technology in a system with high share of RES.  

19 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

As  such,  the  main  question  we  are  trying  to  answer  can  be  summarized  as:  “Are  the 
existing methodologies, models and tools adequate to capture all risks and benefits 
when planning AC/DC hybrid grid”?  

The focus of this study is therefore on the planning stage when the evaluation of the costs 
and benefits of a project candidate takes place. It is important to evaluate whether some 
of  these  costs  or  benefits  are  under-estimated  using  classical  CBA  methodologies. 
Commonly used CBA methods do not capture all technical risks related to operation of a 
system  with  high  penetration  of  IBRs.  Therefore,  operating  conditions  considered  might 
not  be  stable  and  would  require  additional  investment  or  redispatch  to  be  viable.  VSC 
HVDC technology can provide system stability services that would allow stable operation 
at high penetration of IBRs. This must be accounted for in the CBA analysis, in order to 
correctly capture the benefits of HVDC technology. Also, the lower losses and power flow 
control  capabilities  of  HVDC  technology  are  not  always  considered  in  typical  CBA 
approaches. 

This  study  tries  to  identify  the  limitations  of  the  classical  CBA  methodologies  and  to 
provide  implementation  guidelines.  To  that  end  a  proof-of-concept  optimization  model  is 
developed and implemented as an open-source optimization tool and is clearly described 
in  the  report.  Specific  use  cases  were  carefully  chosen  to  test  and  fine-tune  our 
implementation. 

The report is further structured as follows: 

•  Chapter  5  describes  the  proposed  “enhanced  CBA”  methodology.  First,  the 
existing CBA proposed by ENTSO-E is analysed. Then, additional or updated KPIs 
are discussed. Next, the recommended methodology is explained in more detail.  
•  Chapter 6 focuses on the modelling requirements and implementation guidelines. 
The  section  starts  by  a  review  of  the  different  classes  of  models  and  describes 
which  level  of  detail  is  recommend  depending  on  the  studied  phenomenon.  The 
second part of the section details the modelling requirements for the steady-state 
optimization  problem  while  the  last  part  details  the  requirements  for  the  stability 
indicators.  

•  Chapter  7  shows  the simulation  results  on the selected  use  cases.  First, the  use 
case selection process is described. Different use cases are highlighted to quantify 
specific  indicators  with  the  goal  of  illustrating  the  methodology,  test  the 
implementation and demonstrate the feasibility of future applications. 

•  Chapter 8 finally gives an overview of the main findings and recommendations 

Additional information on the stakeholder interaction (during a workshop which took place 
on 31st March 2022), on the use case selection and on the data resources for the zonal 
economic dispatch model can be found in appendix. 

20 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

5. 

“Enhanced” CBA methodology 

5.1. Description of the existing ENTSO-E CBA approach 

The following section briefly describes the current CBA methodology employed within the 
TYNDP process and pinpoints, (1) how the representation of additional benefits and costs 
through  HVDC  (grids)  can  be  improved,  (2)  how  some  of  the  KPIs  deemed  not 
quantifiable within the current approach could be quantified in a uniform way. 

The starting point for the analysis of the CBA KPI is the 3rd ENTSO-E Guideline for Cost 
Benefit  Analysis  of  Grid  Development  projects  [3],  currently  under  public  consultation. 
Figure 6 shows the current set of KPIs defined for conducting the CBA and if the KPIs are 
computed  based  on  a  zonal  or  nodal  model.  It  is  also  already  outlined  that  the  stability 
KPIs (B8) are updated in this study. 

Figure 6 – CBA KPI according to the 3rd ENTSO-E guideline for cost benefit analysis of grid development projects 

In the following paragraphs, the calculation of the different KPIs will be introduced briefly, 
for the detailed calculation of the parameters, the readers are referred to [3]. Table 1 gives 
an overview of the KPIs B1 to B10. 

21 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Cat. 

Name 

Unit 

Monetized? 

Table 1 - Overview of KPIs B1 to B10 

Qualitative/ 
Quantitative 

B1 

B2 

B3 

B4 

Socio-economic 
welfare 

€/yr 

Yes 

Quantitative 

CO2 emissions 

t/yr or €/yr 

No / Yes 

Quantitative 

RES integration 

MW or 
MWh/yr 

Yes 

Quantitative 

Non CO2 
emissions 

t/yr 

No 

Quantitative 

B5 

Grid losses 

MWh / yr 

Implicit or 
explicit 

Quantitative 

B6 

B7 

B8 

B9 

Adequacy 

MWh / yr 

Yes 

Quantitative 

Flexibility 

0/+/++ 

Stability 

Avoidance of 
renewal / 
replacement 

- 

€ 

No 

No 

Yes 

Qualitative 

Qualitative 

Quantitative 

B10 

Redispatch 
reserves 

€ / yr 

Yes 

Quantitative 

Although the KPIs B1 – B6 as well as B9 – B10 can be determined in a quantitative way, 
KPIs B7 and B8 related to enhancing system flexibility and impacting system stability have 
been  defined 
the  computational 
requirements  to  calculate  the  listed  KPIs  and  provides  improvement  needs  for  the 
determination of the KPIs. 

in  a  qualitative  manner.  Table  2  summarizes 

Table 2 - Computational requirements to calculate the listed KPIs 

Cat.  Name 

Computational requirements 

Improvement needs 

B1 

B2 

B3 

Socio-
economic 
welfare 

Can be obtained via zonal and/or nodal 
economic dispatch model depending on 
use-case, efficiently solvable using linear 
models 

Power flow control 
through HVDC links in 
the modelling 
framework.  

CO2 
emissions 

No additional optimisation needed w.r.t. 
B2, translation of dispatch to emissions  

RES 
integration 

No additional optimisation needed w.r.t. 
B3, translation of dispatch to additional 
RES integration 

/ 

/ 

22 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Cat.  Name 

Computational requirements 

Improvement needs 

B4 

Non CO2 
emissions 

No additional optimisation needed w.r.t. 
B4, translation of dispatch to emissions. 

/ 

B5 

Grid losses 

Solution of ‘AC’ power flow based on 
dispatch (prone to non-convergence), or 
estimation of losses with subsequent 
power flow calculations. 

Representation of HVDC 
converter and line 
losses. 

B6 

Adequacy 

No additional optimisation needed w.r.t. 
B6, however explicit demand curtailment to 
be modelled using VOLL. 

/ 

B7 

Flexibility 

Stochastic model to determine optimal size 
of FRR and RR for different climatic 
conditions and contingencies.  

B8 

Stability 

Maximum frequency deviation or minimum 
inertia constraints within OPF/ED needed 
for frequency stability for optimisation. As 
an alternative, dynamic simulations for 
various operating points can be performed. 

Voltage stability can be assessed using 
continuation ‘AC’ power flow (convergence 
prone).  

Black-start modelling is very case specific 
requiring dynamic/transient models. 

B9 

Avoidance of 
renewal / 
replacement 

Very project / TSO specific. Can only be 
modelled using nodal models. Ideally 
modelled with TNEP model using 
exclusivity constraints. 

B10  Redispatch 

reserves 

Two stage model consisting of market 
clearing, and detailed redispatch – OPF 
needed. Detailed information on N-1 
contingency set, and control actions 
needed. Potentially discrete model if 
topological actions considered (high 
computational requirement). 

Power flow control 
through HVDC links in 
the modelling 
framework.  

Methodology based on 
stability / inertia 
constraints to 
approximate stability 
constraints based on 
dimensioning incident. 

Multi-step transmission 
expansion optimisation 
to determine potential 
for investment deferral 
between multiple 
options. 

Clear guidelines on 
usage of HVDC for 
cross-border exchange 
and as preventive/ 
curative measure 
needed. 

In  fact,  for  the  determination  of  the  KPIs  B1  throughout  B6,  the  same  underlying 
optimisation model can be used.  

KPI  B1  –  Socio  economical  welfare,  is  calculated  using  an  economic  dispatch  or  unit 
commitment  model,  which  can  be  applied to  either  a zonal  or  detailed nodal  grid  model. 
The  main  idea  behind  such  an  optimisation  model  is  to  determine  the  least  cost 
generation dispatch (or market outcome) for a given RES and demand scenario. The main 
inputs to the optimisation problem are the installed generation capacity for different types 

23 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

of  generation  in  each  zone  /  node,  the  zonal  /  nodal  electricity  demand,  the  cost  of 
electricity generation for the different generators (generator types), and a network model 
including  the  zonal  /  nodal  connectivity  of  generators  and  demand.  In  case  of  zonal 
models,  the  network  is  often  represented  with  transfer  capacities  available  between  the 
different  market  zones,  whereas  in  detailed  nodal  models,  the  high  voltage  network  is 
represented  through  line  impedances  governing  the  power  flows  and  the  respective  line 
limits.  A  more  detailed  explanation  of  the  two  types  of  models  is  presented  within  the 
section 6.2. Thus, KPI B1 is calculated by applying such an optimisation model, where the 
generation  dispatch  cost  is  determined  for  a  number  of  different  operating  conditions 
using RES and demand time series for a number of different climate years. By running the 
same  optimisation  model  for  the  case  without  the  investment  and  with  investment  and 
comparing to total electricity generation cost in both cases, the socio – economic benefits 
of  the  investments  can  be  obtained.  In  the  case  of  HVDC  technology,  its  power  flow 
control capability can help to avoid congestion in the system, and so have a higher impact 
on the minimisation of the total generation dispatch cost. However, this aspect can hardly 
be  captured  in  zonal  models,  as  in  such  models,  the  interzonal  transmission  capacity  is 
often  modelled  without  accounting for  the  distribution of  power flows  and only making  of 
Net Transfer Capacities (NTCs) between the zones, and zones themselves are assumed 
to  be  congestion  free.  As  such,  this  KPI  can  be  improved  by  applying  detailed  nodal 
network  models,  as  well  as  explicitly  modelling  the  control  capabilities  of  HVDC 
connections.  The  NTC  based  model  can  be  improved  using  power  transfer  distribution 
factors  (PTDF)  which  use  representative  impedances  within  the  zones,  and  can 
approximate  power  flow  constraints.  However,  in  presence  of  controllable  devices  such 
models  need to be  extended  with  additional  distribution  factors  for  PSTs  or  HVDC  links. 
Section 6.2 shows how such models can be improved using linearized power flow models.    

KPI B2 – CO2 emissions is a KPI that can directly be calculated from the output of the 
optimisation model used for B1. As the dispatch of each generator (type) is optimised on 
an hourly basis, the emissions of each generator can be calculated in a post-processing 
step, in case the emission factors of the generators expressed in tCO2 / MWh are known. 
Thus, again by comparing the results of the optimisation for the case with and without the 
investment, the contribution to CO2 savings can be calculated.  

KPI B3 – RES integration indicates how many additional MWh of RES generation can be 
accommodated in the system if the investment takes place. Just as in case of B2, this KPI 
can  be  calculated  in  a  post  –  processing  step  by  comparing  the  total  amount  of  RES 
generation between the case with and without the grid investment. 

KPI  B4  –  Non  –  CO2  emissions  is  an  extension  of  B2,  which  also  accounts  for  other 
types  of  emissions  associated  with  electricity  generation,  such  as  NOx  and  SOx 
emissions. Similar to B2, using appropriate emission factors tNOx / MWh and tSOx / MWh 
for  conventional  generators,  the  non-CO2  emissions  between  the  case  with  and  without 
the grid investment can be compared.  

KPI  B5  –  Grid losses  can  be  calculated  in  several  different  ways.  If  a  detailed  network 
model and a lossy power flow formulation are used, the transmission losses attributed to 
AC and DC grid components will be implicitly considered by the optimisation model as will 
be  explained  in  section  6.2  in  detail.  However,  such  models  are  usually  nonlinear  and 
nonconvex in nature, and as such are seldom applied to large power systems, for many 
different  generation  and  demand  scenarios  as  being  done  within  the  TYNDP  CBA 
process.  Thus,  even  if  detailed  nodal  grid  model  is  used,  very  often  a  linearised  power 
flow  (DC)  formulation  is  used  in  practice  to  conduct  the  socio-economic  welfare 
optimisation, which neglects the network losses. When zonal models are used, generally 
losses  cannot  be  accounted  for.  One  way  of  calculating  the  transmission  losses  is  to 
perform power flow calculations using the obtained generation dispatch as a starting point. 
In  the  power  flow  calculation,  a  subset  of  the  generators  in  the  system  are  defined  as 

24 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

slack generators which can provide the additional energy to compensate for losses. This 
way  a  feasible  system  state  fulfilling  the  nonlinear  nonconvex  equations  is  determined. 
Another  possible  way  of  calculating  the  transmission  losses  is  to  start  from  the 
transmission line flows obtained in the first optimisation stage, and to multiply these with 
certain  loss factors  in  order  to  estimate  the  actual  amount  of  expected  losses.  Although 
this  approach  is  widely  used  for  AC  lines,  there  are  standardised  loss factors  which  are 
being used for HVDC connections. 

KPI  B6  –  Adequacy  relates  to  the  expected  energy  not  served,  due  to  unavailability  of 
generation sources in certain parts of the grid and lacking transmission capacity to supply 
these parts from neighbouring parts. This KPI can be calculated by extending the model 
briefly  introduced  for  B1.  Therefore,  a  zonal  /  nodal  demand  curtailment  variable  is 
introduced to the optimisation problem, to reduce the demand in hours where there is not 
enough  generation  and  transmission  capacity  available.  Obviously,  the  cost  of  such 
demand curtailment should be very high, to be only used as last resort action. In practice, 
the  value  of  lost  load  is  considered  to  be  1-2  order  of  magnitude  higher  than  the 
generation costs. The zonal optimisation model with such a demand curtailment model is 
outlined in detail in section 6.2. 

KPI B7 – Flexibility is only considered to be a qualitative parameter in the proposed CBA 
framework. This KPI related to the usage of unused zonal capacity to exchange balancing 
energy across national balancing markets. System balancing can be provided by different 
types  of  reserve  products  such  as  automatic  or  manual  frequency  restoration  reserves 
(aFRR,  mFRR)  or  replacement  reserves  (RR),  often  also  called  tertiary  reserves.  The 
calculation of the improvement of system flexibility through grid investments requires the 
utilisation  of  optimisation  models,  which  can  incorporate  redispatch  actions  from 
generators.  Also,  considering  the  stochastic  nature  of  system  imbalance,  either  through 
deviations from forecasted generation and demand values or through system outages, a 
probabilistic calculation of redispatch needs is required to quantify flexibility improvement. 

KPI  B8  –  Stability  indicates  the  change  in  system  stability  as  a  result  of  grid 
reinforcement  from  the  perspective  of  transient  stability,  voltage  stability,  frequency 
stability  and  provision  of  system  restoration  services,  e.g.,  black  start  capability. 
Generally,  dynamic  analysis  is  required  in  order  to  assess  the  stability  of  the  system. 
HVDC connections can provide improvements in all aforementioned aspects, and such, a 
quantitative  analysis  of  this  indicator  would  highlight  the  benefits  of  HVDC  technology. 
However,  generally,  detailed  time-consuming  dynamic  simulation  studies  are  required  to 
assess the stability of the system (provided that adequate dynamic model is used). Thus, 
such  analysis  cannot  be  conducted  for  a  large  number  of  operational  states,  such  as 
different grid loading conditions or different contingencies.  

KPI  B9  –  Avoidance  of  renewal  /  replacement  cost  of  infrastructure  indicates  the 
avoidance of new investments in generation capacity, refurbishment of existing generation 
fleet or avoidance in construction of other transmission / distribution lines. Aspects related 
to generation expansion can be derived from the outcome of the socio – economic welfare 
model,  by  analysis  of  the  utilisation  of  generators  in  the  system.  In  order  to  assess  the 
avoidance  of 
transmission  expansion 
optimisation  models  would  be  required,  which  treat  different  expansion  options  as 
candidates,  and  select  the  most  suitable  set  of  candidates  considering  their  investment 
costs.  However,  such  approach  implicitly  performs  a  CBA  within  optimisation  model,  to 
select the best subset of candidate lines. As such, in practise this type of quantification is 
only  be  done  on  a  case-by-case  approach,  by  adding  (or  removing)  additional  grid 
expansion, replacement options besides the actually analysed investment. 

replacements,  dedicated 

transmission 

line 

KPI  B10  –  Reduction  of  necessary  reserve  for  redispatch  power  plants  can  be 
calculated by extending the model used for B1 by means of a redispatch optimisation as 

25 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

outlined  in  section  6.2.3.  In  this  case,  for  all  operating  conditions  throughout  a  year,  the 
maximum  amount  of  required  redispatch  power  within  the  year  is  calculated.  By 
comparing  the  maximum  redispatch  requirement  for  the  case  with  and  without  the  grid 
investment, it can be determined if the redispatch need is increased or decreased, as well 
as what the costs (benefits) of the increase (decrease) would be. HVDC connections can 
help to decrease the redispatch need, due to the power flow control capability they offer, 
and  therefore  this  KPI  is  important  to  be  quantified  to  highlight  the  benefits  of  HVDC 
technology.  

5.2. Drivers for an “enhanced” CBA approach 

As  highlighted  in the  introduction, the  goal  of this  work  is  to  adequately capture  all  risks 
and benefits in an enhanced CBA for planning an AC/DC hybrid grid with high penetration 
of IBRs. Before giving an overview of this enhanced CBA and the proposed additional or 
updated  associated  KPIs,  the  following  section  provide  first  an  overview  of  the  benefits, 
costs and risks of HVDC together with the stability challenges in a system with high IBR 
penetration.  Also,  some  new  or  updated  stability  KPIs  are  introduced  which  will  be 
incorporated in the “enhanced” CBA. 

5.2.1. Benefits from HVDC functionalities 

Power  flow  control  capability:  The  power  flow  control  capability  is  one  of  the  most 
valued technical features of HVDC technology for grid expansion. The fast power control 
capability  of  HVDC  can  help  to  avoid  congestion,  optimize  use  of  existing  assets  and 
increase RES  integration,  reduce system  losses  and reduce  redispatch needs.  Although 
benefits  with  respect  to  congestion  management  and  RES  integration  are  already 
accounted for within KPI B1, KPI B10 could be assessed in a different way to explore the 
benefits  of  power  flow  control  capability  of  HVDC  to  reduce  redispatch  costs.  In  this 
respect,  instead  of  only  comparing  the  redispatch  needs  with  and  without  the  HVDC 
investment,  the  comparison  can  be  done  threefold,  (1)  determination  of  redispatch  need 
without  the  HVDC  investment,  (2)  determination  of  the  redispatch  need  with  the  HVDC 
investment  without  power  flow  control,  (3)  determination  of  the  redispatch  need  with  the 
HVDC investment with power flow control. 

Inertial 
through 
response  provision  capability:  HVDC  can  offer  benefits 
asynchronously  connected  HVDC  systems  with  respect  to  inertia  provision  (or  fast 
frequency  reserves).  Using  dynamic  simulations,  the  rate  of  change  of  frequency 
(ROCOF)  can  be  determined  for  a  number  of  predefined  dimensioning  incidents  and 
operational conditions. As quantitative KPI, different metrics such as the inertia provision 
speed in MW / s, the inertia provision capability in MW / Hz and/or the improvement of the 
ROCOF in Hz / s can be provided. However, it is difficult to monetize the inertial response 
provision  capability  from  HVDC  systems  due  to  the  stochastic  nature  of  the  incidents 
happening  in  system  operation,  and  the  large  number  of  possible  system  operational 
states.  In  this  study  we  use  minimum  inertia  constraints,  which  are  based  on  a  given 
allowable  ROCOF  in  the  network  and  determine  the  generation  dispatch  costs  for  the 
cases  (1)  without  the  inertia  constraint,  (2)  with the  inertia  constraint  but  no  contribution 
from  HVDC  and  (3)  with  an  inertia  constraint  which  considers  HVDC  contribution.  By 
analysing the difference in costs, we can derive the benefits of inertial response provision. 

Improvement of resilience: HVDC technology can help to increase the resilience of the 
power system in two fundamental ways. 

Firstly,  by  decreasing  the  vulnerability  of  the  system,  by  for  instance  improving  system 
stability through more robust control and application of special protection schemes. HVDC 
can  act  as  firewalls  between  different  parts  of  the  power  system  and  help  to  isolate 

26 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

healthy  parts  of  the  system  in  a  fast  way,  in  case  of  wide-spread  disturbances  in  the 
system.  Other  technical  features,  such  as  oscillation  damping,  provision  of  short  circuit 
current, and voltage control, can further improve the quality of service and the system. 

Secondly, the resilience of the system can be improved through faster system restoration 
after major events, for instance through provision of black-start services. When equipped 
with grid forming functionality, HVDC converters can provide a stable voltage reference, to 
which other parts / devices of the system can be synchronized to.   

Although in theory quantitative KPIs such as MWh / year of avoided service interruptions, 
or  their  societal  cost  in  €  /  year,  can  be  defined,  the  calculation  of  such  KPIs  is  very 
difficult.  To  analyze  the  improvement  of  the  system  vulnerability,  detailed  dynamic 
simulations  can  be  performed  for  a  number  of  critical  contingencies  and  operating 
conditions. This way the frequency and voltage stability of the system can be assessed.  

For  the  improvement  of  the  system  restoration,  even  though  a  number  of  steady-state 
analysis  tools  exist  to  analyse  the  system  restoration  from  the  power  flow  and  power 
balance  points  of  view,  the  main  challenge  in  system  restoration  is  ensuring  dynamic 
stability.  As  such  many  different  types  of  dynamic  simulations  would  be  required  to 
analyse the system restoration process in detail, covering different operational scenarios 
as  well  a  number  of  emergency  situations,  such  as  different  system  restoration 
sequences.  Considering  that  black  start  services  could  be  delivered  by  different  HVDC 
connections to different countries at the same time, large scale simulation models would 
be needed. As such, this KPI better is suited to be defined in a qualitative manner for high 
level  CBA,  whereas  TSOs  can  quantify  this  parameter  through  more  detailed  simulation 
models for known system restoration sequences.  

Improvement  of  system  stability:  HVDC  converters  can  provide  several  system 
services  that  will  improve  system  stability.  These  services,  such  as  voltage  control, 
frequency response or grid forming controls can be beneficial for the system and reduce 
the  need  of  investment  in  other  assets.  It  is  important  to  note  that  the  classical  zonal 
approach typically ignores network constraints. Therefore, additional constraints or nodal 
network model would need to be considered, to observe the benefits of HVDC technology 
for  improving  system  stability.  It  must  also  be  kept  in  mind  that  the  goal  is  to  integrate 
more  RES  in  the  system  and  that  more  IBR  based  RES  poses  challenges  to  system 
stability.  Therefore,  this KPI  can  be  quantified  by  evaluating  the  percentage of  operating 
conditions which are at risk of being unstable. 

Public  acceptance: HVDC  technology  overhead  lines  have  a  smaller  footprint  than  AC 
overhead  lines.  Also,  HVDC  cables  (underground  or  undersea)  can  be  used  on  much 
longer  distance  than  AC  cables.  It  is  therefore  believed  that  HVDC  will  be  more  easily 
accepted by the public and that the permitting process will potentially be quicker than for 
AC lines. Such public acceptance is very difficult to be translated in a quantitative KPI, but 
should  be  taking  into  account  in  future  CBA  in  a  qualitative  manner  when  comparing 
different network expansion options. Although not further  elaborated in this report, public 
acceptance  may  become  one  of  the  bottlenecks/key  decision  points  in  future  network 
expansion. 

5.2.2. Risks and Costs of HVDC 

HVDC protection strategy cost:  The costs for AC protection systems are relatively low 
when  compared  to  the  total  investment  cost  of  grid  expansion.  However,  HVDC  circuit 
breakers  can  be  costly,  and  especially  in  large  multi-terminal  and  meshed  HVDC  grid 
expansion projects, their costs should be taken into account. This can be done based on 
existing studies on HVDC protection systems, such as proposed within the PROMOTioN 
project [4].  

27 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Interoperability: Multi-vendor interoperability of HVDC systems is, at the time of writing of 
this  document,  still  an  important  challenge.  There  are  several  ways  to  de-risk  potential 
interoperability  problems,  but  some  include  additional  costs  (e.g.  use  of  replica).  As  it  is 
not clear what will be the best way to mitigate interoperability issues, no additional cost is 
foreseen in our calculation. 

Extendibility4:  HVDC  systems  are  currently  not  built  to  be  extended.  Allowing 
extendibility might require additional costs (e.g. spare place on DC-busbar, spare place for 
DCCB,  etc.)  and  also  clear  specifications  for  the  control  systems.  For  modelling,  an 
additional margin on the cost could be considered to allow for future extension.  

Technology  maturity:  The  technology  is  still  evolving  (e.g.  DCCB,  XLPE  cables, 
converters,  etc.)  and  is  not  yet  at  a  fully  mature  stage.  However,  it  is  assumed  that  the 
technology will be ready at the time horizon considered in this project (i.e. 2030 onwards). 

5.2.3. System stability challenges with high penetration of IBRs 

Stability of power systems with high penetration of IBRs is an important challenge which 
might require mitigation means such as new investments (e.g. synchronous  condensers, 
BESS, etc.), advanced controls (e.g. grid forming) and/or operational constraints. In [5], it 
is  noted  that  “In  the  midterm,  until  new  technical  solutions  are  implemented,  it  may  be 
necessary to take additional measures (e. g. RES curtailment or power flow limitations) to 
ensure system security. As such, there is a need to work decisively on the target solutions 
and  to  make  them  available  when  necessary,  so  that  the  midterm  and  probably  costly 
limitations  does  not  last  too  long”.  There  is  therefore  uncertainty  on  costs  for  securing 
future  system  operations  with  high  RES,  which  will  require  more  simulations,  advanced 
control loops, operational measures and/or additional assets.  

The  main  technical  challenges  related  to  stability  in  power  system  with  high  IBR 
penetration are the following: 

•  Reduced inertia and frequency stability 
•  Low system strength5 which can impact:  
o  Functioning of protection devices 
o  Power Quality 
o  Transient stability of synchronous machines 
o  Converter-driven stability 

•  Voltage control 
•  Potential control interactions 

The currently proposed stability KPIs in the ENTSO-E methodology are qualitative and are 
based  on  the  theoretical  benefits  of  a  technology  with  respect  to  transient,  voltage  and 
frequency  stability  [3].  While  this  provides  some  information,  it  is  important  to  not  only 
focus  on  the  technology  but  also  to  consider  some  more  project-specific  characteristics. 
Moreover, the KPIs used by ENTSO-E focus on classical stability aspects (i.e. Transient, 
Voltage and Frequency) while the stability challenges of IBRs in weak grid has to also be 
specifically considered.  

Table 3 proposes therefore two additional KPIs allowing to quantify the risks related to a 
grid with high penetration of power electronics. The quantification is based on the number 
of  hours  where  the  system  is  considered  at  risk.  It  should  be  noted  that  the  KPI  B.4 

4  Extendibility  defined  as  “The  design  should  allow  for  the  forecast  need  for  future  extensions”  (from  National  Grid  ESO, 
https://www.nationalgrideso.com/industry-information/codes/security-and-quality-supply-standards/code-documents)  

5 system strength refers to the “characteristic of an electrical power system that relates to the size of the change in voltage 
following a fault or disturbance on the power system” [32] 

28 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

(converter-driven  stability)  is  really  a  new  KPI,  while  the  assessment  of  existing  KPI  8.1 
frequency stability is extended/updated with some new metrics. 

Table 3 - Proposed Stability KPIs to be incorporated in the “enhanced” CBA 

Proposed KPI 

Metrics 

How to calculate? 

Comments 

B 8.1.Frequency 
stability: 
Percentage of 
hours per year 
where frequency 
stability is at risk 

Estimated inertia 

Unit dispatch 

RoCoF 

Use of swing equation 

Frequency nadir 

Use of (simplified) time-
domain simulations 

Simplified time-
domain simulations 
on single-node 
network can be used 
but lead generally to 
optimistic results. 

B 8.4. 
Converter-driven 
stability: 
Percentage of 
hours or RES 
energy per year 
where 
Converter-driven 
stability is at risk 

Percentage of 
hours at risk 

SCR 

Use of time-domain 
simulations or use of 
inertia/RoCoF constraint 
Using network static data 

Risk indicator 

Converter-driven 
instability risk 
indicator 

Using network static data 
and simplified grid 
following control 
parameters 

Indicator considering 
not only grid strength 
but also IBR control 
loop 

Converter-driven 
instability from 
RMS simulation 

Converter-driven 
instability (EMT + 
modal analysis) 

Using RMS simulations 

Using EMT simulations + 
frequency-scan 

To be used on a 
selection of operating 
conditions and with 
adequate model 
parameters. 

In the  example  of  the  reduced  inertia  challenge,  it  is  therefore  needed  to  estimate  the 
inertia of each operating condition and also the minimum inertia constraint. The proposed 
KPIs require to therefore evaluate the percentage of operating conditions being below the 
inertia  constraint.  A  monetary  value  can  also  be  linked  to  this  KPI  by  adding  a  stability 
constraint  based  on  an  allowable  minimum  inertia  level  within  economic  dispatch  or 
redispatch calculations (as described in section 6.2).  

Regarding  the  KPI  for  converter-driven  stability  (in  weak  grid),  it  is  also  proposed  to 
quantify the number of operating conditions or the amount of energy produced by RES for 
which a stability risk was identified. The  stability of inverter based resources is driven by 
their  control  loops.  With  that  regards,  typical  controls  of  inverters  are  grid-following  and 
require therefore  a  stable  source of voltage to  synchronize to  the  grid.  Theoretically, the 
stability  of  IBRs  has  to  be  assessed  via  EMT  simulations.  This  is  the  only  type  of 
simulations  which  can  fully  capture  the  potential  instability  in  the  different  control  loops 
and  in  the  dynamics  of  the  inverters.  However,  accurate  models,  which are  typically  not 
available at the CBA stage of projects, are required. Another option would be to use RMS 
simulations to capture some aspects of converter-driven instability (such as stability of the 
PLL  in  weak  grid).  However,  RMS  simulations  also  require  adequate  models  (including 
PLL  control  loops  of  grid  following  inverters,  current  limiter  loops  and  grid  forming 
implementations).  While  having  limitations,  the  mostly  used  indicator  is  the  short-circuit 
level  which  represents  the  “strength”  of  the  network.  Therefore,  it  is  proposed  to  use 
indicators such as the short-circuit ratio (SCR) or more advanced metrics considering the 
SCR  but  also  some  basic  control  loops  of  the  inverters  and  their  setpoint  (such  as  the 
CCT-IBR described in [6] [7]). Based on these metrics, a threshold can be used (e.g. SCR 
<  3)  and  the  number  of  operating  conditions  for  which  the  threshold  is  not  reached  are 
29 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

considered  as  at  risk  of  being  unstable.  Figure  7  illustrates  that  there  are  more  stability 
challenges  when  the  SCR  is  below  3  and  that  advanced  controls  or  even  new 
assets/hardware are required when SCR goes below 2. Since converter-driven instability 
can also affect HVDC systems, from the same figure it becomes evident that grid forming 
control  in  HVDC  can  increase  their  range  of  stable  operating  conditions  and  therefore 
allow to integrate more RES.  

Figure 7 - Impact of SCR on Converter-driven stability (from [8]) 

5.3. Overview of “enhanced” CBA approach 

The  “enhanced”  CBA  as  proposed  in  this  work  has  two  main  aspects.  First  of  all,  it 
introduces new KPIs or updates existing ones to capture not only the benefits, but also the 
cost  and  risks  associated  with  HVDC.  An  overview  of  the  way  the  benefits  provided  by 
HVDC are incorporated in the “enhanced” CBA is presented in Table 4 at the end of the 
section  (not  all  of  them  will  be  further  elaborated  in  this  project,  but  a  first  proposal  has 
been included on future KPIs). The computational requirements, e.g. the way to monetize 
the corresponding KPIs are also presented in this table. 

Secondly, as it is a fact that operating a system with high penetration of power electronics 
interfaced devices is a fundamental shift from the current system operations, the question 
is  to  know  which  assets  will  be  required,  which  functionalities  are  required  in  order  to 
ensure  security  and  reliability  of  the  system  and,  last  but  not  least,  which  tools  and 
methodologies  are  required  to  study  them.  Therefore,  the  “enhanced”  CBA  sets  also  a 
framework  to  assess  the  KPIs  in  future  power  systems  building  upon  the  existing  CBA 
approach, see also Figure 8. 

30 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 8 - Overview "enhanced" CBA approach 

As shown in this figure, the existing framework focuses on zonal market simulations. This 
is  the  basis  of  the  pyramid  and  stays  the  main  key  element  in  the  CBA  assessment. 
However,  there  are  some  additional  aspects  that  should  be  evaluated.  In  particular,  it  is 
needed to verify whether large power flows over long distance do not cause any thermal 
violations  and  whether  system  stability  is  maintained  for  a  wide  range  of  operating 
conditions. 

Section 5.2.3 described the additional stability KPIs that we recommend for integrating in 
the “enhanced CBA” while sections 6.2 and 6.3 provide more details on how to compute 
them. It is important to note that the proposed approach has several layers of complexity 
and  it  is  shown  how  the  complexity  of  the  model  should  be  increased  to  compute 
additional  KPIs  or  to  quantify  KPIs  that  are  currently  assessed  only  in  a  qualitative 
manner. 

the  overall  dispatch  costs  with 

The  first  layer  of  the  proposed  approach  is  the  zonal  market  simulation.  On  this  aspect 
there  is  no  change  compared  to  the  existing  CBA  framework  (i.e.  energy  simulations, 
minimizing 
is 
recommended  to  complement  this  zonal  market  simulation  step  by  an  inertia 
calculation  and  simplified  frequency  stability  assessment.  The  main  reason  is  that 
reduced  inertia  presents  a  significant  challenge  for  future  system  operations  and  it  is 
important to at least identify whether the planned operating conditions will be at risk or not. 

transfer  capacity  constraints). 

It 

The  second  layer  consists  of  nodal  market  simulations  based  on  the  European  static 
network model. It is understood that the European network model is currently not widely 
used during the CBA calculation, except for calculation of losses or redispatch simulations 
in  a  limited  number  of  operating  conditions.  It  is  proposed  to  considerably  extend this 
second layer by: 

• 

Including power flow control capabilities of HVDC 

•  Adding stability constraints (such as inertia)   

31 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Therefore, the network model needs to be more intensively used in the economic dispatch 
optimization.  This  will  allow  to  quantify  the  redispatch  costs  for  each  thermal  and/or 
stability  constraint,  and  by  consequence,  give  a  clear  order  of  magnitude  on  what 
mitigation actions need to be put in place to ensure stability. More mathematical details on 
the  implementation  of  the  network  model  optimization  problem  can  be  found  in  section 
6.2. 

The  third  layer  which  is  recommended  in  this  work,  consists  of  a  more  detailed  stability 
assessment.  As  already  outlined,  stability  of  systems  with  high  penetration  of  IBRs  is 
currently a challenge. It is also commonly agreed that the converter-driven stability must 
be assessed using very detailed and representative models that are typically not available 
when performing a CBA study. Our approach is thus to use indicators that can represent 
operating  conditions  at  risk  of  being  unstable.  More  details  on  these  indicators  are 
presented in section 6.3.2. 

On  top  of  these  recommended  three  first  layers,  additional  more  complex  layers  are 
proposed. These include time-domain simulations in RMS or EMT domain. As illustrated 
in  Figure  9,  RMS  simulation  (also  called  phasor-mode  simulation)  is  suitable  for  the 
classical types of power system stability and slow interactions, whereas EMT is necessary 
for faster stability phenomena. 

Figure 9 - Power system stability classification and simulation type for each type of stability (Figure inspired by [8] and [9]) 

It  must  be  evaluated  for  each  project  which  simulations  are  required.  These  simulations 
will typically be performed closer to the design stage of the project and therefore after the 
CBA  approach  which  is  the  scope  of  this  report.  It  is  however  important  that,  during  the 
CBA, projects which will require more advanced simulations are identified. This will allow 
to include a cost margin for further studies and de-risking potential stability issues. 

Finally,  the  use  of  real-time  simulations  or  even  hardware-in-the-loop  is  recommended 
when  knowing  the  design  of  the  project  under  consideration.  These  simulations  are 
extremely important for understanding the behaviour of power electronics assets in weak 
grids.  Also,  the  use  of  replica  for  HVDC  systems  has  shown  great  benefits  to  prevent 
adverse  interactions  or  for  root-cause  analysis,  and  for  allowing  simulations  on  the 
protection  system  design  of  multi-terminal  HVDC  and  HVDC  grids.  However,  these 
simulations are project specific and not to be used at a European scale CBA. 

32 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Table 4 - Benefits provided by HVDC incorporated in “enhanced” CBA 

Unit 

Monetized  Qualitative/ 
Quantitative 

Computational 
requirements 

Comments 

€ / year 

Yes 

Quantitative  Redispatch OPF 

Additional 
benefits 
considered 
in this work  

Power flow 
control 
capability 

Link 
to 
KPI 

B.10 

B.8 
or 
B.10 

B.8 
or 
B.10 

Would be too 
excessive to 
calculate for N-1 
contingency sets 
and large number of 
operating 
conditions. 
Sampling/clustering 
would be needed.  
No unified definition 
of the SCOPF. 

Swing equation can 
be used in 
"conventional" 
systems where the 
main inertia 
provision comes 
from rotating 
masses. Frequency 
time-domain 
simulations 
recommended in 
systems with high 
penetration of virtual 
inertia or fast-
frequency 
responses. For 
monetizing, inertia 
constraints can be 
embedded in steady 
state optimisation 
models. 

"New" type of 
stability 
classification. The 
most important is to 
identify risk of 
instability operating 
conditions. 
Depending on the 
project, simplified or 
more detailed 
assessment can be 
performed. For 
monetizing, stability 
constraints can be 
embedded in steady 
state optimisation 
models.  

Improvement 
of frequency 
stability 

Percentage 
of 
operation 
conditions / 
year  

Or  

€ / year (if 
redispatch) 

for a set of N-1 
contingencies, 
similar to B10. 
Two sets of 
calculations, with 
and without 
HVDC set point 
changes. 
Possibly 
SCOPF. 

No 

Quantitative  Dynamic 

Yes 

 Quantitative 

simulations or 
swing equation 
needed to 
determine 
ROCOF. 
Provision of 
inertial or fast-
frequency 
response 
through 
asynchronous 
HVDC. 
Addition of 
inertia constraint 
in redispatch 
calculation 
needed if 
monetary is 
required.  

Improvement 
of converter-
driven 
stability 

Percentage 
of 
operation 
conditions / 
year  

Or  

€ / year (if 
redispatch) 

No 

Quantitative  Simplified 

assessment, 
RMS or EMT 
simulations 
required 
depending on 
the phenomenon 
under 
assessment and 
available 
dataset..  

Yes 

Quantitative 

33 

 
  
  
  
  
  
  
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Additional 
benefits to 
be 
assessed in 
future work 

Resilience 
improvement 

Public 
acceptance 
and 
permitting 

Protection 
system  cost 
and 
extendibility 
as  part  of 
CAPEX  

Unit 

Monetized  Qualitative/ 
Quantitative 

Computational 
requirements 

Comments 

MWh/year 

Yes 

Quantitative  Dynamic 

€ /year 

- 

No 

Qualitative 

simulations for 
firewalling. 
Black-start 
simulations. In 
both cases the 
avoided 
expected energy 
not served 
through HVDC 
could be used as 
KPI  

Expected 
duration for 
permitting 
process 

Difficult to model in 
detail in a 
harmonised way. 
Future work needed 
to have a common 
agreement by 
stakeholders on 
what to include in 
resilience 
assessment. 

Non-technical 
indicator, very 
project specific. 

Link 
to 
KPI 

/ 

/ 

€  

Yes 

Quantitative  Additional cost 

of protection 
system or multi-
terminal 
readiness as 
part of the 
CAPEX. 

C.1 

Reliable  cost  data 
on 
(projections) 
HVDC 
equipment 
needed.  

5.4. Data for determining CBA-KPIs of the selected use 

cases 

The  data  being  used  in  the  optimization  process  from  the  following  sections  are  coming 
from the ENTSO-E database. In fact, the reference grid, generation and demand data are 
taken from the TYNDP 2020. The reference grid data help to give an overview about how 
the transmission lines are connected in the system. Knowing the level of interconnection 
between  areas  is  fundamental  to  evaluate  the  effects  of  new  investments  on  the  grid. 
Regarding  generation,  the  installed  capacity  for  each  bidding  zone  in  the  European 
system is used as input data. Information regarding renewables, conventional generators, 
power  to  grid  technologies  (P2G)  and  flexibility  providers  such  as  electric  storage  and 
demand side response (DSR) are listed based on the DE2040 scenario from [10]. Among 
the renewables (RES), data can be found for wind (offshore and onshore), solar PV, solar 
thermal, hydro reservoir and run-of-river. All the other RES sources are grouped in ‘other 
RES’.  On  the  conventional  generators  side,  the  sources  being  included  are  coal  lignite 
(new  and  old  1-2),  hard coal  new  and  old (1-2- +Bio),  gas (conventional  old  1-2,  CCGT, 
CCGT  new  CCS  and  present  1-2  CCS,  OCGT new  and  old),  oil  (heavy,  light  and  shale 
new), PS (closed and open) and nuclear power plants. All the other kinds of conventional 
generator  capacities  are  summed  up  in  ‘Other  non-RES’.  The  demand  data  contain  the 
load for each bidding zone for an entire climate year, i.e. 8760 hours.  

34 

 
  
  
  
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

When developing a nodal balance model, it becomes clear how there is a lack in precise 
data for each node in the system. As anticipated, the ENTSO-E data set is based on the 
European zonal model, which assumes the electricity price to be constant for buses in the 
same bidding zone. Furthermore, the Kirchoff’s and Ohm’s laws behind the nodal model 
are not considered. The only limiting factor for the power transfer is the computed NTC for 
the different zones. In order to have a better overview about the status of the power grid, 
the demand and generation data need to be distributed to the nodes in each zone. With 
such a nodal balance model, the loading of each line is analyzed and the power flows to 
each bus are investigated. The main reason to use this kind of model is the more reliable 
picture of the power system that is computed. As a result, it is possible to study the cost of 
electricity  in  a  more  detailed  way  and  spot  possible  additional  benefits  of  HVDC 
technologies  which  cannot  be  fully  grasped  in  the  original  zonal  model.  For  example,  a 
selected line which is not considered in the zonal model could turn out to be overloaded 
for most of the time in the nodal balance model. For this reason, installing a new HVDC 
link  near  the  selected  line  could  lead  to  a  more  optimal  power  dispatch  in  the  grid  and 
improve results for both reliability indexes and the computed KPIs. 

5.5. Interface between steady-state optimization and power 

system simulations 

The  highly  detailed  European  high  voltage  network  model  (which  can  be  obtained  from 
ENTSO-E  under  confidentiality  agreement)  consists  of  more  than  7000  substations  and 
10000 transmission  lines  (and  cables)  and  7000  generating  units.  The calculation  of  the 
CBA-KPIs by applying hourly optimal power flow calculations on this large network model 
would be too time consuming on the one hand, and has a higher risk of non-convergence 
on the other. As such, a two-step approach is used for determining the CBA-KPIs.  

First, the NTC based economic dispatch model as described in section 6.2.1 is solved for 
the  whole  European  region  to  determine  the  hourly  dispatch  of  each  generation  type  on 
an  hourly  basis,  for  the  selected  scenarios  and  planning  horizons.  This  way,  the  net 
positions of each market zone, and the total power exchange between the market zones 
are determined. All data to conduct this zonal analysis are publicly available at ENTSO-E 
and  the  location  of  data  is  provided  in  the  appendix.  The  data  contain  the  aggregated 
generation capacity per generation type for each market zone per planning year, climate 
year  and  scenario.  Additionally,  time  series  for  RES  capacity  factors  and  demand  are 
available for each market zone. 

In  a  second  step,  the  detailed  high  voltage  network  model  is  used  to  perform  OPF 
calculations  where  controllability  of  HVDC  can  be  taken  into  account.  Depending  on  the 
use case, e.g., the location of the HVDC link, the detailed networks of the countries where 
the  HVDC  connections  are  located  are  used.  All  other  countries/market  zones  are 
represented  by  equivalent  single  nodes.  For  instance,  for  the  Navarra  –  Landes  link 
connecting Spain and France, it is sufficient to use the detailed network models for Spain 
and  France,  and  use  equivalent  nodes  for  all  other  neighbouring  networks.  In  order  to 
maintain consistency between the zonal and the nodal network models, a disaggregation 
of  the  zonal  model  is  performed  which  is  described  in  section  7.  The  demand  is 
disaggregated  linearly  from  the  zonal  model  to  the  nodal  model,  whereas  the  hourly 
generation dispatch is disaggregated based on the maximum generation capacity of each 
unit. 

Beside the nodal and zonal simulations, also a sequential approach is applied by means 
of  an  iterative  procedure  between  optimal  power  flow  calculations  and  the  dynamic 
simulation performed for validating system stability. This procedure is visualized in Figure 
10. 

35 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 10 - Iterative procedure between steady state and dynamic calculations 

In  the  first  instance,  optimal  power  flow  calculations  are  used  (either  on  zonal  or  nodal 
network  models  depending  on  the  nature  of  the  use  case),  which  determines  the 
generation set points under various operational conditions. Using this information dynamic 
simulations  are  performed  to  identify  potentially  unstable  cases,  as  well  as  the  required 
level of system inertia to ensure system stability in such cases. This information is passed 
back to the steady state calculation routine, which can determine a new set of generator 
and HVDC converter set points considering the inertia constraints. 

Dynamic  simulations  are  performed  on  the  results  of  the  AC/DC  grid  OPF  described  in 
section  6.2.  It  is  hence  expected  to  receive  from  the  OPF  a  series  of  generation 
dispatches optimized on an hourly basis for at least one year which yields 8760 different 
network conditions. It is not relevant nor realistic to perform the time-domain simulations 
on each dispatch, for the following reasons: 

•  The interest of the time-domain simulations lies in the identification of weaknesses 
in  the  grid  leading  to  instabilities.  These  weaknesses  can  only  be  highlighted 
during periods of significant stress on the system, which should occur only during 
a  limited  period  of  time  throughout  the  year.  In  other  words,  most  generation 
dispatches extracted from the OPF will be far away from the stability limits of the 
system and hence bring limited added value to the time-domain results. 

•  Most  dispatches  will  be  redundant,  for  instance  due  to  daily,  weekly  or  monthly 

periodicity.  

•  Considering  the  size  of  the  systems  envisaged  (multi-country  scale),  the  time-
domain  simulations  will  be  time-extensive.  It  is  key  to  reduce  the  number  of 
simulations required for efficiency purposes. 

Consequently,  the  time-domain  simulations  are  performed  on  a  selection  of  cases 
amongst the hourly dispatches provided by the OPF. The dimensions used to perform the 
selection  will  be  key  to  ensure  that  the  simulations  consider  the  worst-case  dispatch 
scenarios for each instability envisaged. For instance, the total inertia of the system is to 
be  considered  if  frequency  stability  is  of  concern.  For  the  purpose  of  AC/DC  system 
studies, the following dimensions are suggested: 

•  Level of AC short-circuit at key nodes of the network; 
•  Power Flow through the DC link(s) and on parallel AC lines (if relevant); 
•  Overall demand of the system; 
•  Ratio RES production over overall demand; 
•  System inertia (in MW.s); 

36 

Nodal OPF and redispatch (including thermal, inertia and stability risk constraints*)Identification of unstable cases and grouping/clustering of similar hourly dispatchsZonal and Nodal SimulationsIdentification of stable casesDetermining stability constraint 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Once the N dimensions have been selected, each dispatch scenario is then associated to 
a  n-tuple  and  might  have  to  be  processed  into  a  normal  distribution  for  uniformity  of 
dimensions  purposes.  Finally,  each  n-tuple  can  be  plotted  in  a  multi-dimensional 
environment where each axis corresponds to one dimension, then we can use clustering 
methods to select either representative scenarios (which lie in “the middle of the cloud” of 
points), or extreme scenarios (which lie at the edge of the cloud of points).  

Two clustering methods have been used in this work. The first clustering method is based 
on the K-means algorithm and aims at grouping similar operating conditions into clusters. 
The main goal is to perform more advanced simulations on representative samples from 
each  cluster  rather  than  on  each  operating  point.  These  advanced  simulations  can  be 
power  system  time-domain  simulations  or  redispatch  calculations.  When  using  this 
clustering technique, it is recommended to set a relatively high number of clusters (ideally 
equal to the highest number of advanced simulations that can be handled by the user).  

The  second  clustering  technique  is  based  on  the  DBSCAN  algorithm.  This  algorithm 
analyses the density of points in the n-dimensional space. It is therefore a good algorithm 
to identify a representative set of operating conditions (i.e. operating conditions that occur 
regularly  over  the  year).  The  overall  methodology  is  summarized  in  Figure  11.  The 
clustering process itself is illustrated in Figure 12 and Figure 13, which show the different 
types of results obtained by the two proposed clustering approaches. 

OPF hourly 
dispatch DB

Dimension 
selection

Dimension 
value 
extraction from 
DB

Distribution 
normalisation

Scatter plot 
and clustering

Figure 11 – Dispatch scenario selection process 

Figure 12 – Example of an hourly dispatch selection through K-means clustering. This example counts 20 cluster (each 
cluster is indicated by a color). Advanced simulations can be performed on each of these clusters. 

37 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 13 – Example of an hourly dispatch selection through DBSCAN clustering. This example counts 3 representative 
clusters (e.g. low, intermediate and high RES penetration). It can be seen that a significant number of points are not 
assigned to these clusters.

38 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

6. Modelling and implementation guidelines 

6.1. Technical Aspects of HVDC and Modelling Requirements 

6.1.1. HVDC technologies, configurations, and technical features 

Two dominant HVDC technologies are used currently: Line Commutated Converter (LCC) 
and  Voltage  Source  Converter  (VSC).  Most  of  the  HVDC  connections  in  operation 
worldwide  use  the  LCC  technology,  which  relies  on  thyristor  semiconductor  switches. 
Their  power  and  voltage  ratings  keep  increasing  over  time  with  voltages  up  to  1100  kV 
and  rating  up  to  10  GW  in  China.  On  the  other  hand,  VSCs  have  gained  momentum 
during  the  recent  years  and  are  the  most  used  technology  in  Europe.  VSCs  rely  on 
Insulated  Gate  Bipolar  Transistors  (IGBT)  for  the  conversion  process,  which  allows  to 
generate an independent AC voltage waveform.  

Although  LCC  technology  is  mature  and  offers  several  benefits,  VSC  technology  offers 
additional advantages, such as [11]: 

•  Four-quadrant  operation:  LCCs  consume  large  amounts  of  reactive  power.  In 
contrast,  VSCs  can  absorb  or  consume  reactive  power  depending  on the  system 
requirements, thus achieving independent active and reactive power control. 

•  Power  reversal:  VSCs  can  almost  instantaneously  change  the  power  ﬂow 
direction,  whereas  in  LCC  connections  this  requires  shutting  down  the  link  and 
reversing the DC voltage polarity. 

•  Possibility to connect to weak AC grids: LCCs require a strong enough AC grid 

to operate correctly. VSCs do not necessarily face such a limitation. 

•  Grid forming and black-start capability: VSCs can generate a voltage output to 
which  other  devices  can  synchronize.  This  makes  it  extremely  attractive  for 
offshore applications. 

•  Fault-ride through capability: VSCs can ride through low AC voltages, whereas 

LCCs are prone to commutation failures. 

•  Harmonics:  VSCs  generate  less  harmonic  content  than  LCCs.  Therefore,  the 

need for AC and DC ﬁlters is smaller. 

•  Footprint:  VSC  stations  are  generally  less  bulky  than  LCC  stations  of  the  same 

rating, mainly due to the smaller requirements for ﬁlters. 

•  Cheaper  cables:  VSCs  can  be  connected  with  XLPE  cables,  instead  of  the  oil-

based (mass impregnated) cables required for LCC connections. 

The  state-of-the-art  ratings  currently  considered  in  Europe  for  offshore  VSC-HVDC 
transmission  are  2  GW  at  ±525  kV  assuming  a  bipolar  topology  and  Modular  Multilevel 
Converters (MMC).  

Attractive  system-level  features  and  the  related  functionalities  that  VSC-HVDC  can  offer 
are  key  to  many  of  the  drivers  for  the  increasing  use  of  HVDC  systems.  Many  of  these 
features  are  beneficial  to  increased  system  flexibility,  controllability,  resilience,  and 
security  as  time  constraints  to  get  system  back  to  normal  operating  conditions  are 
becoming  tighter.  Nevertheless, these benefits  are  often  not  properly reflected  in holistic 
planning  approaches  such  as  CBAs  that  is  key  to  adopting  and  investing  in  HVDC 
technologies  at  the  planning  stages.  Thus,  the  benefits  and  potential  cost  impacts  are 
often not completely captured. 

The precursor to assessing how the current CBA should be extended is highly dependent 
on the foreseen impact on the system by a feature and its functionalities, and how these 
may  influence  analyses.  The  benefits  of  HVDC  technologies  for  hybridization  are  not  in 
question  as  they  are  well-promoted  and  are  major  drivers  for  these  technologies.  The 
major challenge is the potential cost implications (savings or expenditure) and how these 
39 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

trades-off  with  the  potential  benefits,  and  by  how  much  these  costs  are  high  enough  to 
influence  the  CBA.  Importantly,  the  system  impact  is  dependent  on  the  expected 
functionality,  implementation  details  (generic  or  specific),  initial  speed  of  response, 
duration  of  response,  and  repeatability.  These  in  turn  influence  modelling  requirements, 
tools, and necessary studies — all related. 

This section aims at highlighting some of the most important features and functionalities, 
and some key benefits they provide. Subsequently, the minimum modelling requirements 
to  adequately  represent  and  capture  the  benefits  of  these  features  and  typical  tools  to 
adopt  in representing them  are  discussed relative  to  the  desired  level  of  detail.  Some  of 
the  most  important  features  and  the  related  functionalities  of  each  (traditional  and 
emerging) include: 

1.  Frequency regulation and inertia-emulation. 
2.  Voltage regulation and reactive support. 
3.  Power flow control and transient stability enhancement. 
4.  Black-start capability 
5.  Grid-forming capability 

Considering  that  the  response  and  behavior  of  HVDC  systems  are  inherently  control 
driven,  many  of  the  features  and  functionalities are  at  the  lowest  levels  implemented  by 
device-control structures based on a hierarchical structure. Figure 14 shows a high-level 
block diagram from the external terminals of the HVDC converter to the inner-most control 
block that actuates the converters. The figure also roughly highlights in color the level of 
detail generally required to represent these blocks in simulations. However, from another 
perspective  it  also  suggests  which  blocks  are  generally  not  required  to  be  modelled  in 
basic  simulations;  by  basic  we  mean  first-level  representations  for  high-level  insights.  In 
the  following,  we  dive  deeper  into  each  feature  identified  previously,  short  description  of 
each,  typical  related  functionalities  under  each  feature,  and  generic  implementation 
details. 

Figure 14 – High-level abstract of an HVDC converter from external terminals to inner-most functionalities 

40 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Table 5 – Color legend for qualitative level of details 

Frequency 
spectrum of 
phenomena 

Remarks 

A+ 

> 10 kHz 

A high-level of detail is required to fully capture the phenomena 
that most characterize the said component or their system-level 
impact. 

A 

< 10 kHz 

Further  simplifications  to  previous  level,  though  the  level  of 
detail is still significantly high.  

B 

100 – 1 kHz 

Level  of  detail  required  to  capture  the  behaviour  of  control 
structures typical of PE and their system impact. The system is 
correspondingly modelled. 

C 

< 500 Hz 

Typical  level  of  detail  required  in  EMT  simulations  to  model 
generic PE devices, their controllers, and system impact. 

D 

1- 10 Hz 

Traditional domain of RMS simulation. 

D- 

< 1 Hz 

Lowest  level  of  detail.  Traditional  domain  of  system-adequacy 
and  load-flow  tools.  This  level  of  detail  is  synonymous  with 
typical CBA. 

6.1.2. Frequency  Regulation  and  Inertia-emulation  Capabilities 

from HVDC 

Frequency regulation is at the core of power system operation and security in its entirety. 
In  the  conventional  system,  synchronous  generators  have  been  at  the  core  of  nearly  all 
frequency  regulation  activities  —  inertia,  frequency  response,  balancing,  reserves,  etc. 
Large-scale  efforts  aimed  at  transitioning  the  system  to  a  renewable-based  system  is 
leading to a progressive decommissioning of these generators, while replacing them with 
power electronic (PE) interfaced generation without a natural capability to regulate system 
frequency.  Thus,  the  system  is  being  deprived  of  its  natural  capability  to  regulate 
frequency.  On  the  other  hand,  these  PE  interfaces  can  be  purposefully  designed  to 
support  and  regulate  system  frequency  with  superior  flexibility  and  controllability  than 
conventional generators. 

Frequency  regulation  with  HVDC  systems  is  generally  achieved  by  the  adjustment  of 
power  flow  between  areas  interfacing  converters  and  the  availability  of  containment 
reserves  or  access  to  readily  available  energy  sources.  This  adjustment  can  be 
automated  based  on  pre-defined  system  conditions,  manually  activated,  or  both 
depending on circumstances, timing of operations, and energy reserves at the moment of 
activation. The activation of frequency regulation by asynchronous HVDC systems results 
in a coupling of the frequency of the two synchronous areas. The actual type of coupling 
could  be  static  (stepwise  adjustment)  or  dynamic,  as  defined  by  ENTSO-E  in  [13].  The 
latter could fall into one of the following three classes i.e.: frequency containment reserves 
(FCR) exchange, frequency netting or frequency optimization.  

41 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Specific functionalities related to frequency regulation capabilities include:  

•  Generic frequency control including frequency containment, frequency restoration.  
•  Fast-frequency regulation.  
• 
•  Grid-forming.  

Inertia response and emulation.  

Implementation 

Frequency regulation activities can be broadly split into short-term (in order of seconds), 
mid-term (in order of minutes), and long-term (in order of hours or longer). In conventional 
generators,  short-term 
inertia  and  primary  frequency  response. 
Immediately following this is the mid-term period marked with a sustained period of power 
injection,  maintained  for  up  to  a  few  minutes  before  tertiary  reserves  are  activated  to 
return the system close to the pre-disturbance status.  

involves 

typically 

Since  HVDC  systems  do  not  have  a  natural  rotary  dynamic  and  cannot  independently 
generate  power,  there  are  several  ways  in  which  frequency  regulation  activities  can  be 
implemented.  In  most  implementations  of  this  feature  in  HVDC  systems,  at  least  one 
control loop is invariably involved in the most basic of cases as shown in Figure 15. From 
the  perspective  of  HVDC  control  design,  the  control  system  can  be  designed  to  have 
responses that range from milliseconds (ms) to several minutes to flexibly mimic the short 
and mid-term responses of synchronous generators. Additionally, these responses can be 
implemented  either  as  a  step,  ramp,  or  proportional-based  responses  in  any  of  these 
temporal periods. 

Benefits  

The  core  of  the  benefits  of  frequency  regulation  from  HVDC  systems  are  the  speed, 
flexibility, and controllability of responses, while improving frequency stability properties of 
the  host  network.  Generally,  HVDC  can  provide  a  tuneable  and  arbitrarily  fast  response 
that can arrest frequency deviation faster than synchronous generation (containment) and 
that  can  support  multiple  networks  simultaneously  (containment  and  restoration). 
Furthermore, considering that the physical implementation is inherently based on control 
systems,  it  is  always  possible  to  include damping functionalities without additional  costs. 
With  additional  investments  in  dedicated  energy  storage  for  instance,  even  additional 
flexibility  and controllability  can  be  achieved  and more  functionalities can  emerge  whose 
cost can be compensated by the added benefits.  

Modelling Requirements  

Frequency  control  which  includes  generic  frequency  control  and  inertia  responses,  fast-
frequency  response,  are  usually  implemented  in  HVDC  systems  as  a  supplementary 
control  at  a  higher  hierarchical  level  to  local  control.  Due  to  hierarchical  considerations 
and the relatively slow behaviour of AC system frequency (Δf), the control system is at the 
very least an order of magnitude slower than the next group of downstream controllers.   

Figure 15 – Generic block-diagram of frequency and inertia-response control 

42 

 
 
  
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

There  are  several  factors  that  can  influence  the  level  of  detail  required  to  represent  the 
behaviour  of  frequency  regulation  functionality  and  this  includes  the  expected  system 
impact  and  the  desired  study  of  interest,  and  by  extension  the  modelling  requirements. 
Table  6  provides  the  minimum  modelling  requirements  and  a  qualitative  labelling  of  the 
level of modelling details required relative to CBA analysis. That is, for greenish coloured 
labels, generic models may suffice, and they require less detail in representation. These 
are typically adequate for CBA and should be reflected in the modified CBA. Whereas the 
brighter  colours  (orange,  red)  indicate  that  generic  models  may  no  longer  be  sufficient  if 
the  corresponding  studies  are  required  to  establish  the  potential  costs  and  benefits. 
However, more often than not, these levels of details are not necessary for first-level CBA 
at the planning stage unless they are shown to affect investment choices.  

Table 6 - Minimum modelling requirements for frequency regulation and inertia-
emulation capabilities 

System impact 

Typical studies of 
interest 

Minimum 
modelling 
requirements 

Qualitative level of 
details 

Area power 
exchanges 

System adequacy: 
    - load-flow 

Fundamental 
frequency models 
(voltage and 
current sources) 

Transient stability: 
    - Angle stability 

Phasor based 
models 

Frequency stability 
and transient power 
exchange 

Control interactions 

Synchronization, 
fast-frequency 
response, and 
voltage source 
behaviour 

Dynamic stability: 
- dynamic 
performance 
- oscillatory 
phenomena 

Dynamic stability: 

-oscillatory 
phenomena 

-resonances 

-interaction risks 

-harmonic stability 

Dynamic stability 

D- 

D 

C 

B 

AVM models of 
outer loops and 
cables up to a 
bandwidth of 100 
Hz 

- More accurate 
AVM models of 
outer loops and 
cables 
- possibly inner-
loops (up to 
bandwidth of 500 
Hz) depending on 
system 
peculiarities. 

A 

High-fidelity models 
are recommended 
depending on 
implementation 
details. Model detail 
of class B at the 
minimum. 

43 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

System impact 

Typical studies of 
interest 

Minimum 
modelling 
requirements 

Qualitative level of 
details 

Momentary overloading 

Any of the above depending on time 
duration of overloading 

6.1.3. Voltage regulation and reactive power support capabilities 

from HVDC 

With  as  much  importance  as  frequency  regulation  in  a  hybrid  AC/DC  system,  voltage 
regulation is also at the core of power system operation, security, and power quality. With 
the proliferation of PE interfaced systems, HVDC inclusive, it is now being demanded that 
these devices should in the least not contribute to detrimental behaviours that may lead to 
voltage collapse and at the same time contributing to valuable voltage stability.   
Voltage  regulation  by  HVDC  is  achieved  by  the  adjustment  of  reactive  current/power 
(absorption  or  generation)  through  dedicated  control  strategies  which  is  possible 
independent  of  active  power  flow  (within  the  converter’s  capability).  Thus,  voltage 
regulation and reactive support can, in general, be decoupled from other features without 
need for coordination.  
Specific functionalities related to voltage regulation and reactive power support include:  

•  Fast static and dynamic voltage regulation.  
•  Reactive power control.  
•  Generation of network driving voltage — grid-forming functionality.  
•  STATCOM operation.  

Implementation  

Voltage  regulation  activities  can  be  broadly  split  into  static  regulation  and  dynamic 
regulation.  The  former  requires  relatively  static  setpoints  for  operation  based  on  fixed 
reactive power or voltage references. Implementation examples include, but not limited to 
reactive  power  control,  AC  voltage  control  (local  and  area  mode  and/or  STATCOM 
operation), and power factor control. Whereas, the dynamic voltage regulation allows on-
the-spot regulation of voltage depending on the network and pre-defined conditions, with 
possibilities to include fixed setpoints. Implementation examples include, but not limited to, 
droop-based/supplementary  control-based  structures,  fast  current  injection  mechanisms, 
and grid-forming control approaches to voltage generation and support.  

44 

 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Benefits  

While  synchronous  generators  generally  have  a  good  control  of  network  voltages,  the 
increasing adoption of intermittent power sources and PE interfaces is resulting to voltage 
control  issues  that  synchronous  generators  are  not  adequately  equipped  to  mitigate. 
However,  PE  devices  themselves  such  as  HVDC  systems  can  be  designed  to  mitigate 
emerging  voltage  and  power  quality  issues  with  a  superior  speed  of  response  and 
flexibility than synchronous generators without additional costs. Importantly, the capability 
to fully decouple active and reactive power control in the case of VSC technology provides 
more  flexibility  especially  in  emergent  conditions.   Furthermore,  HVDC  systems,  can 
potentially save on costs of investing in additional equipment. For instance, a VSC-HVDC 
converter  can  reliably  operate  in  STATCOM  mode  even  when  the  DC-side  is  out  of 
service,  which  can  reduce  the  need  for  additional  physical  component  in  proximity  to 
support reactive power. Overall, HVDC systems can support and improve the voltage and 
transient  stability  of  a  network  better  than  an  equivalent  synchronous  generation.  With 
additional investment, there is further potential for additional functionalities to enhance the 
performance  of  the  network  across  varying  temporal  periods;  for  example,  the  VSC  can 
be upgraded to provide active harmonic filtering capability and act as a harmonic sink to 
improve power quality. Therefore, when the HVDC system is properly located, the benefits 
for voltage and reactive power support can be immense.  

Modelling Requirements 

Voltage  regulation  involves  all  activities  aimed  at  maintaining  the  evolution  of  voltages 
within acceptable bounds in normal and emergency conditions. Like frequency regulation 
activities,  several  factors  will  influence  the  level  of  detail  required  to  represent  voltage 
regulation capabilities mainly due to the significant flexibility afforded by PE. As a result, 
there  is  no  fixed  or  clear-cut  minimum  modelling  requirement  without  additional 
information, particularly, the system impact and study of interest.  

Table 7 – Minimum modelling requirements for voltage regulation and reactive 
support capabilities 

System impact  

Typical studies of 
interest  

Minimum modelling 
requirements  

Qualitative level of 
details  

Long-term power 
transfer capability  

System adequacy:  
 - load flow  

Voltage and rotor-
angle stability  

Short-term power 
transfer capability  

Transient stability  

Dynamic stability:  
- dynamic 
performance  
- oscillatory 
phenomena  
- multi-infeed stability  

Control interactions   Dynamic stability:  

 - dynamic 
performance  
 - oscillatory 
phenomena  
 - faster interactions  

Fundamental 
frequency models 
(voltage and current 
sources)  
Phasor based 
models  

AVM models of outer 
loops and cables up 
to a bandwidth well 
below 100 Hz 
especially if grid 
expected to be weak.  
- AVM models of 
outer loops and 
cables up to a 
bandwidth well below 
100 Hz.  
- detailed dc-side 
45 

D 

D- 

C 

C 

B 

 
 
  
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

System impact  

Typical studies of 
interest  

Minimum modelling 
requirements  

Qualitative level of 
details  

model if POC is 
expected to be weak.  
NB: Overall transfer 
capability of the 
hybrid system is 
limited in weak 
condition without 
additional investment 
e.g., specialized non-
generic control.  
- detailed model of 
surrounding AC 
network and 
components in 
proximity.  
- high-fidelity models 
of inner and outer 
loops involved in 
voltage control up to 
bandwidth of 1 kHz  
- network harmonic 
impedance model  
- switched model of 
the converter  
- detailed inner loops 
(up to 10 kHz)  

A 

A+ 

Transient over-
voltages  

EMT studies:  
- resonances  
- harmonic coupling  
- some protection 
studies  

Harmonic 
propagation  

EMT studies:  
- harmonics  

6.1.4. Power  flow  control  and  transient  stability  enhancement 

Capabilities 

Without  a  possibility  to  control  the  power  flow  in  transmission  paths,  the  natural  power 
transfer  capability  of  a  network  is  generally  limited.  The  implementation  of  dedicated 
power flow control devices in a conventional grid has been shown to significantly enhance 
the  capabilities  and  stability  properties  of  the  system.  In  today’s  networks,  PE  devices 
have  been  at  the  core  of  sophisticated  power  flow  control  mechanisms.  Therefore,  an 
HVDC system can inherently contribute with little to no modification. On the long term, this 
power  flow  capability  of  HVDC  will  reduce  the  need  for  investments  elsewhere  for 
dedicated  power flow  controlling  devices and  is  thus  a  feature  of  significant  interest.  For 
HVDC in particular, one of the most important characteristics of power-flow control is the 
superior speed of response that can be flexibly set to meet demanding conditions during 
emergencies.  

Specific functionalities related to power-flow control capabilities include:  

•  Fast power flow reversal and ramp facilities.  
•  P/Q modulator and emergency power control.  
•  AC-line emulation (HVDC links).  
•  Provision of an asynchronous tie.  

46 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Implementation  

There  are  several  ways  in  which  power  flow  may  be  enforced  from  an  HVDC.  Known 
techniques include (but not limited to) emulation of an AC line (by an HVDC link), setpoint 
enforcement  according  to  a  centralized  control,  manual  adjustment  of  setpoints  (as  in 
redispatch  cases),  keeping  the  power  setpoints  constant,  among  others.  Power  flow 
control  capability  may  involve  one  converter  and  its  adjacent  AC  grid,  or  multiple 
converters  and  their  adjacent  AC  grids.  Furthermore,  power  flow  in  other  lines  in  the 
system  can  be  indirectly  influenced  by  a  converter  providing  dynamic reactive  power  so 
those  lines  can  be  loaded  up to their thermal  limits,  e.g.,  long parallel  AC  lines.  Another 
method for implementation of power flow control from HVDC is through the manipulation 
of  firing  angle  of  the  converter.  However,  this  implementation  is  only  applicable  for  LCC 
implementations  based  on  thyristor  technology.  Power  flow  control  can  also  be 
implemented  on  the  DC-side  using  dedicated,  fractionally  rated  current  flow  controllers 
that offer more capabilities and functionality.  

Benefits  

When properly utilized, power flow control capability is one of the most powerful benefits 
of HVDC systems. In addition to obvious improvement in transient stability properties and 
better  utilization  of  network  capacity,  other  benefits  from  power  flow  control  include,  but 
not limited to:  

•  Arbitrary control of active power in either direction.  
•  Fast and full reversal of power flow in normal and emergency conditions.  
•  Significant improvements in network flexibility and controllability.  
•  Mitigation of power flow constraints on AC corridors.  
•  Full independent control at each AC terminal in any of the four quadrants. 

Modelling Requirements  

The  modelling  requirements  for  power  flow  control  will  depend  on  the  required 
functionality  and  the  actual  implementation  of  the  mechanism.  Considering  that  power 
flow control mainly impacts on the transient stability properties of a network in normal and 
emergency conditions, its impacts often transcend the actuating device and can be felt in 
the entire network depending relative size of the HVDC system. In essence, this requires 
an extensive model of the network or the part of the network where the impacts are most 
felt.  Therefore,  at  the  initial  stages  of  development,  fundamental  frequency  models  are 
required  for  system  adequacy  studies  and  at  the  minimum  phasor-based  models  to 
assess  angle-stability  and  damping  properties  in  response  to  power  flow  changes 
enforced by the HVDC system. At a second stage, AVM models of outer control loops (up 
to  a  bandwidth  of  100  Hz)  are  required  to  assess  the  impact  of  power  flow  control  on 
stability  properties  when  a  faster  than  normal  response  is  desired  e.g.,  fast  power  flow 
reversals, emergency power control, or in the moments after unexpected conditions occur. 
Table  8  summarizes  the  minimum  modelling  requirements  based  on  potential  system 
impacts and the related study.  

47 

 
 
 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Table 8 – Minimum modelling requirements for power flow control 

System impact  

Power flow control 
capability  

Stability  

Typical studies 
of interest  
System 
adequacy :  
- load flow  
Transient 
stability  
Dynamic 
stability :  
- dynamic 
performance  
- oscillatory 
phenomena  
- multi-infeed 
stability  

Minimum modelling 
requirements  
Fundamental frequency 
models (voltage and current 
sources)  
Phasor-based models  

AVM models of outer loops 
and cables up to a bandwidth 
well below 100 Hz.  

Qualitative level 
of details  

D 

D- 

C 

6.1.5. Blackstart Capabilities 

Since 2017, the network code on electricity emergency and restoration  [12] has become 
part of the European Commission regulation, setting the rules and responsibilities of each 
Member state (MS) in case of a blackout. In case of a blackout in Europe, either complete 
or partial, each of the MSs must have a restoration plan in place in order to progressively 
restore its network to the normal operating state, thus minimizing customer interruption.  

Each  MS  typically  considers  two  approaches  for  the  restoration  of  its  system  or  a 
combination of these two approaches. The first and most commonly used is the so-called 
“bottom-up” approach. This approach relies on a restoration using internal energy sources 
without  any  external  support  from  other  MSs.  The  internal  sources  should  be  equipped 
with  the  black-start  functionality  that  allows  them  to  form  a  stable  voltage  waveform  of 
constant  magnitude  and  frequency,  to  which  the  rest  of  the  system  (loads,  generators, 
transmission elements) can synchronize/connect. The TSO responsible for the restoration 
should  thus  have  available  at  all  times  a  minimum  number  of  units  capable  of  black-
starting the system. Hydro and gas units are commonly used in a bottom-up approach. 

The second method is the “top-down” approach where the restoration is performed using 
external  sources.  In  this  case,  interconnections  are  utilized  to  energize  the  backbone  of 
the  transmission  system,  with  internal  equipment  being  progressively  synchronized.  AC 
interconnections and embedded HVDC links can be used in case of a partial blackout (i.e. 
when  only  a  part  of  a  synchronous  area  is  blacked  out).  However,  it  is  rather  uncertain 
whether in case of a black out, the other end of an embedded HVDC link is healthy. On 
the other hand, asynchronous HVDC interconnections can be more reliably used as black 
start  units  taking  into  account  that  the  probability  of  two  different  synchronous  areas 
suffering  a  blackout  at  the  same  time  is  negligible.  An  agreement  between  the  MSs  is 
required in such a case for provision of the required restoration power. 

The  capability  of  HVDC  to  provide  black  start  services  was  first  field-tested  in  2008  by 
ABB [13]. A successful black-start test with Skagerrak 4 establishing and supplying a load 
of  approximately  100 MW  has  been  reported  in  the  literature  [14].  According  to  the 
European regulation, the black-start capability of an HVDC link should be tested at least 
once every three years [12].  

Considering  that  complete  black-start  capability  from  HVDC  is  still  at  a  relatively 
developmental stage, desirable functionalities may include:  

48 

 
 
  
  
  
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

•  Black-start control mode, i.e. possibility to generate a voltage waveform of specific 

magnitude and frequency.  

•  Parallel operation with other units in black-start mode.  
•  Soft and/or hard energization.  
•  Fast voltage and frequency control to limit the voltage and frequency transients.  
•  Fast  DC  voltage  control  from  the  VSC-HVDC  on  the  healthy  side  of  the  link 

(requires a relatively stiff AC system).  

•  Availability  of  back-up  power  source  (e.g.  small  battery)  sufficient  to  power  the 
auxiliary  equipment  (such  as  control  and  protection  systems)  of  the  HVDC 
station.   

Implementation 

In short, the black-start capability of an HVDC converter is provided by the manufacturer, 
if requested in the specifications stage of the HVDC project.  HVDC systems based on the 
LCC  technology  cannot  provide  black-start  services  because  they  need  a  strong  grid  in 
order to operate. Nevertheless, LCC links can still support in the faster restoration of the 
network after a stable voltage has been established. 

There should be at least one HVDC converter connected to a healthy AC system in order 
to  be  able  to  provide  this  service.  The  black-start  functionality  refers  to  an  additional 
control  mode  of  the  VSC  that  allows  it  to  use  the  DC  voltage  to  generate  a  voltage 
waveform  of  a  pre-defined  magnitude  and  frequency.  The  VSC  should  be  able  to 
withstand the connection of the rest of the system elements (transformers, loads, etc.) by 
injecting  the  required  current  and  power  while  ensuring  that  the  system  variables 
(frequency, voltage) remain between limits. Parallel operation with other generating units 
should be possible and stable. A VSC can perform hard and soft energization. In case of 
hard energization, the VSC should be able to provide the inrush currents during line and 
transformer  connection.  Such  currents  can  be  minimized  by  using  the  soft  energization 
functionality,  where  the  VSC  progressively  ramps  up  the  voltages  in  the  grid.  Soft 
energization also allows to energize multiple elements at once. However, in such a case it 
is  necessary  to  coordinate  the  protection  relays  to  avoid  protection  actions  that 
inadvertently trip the equipment to be energized.  

Benefits  

•  The capability to perform both soft and hard energization (not always possible with 

other conventional black-start units)  

•  Possibility to blackstart from another asynchronous AC area (not the case with AC 

connections), which is unlikely to have suffered simultaneously a blackout.  

•  HVDC systems have in general very high availability.  
•  Very fast voltage and frequency control that leads to better system performance.  
•  No  diesel  generators  are  required  to  start-up,  except  for  small  units  (diesel  or 

batteries) to start up the auxiliaries.  

•  Possibility  to  provide  black-start  capability  in  a  system  without  synchronous 

machines.   

•  Due to the absence of mechanical parts, multiple self-start attempts can be made 

at a very short time [15].  

•  The  black-start  capability  from  an  HVDC  system  can  be  provided  without 

significant additional investment cost. 

Modelling Requirements  

In order to capitalize on the benefits of black start services from HVDC, it is a prerequisite 
that  the  HVDC  is  included  in  the  restoration  plan  established  by  the  responsible  TSO. 
Devising such a restoration plan requires dedicated studies that demonstrate its feasibility 

49 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

to  manage  the  system  transients  taking  place  during  the  switching  events  of  the 
restoration  sequence.  As  discussed  in  [16],  a  black-start  involving  an  HVDC  converter 
requires very detailed simulations using either a real-time simulator or an offline EMT-type 
simulation tool, also shown in Table 9. 

Table 9 – Minimum modelling requirements for black-start simulation study 

System impact  

Power system 
restoration  

Typical 
studies of 
interest  
EMT study, 
switching 
transients  

Minimum modelling 
requirements  

Qualitative level of details  

A+  

A  

- Real-time model with 
actual control and 
protection replica of 
HVDC equipment  
- Simplified 
representation of the 
system part that is 
involved in the restoration 
scenario  
- Offline EMT simulation 
tools with the black-start 
control mode of the 
HVDC link  
- Generic representation 
of the connected system  

A simplification could be considered at this point, assuming that a feasible restoration plan 
can  be  set-up  including  the  HVDC  link.  As  a  result,  the  study  of  the  benefits  from  black 
start by HVDC would be restricted to a much simpler economic analysis, where the HVDC 
system would replace the black start service of another, more expensive, black start unit. 
Obviously,  this  would  require  incorporating  in  the  current  CBA  methodology  the  costs  of 
having black-start units (and the cost of the black-start service from the HVDC).  

As illustrated in [17] and [18], there is no clear trend neither on the method the black-start 
service  is  sourced  (mandatory  service,  tendered  service,  bilateral  agreements,  etc.)  nor 
on  how  and  if  the  method  is  remunerated.  As  a  result,  this  makes  it  particularly 
challenging  to  develop  a  generic  enough  method  to  include  black  start  costs  in  the 
ENTSO-E CBA methodology. Assessing the benefits of black start services from HVDC is 
even  more  difficult  since  they  will  be  connected  between  different  zones,  so  information 
on the cost of this service is needed.   

6.1.6. Grid-Forming Capabilities 

Most  of  the  existing  IBR  generation  and  HVDC  converters  uses  the  so-called  grid-
following control mode, where the converter measures the grid voltage and frequency and 
adjusts  the  injected  currents  in  order  to  reach  the  desired  active  and  reactive  power 
setpoints. In order to enable such sources to contribute to the system security and stability 
during  voltage  and  frequency  excursions,  the  TSOs  developed  specific  requirements  in 
the  grid  codes.  Nevertheless,  the  control  structure  of  these  converters  remained  largely 
the same. As has been highlighted in several parts of this document, the replacement of 
conventional generating units by such PE-based sources poses several challenges in the 
planning and operation of power systems. Amongst others, ENTSO-E has identified these 
challenges in a technical report [19] and has described a roadmap to address them in the 
short and long-term. For example, the behavior of grid following converters becomes more 
important in case of weak grids, i.e. when the short circuit level at the point of connection 
of  the  HVDC  converter  is  low  in  relation  to  the  size  of  the  converter.  A  typical  rule  of 
thumb specifies that a system is weak if the short circuit power is less than two or three 

50 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

times  the  rating  of  the  converter.  In  such  operating  conditions  the  behavior  of  grid 
following converters cannot be ensured and instability might arise. The use of grid forming 
control  on  HVDC  systems  (along  with  other  PE-based  sources)  appears  as  a  promising 
countermeasure in the long-term. 

The  grid  forming  control  refers  to  a  different  control  philosophy  for  the  converter  that 
allows  it  to form  its  own voltage  and  frequency and is  expected  to lead to better  system 
performance.  The  early  generation  of  grid  forming  control  from  HVDC  converters  has 
already  seen  some  applications.  Offshore  wind  systems  require  that  the  offshore  HVDC 
converter  forms  the  offshore  AC  grid  for  the  wind  turbines  to  synchronize  and  produce 
power. In addition, the black-start control mode described previously is also a type of grid 
forming  control,  employed  in  special  circumstances.  However,  there  are  very  few  grid 
forming  control  applications  in  bulk  power  systems,  which  concern  (mainly)  Battery 
Energy  Storage  Systems  (BESS)  and  not  HVDC  converters.  The  current  generation  of 
grid forming control is expected to allow better coupling of the converter to a large AC grid 
consisting  of  several  other  grid  forming  elements  and  synchronous  machines.  For 
example, the converter can be controlled to behave virtually as a synchronous machine, 
as shown in Figure 16. 

Figure 16 – Grid following and Grid forming inverter types [20] 

to  black-start  capability,  grid-forming  capability 

Similar 
the 
developmental stages with several large-scale demonstrations completed or in operation 
(see  WP3,  Deliverable  3.2  of  the  OSMOSE  project  [21])  to  validate  proof-of-concept. 
Hence, desired functionalities include, but not limited to:  

is  still  at 

from  PE 

•  Enforcement of network driving voltages, synchronizing angle, and frequency;  
•  Reliable voltage source behaviour;  
•  The current limitation strategy;  
•  Short circuit current contribution and any temporary overload capability;  
•  Fast-frequency regulation and inertia response capabilities.  

Implementation  

The  grid  forming  control  requires  implementing  different  control  algorithms  inside  the 
converter. There have been several methods proposed in the literature [22] [23] [24], such 
as the Power Synchronization Loop (PSL) or the so-called Virtual Synchronous Machine 
(VSM)  scheme, where the converter is controlled to behave as a synchronous generator. 
Each  of  these  methods comes  with  its  own  benefits  and  drawbacks.  This  document  will 
not  go  through  the  details  of  such  schemes,  which  can  be  found  in  the  provided 
references.  However,  the  general  principle  is  similar  in  all  methods.  In  contrast  to  grid 
following converters that rely on a Phase-Locked Loop (PLL) scheme for synchronization 
and to calculate the phase angle of the injected current, grid forming converters generate 
a  voltage  waveform  of  specific  magnitude  and  frequency.  Then,  the  magnitude  and  the 
phase of this voltage are adjusted to control the reactive and active power injected into the 
network,  respectively.  During  faults  in  the  system,  the  grid  forming  converter  should  be 
able to ride-through without disconnecting or any equipment damage, and minimal time to 
51 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

full power transfer recovery. A grid forming converter should also be able to provide short-
circuit  current.  Typically,  the  contribution  of  converters  to  short  circuit  level  is  much 
smaller compared to synchronous machines (~1.2 pu instead of ~6-7 pu). Hence, if higher 
short  circuit  current  is  required,  investments  in  hardware  would  be  needed.  It  should  be 
noted  that  the  rest  of  the  features  described  in  this  chapter  (i.e.,  frequency/voltage 
regulation,  power  flow  control)  can  be  also  provided  by  a  converter  operated  in  grid 
forming mode. The main difference would be in the (short-term) dynamic performance of 
the  converter,  where  the  grid-forming  scheme  is  expected  to  be  superior,  especially  in 
weak grid conditions.   

The actual implementation is expected to vary from manufacturer to manufacturer and on 
a  case-by-case  basis.  It  has  to  be  noted  though  that  grid  forming  control  for  bulk  power 
systems  is  a  relatively  new  feature  and  there  are  currently  no  clear  requirements 
regarding  the  performance  that  should  be  satisfied.  This  also  makes  the  modelling  and 
tuning  of  such  converters  for  inclusion  in  planning  studies  more  challenging.  To  define 
such  requirements  and  allow  large  scale  deployment  of  grid  forming  converters,  close 
cooperation  between  system  operators  and  manufacturers  is  critical  in  the  near  future 
[25].  

Benefits  

In  principle,  a  grid  following  converter  can  provide  the  same  features  as  a  grid  forming 
converter  (e.g.  frequency/voltage  control,  oscillation  damping,  etc.).  However,  according 
to the current industry practice, a grid following converter cannot reliably operate in case 
of low system strength, whereas a grid forming converter does not face such a limitation.  

Although  it  is  still  not  certain  if  grid-forming  capability  will  be  offered  predominantly  as  a 
grid service and/or as a standard feature and when, it is at present being considered as 
one of the most important features of next generation converters. The foremost important 
benefit  of  grid-forming  as  a  feature  is  the  capability  to  replicate  grid-control  functions 
provided  by  synchronous  generators.  Thus,  in  line  with  hybridization  efforts  and 
decommissioning  of  existing  synchronous  generators,  system  reliability  and  security  can 
be maintained. Furthermore, since implementation will be in PE converters, most benefits 
of PE apply. More specific benefits with respect to HVDC include, but not limited to:  

• 

Increase of stable operating region of HVDC converter. The converter can operate 
reliably and transfer more power in operating points with low short circuit level and 
low system inertia.  

•  Decrease of need to invest in means to ensure stable system operation, such as 

synchronous condensers.  

•  Apart from the connection of the HVDC converter, grid forming control can enable 
higher  penetration  of  other  PE-sources,  which  would  not  be  possible  with  a  grid 
following HVDC converter.  

•  Operation of islanded systems without must-run synchronous units.  

Modelling Requirements  

The  modelling  requirements  of  a  grid  forming  converter  do  not  significantly  differ  from 
what  has  already  been  listed  in  the  previous  sub-sections  for  frequency  and  voltage 
control.  The  main  difference  lies  in  the  control  structure  of  the  converter,  which  should 
correspond  to  the  grid  forming  type.  As  already  discussed,  the  modelling  and  control  of 
grid  forming  HVDC  converters  is  an  ongoing  research topic  that  has  received  significant 
attention in the recent years. A generic model of an HVDC grid forming converter is shown 
in Figure 17. It includes:  

•  The outer loops:  

a.  The power synchronization loop that provides the internal phase angle and 
frequency of the converter. If frequency regulation capability is required, it 

52 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

can  be  achieved  by  selecting  appropriately  the  parameters  of  this  loop. 
Regulation of DC voltage can be also added (not shown in Figure 17).  
b.  The voltage profile management that provides the magnitude of the voltage 
output of the converter. Reactive power control or terminal voltage control 
is performed through this loop, if required.  

•  The inner loop receives as inputs the outputs of the outer loops and the currents of 
the  converter.  The  outputs  are  the  modulation  signals  that  are  passed  to  the 
internal switching logic of the converter. An important part of the inner loop is the 
current  limitation  strategy,  that  is  activated  in  case  of  overcurrent  (e.g.  during  a 
nearby fault).  

Figure 17 – Generalized control structure of grid forming converter (inspired from [26]) 

The level of detail that is required depends on the phenomenon of concern. For example, 
RMS simulations are sufficient to investigate the classical types of power system stability, 
i.e. frequency, voltage and angle stability. Hence, a simplified model of the converter that 
ignores  the  very  fast  dynamics  of  the  inner  loop  and  focuses  on  frequency/voltage 
regulation could be sufficient. However, for the investigation of faster phenomena, such as 
the response to AC and DC faults or the possible interactions between several converters 
in proximity (especially in weak systems), the modelling of converters in detail for the use 
in EMT tools is necessary. Typically, such problems are solved during the project design 
phase. However, even if they cannot be fully addressed during the system planning, the 
operator  should  be  able  to  detect  the  possibility  of  such  problems  arising  and  set 
appropriately the system requirements and specifications. 

6.1.7. HVDC grid protection aspects 

The  protection  of  HVDC  grids  is  a  challenging  part  of  their  operation  that  has  received 
significant attention in the literature, but has not seen extended practical applications yet. 
In contrast to AC grids, where there is a natural zero crossing of the current that allows to 
open  the  protection  breakers  in  case  of  faults,  the  breaking  of  DC  faults  is  much  more 

53 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

complex  and  challenging,  since  it  requires  to  employ  measures  that  bring  the  DC  fault 
current to zero first before opening the breakers.  

In  contrast  to  the  previously  discussed functionalities,  it  is  uncertain  whether  HVDC  grid 
protection  will  bring  additional  benefits  to  the  AC  system.  However,  it  can  have  a 
significant impact on the cost and risk of HVDC projects.  

On the one hand, if an HVDC system is planned from the beginning with the final topology 
in mind,  its  protection  costs  can  also  be  incorporated  and  optimized  from  the  beginning. 
On  the  other  hand,  the  connection  of  several  pre-existing  HVDC  point-to-point  links  to 
form an HVDC grid may come with a much larger (or even prohibitive) cost. The reason 
for  this  is  that  typically,  point-to-point  HVDC  did  not  require  any  dedicated  HVDC 
protection  apart  from  conventional  AC  breakers.  Such  systems  were  usually  turnkey 
projects,  optimized  for  a  particular  configuration,  and  no  arrangements  were  made  to 
accommodate  extension  to  HVDC  grids  (e.g.  no  additional  space  for  DC  breakers  was 
foreseen).  

Implementation  

Design of HVDC grid protection requires two choices, i.e., choice of protection philosophy 
and choice of technology within the protection philosophy. 

Within  the  protection  philosophy,  three  main  options  exist.  First,  the  fully  selective 
protection  philosophy  works  similar  to  the  present  practice  in  AC  systems,  that  is, 
considering each transmission line and bus as independent protection zones. This option 
requires DC-side breakers at every transmission line end and makes sure that continuity 
of  supply  within  the  HVDC  grid  is  guaranteed.  Second,  a  non-selective  protection 
philosophy  can  be  used,  where  the  entire  HVDC  grid  is  treated  as  one protection  zone. 
This  requires  equipment  to  interrupt  fault  currents  at  each  converter  station,  e.g.,  AC 
breakers, DC breakers or converters with fault blocking capability. A fault at the DC side 
results  in  a  temporary  loss  of  the  entire  HVDC  grid.  Third,  an  intermediate  strategy  is 
putting DC-side breakers at strategic locations in the HVDC grid, forming protection zones 
consisting  of  multiple  transmission  lines  and  buses.  In  case  of  a  DC-side  fault,  only  the 
affected  protection  zone  is  temporarily  lost,  whereas  other  protection  zones  continue 
operation. 

As an alternative to HVDC grids, the option to form reconfigurable point-to-point or multi-
terminal  HVDC  systems  also  exists.  In  this  option,  HVDC  links  can  be  grouped  in  small 
multi-terminal  systems  and  reconfigured  according  to  the  system  needs  for  power 
transfer. 

To interrupt DC-side fault currents, several technologies exist, which are listed below: 

•  AC-side circuit breakers: can be used at the AC-side of every converter, in a non- 

or partially selective protection philosophy 

•  Converters  with  fault  blocking  capability,  such  as  hybrid  or  full-bridge  modular 
multilevel  converter,  which  can  be  used  in  a  non-  or  partially  selective  protection 
philosophy 

•  DC-side  circuit  breakers,  such  as  resonance-type  or  hybrid  DC  circuit  breakers, 
which can be used in any protection philosophy. DC-side circuit breakers are more 
complex and bulky counterparts compared to AC-side circuit breakers because of 
additional  circuitry  (resonant  circuits  or  power-electronic  circuits,  surge  arresters) 
and the need for series inductors. 

•  DC-DC  converters  with  fault  blocking  capability,  which  can  be  used  in  any 

protection philosophy 

Each  philosophy  with  used  technologies  will  lead  to  a  profile  of  “loss  of  active  power 
transfer” and “loss of reactive power transfer” at HVDC nodes, which will allow to quantify 

54 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

the  impacts  of  a  DC-side  fault  on  the  AC-  and  DC-systems  connected  to  the  faulted 
component or protection zone. 

Costs  

Cost drivers of HVDC grid protection can be classified into capital expenditures and 
operational expenditures.  

Non-negligible capital expenditures related to HVDC grid protection are: 

•  DC-side  circuit  breakers:  DC-side  circuit  breakers  are  typically  more  expensive 
compared  to  their  AC  counterparts  and  require  more  space  in  substations  or 
platform space offshore. 

•  Converters with fault blocking capability typically require a higher amount of power 

electronics compared to their non-fault blocking counterparts. 

Non-negligible operational expenditures related to HVDC grid protection are: 

•  DC-side  circuit  breaker  losses:  certain  DC-side  circuit  breakers  insert  power-

electronics in the main circuit, incurring extra losses in the system. 

•  Converters  with  fault  blocking  capability  are  typically  less  efficient  compared  to 

their non-fault blocking counterparts. 

•  AC-side  impact:  HVDC  grid  protection  philosophies  that  shut  down  the  entire  or 
part  of  the  HVDC  system  may  have  an  impact  on  dimensioning  of  frequency 
reserves. 

•  DC-side  impact:  HVDC  grid  protection  philosophies  that  shut  down  part  of  the 
HVDC  system  may  have  an  impact  on  the  dimensioning  of  DC-side  voltage 
balancing reserves. 

Modelling Requirements and Studies  

To identify the most suitable protection strategy, design the equipment, and minimize the 
costs, several studies have to be performed. These are listed hereafter: 

•  Short-circuit studies at the DC-side: Short-circuit studies at the DC side should be 
performed  using  either  EMT-type  simulation  tools  (time  domain)  or  frequency 
domain  studies.  The  most  important  aspects  to  gather  from  these  studies 
(considering low-impedance grounded systems) are the rate-of-rise of the DC-side 
current  and  the  value  of  the  DC-side  current.  Analytical  solutions  have  been 
proposed  in  the  literature  but  are  either  not  accurate  or  confined  to  specific 
systems.  These  studies  will  feed  into  the  CBA  as  “cost  of  DC  breaker”  or  as  a 
variable  that  should be checked  against  the  constraint  on  short-circuit  currents  in 
the DC system. The cost of the DC breaker will depend on the current rate-of-rise 
and value of the current at interruption time. These variables will provide inputs to 
the  required  size  for  series  inductors,  breaker  interruptible  capacity  and  surge 
arrester energy. 

•  Short-circuit studies at the AC-side: Short-circuit studies at the AC-side may reveal 
the  AC-side  breaker  requirements  and  the  impact  on  AC-side  protection.  First, 
steady-state AC-side short-circuit studies can be performed, to check in a CBA for 
compatibility against minimum and maximum AC-side short-circuit currents.  

•  Dynamic studies at AC- and DC-side: Dynamic studies checking the needs for AC 
frequency  regulation  and  DC  voltage  regulation  will  feed  in  the  CBA  as  costs 

55 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

incurred  when  adopting  a  certain  HVDC  grid  protection  strategy,  especially  for 
non-selective or partially selective protection methods. These dynamic studies can 
be performed by considering loss of infeed of the terminals that are grouped within 
one  protection  zone.  The  studies  can  be  performed  using  the  profiles  for  loss  of 
active  power  associated  with  the  chosen  HVDC  grid  protection  philosophy  and 
technology. 

•  Dynamic  studies  on  transient  AC  stability:  Simultaneous  loss  of  multiple  HVDC 
nodes  may  result  in  loss  of  AC  system  stability.  Therefore,  dynamic  studies  may 
feed in the CBA as to check for stability limits of certain system states. 

6.1.8. Overview of Typical Tools Based on Recommended Level 

of Detail 

Tools  for  power  system  simulation  range  from  those  adopted  for  system  planning, 
decades  before  the  actual  commissioning,  to  those  adopted  in  real-time  operational 
scenarios,  and  many  in  between  these  extremes.  One  key  defining  paradigm  of  these 
tools  is  the  level  of  detail  they  require  to  provide  accurate,  plausible,  and  reasonable 
conclusions  subject  to  the  study  at  hand.  The  size  and  complexity  of  the  power  system 
has meant that modelling at a mathematical level has been at the core of power system 
analysis.  Due  to  these  complexities,  simplifications  at  various  levels  are  of  utmost 
necessity  to  represent  various  phenomena.  Traditionally,  when  representing  these 
phenomena,  the  philosophy  of  timescale  separation  has  been  adopted  (as  illustrated  in 
Figure  18),  which  allows  to  neglect  very  fast  phenomena  when  slow  dynamics  are  of 
interest and vice versa. This results in a simplified model and reduced computation time.  

As  a  result  of  this  separation,  dedicated  software  routines  have  been  developed 
specifically to exploit this philosophy. Thus, phenomena that require fairly simple models 
are treated as such, resulting in a model that is computationally tractable. However, they 
may  lack  generality  and  can  only  be  applied  specifically  to  these  phenomena  that  occur 
within the timescale of the studied dynamics. On the other hand, phenomena that require 
more  detailed  model  can  be  handled  by  another  class  of  software  routine  designed  to 
cater for these. However, computational tractability is often lost, and it could take hours to 
complete a few seconds of simulations. 

Nevertheless, the advent of PE devices today is challenging this timescale of separation 
idea as PE devices can influence dynamics across the entire spectrum of power system 
dynamics. As a result, simple models are becoming inaccurate, resulting in misleading or 
incomplete  conclusions,  and  fine-grained  model  are  too  detailed  and  computationally 
intractable  to  model  long-term  behaviour.  Although  there  are  advancements  today  in 
computational tractability of fine-grained models, the cost is still significant.  

56 

 
 
  
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 18 – Power system time scales [27]  

In terms of long-term system planning, when several scenarios are considered with high 
uncertainty,  it  makes  little  sense  to  pursue  such  high  accuracy  using  high-fidelity 
simulation models. This is further supported by the fact that the technology of converters 
has  undergone  tremendous  developments  in  the  latest  30  years  in  hardware  and 
software, and more developments are on the way. As a result, modelling the current state-
of-the-art of control and functionalities of converters in high detail and investing significant 
effort  for  high-fidelity  simulations  is  of  questionable  benefit.  Nevertheless,  it  is  of  utmost 
importance  to  be  able  to  identify  cases  of  concern  based  on  simplified  metrics  derived 
from  static  calculations  (load  flows)  or  from  dynamic  simulations  (i.e.  phasor-mode 
simulations). In essence, great skill is required in selecting the most appropriate tool given 
accuracy  and  computational  tractability  subject  to  the  requirements  of  the  study  in 
question.  

Table 10 – Summary of typical tools subject to the level of detail 

Qualitative level 
of details/Model 
classes  
A+  

System impact  Typical tools Update 

Remarks  

potential  

Currently the 
state-of-the art  

Not recommended for CBA 
except if initial analysis show a 
need for a very small subset of 
scenarios to be verified.  

- Harmonic 
propagation  
- Harmonic 
stability issues 
with frequency > 
5-10 kHz  
- power quality  

- EMT tools + 
real-time 
tools  
- emerging 
high fidelity 
frequency 
domain tools  

57 

 
 
  
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Qualitative level 
of details/Model 
classes  
A  

B  

C  

D- 

D 

System impact  Typical tools Update 

Remarks  

- EMT tools  
- emerging 
high-fidelity 
small-signal 
tools  

- High-fidelity 
small-signal 
tools  
- AVM for 
control 
design/ 
studies  

Standard 
small-signal 
tools  

- Resonance  
- Harmonic 
coupling  
- extremely fast 
control 
interactions (< 
10 kHz)  
- Transient over-
voltages due to 
control and 
peculiar network  
- Converter-
driven control 
interactions  
- dynamic 
performance  
- oscillatory 
phenomena (< 1 
kHz)  
- dynamic 
performance  
- fast converter 
driven oscillatory 
phenomena 
(bandwidth < 
500 Hz)  

Transient, 
voltage & 
frequency 
stability in the 
presence of 
HVDC systems  
System 
adequacy  

Standard 
RMS tools  

Load-flow 
tools  

potential  

Currently the 
state-of-the art  

Not necessary for CBA unless 
specificity of implementation 
warrants such studies. This is 
the case as of these impacts 
may have cost implications if 
they must be mitigated with 
additional investments (which 
may be significant enough) to 
get the full benefits of a feature.  

State-of-the-art  Possible for a slightly larger 

subset of scenarios considering 
the increasing adoption of 
converters  

Recommended depending on 
the expected number of HVDC 
system and their role in the 
network. The more the number 
of converters and system 
functionalities required, the more 
the need for a reasonably 
accurate small-signal analysis  
Highly recommended for coarse-
grained stability metrics for 
hybrid AC/DC grids that can 
establish if simulation with higher 
model classes is required.  

Already part of CBA  

Can be 
upgraded to 
have a 
configurable 
bandwidth of 
accuracy  

Can be 
upgraded to 
include better 
representative 
models of PE 
systems  
Can be 
upgraded to 
include some 
details 
regarding 
converters or 
high-level 
system 
computations 
such as inertia 
estimation  

Although hybrid AC/DC grids are still emerging in power system infrastructure and still far 
from  being  fully  adopted,  the  previous  subsections  show  that  the  benefits  that  can  be 
derived  even  today  are  significant.  Table  11  summarizes  the  generic  implementation 
methods  of  the  previously  discussed  features  and  their  related  functionalities,  and  the 
high-level system impacts.  

58 

 
 
  
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Table 11 – Summary of technical features, functionalities, and basic modelling 
requirements 

Related functionalities  

Generic implementation 
methods  

Technical 
feature  

Frequency 
regulation  

Generic frequency control  

Fast-frequency regulation  
Inertia response and 
emulation  
Frequency balancing  

Grid-forming  

Voltage 
regulation 

Static and dynamic voltage 
regulation  
Reactive power control  
Generation of network driving  
Harmonic sink/filtering  
Reactive power support  

Step, ramp, or proportional-
based control:  
- Inertia emulation strategies 
(with and without storage)  
- Supplementary frequency 
control  
Feedback-based control:  
- Closed-loop synchronizing 
frequency and angle  
- Closed-loop inertia emulation 
strategies  

Static control:  
- Reactive power  
- Voltage  
- Power factor  
Dynamic control:  
- Grid-forming approaches  
- Fast current injection  
- Droop/supplementary control-
based  

Power flow 
control and 
transient 
stability 
enhancement 
features  

Fast power flow reversal  
Dynamic reactive power 
control  
Provision of an asynchronous 
tie  
Fast speed of response  

Closed-loop P/Q modulator  
Ramp functions  
Angle/AC-line emulation (HVDC 
links)  
Dedicated DC-side power flow 
control  

P/Q modulator  
Emergency power control  

Provision of damping 

Blackstart 

Blackstart control mode  

- Inclusion of HVDC converter in 

59 

Overview of 
System 
impacts  

Frequency 
stability  
Power 
exchange:  
- Transient 
exchange  
- Area 
exchanges  
Control 
interactions  
Momentary 
overloading 
(ms-s)  

Stability  
- Voltage 
stability  
- Rotor-angle 
stability  
Control 
interactions 
(AC-AC, AC-
DC)  
Harmonic 
propagation  
System 
dynamic 
performance  
Nonlinear 
impacts:  
- limits  
- Transient 
over-
voltages  
- Transient 
stability  
- Damping 
properties  
- Power 
balance  
- Network 
dynamic 
performance  
- Network 
power 
routing 
flexibility  
- Damping 
properties  
- Shorter 

 
  
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Technical 
feature  

Related functionalities  

Generic implementation 
methods  

capabilities    Parallel operation during 

synchronization  
Fast voltage/frequency 
control  
Soft/hard energization  
DC voltage control from 
healthy side of link  
Small back-up power source   

restoration plan  
- Capability to provide inrush 
currents   
- Capability to inject/absorb 
reactive power during 
energization  

Grid-forming 
capabilities   

- Synchronization control 
scheme  
- Frequency/voltage and other 
supplementary control loops  
- Current limitation strategy  
- Overload capability  

- Virtual synchronous machine, 
power synchronization loop, etc.  
- hardware oversizing   
- switch to grid following during 
faults, virtual impedance  

Overview of 
System 
impacts  

restoration 
times  
- Adjustment 
of protection 
settings  
- Less 
investment in 
synchronous 
condensers  
- Higher 
penetration 
of RES  
- Operation 
in operating 
points with 
lower short-
circuit and 
inertia levels  
- Higher 
stress on 
DC-side 
variables  

6.2. Steady-state Optimization:  Modelling Requirements to 

determine Techno-economic KPIs 

A number of different steady state optimization models can be used to determine specific 
KPIs  of  the  CBA.  Firstly,  an  NTC  based  zonal  economic dispatch  model  can  be  used  to 
determine  the  expected  interzonal  flows  between  different  market  zones,  using  the 
installed generation capacity and RES and demand time series as inputs. This provides a 
base case where the generation dispatch is determined per generation type, and zone as 
well as expected interconnector flows. 

Secondly, an optimal power flow model (OPF) can be used, to determine the generation 
dispatch  and  the  line  flows  within  the  high  voltage  network(s)  of  different  zones.  To  do 
that,  a  detailed  nodal  network  model  is  needed,  including  a  nodal  mapping  of  installed 
generation  capacities  and  nodal  demand  and  RES  time  series.  The  OPF  model  then 
determines the least cost generation dispatch considering Ohm’s and Kirchhoff’s laws and 
technical limits of grid equipment, such as current/power flow limits in transmission lines, 
or nodal voltage limits. Within such an OPF model, different possible control actions can 
be  modelled,  such  as  optimizing  tap  settings  of  PST,  and  active  and  reactive  power 
control of HVDC converters.   

An  optimal  power  flow  model  can  also  be  used  to  determine  the  optimal  amount  of 
redispatch need, either for balancing the system w.r.t. forecast errors between day-ahead 
and real-time operation, or to compensate for outages of transmission lines or generators. 
As such, a basic redispatch optimal power flow model is introduced, with the objective of 
minimizing  the  redispatch  w.r.t.  a  reference  generation  dispatch,  to  compensate  for 
system  imbalances  due to RES  and  demand forecast  errors  or  generation  outages.  The 
following  paragraphs  will  outline 
the  different 
optimization models. 

the  mathematical 

formulations  of 

60 

 
  
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

6.2.1. NTC based zonal economic dispatch model 

In this model, each market zone is represented by a single node.  As such we can denote 
the  set  of  zones  as 𝑧 ∈ 𝑍,  where 𝑧  represents  a  particular  market  zone,  within  the  given 
set of market zones 𝑍. Further, the installed generation capacity per generation type  𝑔𝑡 ∈
𝐺𝑇  is  known  for  each  zone,  where  𝐺𝑇  is  the  set  of  different  generation  types.  The 
objective  of  the  optimization  is  to  minimize  the  cost  of  generation  for  each  hour  𝑡  of  a 
given  time  horizon  𝑇,  e.g.,  8760  hours.  Two  additional  components  namely,  demand 
response  actions  𝐷𝑅𝑧  and  possible  demand  curtailment  𝐷𝐶𝑧  should  be  accounted  for  to 
avoid model infeasibility in cases of adequacy problems. 

The objective of the optimization can be written as: 

min ∑ ∑ 𝐶𝑔𝑡,𝑧,𝑡𝑃𝑔𝑡,𝑧,𝑡

+ 𝐷𝑅𝑧,𝑡𝐶𝑑𝑟,𝑧,𝑡 + 𝐶𝑢𝑟𝑡𝑧,𝑡𝑉𝑂𝐿𝐿𝑧,𝑡     ∀ 𝑡 ∈ 𝑇

𝑧∈𝑍

𝑔𝑡∈𝐺𝑇

where 𝑃𝑔𝑡,𝑧,𝑡 denotes the power generation of type 𝑔𝑐 in zone 𝑧 for the time point 𝑡, and 
𝐶𝑔𝑡,𝑧,𝑡 its  associated  generation  cost.  Similarly,  𝐷𝑅𝑧,𝑡  is  the  amount  of  demand  response 
activation within zone 𝑧 in time point 𝑡, and 𝐶𝑑𝑟,𝑧,𝑡 is its associated cost. Lastly, 𝐶𝑢𝑟𝑡𝑧,𝑡 the 
amount of possible demand shedding in zone 𝑧 in time point 𝑡, with the associated value 
of lost load 𝑉𝑂𝐿𝐿𝑧,𝑡.  

The following optimization constraints need to be fulfilled. Firstly, the nodal power balance 
in each zone needs to be respected as given below: 

∑ 𝑃𝑔𝑐,𝑧,𝑡
𝑔𝑐∈𝐺𝐶

+ 𝐷𝑅𝑧,𝑡 + 𝐶𝑢𝑟𝑡𝑧,𝑡 − 𝐷𝑧,𝑡 − ∑ 𝑃𝑓𝑖𝑗,𝑡

= 0         ∀ 𝑧 ∈ 𝑍, 𝑡 ∈ 𝑇  

𝑧=𝑖,𝑗≠𝑧

where 𝐷𝑧,𝑡  denotes  the expected  total zonal  demand in  zone  𝑧  in time  point 𝑡, and  𝑃𝑓𝑖𝑗,𝑡 
denotes the power flow from zone 𝑧 to any other connected zone 𝑗.  

Secondly,  the  power  flows  between  different  zones  need  to  be  limited  by  the  given  net 
transfer capacity (NTC) as follows: 

−𝑁𝑇𝐶𝑖𝑗 ≤ 𝑃𝑓𝑖𝑗,𝑡 ≤ 𝑁𝑇𝐶𝑖𝑗        ∀ (𝑖, 𝑗)   ∈  𝑍, 𝑡 ∈ 𝑇 

Finally,  capacity  limits  for the  different  generator types  in each  zone  as  well  as limits for 
providing demand response as well as demand curtailment need to be defined as follows: 

0 ≤ 𝐷𝑅𝑧,𝑡 ≤ 𝐷𝑅𝑧

𝑚𝑎𝑥       ∀ 𝑧 ∈ 𝑍, 𝑡 ∈ 𝑡 

0 ≤ 𝐶𝑢𝑟𝑡𝑧,𝑡 ≤ 𝐶𝑢𝑟𝑡𝑧

𝑚𝑎𝑥       ∀ 𝑧 ∈ 𝑍, 𝑡 ∈ 𝑡 

0 ≤ 𝑃𝑔𝑐,𝑧,𝑡 ≤ 𝑃𝑔𝑐,𝑧

𝑚𝑎𝑥       ∀ 𝑔𝑐 ∈ 𝐺𝐶𝑛𝑜𝑛𝑟𝑒𝑠, 𝑧 ∈ 𝑍, 𝑡 ∈ 𝑇 

0 ≤ 𝑃𝑔𝑐,𝑧,𝑡 ≤ 𝑃𝑔𝑐,𝑧,𝑡

𝑚𝑎𝑥        ∀ 𝑔𝑐 ∈ 𝐺𝐶𝑟𝑒𝑠, 𝑧 ∈ 𝑍, 𝑡 ∈ 𝑇 

Note  that  in  this  case  a  distinction  between  RES  generation  and  non-RES  generation 
needs to be made, as the maximum generation capacity for RES generators in each hour 
is determined by the hourly solar irradiation and wind speeds.  

As  there  are  no  time  coupling  constraints,  e.g.,  to  model  storage  or  specific  unit 
commitment  constraints,  the  optimization  problem  is  solved  as  a  sequence  of  hourly 
optimization problems. Figure 19 shows the outcome of the optimization model, applied to 
the zonal TYNDP model under the Global Ambition (GA) scenario.  The figure depicts the 
61 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

total amount of demand across all European market zones for each hour of the planning 
year  2030,  for  which  the  RES  generation  and  demand  time  series  have  been  based  on 
the climate year 1982. The figure also depicts the amount of curtailed RES generation on 
an  hourly  basis  due  to  limited  transmission  capacity  between  the  market  zones,  as  the 
RES  generation  costs  have  been  modelled  as  the  cheapest  option.  The  detailed 
description of all input data is provided in Appendix III.   

In comparison, in Figure 20 we can observe a much higher RES curtailment need for the 
planning year 2040, where the total installed RES generation capacity is 300 GW higher 
than in 2030, namely 1032 GW in 2040 instead of 737 GW in 2030. This is also reflected 
in the interzonal flows. Figure 21 and Figure 22 show the number of hours within a year, 
where the interconnection flows are larger than 90% of the interzonal NTC values. We can 
observe  that  the  number  of  hours  where  the  NTC  between  the  zones  is  utilized  fully, 
increases  with  the  amount  of  RES  in  the  system,  especially  observable  between  the 
Nordic region and Continental Europe, in the Balkan region and around Germany. 

Figure 19 – Total demand and RES curtailment for the GA2030 scenario, for climate year 1982 

Figure 20 – Total demand and RES curtailment for the GA2040 scenario, for climate year 1982 

62 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 21 – Number of hours with interconnection flow larger than 90% of NTC for GA2030 scenario, climate year 1982 

Figure 22 – Number of hours with interconnection flow larger than 90% of NTC for GA2040 scenario, climate year 1982 

In order to determine the generation dispatch while considering the power flows on both 
the  interconnectors  as  well  as  within  the  market  zones,  an  optimal  power  flow  model  is 
needed,  which  determines  the  least  cost  generation  dispatch  in  a  given  hour,  while 
respecting  Ohm’s  and  Kirchhoff’s  laws  and  the  operational  and  technical  limits  in  the 
system.  By  doing  so,  also the  optimal set  points for  HVDC  converters  and PSTs can be 
determined  to  maximally  utilize  the  transmission  lines,  thus  reduce  congestion,  and 
achieve a lower total generation cost in the system. 

6.2.2. AC/DC grid optimal power flow modelling 

Firstly, the most detailed generic nonlinear, nonconvex (NLP) optimal power flow model is 
introduced which is able to represent the nonlinearity of the system, when reactive power 
and  voltage  magnitudes  are  considered,  and  transmission  losses  are  considered  in  the 
network  equations.  This  OPF  model  is  applicable  on  a  nodal  level,  where  the  total 
generation  cost  in  the  transmission  system  is  minimized  while  considering  the  circuit 
physics  and  limits  of  the  network.  The  objective  function  of  the  optimization  problem  is 
given as: 

min ∑ 𝐶𝑔 𝑃𝑔,𝑡 + ∑ (𝐶𝑢

𝑑𝑟𝑃𝑢,𝑡

𝑑𝑟 + 𝑉𝑂𝐿𝐿𝑢𝑃𝑢,𝑡

𝑐𝑢𝑟𝑡)

    ∀ 𝑡 ∈ 𝑇 

𝑔∈𝑆𝑔

𝑢∈𝑆𝑢

63 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

where  𝑔 ∈ 𝑆𝑔  denotes  the  set  of  generators  in  the  system,  𝑃𝑔,𝑡  denotes  the  dispatch  of 
generator 𝑔 at time point 𝑡,  𝐶𝑔 denotes the cost of generator 𝑔 in €/MWh, 𝑢 ∈ 𝑆𝑢 denotes 
𝑑𝑟  the  demand  response  of  load  𝑢 at  time  point  𝑡  with  the  associated 
the  set  of  loads,  𝑃𝑢,𝑡
𝑐𝑢𝑟𝑡 denotes the possible demand curtailment of load 𝑢 at time point 𝑡 with 
𝑑𝑟, and 𝑃𝑢,𝑡
cost 𝐶𝑢
the  associated  value  of  lost  load  𝑉𝑂𝐿𝐿𝑢.  Note  that  to  represent  the  active  power 
generation  cost,  also  polynomial  or  other  types  of  nonlinear  cost  functions  can  be 
incorporated in the optimization model. 

To model all network constraints, we first start with the modelling of AC nodes. Each AC 
𝑎𝑐  is 
node  is  characterized  with  a  complex  valued  nodal  voltage  𝑈𝑘∠𝜃𝑘, 𝑘 ∈ 𝑆𝑛
the set of network nodes. The operational limits of the AC nodal voltages are defined as 
follows: 

𝑎𝑐,  where  𝑆𝑛

𝑈𝑚,𝑡,𝑦

𝑚𝑖𝑛 ≤ U𝑚,𝑡,𝑦 ≤ 𝑈𝑚,𝑡,𝑦

𝑚𝑎𝑥    ∀𝑚 ∈ 𝑆𝑛

𝑎𝑐, ∀𝑡 ∈ 𝑇 

𝑚𝑖𝑛 ≤ θ𝑚,𝑡,𝑦 ≤ 𝜃𝑚,𝑡,𝑦
𝜃𝑚,𝑡,𝑦

𝑚𝑎𝑥    ∀𝑚 ∈ 𝑆𝑛

𝑎𝑐, ∀𝑡 ∈ 𝑇, 

where  these  operational  limits  need  to  hold  for  each  time  step  of  each  planning  horizon 
considered.  An  AC  branch  connects  two  different  AC  nodes  𝑘  and  𝑚.  As  such,  the  AC 
branch  model  consists  of  AC  lines  and  cables  and  power  transformers,  e.g.,  found  in 
primary  substations.  A  generic  PI-model  representation  of  AC  branches  is  chosen,  as 
depicted  in  Figure  23.  𝑔𝑙  and  𝑏𝑙  are  the  resistive  and  inductive  series  admittances, 
whereas 𝑏𝑐𝑙 is the shunt susceptance. For the representation of power transformers, the 
AC branch model is generalized with an ideal transformer with the voltage tap ratio 𝜏𝑙. For 
an AC line or cable, 𝜏𝑙 = 1 holds. 

Figure 23 – Generic AC branch model for optimal power flow models 

The  active  and  reactive  power  flow  through  an  existing  AC  branch  in  the  from  direction 

𝑘 → 𝑚 are defined as follows: 

𝑓𝑟 = 𝑔𝑙 (
𝑃𝑙,𝑡

2
)

𝑈𝑘,𝑡
𝜏𝑙

− 𝑔𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑐𝑜𝑠(𝜃𝑘,𝑡 − 𝜃𝑚,𝑡) − 𝑏𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑠𝑖𝑛(𝜃𝑘,𝑡 − 𝜃𝑚,𝑡)  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, 𝑡 ∈ 𝑇 

𝑓𝑟 = −𝑏𝑙 (

𝑄𝑙,𝑡

2
)

𝑈𝑘,𝑡
𝜏𝑙

+ 𝑏𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑐𝑜𝑠(𝜃𝑘,𝑡 − 𝜃𝑚,𝑡) − 𝑔𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑠𝑖𝑛(𝜃𝑘,𝑡 − 𝜃𝑚,𝑡)  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, 𝑡 ∈ 𝑇 

𝑓𝑟  and  𝑄𝑙,𝑡

𝑓𝑟  are  the  active  and  reactive  power  flows  through  the  line  𝑙  in  time 
where,    𝑃𝑙,𝑡
point 𝑡 respectively. Similarly, the active and reactive power flow through an existing AC 
branch in the to direction 𝑚 → 𝑘 are defined as follows: 

𝑡𝑜 = 𝑔𝑙 (
𝑃𝑙,𝑡

2
)

𝑈𝑚,𝑡
𝜏𝑙

− 𝑔𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑐𝑜𝑠(𝜃𝑚,𝑡 − 𝜃𝑘,𝑡) − 𝑏𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑠𝑖𝑛(𝜃𝑚,𝑡 − 𝜃𝑘,𝑡)  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

64 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

𝑄𝑙,𝑡

𝑡𝑜 = −𝑏𝑙 (

2
)

𝑈𝑚,𝑡
𝜏𝑙

+ 𝑏𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑐𝑜𝑠(𝜃𝑚,𝑡 − 𝜃𝑘,𝑡) − 𝑔𝑙

𝑈𝑘,𝑡𝑈𝑚,𝑡
𝜏𝑙

𝑠𝑖𝑛(𝜃𝑚,𝑡 − 𝜃𝑘,𝑡)  ∀𝑙 ∈ 𝑆𝑙, ∀𝑡 ∈ T 

The apparent  power flow  through  AC  branches is  bounded by  the MVA rating of  branch 
the branch 𝑆𝑙

𝑟𝑎𝑡𝑒𝑑 as follows: 

(𝑃𝑙,𝑡

𝑓𝑟) 2 + (𝑄𝑙,𝑡

𝑓𝑟) 2   ≤ (𝑆𝑙

𝑟𝑎𝑡𝑒𝑑)2            ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

(𝑃𝑙,𝑡

𝑡𝑜) 2 + (𝑄𝑙,𝑡

𝑡𝑜) 2   ≤ (𝑆𝑙

𝑟𝑎𝑡𝑒𝑑)2             ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

Additionally, voltage phase angle deviation limits across AC nodes can be defined, which 
𝑚𝑎𝑥  denotes  the  maximum 
are  used  as  a  proxy  of  dynamic  stability  limits,  where  𝛥𝜃𝑙
allowable phase angle deviation across an AC branch: 

𝜃𝑘,𝑡 − 𝜃𝑚,𝑡 ≤ 𝛥𝜃𝑙

𝑚𝑎𝑥      ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

𝜃𝑚,𝑡 − 𝜃𝑘,𝑡 ≤ 𝛥𝜃𝑙

𝑚𝑎𝑥       ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

A  phase  shifting  transformer  (PST)  which  can  be  used  to  provide  power  flow 

controllability,  can  be  represented  by  a  series  impedance  connected  in  series  to  an 

existing  transmission  line  as  shown  in  Figure  24.  Where  𝑔𝑏  denotes  its  series 
conductance  and  𝑏𝑑  denotes  it  series  admittance.  The  PST  adds  an  additional  variable 
phase shift 𝜑𝑏 to control the power flow through the in series connected branch.  

Figure 24: Steady state PST representation for OPF modelling 

The PST is located between the nodes 𝑘 and 𝑘′ connected in series with a line 𝑘′ → 𝑘. A 
PST introduces  a  voltage  angle shift  𝜑𝑏  along  the PST impedance,  such  that  the  power 
flow through an existing PST becomes, 

2
𝑓𝑟 = 𝑔𝑏(𝑈𝑘,𝑡)
𝑃𝑏,𝑡

− 𝑔𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑐𝑜𝑠(𝜃𝑘,𝑡 − 𝜃𝑘′,𝑡 + 𝜑𝑏,𝑡)

− 𝑏𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑠𝑖𝑛(𝜃𝑘,𝑡 − 𝜃𝑘′,𝑡 + 𝜑𝑏,𝑡)  ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T 

2
𝑓𝑟 = −𝑏𝑏(𝑈𝑘,𝑡)

𝑄𝑏,𝑡

+ 𝑏𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑐𝑜𝑠(𝜃𝑘,𝑡 − 𝜃𝑘′,𝑡 + 𝜑𝑏,𝑡)

− 𝑔𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑠𝑖𝑛(𝜃𝑘,𝑡 − 𝜃𝑘′,𝑡 + 𝜑𝑏,𝑡)  ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T 

65 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

2
𝑡𝑜 = 𝑔𝑏(𝑈𝑘′,𝑡)
𝑃𝑏,𝑡

− 𝑔𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑐𝑜𝑠(𝜃𝑘′,𝑡 − 𝜃𝑘,𝑡 − 𝜑𝑏,𝑡)

− 𝑏𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑠𝑖𝑛(𝜃𝑘′,𝑡 − 𝜃𝑘,𝑡 − 𝜑𝑏,𝑡)  ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T 

2
𝑡𝑜 = −𝑏𝑏(𝑈𝑘′,𝑡)

𝑄𝑏,𝑡
𝜑𝑏,𝑡)  ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T. 

+ 𝑏𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑐𝑜𝑠(𝜃𝑘′,𝑡 − 𝜃𝑘,𝑡 − 𝜑𝑏,𝑡) − 𝑔𝑏𝑈𝑘,𝑡𝑈𝑘′,𝑡 𝑠𝑖𝑛(𝜃𝑘′,𝑡 − 𝜃𝑘,𝑡 −

The  phase  angle  shift  is  bounded  with  the  maximum  and  minimum  phase  angle  shift  of 
the PST, 

𝜑𝑏

𝑚𝑖𝑛 ≤ 𝜑𝑏,𝑡 ≤ 𝜑𝑏

𝑚𝑎𝑥      ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T. 

Also,  the  apparent  power  flow  across  the  PST  is  bounded  by  its  MVA  rating  𝑆𝑏
follows, 

𝑟𝑎𝑡𝑒𝑑  as 

(𝑃𝑏,𝑡

𝑓𝑟) 2 + (𝑄𝑏,𝑡

𝑓𝑟) 2   ≤ (𝑆𝑏

𝑟𝑎𝑡𝑒𝑑)2            ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ T 

(𝑃𝑏,𝑡

𝑡𝑜 ) 2 + (𝑄𝑏,𝑡

𝑡𝑜 ) 2   ≤ (𝑆𝑏

𝑟𝑎𝑡𝑒𝑑)2             ∀𝑏 ∈ 𝑆𝑏, ∀𝑡 ∈ 𝑇 

According to Kirchhoff’s current law, all active and reactive power injections in a node 𝑚 
need to balance to zero, 

∑ 𝑃𝑔,𝑡 

𝑔𝑚  ∈ 𝑇𝑔𝑒𝑛

𝑎𝑐
+ ∑ 𝑃𝑐,𝑡
𝑐𝑚𝑒 ∈ 𝑇𝑎𝑐𝑑𝑐

𝑓𝑟
− ∑ 𝑃𝑙,𝑡
𝑙𝑚𝑘 ∈ 𝑇𝑎𝑐

𝑓𝑟
− ∑ 𝑃𝑏,𝑡
𝑏𝑚𝑘 ∈ 𝑇𝑏

  − ∑ 𝑃𝑢,𝑡
𝑢𝑚 ∈𝑇𝑙𝑜𝑎𝑑

= 0 ∀𝑚 ∈ 𝑆𝑚, 𝑡

∈ 𝑇  

∑ 𝑄𝑔,𝑡 

𝑔𝑚  ∈ 𝑇𝑔𝑒𝑛

𝑎𝑐
+ ∑ 𝑄𝑐,𝑡
𝑐𝑚𝑒 ∈ 𝑇𝑎𝑐𝑑𝑐

𝑓𝑟
− ∑ 𝑄𝑙,𝑡
𝑙𝑚𝑘 ∈ 𝑇𝑎𝑐

𝑓𝑟
− ∑ 𝑄𝑏,𝑡
𝑏𝑚𝑘 ∈ 𝑇𝑏

  − ∑ 𝑄𝑢,𝑡
𝑢𝑚 ∈𝑇𝑙𝑜𝑎𝑑

= 0 ∀𝑚 ∈ 𝑆𝑚, 𝑡

∈ 𝑇 

where, 

•  𝑃𝑐,𝑡

•  𝑃𝑔,𝑡 and 𝑄𝑔,𝑡 are the active and reactive power injections of generators connected 
 represents the nodal connectivity of 

𝑎𝑐  are  the  AC  side  active  and  reactive  power  injections  of  HVDC 

to node 𝑚, in time point 𝑡, where 𝑔𝑚   ∈   𝑇𝑔𝑒𝑛
generators 
𝑎𝑐  and  𝑄𝑐,𝑡
converters  connected  to  node  𝑚,  in  time  point  𝑡,  𝑐𝑚𝑒   ∈   𝑇𝑎𝑐𝑑𝑐
nodal connectivity of HVDC converters between AC nodes 𝑚 and DC nodes 𝑒 
𝑓𝑟 are the active power flows leaving from node 𝑚, in time point 𝑡, where 
𝑓𝑟 and 𝑄𝑙,𝑡
𝑙𝑚𝑘  ∈  𝑇𝑎𝑐  represents the  nodal  connectivity  of  AC  branches  between AC  nodes 
𝑚 and 𝑘  

  represents  the 

•  𝑃𝑙,𝑡

𝑓𝑟
•  𝑃𝑏,𝑡

   and 𝑄𝑏,𝑡

𝑓𝑟  are  the  active flows  and  reactive  power flows  of  PSTs  leaving from 

node 𝑚,  in  time  point  𝑡,    where  𝑏𝑚𝑘  ∈  𝑇𝑏
between nodes 𝑚 and 𝑘 

  represents  the  connectivity  of  PST 

66 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

•  𝑃𝑢,𝑡  and 

  𝑄𝑢,𝑡  are 

the  active  and  reactive  power  demands  of 

loads 

connected to node 𝑚,  in  time  point  𝑡,  where  𝑢𝑚   ∈   𝑇𝑙𝑜𝑎𝑑
connectivity of loads 

  represents  the  nodal 

Both dispatchable and renewable generators are subject to operational limits, 

𝑚𝑖𝑛 ≤ 𝑃𝑔,𝑡 ≤ 𝑃𝑔,𝑡
𝑃𝑔,𝑡

𝑚𝑎𝑥   ∀𝑔 ∈ 𝑆𝑔, 𝑡 ∈ 𝑇 

𝑄𝑔,𝑡

𝑚𝑖𝑛 ≤ 𝑄𝑔,𝑡 ≤ 𝑄𝑔,𝑡

𝑚𝑎𝑥   ∀𝑔 ∈ 𝑆𝑔, 𝑡 ∈ 𝑇 

where the active and reactive power limits of the renewable generators are defined by the 
climatic  conditions  at  time  instance  t.  Similarly,  the  nodal  demand  including  demand 
response and possible demand curtailment can be modelled using following relationships: 

𝑃𝑢,𝑡 = 𝑃𝑢,𝑡

𝑟𝑒𝑓 − 𝑃𝑢,𝑡

𝑑𝑟 − 𝑃𝑢,𝑡

𝑐𝑢𝑟𝑡     ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇  

𝑟𝑒𝑓 is the reference demand of load 𝑢 at time point 𝑡, and 𝑃𝑢,𝑡

𝑐𝑢𝑟𝑡 are the 
where  𝑃𝑢,𝑡
demand  response  and  curtailment,  respectively.  Similarly,  the  reactive  power  demand  is 
modelled using : 

𝑑𝑟 and 𝑃𝑢,𝑡

𝑄𝑢,𝑡 = 𝑄𝑢,𝑡

𝑟𝑒𝑓 − 𝑄𝑢,𝑡

𝑑𝑟 − 𝑄𝑢,𝑡

𝑐𝑢𝑟𝑡     ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇  

Active  and  reactive  demand  response,  as  well  as  curtailment  are  subject  to  upper  and 
lower bounds: 

0 ≤ 𝑃𝑢,𝑡

𝑑𝑟 ≤ 𝑃𝑢,𝑡

𝑟𝑒𝑓       ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇 

0 ≤ 𝑃𝑢,𝑡

𝑐𝑢𝑟𝑡 ≤ 𝑃𝑢,𝑡

𝑟𝑒𝑓       ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇 

0 ≤ 𝑄𝑢,𝑡

𝑑𝑟 ≤ 𝑃𝑢,𝑡

𝑟𝑒𝑓       ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇 

0 ≤ 𝑄𝑢,𝑡

𝑐𝑢𝑟𝑡 ≤ 𝑃𝑢,𝑡

𝑟𝑒𝑓       ∀ 𝑢 ∈ 𝑆𝑢, 𝑡 ∈ 𝑇 

where  the  reference  power  factor  is  preserved  through 

𝑑𝑟
𝑃𝑢,𝑡
𝑑𝑟 =  
𝑄𝑢,𝑡

𝑟𝑒𝑓
𝑃𝑢,𝑡
𝑟𝑒𝑓  and 
𝑄𝑢,𝑡

𝑐𝑢𝑟𝑡
𝑃𝑢,𝑡
𝑐𝑢𝑟𝑡 =  
𝑄𝑢,𝑡

𝑟𝑒𝑓
𝑃𝑢,𝑡
𝑟𝑒𝑓  ∀ 𝑢 ∈
𝑄𝑢,𝑡

𝑆𝑢, 𝑡 ∈ 𝑇. 
Figure  25  depicts  the  HVDC  converter  station  model  as  part  of  the  AC/DC  grid  optimal 
power  flow  model.  The  generic  converter  station  model  consists  of  a  converter 
transformer,  an  inductive and  capacitive  filter,  and  the  power  electronic HVDC  converter 
itself. 

67 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 25 - Generic HVDC converter station model 

The depicted converter station is located between an AC node 𝑖 and a DC node 𝑒. On the 
AC  side,  the  converter  is  characterized  by  the  complex voltage  𝑈𝑖  of  the AC  node 𝑖,  the 
𝑓 and the complex voltage observed on 
complex voltage after the converter transformer 𝑈𝑐
𝑐𝑣.  
the AC side of the power electronic converter 𝑈𝑐
Using  the  AC  side  voltages,  the  power  flows  through  the  converter  transformer  of  each 
converter  station  𝑐 ∈ 𝑆𝑐  ,  for  each  time  point  𝑡 ∈ 𝑇  are  calculated  using  for  the  from 
direction 𝑖 → 𝑒: 

𝑡𝑓 = 𝑔𝑐
𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 (

2

)

𝑚𝑎𝑔

𝑈𝑖,𝑡
𝜏𝑐

𝑓,𝑚𝑎𝑔

− 𝑔𝑐

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

𝑐𝑜𝑠(𝜃𝑖,𝑡 − 𝜃𝑐,𝑡

𝑓 ) − 𝑏𝑐

𝑓,𝑚𝑎𝑔

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

𝑠𝑖𝑛(𝜃𝑖,𝑡 − 𝜃𝑐,𝑡

𝑓 )  ∀𝑐

∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑡𝑓 = −𝑏𝑐
𝑄𝑐𝑖𝑒,𝑡

𝑡𝑓 (

2

)

𝑚𝑎𝑔

𝑈𝑖,𝑡
𝜏𝑐

𝑓,𝑚𝑎𝑔

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

+ 𝑏𝑐

𝑓 )
𝑐𝑜𝑠(𝜃𝑖,𝑡 − 𝜃𝑐,𝑡

𝑓,𝑚𝑎𝑔

− 𝑔𝑐

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

𝑠𝑖𝑛(𝜃𝑖,𝑡 − 𝜃𝑐,𝑡

𝑓 )  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

And the to direction 𝑒 → 𝑖: 

𝑎𝑐 =   𝑃𝑐𝑒𝑖,𝑡
𝑃𝑐,𝑡

𝑡𝑓 = 𝑔𝑐

𝑡𝑓 (

𝑓,𝑚𝑎𝑔

𝑈𝑐,𝑡
𝜏𝑐

2

)

𝑓,𝑚𝑎𝑔

− 𝑔𝑐

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

𝑐𝑜𝑠(𝜃𝑐,𝑡

𝑓 − 𝜃𝑖,𝑡)

𝑓,𝑚𝑎𝑔

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

− 𝑏𝑐

𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑓 − 𝜃𝑖,𝑡)  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑎𝑐 = 𝑄𝑐𝑒𝑖,𝑡
𝑄𝑐,𝑡

𝑡𝑓 = −𝑏𝑐

𝑡𝑓 (

𝑓,𝑚𝑎𝑔

𝑈𝑐,𝑡
𝜏𝑐

2

)

𝑓,𝑚𝑎𝑔

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

+ 𝑏𝑐

𝑐𝑜𝑠(𝜃𝑐,𝑡

𝑓 − 𝜃𝑖,𝑡)

𝑓,𝑚𝑎𝑔

− 𝑔𝑐

𝑡𝑓 𝑈𝑖,𝑡

𝑚𝑎𝑔𝑈𝑐,𝑡
𝜏𝑐

𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑓 − 𝜃𝑖,𝑡)  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑡𝑓  denotes  the  series  conductance  of  the  transformer,  𝑏𝑐

𝑡𝑓  denotes  its  series 
where,  𝑔𝑐
admittance,  and  𝜏𝑐  denotes  the  tap  setting  of  the  transformer.    In  case,  the  converter 
station does not contain a transformer, the equations can be placed by: 
𝑡𝑓 + 𝑃𝑐𝑒𝑖,𝑡
𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

68 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

𝑡𝑓 + 𝑄𝑐𝑒𝑖,𝑡
𝑄𝑐𝑖𝑒,𝑡

𝑡𝑓 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑚𝑎𝑔 = 𝑈𝑐,𝑡
𝑈𝑖,𝑡

𝑓,𝑚𝑎𝑔   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝜃𝑖,𝑡 = 𝜃𝑐,𝑡

𝑓     ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

The reactive power injected by the capacitive part of the filer is defined as, with 𝑏𝑐
susceptance of the capacitive filter: 

𝑓 as the 

𝑄𝑓,𝑡

𝑐 =   −𝑏𝑐

𝑓(𝑈𝑐,𝑡

2
𝑓,𝑚𝑎𝑔)

    ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

The nodal power balance at the filter node 𝑓 is defined as: 

𝑝𝑟 + 𝑃𝑐𝑒𝑖,𝑡
𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 + 𝑄𝑐𝑒𝑖,𝑡
𝑄𝑐𝑖𝑒,𝑡

𝑡𝑓 + 𝑄𝑐,𝑡

𝑓 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

As  the  inductive  part  of  the  converter  station  filter  behaves  similar  to  the  converter 
transformer  (with the  exception  of the transformer  tap  𝜏𝑐),  the  active  and reactive power 
𝑝𝑟  as  the  series 
flows  across  the  inductive  filter  can  be  written  down  as  with  𝑔𝑐
conductance and susceptance of the inductor: 

𝑝𝑟  and  𝑏𝑐

For the from direction 𝑖 → 𝑒: 

𝑝𝑟(𝑈𝑐,𝑡

𝑝𝑟 = 𝑔𝑐
𝑃𝑐𝑖𝑒,𝑡
𝑝𝑟𝑈𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡

2
𝑓,𝑚𝑎𝑔)

− 𝑔𝑐
𝑐𝑣,𝑚𝑎𝑔 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑝𝑟𝑈𝑐,𝑡
𝑓 − 𝜃𝑐,𝑡

𝑐𝑣,𝑚𝑎𝑔 𝑐𝑜𝑠(𝜃𝑐,𝑡
𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡
𝑐𝑣)  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

− 𝑏𝑐

𝑓 − 𝜃𝑐,𝑡
𝑐𝑣)

𝑝𝑟 = −𝑏𝑐
𝑄𝑐𝑖𝑒,𝑡

𝑝𝑟(𝑈𝑐,𝑡

2
𝑓,𝑚𝑎𝑔)

+ 𝑏𝑐

𝑝𝑟𝑈𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡

𝑐𝑣 𝑐𝑜𝑠(𝜃𝑐,𝑡

𝑓 − 𝜃𝑐,𝑡

𝑐𝑣) − 𝑔𝑐

𝑝𝑟𝑈𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡

𝑐𝑣 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑓 − 𝜃𝑐,𝑡

𝑐𝑣)  ∀𝑐

∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

And the to direction 𝑒 → 𝑖: 

2
𝑓,𝑚𝑎𝑔)

𝑝𝑟 = 𝑔𝑐
𝑃𝑐𝑒𝑖,𝑡
𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡
𝑝𝑟𝑈𝑐,𝑡

𝑝𝑟(𝑈𝑐,𝑡
𝑐𝑣,𝑚𝑎𝑔 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑝𝑟𝑈𝑐,𝑡
𝑐𝑣 − 𝜃𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡
𝑐𝑣 𝑐𝑜𝑠(𝜃𝑐,𝑡
𝑓 )  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

− 𝑔𝑐

− 𝑏𝑐

𝑓 )
𝑐𝑣 − 𝜃𝑐,𝑡

𝑝𝑟 = −𝑏𝑐
𝑄𝑐𝑒𝑖,𝑡
𝑝𝑟𝑈𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡

𝑝𝑟(𝑈𝑐,𝑡

2
𝑓,𝑚𝑎𝑔)

+ 𝑏𝑐
𝑐𝑣,𝑚𝑎𝑔 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑝𝑟𝑈𝑐,𝑡
𝑐𝑣 − 𝜃𝑐,𝑡

− 𝑔𝑐

𝑐𝑣,𝑚𝑎𝑔 𝑐𝑜𝑠(𝜃𝑐,𝑡

𝑓,𝑚𝑎𝑔𝑈𝑐,𝑡
𝑓 )  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑓 )
𝑐𝑣 − 𝜃𝑐,𝑡

According to the notation in Figure 25, the AC side active and reactive power of the HVDC 
converter have opposite signs as the power through the inductive filter, e.g.,  

𝑝𝑟 + 𝑃𝑐,𝑡
𝑃𝑐𝑒𝑖,𝑡

𝑐𝑣,𝑎𝑐 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 + 𝑄𝑐,𝑡
𝑄𝑐𝑒𝑖,𝑡

𝑐𝑣,𝑎𝑐 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

69 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

The  AC  and  DC  side  power  of  the  power  electronic  converter  can  be  linked  via  the 
converter losses, e.g., 

𝑐𝑣,𝑎𝑐 + 𝑃𝑐,𝑡
𝑃𝑐,𝑡

𝑐𝑣,𝑑𝑐 = 𝑃𝑐,𝑡

𝑐𝑣,𝑙𝑜𝑠𝑠  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

with the losses defined as a quadratic function of the current through the power electronic 
converter 𝐼𝑐

𝑎𝑐,𝑚𝑎𝑔∠𝜃𝑐
𝑖: 

𝑎𝑐 = 𝐼𝑐

𝑐𝑣,𝑙𝑜𝑠𝑠 = 𝑎𝑐 + 𝑏𝑐𝐼𝑐,𝑡
𝑃𝑐,𝑡

𝑎𝑐,𝑚𝑎𝑔 + 𝑐𝑐(𝐼𝑐,𝑡

2
𝑎𝑐,𝑚𝑎𝑔)

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

The  active  and  reactive  power  of  the  converter  are  linked  to  the  converter  current  and 
voltage through: 

2
𝑐𝑣,𝑎𝑐)

(𝑃𝑐,𝑡

+ (𝑄𝑐,𝑡

2
𝑐𝑣,𝑎𝑐)

2
𝑎𝑐,𝑚𝑎𝑔)

= (𝐼𝑐,𝑡

2
𝑐𝑣,𝑚𝑎𝑔)

⋅ (𝑈𝑐,𝑡

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

All active and reactive power terms as well voltage magnitudes and currents are subject to 
operational bounds: 

2
𝑡𝑓 )
(𝑃𝑐𝑖𝑒,𝑡

2
𝑡𝑓 )
+ (𝑄𝑐𝑖𝑒,𝑡

2
𝑡𝑓,𝑟𝑎𝑡𝑒𝑑)

≤ (𝑆𝑐

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

2
𝑡𝑓 )
(𝑃𝑐𝑒𝑖,𝑡

2
𝑡𝑓 )
+ (𝑄𝑐𝑒𝑖,𝑡

2
𝑡𝑓,𝑟𝑎𝑡𝑒𝑑)

≤ (𝑆𝑐

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

2
𝑝𝑟 )
(𝑃𝑐𝑖𝑒,𝑡

2
𝑝𝑟 )
+ (𝑄𝑐𝑖𝑒,𝑡

2
𝑝𝑟,𝑟𝑎𝑡𝑒𝑑)

≤ (𝑆𝑐

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

2
𝑝𝑟 )
(𝑃𝑐𝑒𝑖,𝑡

2
𝑝𝑟 )
+ (𝑄𝑐𝑒𝑖,𝑡

2
𝑝𝑟,𝑟𝑎𝑡𝑒𝑑)

≤ (𝑆𝑐

 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

0 ≤ 𝑄𝑐,𝑡

𝑓 ≤ 𝑄𝑐

𝑓,𝑚𝑎𝑥 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑓,𝑚𝑖𝑛 ≤ 𝑈𝑐,𝑡

𝑓,𝑚𝑎𝑔 ≤ 𝑈𝑐

𝑈𝑐

𝑓,𝑚𝑎𝑥 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑐𝑣,𝑚𝑖𝑛 ≤ 𝑈𝑐,𝑡
𝑈𝑐

𝑐𝑣,𝑚𝑎𝑔 ≤ 𝑈𝑐

𝑐𝑣,𝑚𝑎𝑥 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑐𝑣,𝑚𝑖𝑛 ≤ 𝐼𝑐,𝑡
𝐼𝑐

𝑐𝑣,𝑚𝑎𝑔 ≤ 𝐼𝑐

𝑐𝑣,𝑚𝑎𝑥 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑑𝑐,𝑚𝑖𝑛 ≤ 𝑃𝑐,𝑡
𝑃𝑐

𝑐𝑣,𝑑𝑐 ≤ 𝑃𝑐

𝑑𝑐,𝑚𝑎𝑥 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

The HVDC branches, e.g., lines and cables can be modelled using the single line diagram 
shown in Figure 26, which represents the DC branch as a resistance between two DC grid 
nodes 𝑒 and 𝑓. For monopolar HVDC configurations, the power will flow through a single 
conductor, whereas for symmetrical monopoles or bipolar HVDC schemes, the power flow 
through a branch is distributed equally between the two conductors, assuming they have 
the same resistance (𝑟𝑑) / conductance (𝑔𝑑). 

70 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 26 – Generic DC branch model for monopolar and bipolar HVDC 

Considering  the  number  of  poles  𝑁𝑑  (𝑁𝑑 = 1  for  monopolar  and  𝑁𝑑 = 2,  for  symmetrical 
monopolar  or  bipolar  configurations),  the  power  flows  through  the  DC  branches  can  be 
calculated with the Ohm’s law using the nodal DC grid voltages for both directions 𝑒 → 𝑓 
and 𝑓 → 𝑒: 

𝑑𝑐 = 𝑁𝑑𝑔𝑑𝑈𝑒,𝑡
𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐(𝑈𝑒,𝑡

𝑑𝑐 − 𝑈𝑓,𝑡

𝑑𝑐) ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

𝑑𝑐 = 𝑁𝑑𝑔𝑑𝑈𝑓,𝑡
𝑃𝑑𝑓𝑒,𝑡

𝑑𝑐(𝑈𝑓,𝑡

𝑑𝑐 − 𝑈𝑒,𝑡

𝑑𝑐) ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

with the DC branch power flow limits 

−𝑃𝑑

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐 ≤ 𝑃𝑑

𝑟𝑎𝑡𝑒𝑑.    ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

−𝑃𝑑

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑑𝑓𝑒,𝑡

𝑑𝑐 ≤ 𝑃𝑑

𝑟𝑎𝑡𝑒𝑑     ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

Finally,  defining  Kirchhoff’s  current  law  for  DC  nodes  completes  the  AC/DC  grid  optimal 
power  flow  model,  where  𝑆𝑒  denotes  the  set  of  DC  nodes,  and  set  𝑇𝑑𝑐  denotes  the 
connectivity set of DC branches to DC nodes: 

𝑑𝑐
∑ 𝑃𝑐,𝑡

− ∑ 𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐

= 0 ∀𝑒 ∈ 𝑆𝑒, 𝑡 ∈ 𝑇  

𝑐𝑚𝑒 ∈ 𝑇𝑎𝑐𝑑𝑐

𝑑𝑒𝑓 ∈ 𝑇𝑑𝑐

As  in  the  case  of  the  NTC  based  zonal  model,  also  this  optimization  model  does  not 
include  any  time  coupling  constraints,  and  as  such  can  be  solved  for  all  the  hours  in  a 
planning  year  separately.  In  case  unit  commitment  constraints  or  storage  models  are 
introduced  in  model,  time  coupling  constraints  would  be  needed,  and  as  such,  the 
problem would become a single optimization problem solved for the entire planning year. 
Even  if  solved  for  each  time  step  (hour)  separately,  the  problem  remains  a  highly 
nonlinear and nonconvex problem. Although such problems can be solved efficiently with 
interior  point  optimization  solvers,  still  for  large  and  especially  ill  conditioned  cases, 
convergence  problems  or  long  calculation  times  can  occur.  Thus,  as  a  mitigation,  the 
power  flow  equations  can  be  linearized,  providing  a  much  more  tractable  and  compact 
model,  under  the  following  assumptions,  which  are  very  well  known  for  the  linearized 
power flow formulation, often called “DC OPF” (which does not relate to DC grids). 

Firstly,  it  is  assumed  that  the  magnitudes  of  the  nodal  AC  and  DC  grid  nodal  voltage 

magnitudes across the network will only differ slightly such that it can be assumed: 𝑈𝑚,𝑡 =
𝑎𝑐 and 𝑈𝑒,𝑡 = 𝑈𝑓,𝑡 = 𝑈𝑑𝑐 ∀𝑒, 𝑓 ∈ 𝑆𝑒. Another assumption is that the AC 
𝑈𝑘,𝑡 = 𝑈𝑎𝑐 ∀𝑚, 𝑘 ∈ 𝑆𝑛
grid  voltage  angle  differences  are  so  small  such  that  𝑠𝑖𝑛(𝜃𝑚,𝑡,𝑦 − 𝜃𝑘,𝑡,𝑦) ≈ 𝜃𝑚,𝑡,𝑦 − 𝜃𝑘,𝑡,𝑦 

71 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

and  𝑐𝑜𝑠(𝜃𝑚,𝑡,𝑦 − 𝜃𝑘,𝑡,𝑦) ≈ 1  can  be  assumed.  Additionally,  the  resistive  part  of  the  series 
admittance 𝑔𝑙 = 0 is neglected under the assumption that the inductance of AC branches 
is dominant, which is a valid assumption for overhead lines, resulting for AC branches in: 

 (𝜃𝑚,𝑡 − 𝜃𝑘,𝑡) ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

𝑡𝑜 = 𝑏𝑙
𝑃𝑙,𝑡

 (𝜃𝑘,𝑡 − 𝜃𝑚,𝑡) = −𝑃𝑙,𝑡

𝑓𝑟  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

2
𝑈𝑎𝑐
𝜏𝑙

𝑓𝑟 = 𝑏𝑙
𝑃𝑙,𝑡,𝑦
2
𝑈𝑎𝑐
𝜏𝑙
𝑓𝑟 = 𝑄𝑙,𝑡
𝑄𝑙,𝑡

𝑡𝑜 = 0  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T, 

which  means that  all  reactive  power  related  terms  disappear  in the  used  model.  As the 

resistive  part  of  the  impedance/admittance  is  neglected,  this  representation  also 

neglects the network losses occurring. In this case, branch flows are only bound by the 

maximum voltage angle differences and the thermal limits of the AC branches are defined 

in terms of active power only: 

𝜃𝑘,𝑡 − 𝜃𝑚,𝑡 ≤ 𝛥𝜃𝑙

𝑚𝑎𝑥      ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

𝜃𝑚,𝑡 − 𝜃𝑘,𝑡 ≤ 𝛥𝜃𝑙

𝑚𝑎𝑥       ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

−𝑃𝑙

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑙,𝑡,𝑦

𝑓𝑟   ≤ 𝑃𝑙

𝑟𝑎𝑡𝑒𝑑            ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

−𝑃𝑙

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑙,𝑡,𝑦

𝑡𝑜   ≤ 𝑃𝑙

𝑟𝑎𝑡𝑒𝑑               ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

Similarly,  to  AC  branches,  also  the  linearized  equations  for  PSTs  can  be  written  using 

𝑈𝑘,𝑡,𝑦 = 𝑈𝑘′,𝑡,𝑦 = 𝑈𝑎𝑐 ∀𝑘′, 𝑘 ∈ 𝑆𝑛

𝑎𝑐, 

𝑓𝑟 = 𝑏𝑏𝑈𝑎𝑐
𝑃𝑏,𝑡

2  (𝜃𝑘,𝑡 − 𝜃𝑘′,𝑡 + 𝜑𝑏,𝑡)  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

𝑡𝑜 = 𝑏𝑏𝑈𝑎𝑐
𝑃𝑏,𝑡

2  (𝜃𝑘′,𝑡 − 𝜃𝑘,𝑡 − 𝜑𝑏,𝑡)  ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

−𝑃𝑏

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑏,𝑡

𝑓𝑟   ≤ 𝑃𝑏

𝑟𝑎𝑡𝑒𝑑             ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

−𝑃𝑏

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑏,𝑡

𝑡𝑜   ≤ 𝑃𝑏

𝑟𝑎𝑡𝑒𝑑                 ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T 

𝜑𝑏

𝑚𝑖𝑛 ≤ 𝜑𝑏,𝑡 ≤ 𝜑𝑏

𝑚𝑎𝑥       ∀𝑙 ∈ 𝑆𝑙

𝑎𝑐, ∀𝑡 ∈ T. 

The AC nodal power balance is only written in active power: 

∑ 𝑃𝑔,𝑡 

𝑔𝑚  ∈ 𝑇𝑔𝑒𝑛

𝑎𝑐
+ ∑ 𝑃𝑐,𝑡
𝑐𝑚𝑒 ∈ 𝑇𝑎𝑐𝑑𝑐

𝑓𝑟
− ∑ 𝑃𝑙,𝑡
𝑙𝑚𝑘 ∈ 𝑇𝑎𝑐

𝑓𝑟
− ∑ 𝑃𝑏,𝑡
𝑏𝑚𝑘 ∈ 𝑇𝑏

  − ∑ 𝑃𝑢,𝑡
𝑢𝑚 ∈𝑇𝑙𝑜𝑎𝑑

= 0 ∀𝑚 ∈ 𝑆𝑚, 𝑡

∈ 𝑇  

Similarly,  all  equations  describing  the  HVDC  converter  station  can  be  linearized  and 
written in “active power only” terms as follows: 

𝑡𝑓 = −𝑏𝑐
𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 𝑈𝑎𝑐

2  𝑠𝑖𝑛(𝜃𝑖,𝑡 − 𝜃𝑐,𝑡

𝑓 )  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

72 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

𝑎𝑐 =  𝑃𝑐𝑒𝑖,𝑡
𝑃𝑐,𝑡

𝑡𝑓 = −𝑏𝑐

𝑡𝑓 𝑈𝑎𝑐

2 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑓 − 𝜃𝑖,𝑡)  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 + 𝑃𝑐𝑒𝑖,𝑡
𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 = −𝑏𝑐
𝑃𝑐𝑖𝑒,𝑡

𝑝𝑟𝑈𝑎𝑐

2 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑓 − 𝜃𝑐,𝑡

𝑐𝑣)  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 = −𝑏𝑐
𝑃𝑐𝑒𝑖,𝑡

𝑝𝑟𝑈𝑎𝑐

2 𝑠𝑖𝑛(𝜃𝑐,𝑡

𝑐𝑣 − 𝜃𝑐,𝑡

𝑓 )  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

𝑝𝑟 + 𝑃𝑐,𝑡
𝑃𝑐𝑒𝑖,𝑡

𝑐𝑣,𝑎𝑐 = 0   ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

Considering that the AC grid and AC equipment of the HVDC substations are considered 
to be lossless, and the power electronic converter losses are assumed to be zero as well 
resulting in: 

𝑐𝑣,𝑎𝑐 + 𝑃𝑐,𝑡
𝑃𝑐,𝑡

𝑐𝑣,𝑑𝑐 = 0  ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

Also, all equipment limits within the HVDC substation can be defined via the active power 
bounds as: 

−𝑃𝑐,𝑡

𝑡𝑓,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐𝑖𝑒,𝑡

𝑡𝑓 ≤ 𝑃𝑐,𝑡

𝑡𝑓,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

−𝑃𝑐,𝑡

𝑡𝑓,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐𝑒𝑖,𝑡

𝑡𝑓 ≤ 𝑃𝑐,𝑡

𝑡𝑓,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

−𝑃𝑐,𝑡

𝑝𝑟,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐𝑖𝑒,𝑡

𝑝𝑟 ≤ 𝑃𝑐,𝑡

𝑝𝑟,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

−𝑃𝑐,𝑡

𝑝𝑟,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐𝑒𝑖,𝑡

𝑝𝑟 ≤ 𝑃𝑐,𝑡

𝑝𝑟,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

−𝑃𝑐

𝑎𝑐,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐,𝑡

𝑐𝑣,𝑎𝑐 ≤ 𝑃𝑐

𝑎𝑐,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

−𝑃𝑐

𝑑𝑐,𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑐,𝑡

𝑐𝑣,𝑑𝑐 ≤ 𝑃𝑐

𝑑𝑐,𝑟𝑎𝑡𝑒𝑑 ∀𝑐 ∈ 𝑆𝑐, 𝑡 ∈ 𝑇 

As  for  the  DC  branches,  considering  that  the  voltage  difference  between  the  nodes 
reduces to zero, the DC power flow reduces to a network flow model, i.e., an NTC based 
model  which  is  a  valid  approximation  under  the  assumption  that  the  injections  from  the 
converters can be controlled largely, 

𝑑𝑐 + 𝑃𝑑𝑓𝑒,𝑡
𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐 = 0 ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

−𝑃𝑑

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐 ≤ 𝑃𝑑

𝑟𝑎𝑡𝑒𝑑.    ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

−𝑃𝑑

𝑟𝑎𝑡𝑒𝑑 ≤ 𝑃𝑑𝑓𝑒,𝑡

𝑑𝑐 ≤ 𝑃𝑑

𝑟𝑎𝑡𝑒𝑑.    ∀𝑑 ∈ 𝑆𝑑, 𝑡 ∈ 𝑇 

The DC grid nodal power equations remain unchanged: 

𝑑𝑐
∑ 𝑃𝑐,𝑡

− ∑ 𝑃𝑑𝑒𝑓,𝑡

𝑑𝑐

= 0 ∀𝑒 ∈ 𝑆𝑒, 𝑡 ∈ 𝑇  

𝑐𝑚𝑒 ∈ 𝑇𝑎𝑐𝑑𝑐

𝑑𝑒𝑓 ∈ 𝑇𝑑𝑐

73 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

It  needs  to  be  noted  that  in  the  literature  many  different  formulations  of  the  power  flow 
equations  exist,  which  lead  to  different  computational  complexities,  accuracy  in  system 
representation  and  computation  time.  The  introduced  OPF  models  can  further  be 
extended in order to model different aspects of system operation. For instance, one such 
application  is  the  determination  of  the  optimal  redispatch  actions  both  for  balancing  the 
power  mismatch  stemming  from  the  day  ahead  renewable  forecast  error  as  well  as  in 
cases of outages. 

6.2.3. AC/DC grid optimal redispatch power flow modelling 

Considering  possible  outages  in  the  network,  or  potential  inertia  constraints,  an  optimal 
redispatch  model  can  be  used  to  determine  the  minimal  redispatch  to  be  performed  to 
avoid  thermal  overloads  in  the  grid  due  to  outages,  or  potential  dispatch/start-up  of 
conventional synchronous machine based generation to ensure a minimum inertia level in 
the grid. 

Let  us  first  start  with  the  case  of  possible  contingencies  in  the  grid.  In  case  of  a  line 
contingency,  the  power  flows  in  the  grid  will  be  changed  due  to  the  change  in  the  grid 
impedances.  This could potentially  lead to overloading  of  other  lines  in  the system,  e.g., 
most notable on parallel lines which are highly loaded. In such cases, the active power set 
points  of  generators,  PSTs  and  HVDC  links  can  be  changed  in  order  to  obtain  a  power 
flow solution which respects thermal line limits. In order to minimize the necessary active 
power re-dispatch costs, the following model can be utilized.  

Starting  from  the  pre-contingency  (N-0)  situation,  e.g.,  the  solution  of  the  optimal  power 
flow  problem  denoted  with  the  superscript  𝑟𝑒𝑓,  we  can  deactivate  a  critical  set  of 
transmission  lines  one-by-one  in  the  system,  e.g.,  create  a  number  of  n-1  contingency 
situations. In this case, our objective is to minimize the cost for upwards and downwards 
𝑑𝑜𝑤𝑛.  Thus,  the  objective  function  of  the 
redispatch  which  is  denoted  by  Δ𝑃𝑔,𝑡
optimisation model becomes: 

𝑢𝑝and  Δ𝑃𝑔,𝑡

min ∑

𝑔∈𝑆𝑔

(𝐶𝑔

𝑢𝑝Δ𝑃𝑔,𝑡

𝑢𝑝 + 𝐶𝑔

𝑑𝑜𝑤𝑛Δ𝑃𝑔,𝑡

𝑑𝑜𝑤𝑛)  + ∑

𝑢∈𝑆𝑢

(𝐶𝑢

𝑑𝑟𝑃𝑢,𝑡

𝑑𝑟 + 𝑉𝑂𝐿𝐿𝑢𝑃𝑢,𝑡

𝑐𝑢𝑟𝑡

)    ∀ 𝑡 ∈ 𝑇, 

𝑑𝑜𝑤𝑛 ≥ 0. We can then write the 
with the two newly introduced variables Δ𝑃𝑔
relationship between the active power generation and the redispatch need with respect to 
the reference (N-0) case as: 

𝑢𝑝 ≥ 0 and Δ𝑃𝑔

𝑃𝑔,𝑡 = 𝑃𝑔

𝑟𝑒𝑓 + Δ𝑃𝑔

𝑢𝑝 −  Δ𝑃𝑔

𝑑𝑜𝑤𝑛     ∀𝑔 ∈ 𝑆𝑔, 𝑡 ∈ 𝑇 

By  adding further  constraints to the  optimization  problem  defined in  the previous  section 
for  not  altering  the  net  position  of  a  certain  market  zone  the  redispatch  –  optimization 
problem is fully defined. These constraints are only defined over a set of interconnecting 
AC and DC lines of the considered market zone and given as: 

∑ 𝑃𝑙,𝑡,𝑧
𝑙∈𝑆𝑙

𝑓𝑟 + ∑ 𝑃𝑑𝑒𝑓,𝑡,𝑧
𝑑∈𝑆𝑑

𝑑𝑐

𝑎𝑐

=

𝑓𝑟,𝑟𝑒𝑓

∑ 𝑃𝑙,𝑡,𝑧
𝑙∈𝑆𝑙

𝑎𝑐

𝑑𝑐,𝑟𝑒𝑓
+ ∑ 𝑃𝑑𝑒𝑓,𝑡,𝑧

     ∀𝑡 ∈ 𝑇, 𝑧 ∈ 𝑍.   

𝑑∈𝑆𝑑

Note  that  the  above  constraint  might  need  to  be  defined  on  a  zone-by-zone  basis  if  the 
considered market zone is connected to multiple other market zones, thus for each 𝑧 ∈ 𝑍. 

This  optimization  model  is  used  to  determine  the  benefits  of  power  flow  controllability 
through HVDC links in the Ultranet use case illustrated in section 7.4. 

A similar optimisation model can be derived to determine the minimum redispatch/start-up 
costs conventional generation in order to fulfil minimum system inertia requirements as a 
proxy for frequency stability.  

74 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

In this case first a distinction needs to be made for generators that are already online, and 
thus can provide inertial support, versus generators that are offline and would need to be 
started up. Therefore, a binary parameter 𝑠𝑔 is introduced which indicates the on/off state 
of  the  generator  in  the  reference  case  (e.g.,  the  solution  of  the  optimal  power  flow 
problem). In this case, our aim is to minimize the start-up costs to provide the necessary 
inertia in the system, thus the objective of the optimisation becomes, 

min ∑

𝑔∈𝐺 

𝑟𝑎𝑡𝑒𝑑  ⋅ 𝐶𝑔
𝑃𝑔

𝑠𝑡𝑎𝑟𝑡−𝑢𝑝 ⋅ (𝛼𝑔 − 𝑠𝑔)
, 

𝑟𝑎𝑡𝑒𝑑  is  the  rated  active  power  generation  of  generator  𝑔,  and  𝛼𝑔  is  a  binary 
where  𝑃𝑔
decision  variable,  𝛼𝑔 ∈ {0, 1},  for  the  start-up  of  a  generator.  The  following  additional 
constraints  w.r.t  the  optimal  power  flow  problem  needs  to  be  introduced  to  ensure  that 
both  grid  constraints,  and  inertia  constraints  are  fulfilled.  Firstly,  the  active  power 
generation needs to be limited by 

𝛼𝑔 ⋅ 𝑃𝑔

𝑚𝑖𝑛 ≤ 𝑃𝑔 ≤ 𝛼𝑔 ⋅ 𝑃𝑔

𝑚𝑎𝑥      ∀ 𝑔 ∈ 𝐺, 

to indicate that generators with an off status cannot generate power. 

Secondly,  the  constraint  𝛼𝑔 ≥ 𝑠𝑔needs  to  be  introduced  to  make  sure  that  generators 
which  were  online  in the  reference  case,  are  not  switched-off.  Finally,  a minimum  inertia 
constraint is introduced, which ensures that the total inertia in a given synchronous zone 𝑧 
is larger or equal to a given minimum inertia limit 𝐻𝑧

𝑚𝑖𝑛, 

∑

𝑔∈𝐺

𝑟𝑎𝑡𝑒𝑑

𝑃𝑔,𝑧

⋅ 𝐻𝑔 ⋅ 𝛼𝑔 ≥ 𝐻𝑧

𝑚𝑖𝑛        ∀𝑧 ∈ 𝑍, 

where 𝐻𝑔 is the inertia constant of generator 𝑔.  

Here it should be noted that the above-described model does not consider any additional 
constraint for  technical  characteristics of  conventional  power  plants  w.r.t.,  start-up times, 
and minimum down times, and as such can only be used as an approximation. 

The  above  described  model  can  be  used  both  in  the  NTC  based  formulation  (section 
6.2.1)  as  well  as  the  linearized  power  flow  formulation  (section  6.2.2)  and  is  applied  to 
determine the benefits of inertia support through HVDC links in sections 7.3 and 7.5 (use 
cases Celtic Interconnector and Eurasian Interconnector).  

Within  this  project,  all  described  optimisation  models  throughout  this  section  have  been 
implemented  as  an  extension  of  the  open-source  AC/DC  grid  optimal  power  flow  tool 
PowerModelsACDC.jl6.  As  such,  a  new  software  package,  CBAOPF.jl  has  been  created 
which includes all optimisation models explained in this section. The CBAOPF.jl package 
can be accessed through https://github.com/Electa-Git/CBAOPF.jl.  

6.3. Modelling Requirements to determine proposed stability 

KPIs 

6.3.1. Frequency stability KPIs 

As indicated in section 5.2.3, frequency stability in a reduced inertia system represents a 
significant  challenge.  There  are  some mitigation  actions  to  ensure  stability  of  low  inertia 
systems but they might require more advanced control loops or additional assets.  

First  of  all,  it  is  important to remind that  the  system  inertia  represents the kinetic  energy 
stored  in  the  rotating  masses  synchronously  connected  to  the  grid.  Therefore,  three 

6 https://github.com/Electa-Git/PowerModelsACDC.jl  

75 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

parameters  are  required  in  order  to  estimate  the  system  inertia  (i.e.  number  of  online 
machines, their MVA rating and inertia constants). Two estimations of inertia were used in 
the project.  

The first estimation is applied to the zonal dispatch when there are aggregated machines 
connected to each zone. In this case, it is not possible to know the unit dispatch and as 
such  accurately  determine  the  inertia.  Therefore,  a  simplification  is  made  by  using  the 
active power dispatched and by approximating the MVA rating per type of generator.  

For example, it is expected that nuclear units have a load factor of at least 0.9 at all time. 
Therefore,  if  the  equivalent  machine  for  nuclear  units  is  dispatched  at  900MW,  it  will  be 
assumed that there are 1000MVA of nuclear units running. This approximation has been 
used in [28] and provides adequate results for large size systems. Estimated load factor 
values per generation type can also be found in [28] 

𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑠𝑦𝑠 = ∑ 𝐻𝑖   ∗

𝑃𝑔𝑒𝑛𝑖
𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟𝑖

where 𝐻 is the inertia constant of machine 𝑖, 𝑃𝑔𝑒𝑛 is the dispatch of machine 𝑖 and 
𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 is the estimated loading factor of machine 𝑖. 

A  second  estimation  of  the  system  inertia  has  been  used  for  the  nodal  dispatch.  In  this 
case, the optimization problem has been slightly adapted to ensure that only the needed 
number  of  machines  are  considered  as  online.  This  allows  to  estimate  the  inertia  by 
looking only at the MVA rating and inertia constants of the online machines.  

𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑠𝑦𝑠 = ∑ 𝐻𝑖   ∗ 𝑆𝑛𝑜𝑚𝑖 ∗ 𝑜𝑛𝑙𝑖𝑛𝑒𝑖 

It can be seen that a binary value (𝑜𝑛𝑙𝑖𝑛𝑒) is used to neglect the offline machines in the 
system inertia calculation. 

Once the inertia is estimated, it allows to approximate the initial RoCoF that will occur in 
the system after a disturbance (before actions of frequency response services).  This can 
be done using the swing equation formulated as per [29]: 

𝑅𝑜𝐶𝑜𝐹 =

𝑓 ∗ Δ𝑃
2 ∗ 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑠𝑦𝑠

where Δ𝑃 represents the difference between generation and loads (in MW), and  𝑓 is the 
nominal  system  frequency.  In  case  of  contingency  (e.g.  loss  of  infeed),  the  Δ𝑃  will  be 
equal to the loss of infeed. 𝑅𝑜𝐶𝑜𝑓 is the rate of change of frequency (expressed in Hz/s) 
while the total system inertia is expressed in 𝑀𝑊𝑠. 

It is important to note that using the swing equation assumes the exact same frequency at 
all  times  in  the  network,  and  should  therefore  be  seen  as  a  representation  of  the 
frequency  behaviour  at  the  centre  of  inertia  of  the  network.  During  a  disturbance,  the 
frequency at each node of the network will experience an oscillatory behaviour around the 
average frequency. 

Similarly to [29], an inertia constraint is derived from the swing equation. This is done by 
considering  the  highest  credible  loss  of  infeed  (e.g.  largest  generating  unit)  and  by 
assuming  a  maximum  RoCoF  withstand  capability  of  assets  connected  to  the  system. 
Using  these  two  parameters  will  directly  provide  the  minimum  inertia  required  to  meet 
maximum acceptable RoCoF.  

In this  work,  fast-frequency response  that  can  be  provided  by  an  (asynchronous)  HVDC 
link  has  been  considered  in  order  to  estimate  the  inertia  constraint.  Assuming  that  the 
frequency response of the HVDC is much faster than the mechanical time constants, the 
following can be expressed:  

Δ𝑃 = 𝑃𝑖𝑛𝑓𝑒𝑒𝑑 𝑙𝑜𝑠𝑠 − min (𝑃𝑚𝑜𝑑, 𝑃𝑚𝑎𝑥 − 𝑃𝐻𝑉𝐷𝐶), 

76 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

where 𝑃𝑖𝑛𝑓𝑒𝑒𝑑 𝑙𝑜𝑠𝑠 is the total loss of infeed, 𝑃𝑚𝑜𝑑  is the active power modulation provided 
by the HVDC link during disturbance, and 𝑃𝑚𝑎𝑥 − 𝑃𝐻𝑉𝐷𝐶 is the available headroom on the 
link.  An  estimation  of  the  inertia  constraint  can  therefore  be  done  based  on  the  active 
power  modulation  capability  of  the  HVDC  link.  However,  because  this  expression  is 
dependent  on  the  HVDC  dispatch,  it  is  proposed  to  model  this  using  a  simplified  2-bus 
system  illustrated  in  Figure  27  (similarly  to  what  has  been  done  in  [30]).  Another 
advantage  of  this  model  is  that  it  can  also  consider  virtual  inertia  contribution  from  RES 
and/or  BESS.  Using  this  2-bus  model  allows  to  perform  a  large  number  of  frequency 
stabilty  simulations  in  order  to  evaluate  which operating  conditions  are stable  and  which 
ones are unstable. 

Figure 27 - 2-bus system for simplified frequency stability assessment 

It is important to remind that the proposed KPI in section 5.2.3 is the percentage of hours 
per  year,  for  which  the  frequency  stability  is  at  risk.  Therefore,  if  an  inertia  constraint  is 
used, it simply requires estimating the inertia of each hourly dispatch and to compare this 
with the pre-determined inertia constraint. The advantage of having an inertia constraint is 
its simplicity and it also allows to add the constraint into the optimization problem defined 
in 6.2.3. 

If the 2-bus system is used, a representative number of time-domain simulations has to be 
performed  in  order  to  evaluate  the  number  of  stable  and  unstable  cases.  This 
representative  number  can  be  determined  via  a  clustering  technique  as  presented  in 
section  5.5.  This  method  has  the  advantage  to  be  more  accurate  than  the  inertia 
constraint  because  it  includes  inertia,  fast-frequency  response,  primary  frequency 
response  and  unit  dispatch.  However,  it  requires  more  interactions  with  the  optimization 
problem described in 6.2.3. 

6.3.2. Converter-driven stability KPIs 

Converter-driven stability is a major challenge in systems with high IBRs penetration. As 
stated  in  [31],  “high-quality  vendor-specific  EMT  models  are  required  […]  as  part  of  the 

77 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

interconnection process to ensure that all resources can reliably operate”. This statement 
clearly  outlines  the  need  to  perform  EMT  simulations  to  ensure  system  stability  but  also 
emphasizes  the  need  to  have  detailed  EMT  models,  which  are  typically  not  available  at 
the CBA stage of a project7. It is also outlined in the same report that RMS simulation can 
only capture a small subset of the potential instabilities that can be driven by converters. 
Therefore,  in  this  work,  it  has  been  decided  to  focus  on  simplified  indicators  quantifying 
the risk of instability of IBRs. For example, the system strength, which can be seen as the 
impact  of  a  fault  or  disturbance  on  the  change  in  voltage  [32],  is  a  clear  candidate  that 
allows  to  identify  this  risk.  When  the  grid  is  “strong”,  the  voltage  waveform  will  be  less 
sensitive to disturbances and therefore the IBRs will be more stable. In  “weak” grids, the 
voltage waveform can be significantly impacted by faults or disturbances, this can cause 
many consequences to IBRs (e.g., PLL loss of synchronism, AC or DC overvoltage, etc.).  

The  first  proposed  indicator  for  quantifying  the  risk  of  converter-driven  instability  is  the 
short-circuit ratio (SCR), defined as the short-circuit power at the point of connection of 
the IBR over its rating. High short-circuit ratio means that the grid is strong. As shown in 
Figure  7,  it  is  generally  assumed  that  when  the  SCR  is  above  3  the  IBR  will  be  stable 
while  SCR  around  1  requires  additional  assets  and/or  grid-forming  control.  To  calculate 
the SCR, the nodal representation of the electrical grid has to be used, including the step-
up transformer of each generating unit.  

A limitation of the SCR as indicator of converter-driven instability is that it does not include 
the IBR operating point nor its control loops. Therefore, another indicator, as introduced in 
[7]  and  [6],  will  be  applied  to  complement  the  SCR.  The  main  objective  of  this  second 
indicator,  referred  to  in  this  report  as  IBR-CCT  (Critical  Clearing  Time  of  IBR),  is  to 
“Identify  operation  conditions  prone  to  IBR  transient  instability  following  a  fault”  [7].  Its 
advantage compared to the SCR is that it includes two additional components which are: 

•  The IBR operating points 
•  Parameters of a simplified PLL control loop 

More information can be found in [7] and [6], but in summary the IBR-CCT is an indicator 
of  the  transient  stability  margin  of  an  IBR  which  can  be  calculated  analytically  by  taking 
the  operating  point,  SCR  and  PLL  parameters  as  main  input  parameters.  The  analytical 
expression  is  based  on the  equal  area-criterion applied  to the  PLL dynamics  during  and 
after the fault. 

It  is  expected  that  additional  improved  indicators  will  be  developed  in  the  future  by 
industry  and  academia  to  further  assess  the  stability  of  converters  as  well  as  to  also 
include  the  contribution  of  grid  forming  inverters  in  the  system  strength.  Therefore,  the 
benefits  of  grid  forming  capability  as  offered  by  HVDC  could  be  more  easily  quantified 
using such stability indicators.   

6.3.3. Selection of operating conditions 

In  section  5.5,  two  clustering  techniques  have  been  proposed.  The  first  one,  based  on    
K-means, allows to reduce the number of operating conditions for which the stability KPIs 
have to be estimated. It is recommended to use this clustering technique with a relatively 
high  number  of  clusters.  By  doing  so,  the  size  of  each  cluster  will  be  small  and  it  can 
therefore be assumed that each point of the same cluster will have the same frequency or 
converter-driven stability performance. Therefore, it allows to simulate a single point within 
each  cluster  and  then  to  weight  the  values  obtained  by  the  cluster  size.  This  clustering 
technique is used for the 2-area frequency stability and for the IBR-CCT assessment.  

7  The  CIGRE  WG  C4.60: “Generic  EMT-Type Modelling  of Inverter-Based  Resources  for  Long Term Planning  Studies”  is 
trying to fill the gap and to propose EMT models to be used in long-term planning. 

78 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

The second approach, based on DBSCAN, allows to identify more dense clouds of points. 
This should be used when it is required to evaluate more in details (e.g. redispatch, RMS 
or even EMT-simulations) extreme but yet representative operating conditions. Depending 
on  the  size  of  the  clusters  obtained  via  the  DBSCAN  method,  it  may  be  needed  to 
simulate multiple points within each cluster (e.g. extremities).  

79 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.  Illustration on use cases 

This  chapter  presents  first  the  process  for  selecting  the  use  cases.  It  can  be  seen  in 
section  7.1  that  each  use  case  was  selected  for  a  particular  reason  (e.g.  embedded 
HVDC within a single market zone, or HVDC link embedded into AC grid connecting two 
market  zones,  or  HVDC  link  connecting  two  asynchronous  areas,  etc.).  Therefore,  the 
proposed  KPIs  were  not  calculated  for  all  use  cases.  Instead,  the  goal  is  to  test  the 
implementation  of  our  KPIs  among  the  selected  use  cases.  This  is  what  is  presented 
throughout  sections  7.2  and  7.6.  Finally,  as  this  work  focuses  on  implementation  and 
modelling  guidelines,  the  main  challenges  encountered  during  implementation  and 
analysis of the use cases are presented in section 7.7. 

7.1. Use case selection 

7.1.1. Goal and methodology 

The  main  objective  is  to  select  relevant  and  representative  use  cases  to  which  the 
developed extended CBA approach can be applied and tested. 

Different steps, which are presented in the schematic overview of Figure 28, are taken to 
select the final set of use cases. The first step within this approach consists of creating a 
long  list  of  use  cases.  The  goal  is  to  gather  all  kinds  of  projects  which  can  be  directly 
taken from the TYNDP2020 or PCI list (projects of common interest, updated in 2021) but 
also  more  academic  use  cases  could  be  included.  Moreover,  also  variations  or 
combinations of projects (e.g., by adding an HVDC bootstrap to an AC grid, by connecting 
several  PCIs  or  by  connecting  offshore  windfarms  to  large  load  centres  further  inland) 
have  been  integrated  as  well.  Study  cases  could  therefore  be  fictive  cases  based  on 
potential future initiatives. 

In order to provide a structured overview of the possible projects within the long list, a first 
high-level  classification  on  the  proposed  AC/DC  systems  is  applied  to  split  up  the  list 
depending on the topology. A preliminary long-list and classification is presented in more 
detail in section 7.1.2 of this report. 

Figure 28 – Use case selection procedure 

Next, a selection/screening process is used to narrowing down the long-list and come up 
with  a  limited  number  of  relevant  use  cases.  To  this  end,  different  selection  criteria  are 
defined  which  are  converted  to  indicators  allowing  to  rank  use  cases  according  to  their 
relevance  for  the  study.  By  applying  such  indicators,  it  is  ensured  that  a  diverse  mix  of 
uses cases is obtained, covering all important aspects (technical, economic, but also the 
time horizon/geographical aspects…).  

To  finally  select  the  use  cases,  a transparent  iterative  process  has  been  followed  which 
involved regular interactions/discussions with the European Commission in order to make 
sure  a  common  agreement  is  made  on  the  selection  of  use-cases.  In  addition,  a  virtual 

80 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

stakeholder workshop (31/03/2022) has been organized to present the list of selected use 
cases and to perform adjustments if needed in order to integrate reasoned stakeholders’ 
feedback.  

The screening and selection procedure are further elaborated in section 7.1.3 and the five 
use cases that were selected are described in more detail in section 7.1.4 of this report. 

7.1.2. Step 1: Long-list of use cases 

Numerous  examples  and  uses  cases  of  AC/DC  hybrids  grids  can  be  found  within  the 
TYNDP and PCI list for the short-term time horizon (i.e., commissioned by 2030). In case 
also  the  long-term  horizon  (i.e.,  2050)  is  considered  and  more  academic  test  cases  are 
considered  as  well,  the  number  of  possible  uses  cases  to  select  from  becomes  even 
higher. 

Therefore, instead of arbitrarily adding all projects to the long list, it is chosen to already 
perform a preselection and to create a well-structured long list which provides a good mix 
in terms of topology set-up and geographical spread (e.g., South, North, East, Central). To 
split  up  the  list  according  to  topology,  the  classification  as  presented  in  Figure  29  is 
applied. As illustrated, HVDC systems are split up in point-to-point connections (PtP) and 
HVDC  grids,  which  are  then  further  divided  into  embedded  and  asynchronous  systems. 
For  asynchronous  HVDC  grids,  a  further  subclassification  is  defined  depending  on 
whether  a  radial  connection  or  a  meshed/interlinked  PtP  is  used.  Interlinked  PtP  is 
referred to the case where the main (offshore) network is operated in AC with DC links to 
the  surrounding  power  systems  (see  also  North  Sea  Wind  Power  hub  for  instance).  As 
such, five main topology categories were obtained. 

Figure  29  –  Topology  classification  applied  to  the  long-list  of  use  cases  (note:  if  there  is  even  a  single  offshore  WF 
connected to the HVDC grid, it is considered asynchronous since there is the possibility of frequency support) 

The long list, consisting of 15 use cases covering all topology categories and the different 
areas in Europe, is presented in Table 12. It must be noted that the list is predominantly 
based  on  the  projects  from  the  ENTSO-E  TYNDP  2020.  The  geographical  location  and 
spread of the cases are finally indicated on a map of Europe as given in Figure 30. 

81 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Table 12 - Long list of use cases 

Use case 

Short description 

Topology 
category 

Embedded PtP 

1. Slovenia-Italy 
link 

2. HVDC 
SuedOstLink 

The  project  consists  of  a  new  HVDC  link  of 
800  MW  between  Salgareda  (Italy)  and 
Divaca/Bericevo (Slovenia) which is planned 
to be commissioned around 2028. 

•  PCI number 3.21 (4th list, 31 Oct. 

2019) 

•  TYNDP 2020: Project nr. 150 

2  GW  HVDC-connection  from  North-East 
Germany (Area of Wolmirstedt), an area with 
high  installed  capacities  of  RES,  to  the 
South of Bavaria (area of Isar), an area with 
high  consumption  and  connections 
to 
storage 
(commissioning 
foreseen in 2025). 

capabilities 

•  PCI number 3.12 (4th list, 31 Oct. 

2019) 

•  TYNDP 2020: Project nr. 130 

3. Navarra-
Landes Link 

A  new  HVDC  interconnection  (2x1000  MW) 
between  the  Western  part  of  the  Pyrenees 
(Spain)  and 
between  Pamplona  area 
Cantegrit  (France).  The  project  is  foreseen 
to be commissioned in 2029. 

4. MONITA 
project 

•  PCI number 2.27.2 (4th list, 31 Oct. 

2019) 

•  TYNDP 2020: Project nr. 276 

Italy-Montenegro 

(MONITA) 
The 
interconnection  project 
includes  a  new 
HVDC  (LCC)  subsea  connection  between 
Villanova  (Italy)  and  Lastva  (Montenegro). 
The project  is  foreseen  to  be  commissioned 
in 2026  and will  have a  final  capacity  of  1.2 
GW. 

•  TYNDP 2020: Project nr. 28 

Asynchronous PtP 

5. Celtic 
interconnector 

the 

Interconnector  will  be 

Celtic 
first 
interconnection between Ireland and France. 
A survey of the route of the HVDC (VSC) link 
with  700  MW  capacity  has  been  done  from 
the  southern  coast  of  Ireland  to  La  Martyre 
is 
in  France. 
(Finistère) 
foreseen to be commissioned in 2026. 

Interconnection 

•  PCI number 1.6 (4th list, 31 Oct. 2019) 

82 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Topology 
category 

Use case 

Short description 

•  TYNDP 2020: Project nr. 107 

6. TUN.ITA. 

of 

project 

The 
new 
consists 
interconnection  between  Tunisia  and  Sicily 
to  be  realized  through  an  HVDC  submarine 
cable with a capacity of 600 MW. The project 
is foreseen to be commissioned in 2027. 

a 

•  PCI number 3.27 (4th list, 31 Oct. 

2019) 

•  TYNDP 2020: Project nr. 29 

7. Viking DKW-
GB 

2x700  MW  HVDC  subsea  link  across  the 
North  Seas  between  Bicker  Fen  (GB)  and 
Revsing  (DK).  The  project  is  foreseen  to  be 
commissioned in 2023. 

•  PCI number 1.14 (4th list, 31 Oct. 

2019) 

•  TYNDP 2020: Project nr. 167 

8. TuNur 

Embedded MTDC 

9. Ultranet + A-
North 

located 

TuNur  aims  at  connecting  a  Concentrated 
(total 
Solar  Power  plant  with  storage 
in  Rejim 
capacity  >2000  MW) 
Maatoug  (Kebili,  Tunisia)  to  the  Continental 
European  power  system.  The  connection 
point  in  Europe  is  located  in  Montalto  di 
Castro,  North  of  Rome.  The  transmission 
project  will  consist  of  a  DC  overhead  line  in 
Tunisia  from  the  power  plant  to  the  shoring 
point  and  submarine  cables 
the 
Tunisian  Northern  coast  to  Italy.  Project  is 
aimed to be finalized around 2028. 

from 

•  TYNDP 2020: Project nr. 283 

Ultranet  together  with  A-North  form  a  large-
scale  transmission  link  from  the  North  Sea 
coast to Baden- Württemberg. 

The  Ultranet  project  consists  of  a  2  GW 
the  Region  of 
HVDC-connection 
from 
Osterath  (Rhineland) 
the  Region  of 
Philippsburg  (Baden-Württemberg)  and  is 
planned to be commissioned in 2024.  

to 

A-North  on  the  other  hand  consists  of  two 
new  HVDC  cables  from  Emden-East  to 
Osterath. This HVDC link also has a transfer 
capacity  of  2  GW  and  is  planned  to  be 
finalized in 2025.  

83 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Topology 
category 

Use case 

Short description 

Asynchronous 
MTDC (radial grid) 

10. EuroAsia 
interconnector 

11. 
MaresConnect 

12. LaSGo Link 

•  PCI number 2.9 (Ultranet) (4th list, 31 

Oct. 2019) 

•  TYNDP 2020: Project nr. 254 (Ultranet) 

and nr. 132 (A-North) 

interconnector 

between  Crete, 
HVDC 
Cyprus and Israel (Consisting of two stages: 
final  capacity  of  2  GW).  Interconnection  is 
foreseen  to  be  commissioned  in  2026.  It  is 
also  planned  to  form  a  four-terminal  MTDC 
grid  in  the  future  with  the  HVDC  link  of  the 
Ariadne  HVDC  connection  between  Attica 
and Crete 

•  PCI number 3.10 (4th list, 31 Oct. 2019) 
•  TYNDP 2020: Project nr. 219 

MaresConnect  is  a  750MW  HVDC  VSC 
Interconnector  between  Great  Britain  and 
Ireland  with  three  node  connections;  (i) 
Bodelwyddan  (Wales), (ii)  Maynooth  (Dublin 
area,  Ireland)  and (iii)  Bellacorick  new  node 
(Mayo  area,  Ireland).  Project  is  foreseen  to 
be commissioned in 2025. 

•  TYNDP 2020: Project nr. 349 

project 

interconnector 

LaSGo  Link  is  a  new  multi  terminal  HVDC 
sub-sea 
linking 
Sweden,  the  Island  of  Gotland  and  Latvia. 
The  project  consists  of  two  sections:  a 
700MW  internal  grid  reinforcement  between 
the  Swedish  mainland  and  the  island  of 
Gotland  and  a  500MW  cross  border 
connection  between  the  island  of  Gotland 
and Latvia. Interconnection is foreseen to be 
commissioned in 2036. 

13. Nautilus 

•  TYNDP 2020: Project nr. 1068 

This  project  considers  the  possibility  of  a 
multi-purpose  HVDC  between  GB  and 
Belgium  with  also  interconnecting  offshore 
wind farms. The capacity of the is still under 
review,  but  is  likely  to  be  in  the  range  of  1 
GW  –  2GW.  The  project  is  foreseen  to  be 
commissioned in 2028. 

•  TYNDP 2020: Project nr. 121 

84 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Topology 
category 

Asynchronous 
MTDC  
(Meshed grid or 
interlinked point-to-
point grid) 

Use case 

Short description 

14. MTDC multi-
country backbone 

15. North Sea 
Wind Power Hub 
(NSWP) 

Large  meshed  (asynchronous)  HVDC  grid 
connecting different member states which is 
foreseen  on 
(i.e.  2050 
horizon).  A  stepwise  approach  could  be 
taken  in  which  the  existing  HVDC  projects 
from the 2030 horizon are linked together to 
form a single meshed system. 

long-term 

the 

North  Sea  Wind  Power  Hub 
is  an 
international  consortium,  run  by  TenneT 
(Germany),  Energinet  (Denmark),  Gasunie 
(Netherlands)  and  Port  of  Rotterdam 
(Netherlands),  which  goal  is  to  develop 
several  farms  in  the  North  Sea  that  are 
connected  to  an  artificial  island  (i.e.  AC 
power 
HVDC 
which 
interconnections  to  surrounding  countries. 
Foreseen  timeline  for  construction  is  2030-
2050. 

hub) 

has 

Figure 30 – Geographical location of the different use case from the long-list 

85 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.1.3. Step 2: Screening 

As previously introduced, the screening process to go from long-list to short-list is done by 
applying indicators which allow to rank and select use cases according to their relevance 
for the study. As such, it is ensured that with a limited number of use-cases, all relevant 
aspects  within  the  scope  of  this  study  are  covered.  In  the  following  subsections,  the 
different indicators are introduced and applied to the long-list of uses cases.  

7.1.3.1. 

Technical indicators 

The main technical indicator used in this study is the topology category as defined in the 
classification of Figure 29. No specific preference is given to a certain set-up, but instead 
it  is  aimed  to  have  a  good  mix  of  HVDC  grids  and  PtP  connections  as  well  as  both 
embedded and asynchronous HVDC connections within the final short-list.  

7.1.3.2. 

Economic indicators 

specific 

through 

The  aim  of  the  economic  indicators  is  to  evaluate  the  additional  benefits  from  HVDC 
systems 
system.  These 
services/capabilities are described in more detail in the previous chapters. For each of the 
use cases in the long list, a grade of 0 to 5 is assigned to each service depending on the 
benefit  that  is  expected  to  be  obtained.  For  example,  a  grade  of  5  for  the  frequency 
regulation capability means that significant benefit is expected by considering this service 
in the CBA. On the other hand, a grade of 0 indicates that the benefit would be negligible. 

capabilities/services 

the  AC 

to 

It has to be noted that in the context of the use case selection, there has been no detailed 
calculation of the benefit from each service. Instead, this is only a preliminary assessment 
based on simplified rules, used exclusively for the screening of the use cases. The aim is 
to  make  an  “educated  guess”  and  to  choose  the  use  cases  in  which  including  the  new 
services  from  HVDC  would  lead  to  a  change  in  the  CBA.  The  simplified  rules  are 
described hereafter: 

•  Frequency regulation 

•  For embedded connections there is no benefit 
•  For asynchronous point-to-point connections between an area and remote 

generation some limited benefit is expected  

•  For asynchronous point-to-point connections between two areas significant benefit  
•  For asynchronous MTDC grids the benefit can be higher depending on the number 

of connected synchronous areas  

•  Voltage regulation: 

•  Embedded point-to-point can provide benefits in voltage regulation through the use 

of active and reactive power 

•  Embedded MTDC grids can provide even better benefits (more options)  
•  Asynchronous point-to-point can provide mainly local reactive power regulation 

(benefit from redirection of active power flow more difficult to assess)  

•  The benefits from asynchronous MTDC grids depend on whether they provide 

parallel paths to AC lines  

•  Blackstart: 

•  Very limited and difficult to assess benefit from embedded point-to-point 

connection 

•  Similar benefit from embedded MTDC grids, however the existence of multiple 

connections provides more options  

•  For asynchronous point-to-point connections between an area and remote 

generation no benefit is expected 

•  For asynchronous point-to-point connections between two areas significant benefit   
86 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

•  For asynchronous MTDC grids the benefit can be even higher depending on the 

number of connected synchronous areas  

•  Power flow control: 

•  Similar to the voltage regulation, embedded point-to-point and MTDC grids provide 

significant benefits 

•  Point-to-point connections provided limited benefits 
•  The benefits of asynchronous MTDC grids depend on the number of connections 

and on whether alternative paths to the AC network are provided. 

•  Grid forming control: 

•  The benefit from grid forming control in a point-to-point connection between an 

area and a remote generation (usually offshore wind farm) is expected to be low. 
In such cases, there is already one grid forming converter (offshore converter), 
hence it is still unclear whether the onshore one can reliably operate also as grid 
forming. 
In all the other cases, the grading depends on a case-by-case basis. In general, if 
an islanded network is included in the configuration (e.g. Cyprus, Ireland) a higher 
benefit is expected. 

• 

The  afore-mentioned  rules  are  summarized  in  Table  13,  where  the  resulting  grades  for 
each topology are also given: 

Table 13 - Preliminary assessment of benefits from HVDC services/capabilities 

HVDC 
capability 

Embedded 
PtP 

Embedded 
MTDC 

Asynchronous PtP 

Asynchronous 
MTDC (radial) 

Asynchronous 
MTDC (meshed) 

Between area and 
remote 
generation/load 

Between 
two areas 

Frequency 
regulation 
Voltage 
regulation 

Black start 

Power flow 
control 

Grid forming 

0 

4 

1 

3 

0 

5 

2 

4 to 5 

To be 
defined on a 
case-by-
case basis 

To be 
defined on a 
case-by-
case basis 

Total score 

8 to 13 

11 to 17 

2 

2 

0 

1 

1 

6 

3 

2 

3 

2 

3 to 5 

2 to 5 

4 to 5 

2 to 5 

3 to 5 

2 to 5 

4 to 5 

2 to 5 

To be 
defined on a 
case-by-
case basis 

To be defined on 
a case-by-case 
basis 

To be defined on a 
case-by-case 
basis 

10 to 16 

11 to 25 

11 to 25  

The following observations are made based on the grading of topologies: 

•  Embedded configurations are expected to provide benefits in terms of voltage 

regulation and power flow control 

•  Connection between asynchronous areas provides higher benefits in terms of 

frequency regulation and black-start services 

•  More complex HVDC topologies will in general provide more benefits by combining 

different aspects 

These general rules are then applied to the use cases of the long list, see in Table 25 in 
Appendix II: use case selection. The sum of the grades for the different benefits is applied 
to rank the use cases and finally select the ones with a high total score. 

87 

 
  
  
  
  
  
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.1.3.1. 

Other indicators 

Finally,  some  other  indicators  were  added  to  the  screening  process,  namely  a 
geographical and a time horizon indicator. The geographical indicator has been applied to 
make sure that the final use cases cover the different parts of Europe (i.e., to avoid that all 
use cases are for instance located in countries around the North Sea) and to ensure that 
also at least one use case with a connection external to Europe is included.  

Looking at the time horizon, it is important to note that some of the operational challenges 
in power systems, such as operation with reduced grid strength (low inertia and low short-
circuit  power),  are  expected  to  become  more  prominent  on  a  longer  time  horizon  (i.e., 
2050).  The  corresponding  benefits from  HVDC  (e.g.,  grid forming  capability  in this  case) 
are  therefore  also  more  relevant/important  in  the  future  power  system  compared  to  its 
application today. Therefore, to illustrate/capture these benefits within a CBA analysis, it is 
proposed to have at least one 2050 (long-term) use case.  

An assessment of the use cases within the long list applying these additional indicators is 
presented in Table 14. 

Table 14 - Assessment of long list considering time horizon and geographical 
aspects (N=North, E=East, S=South, W=West, C=central) 

Use case 

Geographical 
location within 
Europe 

External 
connection 

Time horizon 

1. Slovenia-Italy 
link 

2. HVDC 
SuedOstLink 

3. Navarra-
Landes Link 

4. MONITA 
project 

5. Celtic 
interconnector 

6. TUN.ITA. 

7. Viking DKW-
GB 

8. TuNur 

9. Ultranet + A-
North 

10. EuroAsia 
interconnector 

11. 
MaresConnect 

CS 

NC 

SW 

SW 

NW 

S 

N 

S 

NC 

ES 

NW 

No 

No 

No 

No 

No 

Yes 

No 

Yes 

No 

Yes 

No 

88 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

2030 (short-term) 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

12. LaSGo Link 

13. Nautilus 

14. MTDC multi-
country backbone 

15. North Sea 
Wind Power Hub 
(NSWP) 

NE 

NW 

N/E/S/W/C 

NE 

No 

No 

No 

No 

2030 (short-term) 

2030 (short-term) 

2050 (long-term) 

2050 (long-term) 

7.1.4. Step 3: short-list of use cases 

Using the indicators and the assessment of uses cases presented in the long list, 
five use cases were finally selected: 

1.  Navarra-Landes link 
2.  Celtic interconnector 
3.  Ultranet+A-North 
4.  EuroAsia Interconnector 
5.  MTDC multi-country backbone 

As highlighted in the table below, the different aspects are well covered by these 
five uses cases. Looking at the additional benefits (i.e., economic indicator), they 
all  have  a  medium  to  high  score  (adding  up  the  grades  given  in  section  7.1.3.2) 
the 
and  each  of 
geographical locations of the use cases are more or less spread over Europe and 
there  is  even  one  including  an  external  connection.  Finally,  considering  the  time 
horizon, both use cases planned to be built in the short-term (2030) and the long-
term (2050) are included in the list. In the following subsections, each of the use 
cases from the short-list is described in more detail. 

is  represented.  Additionally, 

topology  categories 

the  5 

Table 15 - Short-list of use cases and a summary of the different indicators 

89 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.1.4.1. 

Navarra-Landes Link 

new  HVDC 

Description:  A 
interconnection 
(embedded  PtP)  between  the  Western  part  of  the 
Pyrenees  between  Pamplona  area  (Spain)  and 
Cantegrit (France).  

Capacity: 2000 MW 

Commissioning year: 2029 

Promotors: REE & RTE 

Why is this a good case? 

•  Benefits expected from power flow control 

and voltage regulation 

7.1.4.2. 

Celtic Interconnector 

Description:  Celtic  Interconnector  will  be  the  first 
interconnection  between 
Ireland  and  France.  A 
survey of the route of the HVDC (VSC) link has been 
done  from  the  southern  coast  of  Ireland  to  La 
Martyre (Finistère) in France.  

Capacity: 700 MW 

Commissioning year: 2026 

Promotors: EIRGRID & RTE 

Why is this a good case? 

•  Frequency services by HVDC can be 

important for Ireland especially with RES 
penetration 

•  A good case for blackstart 
•  Grid forming might play an important role 
due to Ireland being an islanded system 

90 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

7.1.4.3. 

Ultranet + A-North 

Description:  Ultranet  together  with  A-North  form  a 
large-scale  transmission  link  (so-called  “Corridor A”) 
from the North Sea coast to Baden- Württemberg to 
channel  wind  energy  from  the  north  past  the  grid  in 
the Rhineland and down to the south.  

Capacity: 2000 MW 

Commissioning year: 2024-2025 

Promotors: AMPRION & TRANSNET BW 

Why is this a good case? 

•  Combination of two embedded PtP 

projects: only embedded MTDC for 2030 
•  Probably a good use case to demonstrate 
the benefits of power flow control and 
voltage regulation by HVDC 

7.1.4.4. 

EuroAsia Interconnector 

Description:  HVDC  interconnector  between  Crete, 
Cyprus  and  Israel.  It  is  also  planned  to  form  a  four-
terminal MTDC grid in the future with the HVDC link 
of the Ariadne HVDC connection between Attica and 
Crete. 

Capacity: 2000 MW 

Commissioning year: 2026 

Promotors: EuroAsia interconnector Ltd. 

Why is this a good case? 

Includes external connection 

• 
•  South-Eastern Europe (geographical 

indicator) 

•  Another good case for frequency 

regulation, grid forming and black-start 
considering that it involves the isolated 
island of Cyprus and the weakly connected 
island of Crete 

91 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.1.4.5. 

MTDC multi-country backbone 

Description:  Large  meshed  (asynchronous)  HVDC 
grid  connecting  different  member  states. A  stepwise 
approach could be taken in which the existing HVDC 
projects from the 2030 horizon are linked together to 
form a single meshed system. 

Capacity: Not yet known 

Commissioning year: Long-term horizon (2050) 

Why is this a good case? 

•  Large MTDC connection among multiple 

countries 

•  Benefits for 2050 are expected to be 
significant since it connects multiple 
countries 

•  The number of connections can provide 
benefits with all kinds of services: grid 
forming, and power flow control can be 
significant 

The subset of the use cases identified have been analysed to demonstrate the usefulness 
of the enhanced CBA methodology outlined throughout Chapter 5. The main objective of 
the following  sections is  to  quantify  benefits  of HVDC  technology  with  respect  to  system 
stability  improvement  and  power  flow  controllability  in  a  realistic  setting.  To  that  end, 
rather  than  determining  all  additional  KPIs  of  the  enhanced  method  on  all  use  cases, 
certain  use  cases  have  been  selected  to  demonstrate  the  relevant  KPIs,  as  not  all 
potential  benefits  of  HVDC  technology  will  have  a  significant  effect  on  all  types  of 
networks.  For  instance,  the  stability  improvement  through  HVDC  technology  is  more 
relevant  for  asynchronously  connected  networks,  whereas  the  benefits  of  power  flow 
controllability are more relevant for uses cases with embedded HVDC links.   

7.2. Navarra Landes 

7.2.1. Assessment of techno-economic KPIs 

7.2.1.1. 

Overview  of  implementation,  models  and  data 

used 

This test case has been used to validate the NTC based zonal dispatch model, in order to 
investigate  the  sensitivities  with  respect  to  the  capacity  increase  in  RES  generation  as 
well as the increase in transmission capacity and how this is translated to socio-economic 
welfare and emission reduction benefits. 

The Navarra Landes interconnector aims to increase the power transfer capacity between 
France  and  Spain  by  1500  MW.  The  NTC  based  zonal  economic  dispatch  model  as 
introduced in section 6.2.1 is used to calculate the socio-economic KPIs. The calculations 
have  been  performed  for  the  base  case  without  the  NTC  increase  between  the  French 
and the Spanish zone, and the case with the investment. As the NTC based model uses 
an  aggregated  capacity  between  both  zones,  in  the  case  with  the  investment,  the  base 
case capacity is increased by 1500 MW, although the rating of the interconnector itself is 
2000 MW.  

92 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

The  zonal  TYNDP  model  consists  of  64  market  zones,  where  each  market  zone  is 
representing  55  different  types  of  generators,  of  which  53  are  actual  generators,  1 
generator  representing  demand  response,  and  one  generator  representing  energy  not 
served. The used generation cost data is provided in the appendix. 

7.2.1.2. 

Simulations performed 

The  zonal  model  with  and  without  interconnector  is  simulated  for  an  entire  year  (8760 
hours)  for  both  GA2030  and  GA2040  scenarios  from  the  ENTSO-E  TYNDP,  for  the 
climate year 2007 in both scenarios. 

7.2.1.3. 

Comparisons  of  relevant  KPIs  without  the 
project,  with  the  project  (CBA  methodology)  and  with 
the project (proposed CBA) 

Table  16  summarizes  the  KPIs  for  the  zonal  model  when  the  Navarra  –  Landes 
interconnector is included in the European grid. The benefit in the socio-economic welfare 
obtained  thorugh  the  NTC  based  zonal  dispatch  model  is    468  MEUR  for  the  global 
ambition  scenario  (GA)  2030  and  532  MEUR  for  the  GA2040  scenario.  The  difference 
between the two scenarios is mainly attributed to the installed renewable generation (solar 
PV, onshore and offshore wind) in Spain, which is  76.4 GW in 2030 and 114.95 GW in 
2040, respectively. Figure 31 shows the interconnector flows for the GA2030 scenario.  

Counterintuitively,  the  CO2  emissions  related  to  the  French  and  Spanish  zones  do  not 
have a similar  decrease  even though  there is  a higher  RES  integration. Altough  there is 
maximum  export  of  renewable energy  from  Spain  to  France8  as shown in  Figure  31, the 
benefits  of the  CO2 emission  reduction  do  not  increase to the same  extend as the  RES 
integration does. This is mainly attributed to the reduction of nuclear generation in France, 
where the installed capacity is 56.6 GW in 2030 and 37.2 GW in 2040, according to the 
scenario data. 

A second effect that can be observed is that not all CO2 emission benefits are achieved in 
Spain or France through the extension of the transfer capacities between both countries. 
The total emission CO2 reduction across Europe is 495 kton / year through the capacity 
increase, where the emission reduction in Spain and France adds up to 264 kton / year as 
indicated in the table below. Thus the interconnector contributes to CO2 reductions also in 
other market zones, owing it to the objective function where the generation cost (which is 
higher for non RES generation) is minimized over all market zones. 

In Figure 31, we can see the interconnector flows in function of the total RES generation 
in both Spain and France. We observe that, for situations with the highest RES generation 
levels, the interconnector flows are from Spain to France as expected. 

8 Positive sign of the interconnector power flow indicates flows from France to Spain and vice versa 

93 

 
 
 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Table 16 - Computed KPIs for the Navarra-Landes interconnector, zonal model, GA 
scenario for years 2030 and 2040, climate year 2007 

GA2030, cy 2007 

GA2040, cy 2007 

KPIs 

No investment 

Investment  Benefit 

No 
investment 

Investment  Benefit 

B1 – 
Socio-
economic 
welfare  -  
all market 
zones 

B2 – CO2 
emissions 
[Mton/yr]   

B3 – RES 
integration 
[TWh]  

B4 – NOx 
emissions  
[kton/yr]  

B4 – SOx 
emissions  
[ton/yr]  

B6 – 
Adequacy, 
ENS 
[MWh/yr]  

170.93 bn€ 

170.46 bn€   468 M€  186.12 bn€ 

185.58 bn€  532 M€ 

12.27 

12.00 

0.27 

10.68 

10.46 

0.22 

265.87 

 271.02  

 5.15  

339.07 

342.86  

3.79 

19.49  

 20.00 

- 0.51 

15.54 

15.81 

- 0.27 

384.09 

394.28 

- 10.19 

306.19 

311.70 

- 5.51 

0 

0 

0 

5.44  

5.44 

0 

Figure 31-Comparison between the power flow between France and Spain with and without the Navarra-Landes 
interconnector for different RES generation levels, GA2030, climate year 2007 

94 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

7.3. Celtic interconnector 

7.3.1. Assessment of techno-economic KPIs 

7.3.1.1. 

Overview  of  implementation,  models  and  data 

used 

Using  the  Celtic  interconnector,  we  want  to  demonstrate  mainly  two  aspects.  Firstly,  the 
obtained  socio-economic  welfare  benefits  using  an  NTC  based  dispatch  model  versus 
using  an  optimal  power  flow  (OPF)  model  can  differ  significantly,  as  the  OPF  model  is 
capable  of  considering  the  internal  congestion.  Secondly,  Ireland  being  an  island,  the 
effect  of  decreasing  inertia  due  to  RES  integration  will  have  more  severe  impact,  and 
connected  to  that,  the  benefits  provided  through  HVDC  by  means  of  inertia  support  are 
expected  to  be  significant.  In  this  use  case,  we  make  use  of  both  the  NTC  based  zonal 
and the nodal OPF  models  for  the  calculation  of  the social  welfare  benefits  and  quantify 
the  effects  of  considering  internal  congestion.  In  the  same  way,  we  perform  the  zonal 
dispatch and nodal redispatch OPF models by introducing inertia constraints as outlined in 
section  6.2.3  to  calculate  the  benefits  through  inertia  provision  through  HVDC,  with  an 
approximate zonal approach and a detailed nodal approach.  

For the zonal calculations we use the zonal TYNDP model consisting of 64 market zones, 
where each market zone is representing 55 different types of generators, of which 53 are 
actual  generators,  1  generator  representing  demand  response,  and  one  generator 
representing energy not served. The used generation cost data is provided in Appendix III. 
This  results  in  3520  generators  in  total.  The  64  market  zones  are  connected  by  119 
interconnections. For the hourly dispatch calculations, the hourly demand time series from 
ENTSO-E  and  RES  capacity  factor  time  series  from  the  European  climate  database  are 
used. Both time series are given for a number of climate years, with an hourly resolution.  

As  for the  nodal model, the  ENTOS-E  nodal  grid  model  has  been  used. For the  case  of 
the Celtic interconnector, the French grid model consists of, 2764 nodes, 3680 branches 
(including  transformers  and  breakers),  3556  generators  and  8  HVDC  links,  whereas  the 
Irish  grid  model  consists  of  2324  nodes,  2874  branches  (including  transformers  and 
breakers),  672  generators  and  2  HVDC  links.  In  the  next  section  further  information  is 
provided  on  the  particular  calculation  methodologies,  and  the  usage  of  the  grid  models 
within. 

7.3.1.2. 

Simulations performed 

In order to compare the socio-economic welfare KPIs, first the NTC based zonal model is 
used  without  and  with  the  Celtic  interconnector  and  the  KPIs  have  been  calculated  for 
each case separately. As it is computationally too expensive to perform the nodal model 
on  the  full  scale  European  network,  only  the  French  and  the  Irish  networks  have  been 
modelled  in  detail  whereas  their  power  exchanges  with  their  respective  neighbouring 
market  zones  are  approximated  using the  outcome of  the  zonal  dispatch model.  To  that 
end, the following approach has been used. First, the exchanges between the France and 
Ireland and their respective neighbouring countries have been assumed to be equal to the 
exchanges  obtained through  the zonal  model.  As  in the  nodal model,  all  interconnecting 
lines are modelled in detail, an additional constraint is implemented within the OPF model 
outlined  in  section  6.2.2,  which  states  that  the  sum  of  all  power  flows  on  the 
interconnectors with a neighbouring market zone, need to be equal to the interconnector 
flow determined with the zonal model. This way we ensure the consistency between the 
two models.  

Secondly,  the  nodal  ENTSO-E  model  provides  only  one  operational  condition,  e.g.  one 
operating  hour.  To  be  able  to  consistently  use  the  demand  and  RES  time  series  of  the 

95 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

zonal  model  within  the  nodal  model,  a  model  disaggregation  is  performed.  The 
aggregated total demand coming from the zonal model is distributed pro rata among the 
loads  in  the  nodal  model.  In  the  same  way,  the  total  installed  generation  capacity,  and 
capacity  factors  of  RES  generators  are  disaggregated  pro  rata,  based  on  the  generator 
ratings provided in the nodal model. 

Figure 32 visualizes the calculation procedure for the zonal and nodal models and shows 
the model interactions. 

To  perform  inertia  constrained  dispatch  calculations,  following  approach  is  used  as  also 
described  in  Figure  33.  First,  using  the  zonal  model  including  the  Celtic  interconnector, 
inertia constraints for the French and Irish networks are introduced using the methodology 
described  in  section  6.3,  where  the  required  inertia  is  determined  based  on  the  rate  of 
change  of  frequency.  This  is  done  for  two  cases,  namely  for  the  case  that  the  Celtic 
interconnector  provides  inertial/fast-frequency  support  and  for  the  case  that  it  does  not. 
For  both  inertia  constraints,  the  NTC  based  zonal  dispatch  model  is  extended  by  the 
inertia constraint as described 6.2.3 and the zonal calculations are performed. This way, 
the  additional  benefits  of  inertia  provision  through  HVDC  is  determined.  As  the  zonal 
model uses one aggregated generator for each type of generation per country, the inertia 
constraint in the zonal model is defined as  

∑ 𝑃𝑔,𝑧
𝑔∈𝐺

⋅ 𝐻𝑔 ⋅ 𝛼𝑔 ≥ 𝐻𝑧

𝑚𝑖𝑛        ∀𝑧 ∈ 𝑍 

using  the  actual  dispatch  of  each  type  of  generator  𝑃𝑔,𝑧  as  opposed  to  the  installed 
capacity  of  the  generator  as  described  in  section  6.2.3.  Note  that  the  objective  of  this 
optimisation model is the minimization of the generation dispatch cost as  opposed to the 
nodal redispatch optimisation as described below.  

Additionally,  the  inertia  constrained  redispatch  OPF  model  is  performed  for  the  nodal 
model.  The  rationale  therefore  is  that  after  performing  the  nodal  OPF  calculations,  the 
generation  dispatch  is  obtained  per  generating  unit,  and  such,  it  is  known  which 
generators  are  online  for  any  given  operational  hour.  Thus,  by  performing  the  inertia 
constrained redispatch OPF, we can approximate the value of reserves that TSOs would 
have  to  commit  to  ensure  frequency  stability.  In  this  case,  as  optimisation  objective  the 
start-up costs of generators are minimized, which can be one to two orders of magnitude 
higher  than  the  fuel  costs.  Additionally,  as  the  nodal  redispatch  OPF  model  is 
computationally expensive, this calculation has been performed for a selected number of 
operational  points  using  the  clustering  approach  described  in  section  5.5.  As  the  nodal 
model can represent the power generation on the unit level, the original inertia constraint 
𝑚𝑖𝑛   ∀𝑧 ∈ 𝑍  based  on  the  rated  power  of  online  generators  is 
∑
enforced in the redispatch OPF.  

⋅ 𝐻𝑔 ⋅ 𝛼𝑔 ≥ 𝐻𝑧

𝑃𝑔,𝑧

𝑟𝑎𝑡𝑒𝑑

𝑔∈𝐺

96 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 32 - Calculation procedure using zonal and nodal models and their interaction. 

Figure 33 - Inertia constrained (re)dispatch calculations performed on zonal (left) and nodal (right) network models. 

7.3.1.3. 

Comparisons  of  relevant  KPIs  without  the 
project,  with  the  project  (standard  CBA  methodology) 
and with the project (proposed CBA) 

Table 17 and Table 18 below show the computed KPIs for both the zonal and nodal model 
when the Celtic interconnector is included in the European power grid. 

In  the  zonal  model,  the  socio-economic  welfare  benefit  brought  by  the  investment 
increases over time. The social welfare obtained for the Global Ambition (GA) scenario for 
the  planning  year  2030  is  84.9  MEUR,  and  it  is  114.7  MEUR  for  the  GA2040  scenario. 
The results  are comparable  to the results  in ENTSO-E's  2030  sustainable transition  and 
interconnector’ 
distributed  generation 
(https://tyndp.entsoe.eu/tyndp2018/projects/projects/107). 
the 
of 
interconnector  leads  to  an  improvement  in  all  KPIs,  with  all  emissions  (CO2,  NOx  and 
SOx) being reduced.  

‘Project  107  –  Celtic 

scenarios 

presence 

The 

in 

The  nodal  system,  despite  having  higher  computational  requirements  (roughly  24  hours 
for France and Ireland compared to 20 minutes for the whole European zonal grid), offers 
a  deeper  insight  in  the  power  grid.  Aspects  such  as  demand  curtailment,  demand 
reduction,  physical  congestions  of  the  lines  and grid  stability  can  be  investigated.  In the 
nodal model, the improvement in the overall socio-economic welfare increases compared 
to the zonal one only for 2030. The main reason therefore is consideration of the internal 
97 

Zonal TYNDP modelDemand & RES time seriesRun NTC based dispatch modelFor all 8760 hoursGeneration dispatch per type and interzonal exchangesBase caseZonal TYNDP model + Celtic interconnectorDemand & RES time seriesRun NTC based dispatch modelFor all 8760 hoursGeneration dispatch per type and interzonal exchangesCeltic interconnectorNodal TYNDP model of FranceGenerationanddemanddisaggregation Run nodal AC/DC grid OPF modelFor all 8760 hoursGeneration dispatch per unit and AC and DC branch flowsNodal TYNDP model of IrelandCombined nodal network model with Celtic interconnectorFor all 8760 hoursRun nodal AC/DC grid OPF modelRun nodal AC/DC grid OPF modelFor all 8760 hoursGeneration dispatch per unit and AC and DC branch flowsGeneration dispatch per unit and AC and DC branch flowsZonal modelNodal modelZonal TYNDP model + Celtic interconnectorDemand & RES time seriesRun NTC based dispatch model with inertia constraintsGeneration dispatch per typeInertia constraint without HVDC contributionFor all 8760 hoursZonal TYNDP model + Celtic interconnectorDemand & RES time seriesRun NTC based dispatch model with inertia constraintsGeneration dispatch per typeInertia constraint with HVDC contributionFor all 8760 hoursNodal grid of FR and IE + Celtic interconnectorGeneration dispatch and demand from nodal modelRun nodal redispatch OPF model with inertia constraintsGeneration redispatch per generatorInertia constraint without HVDC contributionFor selected operational conditionsNodal grid of FR and IE + Celtic interconnectorGeneration dispatch and demand from nodal modelRun nodal redispatch OPF model with inertia constraintsGeneration redispatch per generatorInertia constraint with HVDC contributionFor selected operational conditions 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

network  congestion,  which  contains  the  integration  of  the  cheaper  RES  resources,  and 
leading  to  higher  levels of  demand  reduction  or curtailment than  anticipated  in  the  zonal 
model.  

The nodal model indicates an increase in the CO2 emissions and lower RES integration 
compared  to  the  zonal  one.  This  fact  is  related  to  the  distributed  nature  of  the  RES 
generators. By not being aggregated in a single node, the power transmission constraints 
lead to an increased generation curtailment near the congested lines. Furthermore, Figure 
34Error!  Reference  source  not  found.  and  Figure  35  show  the  relation  between  the 
RES  generation  in  France  and  Ireland  and  respectively  their  demand  reduction  and 
demand  curtailment  for  the  scenario  GA2030.  The  power  exchange  through  the  HVDC 
link  reduces  both  in  the  intensity  and  frequency  of  demand  reduction  and  demand 
curtailment events for the whole set of RES generation levels in the two countries. In fact, 
as shown by Figure 36, the Celtic interconnector is used at its full capacity of 700 MW for 
most of the hours independent of the RES generation in both directions alike.   

Table 17 - Computed KPIs for the Celtic interconnector, zonal model, GA scenario 
for years 2030 and 2040, climate year 2007 

GA2030, cy 2007 

GA2040, cy 2007 

KPIs 

No 
investment 

Investment  Benefit 

No 
investment 

Investment  Benefit 

B1 – 
Socio-
economic 
welfare – 
all market 
zones 

B2 – CO2 
emissions 
[Mton/yr]   

B3 – RES 
integration 
[TWh]  

B4 – NOx 
emissions  
[kton/yr]  

B4 – SOx 
emissions  
[ton/yr]  

B6 – 
Adequacy, 
ENS 
[TWh/yr]  

170.93 
bn€ 

170.85 
bn€ 

84.92 
M€ 

186.12 
bn€ 

186.00 
bn€ 

114.69 
M€ 

12.27 

11.83 

0.44 

8.9 

8.79 

0.11 

160.54 

164.84 

4.3 

339.07 

339.27 

0.2 

18.99 

18.51 

0.48 

15.54 

15.43 

0.11 

374.22 

364.77 

9.45 

306.2 

304.1 

2.1 

0 

0 

0 

5.55 

5.55 

0 

98 

 
  
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Table 18 - Computed KPIs for the Celtic interconnector, nodal model, GA scenario 
for years 2030 and 2040, climate year 2007 

GA2030, cy 2007 

GA2040, cy 2007 

KPIs 

FR 

IE 

FR_IE 

Benefit 

FR 

IE 

FR_IE 

Benefit 

B1 – Socio-
economic 
welfare – FR 
and IE market 
zones 

B2 – CO2 
emissions 
[Mton/yr]  

B3 – RES 
integration 
[MWh]  

B4 – NOx 
emissions 
[kton/yr]  

B4 – SOx 
emissions 
[ton/yr]  

B5 – Grid 
losses [TWh]  

B6 -
Adequacy, 
ENS [GWh/yr]  

Additional KPI 
– Demand 
curtailment 
[GWh] 

15.36 
bn€ 

1.58 
bn€ 

16.82 
bn€ 

122.9 M€ 

16.16 
bn€ 

15.0 
bn€ 

17.56 bn€  105.9 M€ 

3.78 

2.71 

6.49 

0  

3.32 

2.65 

5.90 

0.07 

242.4 

24.3   

268.5 

1.92 

296.96  

26.88 

325.99 

2.15 

5778.1  3210.0   8972.3 

15.8 

5083.4 

3151.5  

8132.3  

102.6 

113.88  131.54 

211.53 

33.89 

100.19 

140.97 

208.20 

 32.96 

13.92 

2.02 

16.21 

- 0.27 

15.49 

2.29 

18.44 

- 0.66 

0 

0 

0 

0 

0 

0 

0 

0 

0 

206.90 

27.96 

178.94 

0 

55.30 

 2.32 

52.98 

Figure  34  provides  another  interesting  insight.  Considering  that  the  objective  of  the 
optimal  power  flow  calculation  is  to  minimize  the  cost  of  generation,  demand  reduction 
and demand curtailment, we can observe that the demand reduction is being shifted from 
the  Irish  zone  to  the  French  system  if  both  zones  are  interconnected,  and  thus  the 
optimisation is performed on the interconnected system as a whole. The reason therefore 
is  that  the  costs  for  demand  reduction  have  been  assumed  to  be  the  same  in  both 
networks, and as such on the system level no distinction between the countries are made. 
Looking at Figure 35, we can also observe that through the interconnection, the expected 
demand  curtailment  can  be  reduced  by  a  significant  amount  (from  206.9  GWh  to 
approximately 28 GWh as indicated in the above table), both in the Irish and the French 
grids. Again, there is a shift in demand curtailment from Ireland to France, owing it to the 
99 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

price  agnosticism  of  the  model  as  through  the  interconnection  the  optimisation  is 
performed on the combined network as a whole.  

Figure 34 - Comparison between the demand reduction in Ireland (left) and France (right), with and without the Celtic 
interconnector for different RES generation levels, GA2030, climate year 2007. 

Figure 35- Comparison between the demand curtailment in Ireland (left) and France (right), with and without the Celtic 
interconnector for different RES generation levels, GA2030, climate year 2007. 

Figure 36 - Power flow through the Celtic interconnector for different RES generation levels, GA2030, climate year 2007. 

The pattern seen for demand reduction and demand curtailment against RES generation 
in  GA2030  is  also  observed  in the  GA2040  scenario,  as shown  in  Figure  37  and  Figure 
38. The peak intensity of the demand reduction is higher for GA2040 though, with single 
instances  reaching  1600  MW  of  demand  reduction.  Compared  to  the  maximum  value  of 
900  MW  in  GA2030,  there  is  a  78%  increase  of  the  severity  of  the  event.  Demand 
reduction is as well more frequent in both cases with and without investment compared to 

100 

 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

GA2030, owing it to the increased demand (~10% in total for France and Ireland), and the 
increase in RES generation.  

In contrary, demand curtailment is greatly reduced in GA2040 compared to GA2030. The 
benefit  through  demand  curtailment  reduction  is  especially  observed  in  situations  with 
lower  RES  generation.  In  such  cases,  making  use  of  the  power  exchanges  through  the 
interconnector, demand curtailment can be reduced to zero, which is not possible without 
the interconnector.    

Figure 37 - Comparison between the demand reduction in Ireland (left) and France (right), with and without the Celtic 
interconnector for different RES generation levels, GA2040, climate year 2007 

Figure 38 - Comparison between the demand curtailment in Ireland (left) and France (right), with and without the Celtic 
interconnector for different RES generation levels, GA2040, climate year 2007. 

In  the  previous  section  7.3.1.2  the  use  of  the  inertia  constrained  redispatch  OPF  model 
was  described  thoroughly.  In  this  section,  the  effect  of  including  inertia  constraints  is 
quantified. 

The  total  costs  for  one  year  of  operation  of  the  three  different  OPF  models  are 
summarised  in  the  following  Table  19.  As  expected,  the  case  without  inertia  constraints 
but with the Celtic interconnector installed is the cheapest with respect to generation costs 
compared  to  the  other  two  cases  including  inertia  constraints.  We  observe  that  the  total 
generation  costs  increase  with  62  MEuro  and  113  MEuro,  respectively  if  the  HVDC  link 
provides  inertia  or  not.  This  means  that  the  value  of  inertia  provision  through  the  HVDC 
equals  to  51  MEUR,  e.g.,  the  difference  of  the  cost  increase  of  both  inertia  constrained 
cases. 

The hours with low inertia can be seen in Figure 39, where the inertia values for Ireland 
are  shown  for  different  RES  generation  levels.  The  results  suggest  indeed  that  Ireland 
faces  lack  of  inertia  when  there  are  no  inertia  constraints  in  the  OPF  problem  and  high 
RES  generation  is  expected.  When  these  constraints  are  included  in  the  optimization 
problem,  the  minimum  inertia  is  constrained  by  the  inertia  limits  represented  by  the 
horizontal  lines.  The  inertia  limits  obtained  through  the  dynamic  simulations  are  8750 
101 

 
 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

MWs (without frequency support from HVDC, assuming max. RoCoF of 2Hz/s) and 5625 
MWs (with frequency support from HVDC (limited to 250MW) max. RoCoF of 2Hz/s). We 
can observe in Figure 39 that the system inertia remains above the imposed limits for the 
cases  without  (orange  markers)  and  with  (green  markers)  inertia  support.  For  the  case 
where  no  constraints  are  enforced  (blue  markers),  the  system  inertia  can  be  well  below 
5000 MWs.  

Table 19 – Total cost and comparison to the unconstrained zonal model with 
investment of the inertia-based OPF model with and without HVDC Celtic 
interconnector, GA2030, climate year 2007 

Case 

Total cost [bn€] 

Difference with respect to 
unconstrained model [M€] 

Unconstrained model 

Inertia constrained, no HVDC 

Inertia constrained, with HVDC 

170.85 

170.96 

170.91 

- 

113  

62 

Figure 39 – Inertia values for Ireland with different RES generation levels for the zonal model, unconstrained and inertia-
based OPFs, with and without HVDC, GA2030, climate year 2007 

As  already  mentioned  in  the  previous  section,  a  redispatch  calculation  has  been 
performed using the detailed nodal model of both networks where the generator start-up 
costs for conventional generators have been minimized for fulfilling the inertia constraints. 
This  value  can  be  seen  as  an  upper  bound  on  the  costs  needed  to  ensure  the  system 
inertia,  as  generator start-up  costs  are  used  in the objective.  Table  20  provides  the total 
annual generation start-up costs for the Irish network with both inertia constraints. These 
costs  should  be  seen  as  an  upper  bound,  as  it  assumes  that  in  all  low  inertia  hours 
generators would need to be started up as no unit commitment constraints are included in 
the  optimisation  model.  However,  we  can  assume  that  the  effect  of  not  having  included 
such unit commitment constraints would affect both results to the same extend and thus 
can conclude that using the inertia contribution from the HVDC link can reduce the annual 

102 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

generation start-up cost by roughly 50%, which is also in line with results provided in the 
zonal model. 

Table 20 - Total annual generation start-up costs for the Irish network to fulfill 
inertia constraints, for the scenario GA2030, climate year 2007. 

Case 

Annual genertion start-
up costs [M€] 

Inertia constrained, no HVDC 

Inertia constrained, with HVDC 

1073.6 

544.6 

7.3.2. Assessment of stability KPIs 

7.3.2.1. 

Converter driven stability 

The first indicator that has been determined for the different clusters is the SCR. In order 
to obtain the SCR, a short-circuit analysis is firstly performed (according to standard IEC 
60909)  to  obtain  the  short-circuit  power  at  each  connection  point  of  the  wind  turbines  in 
Ireland.  Thereafter  the  SCR  is  calculated  by  taking  the  ratio  of  the  short-circuit  power 
(SCR)  over  the  MVA  rating  of  each  wind  unit.  This  analysis  is  performed  using  the 
operating  points  of  the  different  clusters  both  for  the  case  with  the  Celtic  Interconnector 
and without.  

As  a  first  step,  one  could  investigate  the  amount  of  hours  where  the  converter-driven 
stability is at risk for each wind turbine or wind farm in the system. An example of such a 
duration  curve  (expressing  the  amount  of  time  a  certain  SCR  is  exceeded)  for  a  single 
turbine is presented in Figure 40. For this specific location approximately 28% of the year, 
production is at SCR<3, which can be considered  critical for converter-driven stability. In 
this case, the duration curve with and without the Celtic interconnector looks very similar, 
but this may differ depending on the dispatch and location of the wind turbine.  

Figure 40 - Duration curve of SCR for a single WT in the Irish system 

103 

 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Next, the results of all wind turbines are aggregated and it is determined how much of the 
yearly  total  wind  energy  is  produced  at  SCR  levels  below  3.  As such  an  estimate of the 
yearly  energy  can  be  obtained  at  which  converter-driven  stability  is  at  risk (see  also  KPI 
presented in Table 3). The outcome of this analysis is visualized in Figure 41 where the 
cumulative  yearly  wind  energy  is  presented  in  function  of  increasing  SCR.  It  is  clearly 
shown  in  the  figure  that  for  the  case  with  the  interconnector  more  wind  energy  (2390 
GWh)  is  produced  at  an  SCR<3  compared  to  the  case  without  the  interconnector  (1219 
GWh).  This  can  be  explained  by  the  fact  that  on  the  one  hand  more  wind  energy  is 
produced  with  the  interconnector  but  also  that  the  change  in  dispatch  leads  to  slightly 
lower SCR levels in the case of the interconnector.  

Figure 41 - Cumulative yearly wind energy in function of increasing SCR (results are only presented for SCR<30) 

The second indicator that has been determined for the six considered operating conditions 
of  the  system  (corresponding  to  the  different  clusters)  is  the  IBR  Critical  Clearing  Time 
(CCT).  As  introduced  in  section  6.3.2,  this  indicator  is  applied  to  assess  the  transient 
stability of IBR. We will focus in this report on the power system of Ireland. 

To calculate the IBR-CCT, the operating points of the wind turbines in service (active and 
reactive power) as well as the voltage at their terminals are taken from the AC load flow 
results using the nodal data as input (to do so, an AC power flow calculation is performed 
which uses the active power set points of generators and HVDC links as provided by the 
nodal  OPF  calculations  as  input).  The  external  system  has  been  represented  by  its 
Thévenin equivalent using the short-circuit power at the wind turbine connection point. By 
applying  the  different  analytical  expressions  as  introduced  in  [33]  (neglecting  outer  loop 
controller and current dynamics), the results as presented in Figure 42 are obtained (data 
with and without the Celtic Interconnector is merged). In this figure, the IBR-CCT is given 
in function of the loading of the wind turbines (active power output/rating of the machine) 
and  the  SCR.  The  results  show  the  inversely  proportional  relationship  between  loading 
and IBR-CCT.  The correlation between SCR and IBR-CCT is less clear, although for the 
operating points where the wind turbines are highly loaded (mainly out of cluster 1), lower 
SCR leads in general to a lower IBR-CCT. 

104 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 42- IBR-CCT for wind turbines within the 6 considered clusters (SCR<20) 

7.3.2.2. 

Frequency stability 

The frequency stability is investigated based on the simplified two-area system described 
in  section  6.3.  This  model  allows  to  assess  the  dynamic  performance  of  the  frequency 
regulation  and  whether  the  occurrence  of  the  sizing  incidence  would  lead  to  extreme 
following 
ROCOF  and 
simplifications/assumptions have been made: 

frequency  excursions.  For 

illustrative  purposes, 

the 

•  A threshold of 49 Hz has been considered, below which it is assumed that under-

frequency load shedding would take place.  

•  The sizing incident would be the outage of the complete HVDC link when injecting 
power  higher  than  500  MW  from  France  to  Ireland.  If  power  is  exported  through 
the  Celtic  interconnector,  then  the  sizing  incident  would  be  either  the  outage  of 
another  HVDC  link  (Eastwest  or  Moyle)  or  the  outage  of  a  generator  in  Ireland. 
Since  the  zonal  results  do  not  include  details  about  the  actual  unit  dispatch,  a 
700 MW  disturbance  is  considered  in  all  cases.  This  is  simulated  by  a  sudden 
increase of the system load.  

•  The  contribution  of  the  Celtic  interconnector  to  frequency  regulation  is  modelled 

through a simple frequency droop that modifies its active power reference.  

•  The  converter-based  renewable  units  (wind  and  PV),  as  well  as  the  run-of-river 

hydro units do not provide frequency support. 

The  benefits  from  HVDC  frequency  regulation  depend  on  the  capacity  of  the  HVDC 
allocated  for  this  purpose.  Therefore,  results  are  provided  for  four  cases:  200  MW,  400 
MW,  700 MW  and  1400  MW  (i.e.,  full  range  of  VSC  from  maximum  export  to maximum 
import). In all cases, the maximum power of the HVDC is limited by the maximum current 
rating of 1.1 pu.  

105 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure  43  -  Frequency  of  IE  with  maximum  200  MW  of 
HVDC support. 

Figure  44  -  Frequency  of  IE  with  maximum  400  MW  of 
HVDC support 

Figure  45  -  Frequency  of  IE  with  maximum  700  MW  of 
HVDC support 

Figure  46  -  Frequency  of  IE  with  maximum  1400  MW  of 
HVDC support 

As shown throughout Figure 43 and Figure 46, HVDC frequency support greatly improves 
the  frequency  stability  of  the  Irish  system.  In  particular,  with  200  MW  and  400  MW  of 
support, several cases would lead to collapse of the system frequency and load shedding 
due to insufficient reserves. In practice, the operator would re-dispatch the generators of 
the system to have sufficient reserves. Obviously, this would decrease the penetration of 
renewable units by adding more conventional units to the mix (at partial power) and would 
limit the benefits obtained from the HVDC system.  

When  the  HVDC  link  is  operated  near  its  maximum  import  before  the  disturbance,  the 
obtained benefit is negligible since it cannot further increase its power. That is the reason 
why some of the cases could not be stabilized even with very high maximum contribution 
by the HVDC.  

Figure 47 illustrates the benefit obtained by HVDC frequency support in reducing the risk 
of  having  under-frequency  load  shedding.  When  frequency  regulation  is  not  considered 
(e.g., as in the current version of the CBA), then KPIs such as the renewable integration 
tend to be overestimated and the redispatch costs (to allow for frequency reserves) tend 
to be  underestimated.  Frequency  regulation  by the  HVDC  decreases the  risk  associated 
with these parameters.  

106 

 
 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

The total number of cases in Figure 47 is split into cases where the load shedding occurs 
before 5 s and after 5 s. This time duration is in the order of the typical response time of 
the  governors  of  thermal  power  plants.  It  allows  to  have  a  clearer  insight  of  the  main 
reason  for  load  shedding.  In  particular,  in  the  cases  where  the  load  shedding  occurs 
before 5s after the disturbance, it can be deduced that there is a lack of sufficient inertia in 
the  system.  In  contrast,  when  the  load  shedding  occurs  after  5  s,  there  is  a  lack  of 
sufficient  primary  frequency  reserves.  The  contribution  from  the  HVDC  has  a  positive 
impact on both cases. 

Figure 47 : Percentage of operating points with risk of under frequency load shedding 

7.4. Ultranet + A-North 

7.4.1. Assessment of techno-economic KPIs 

7.4.1.1. 

Overview  of  implementation,  models  and  data 

used 

This  case  is  selected  to  demonstrate  the  additional  benefits  of  power  flow  control 
capability  of  HVDC  links,  especially  to  minimize  the  redispatch  costs  in  case  of 
contingencies.  To  that  end,  the  nodal  ENTSO-E  grid  model  of  the  German  network  is 
used. The network model consists of 2558 nodes, 3127 branches (including transformers 
and circuit breakers), 4954 generators and 8 HVDC links.  

107 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.4.1.2. 

Simulations performed 

As the aim is to demonstrate the benefits of power flow control through HVDC in cases of 
contingencies, first the generation dispatch is determined using the nodal grid model and 
applying AC/DC grid OPF model. By performing the calculations both with and without the 
planned  investment,  the  socio-economic  welfare  indicators  can  be  calculated  (for 
validation),  for  which  the  results  are  shown  in  the  next  section.  After  having  determined 
the  generation  dispatch,  the  redispatch  optimisation  can  be  performed  as  outlined  in 
Figure 48. 

Starting  from  the  generation  dispatch  and  the  HVDC  converter  set  points  obtained  from 
the nodal model, first a clustering of the operational hours has been performed using the 
k-means  approach  as  described  in  section  6.3.3  using  the  RES  generation  and  total 
demand  as  features  for  the  clustering.  The  reason  therefore  is  that  the  simulation  of 
operational hours, e.g. 8760 hours is computationally too expensive. For the case at hand, 
20 different clusters have been built as shown in Figure 49. As such, from each of the 20 
clusters,  5  operating  hours  have  been  sampled,  to  sufficiently  cover  the  entire  range  of 
operational conditions. 

Figure 48 - Calculation procedure to determine the benefits of HVDC power flow control for contingencies 

Figure 49 - RES generation / demand clusters for the German network, GA2030 scenario with climate year 2007 

108 

Generation dispatch and HVDC set points and demand from nodal modelRedispatch cost without HVDC controlFor each selected  operational hour of each clusterClustering of operational hours based on RES generation and demandDetermine set of critical contingenciesPerform redispatch OPF without HVDC controls, e.g. fixed set pointsFor each critical contingency Perform redispatch OPF with HVDC controls, e.g. optimal set pointsRedispatch cost with HVDC control 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

After  performing  the  clustering,  a  sequential  calculation  routine  is  performed  for  each  of 
the 5 operating hours of each of the 20 clusters selected. For each operational hour, first 
the  set  of  critical  contingencies  is  determined.  To  that  end,  all  (AC  and  DC)  lines 
exceeding  a  thermal  rating  of  1600  MVA  (MW  in  case  of  DC  lines)  and  a  line  loading 
above 70% are added to the set of critical contingencies. For the case at hand, depending 
on the selected operational hour, the number of critical contingencies varies between 70 
and  100.  Thereafter,  for  each  critical  contingency  the  optimal  redispatch  calculation  is 
performed  for  two  cases;  first,  where  HVDC  converter  set-points  are  fixed  to  their  pre-
contingency  values,  and  second,  where  the  optimal  HVDC  converter  set-points  are 
optimized.  This  way,  the  redispatch  costs  both  including  and  excluding  HVDC  control  is 
determined,  and  by  calculating  their  difference,  the  benefits  through  HVDC  power  flow 
control  is  determined.  Eventually,  the  determined  costs  are  extrapolated  to  a  full  year, 
both using the average benefits over all considered contingencies, as well as considering 
only the contingencies of each operating hour with the maximum benefits through HVDC 
control. These costs are illustrated in Table 22. 

7.4.1.3. 

Comparisons  of  relevant  KPIs  without  the 
project,  with  the  project  (CBA  methodology)  and  with 
the project (proposed CBA) 

The  following  table  shows  the  computed  KPIs  for  the  German  nodal  model  with  and 
without the UltraNet and A-North interconnectors. This use case highlights one limitation 
of  the  current  ENTSO-E  CBA,  i.e.,  not  being  able  to  evaluate  the  benefits  of  such  an 
investment  within the  zonal  model,  as  this  connection  is  entirely  within  Germany  and  as 
such,  the  determination  of  the  increase  of  the  NTCs  with  different  market  zones  is  not 
easy  to  determine  a  priori.  Without  the  prior  knowledge  of  the  NTC  increase,  the  KPIs 
cannot  be  computed  if  only  one  node  per  market  zone  is  present  in  the  model,  as  it 
happens with the current zonal simulations. 

the  power 

The  project  consists  of  a  multi-terminal  DC  from  the  North  to  the  South  of  Germany, 
the 
enhancing 
neighbouring  countries.  This  aim  reflects  in  the  computed  KPIs.  The  total  costs  are 
reduced by 113 M€ and 307 M€ respectively for GA2030 and GA2040 scenarios using the 
climate  year  2007.  Furthermore,  the  CO2,  SOx  and  NOx  emissions  are  reduced  in  both 
scenarios, as a result of the enhanced transmission power capacity. 

flow  controllability  without  having 

through 

flows 

loop 

Table 21 - Benefits through HVDC power flow control for the UltraNet + A-North 
case 

GA2030, cy 2007 

GA2040, cy 2007 

KPIs 

No 
investment 

Investment 

Benefit 

No 
investment 

Investment 

Benefit 

B1 – Socio-
economic 
welfare  – all 
market zones 

B2 – CO2 
emissions 
[Mton/yr]   

B3 – RES 
integration[TWh]  

17.47 bn€   17.35 bn€ 

113 M€ 

15.96 bn€ 

15.65 bn€ 

307 M€ 

23.57 

20.48 

3.09 

18.78 

18.32 

0.46 

273.00 

271.1  

- 1.9 

290.0 

286.5 

- 3.5 

109 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

GA2030, cy 2007 

GA2040, cy 2007 

No 
investment 

Investment 

Benefit 

No 
investment 

Investment 

Benefit 

30.92 

30.82 

0.10 

29.59 

29.04 

0.55 

128.45 

125.45 

3.00 

189.00 

183.67 

5.33 

2.76 

2.77 

- 0.01 

2.86 

2.86 

0 

0 

132.64 

132.64 

0 

0 

0 

0 

303.60 

303.60 

0 

0 

0 

KPIs 

B4 – Nox 
emissions  
[Mton/yr]  

B4 – Sox 
emissions  
[ton/yr]  

B5 – Grid losses 
[TWh] 

B6 – Adequacy, 
ENS [GWh/yr]  

Additional KPI – 
Demand 
curtailment 
[GWh] 

Table 22 shows the benefits obtained through HVDC grid control in case of contingencies. 
The  table  provides  two  different  values,  namely  the  total  annual  benefits  obtained  by 
taking  the  average  value  of  the  benefits  among  all  contingencies  summed  up  over 
operating hours considered and extrapolated to a full year. The second column provides 
the  total  annual  benefits  obtained  by  taking  the  maximum  achieved  benefits  among  all 
considered  contingencies  summed  up  over  all  operating  hours  and  extrapolated  to  a full 
year.  We  can  observe  that  there  exists  a  significant  gap  of  one  order  of  magnitude 
between the average value and the maximum value. Figure 50 illustrates the benefits of 
power  flow  control  through  HVDC  for  all  clusters,  chosen  operating  hours  and 
contingencies.  The  figure  clearly  demonstrates  that  the  maximum  benefits  are  achieved 
for  certain  specific  contingencies  in  a  given  operating  hour  or  contingency  indicated  as 
outliers  in  the  boxplots.  In  reality  structural  weaknesses  network  resulting  in  such  high 
costs during contingencies would be solved with local reinforcements. As such, it can be 
expected  that  realistically  the  benefits  through  power  flow  control  through  HVDC  will  be 
closer to the average value provided in Table 22. 

Table 22 - Benefits through HVDC power flow control for the UltraNet + A-North 
case 

Using average benefits 
of all contingencies 
[MEUR/year] 

Using contingencies with 
maximum benefits 
[MEUR/year] 

Annual  benefits  through  power 
flow control through HVDC 

33.5 

473.2 

110 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 50 - Benefits of power flow control through HVDC for each RES-demand cluster, each operating hour per cluster and 
each contingency per operating hour. 

111 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

7.5. EuroAsia 

7.5.1. Assessment of techno-economic KPIs 

7.5.1.1. 

Overview  of  implementation,  models  and  data 

used 

The  EuroAsia 
interconnector  (https://tyndp.entsoe.eu/tyndp2018/projects/projects/219) 
aims  to  connect  continental  Greece  (zone  GR00),  Crete  (GR03),  Cyprus  (CY00)  and 
Israel (IL00) with an HVDC interconnection. Even though the rated capacity of the cable is 
2000  MW,  only  1000 MW  will  be  used for  its  preliminary  stage.  For this  reason, the  two 
cables being added to the zonal European grid have a rated capacity of 1000 MW. They 
interconnect  Crete  and  Cyprus  (GR03-CY00)  and  Cyprus  and  Israel  (CY00-IL00).  Since 
Israel is an islanded zone in the zonal model, its demand is assumed to follow the pattern 
of another Mediterranean market zone, ITSI. As the installed power plant capacities and 
peak  demand  for  Israel  are  not  provided  within  the  zonal  TYNDP  model,  the  installed 
capacity  is  obtained  from  the  website  of  International  Trade  Administration9.  The  peak 
demand  assumed  to  be  13.8  GW10.  As  for  the  RES  and  demand  time  series,  the  same 
profiles as for the Southern Italian market zone are used.  

This  case  study  is  chosen  to  demonstrate  the  added  value  of  inertia  provision  through 
HVDC. Considering that power provided by the HVDC link will be higher than the current 
peak demand in Cyprus, as well as the envisaged RES penetration on the island, inertia 
provision  through  this  HVDC  link  will  be  vital  to  maintain  the  stability  of  the  system.  As 
such,  in  this  case  study,  we  are  using  the  same  approach  as  in  the  case  of  the  Celtic 
interconnector to determine the benefits through inertia provision using the zonal model of 
the system. 

7.5.1.2. 

Simulations performed 

In order to validate the assumptions with respect to the assumed demand and generation 
mix in Israel, first the zonal NTC based economic dispatch model is used to calculate the 
socio-economic benefits for the cases, with and without the interconnector. We determine 
the  socio-economic  welfare  KPIs  and  compare  them  to  the  benefits  provided  in  the 
TYNDP for which the KPIs are provided in the next section for validation.  

As in the case of the Celtic interconnector, subsequently, also the inertia constrained NTC 
based dispatch model is performed, for the cases where inertia contribution from HVDC is 
considered  and  omitted.  This  way  the  same  comparison  as  in  the  case  of  the  Celtic 
interconnector  w.r.t  the  costs  associated  with  stability  constraints  can  be  quantified,  as 
well as the benefits achieved through inertia provision through HVDC control.  

7.5.1.3. 

Comparisons  of  relevant  KPIs  without  the 
project,  with  the  project  (CBA  methodology)  and  with 
the project (proposed CBA) 

With the EuroAsia interconnector, all the KPIs improve for scenario GA2030, climate year 
2007. In Table 23, the indicators computed with and without investments are compared to 
the values shown by ENTSO-E TNYDP in its 2030 Sustainable Transition scenario. As a 

9 See also https://www.trade.gov/country-commercial-guides/israel-energy 

10 See also https://sympower.net/demand-peaks-in-israel/ 

112 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

validation of our zonal model, the order of magnitude of all the KPIs falls in the range of 
values  stated  by  ENTSO-E.  The  reason  behind  the  difference  for  B1  (Socio-economic 
welfare)  and  B6  (Adequacy  –  ENS)  resides  probably  in  the  assumptions  made  for  the 
Israel zone IL00. Nevertheless, the difference is not substantial. 

The benefits brought by the interconnector in terms of ENS reduction are shown in Figure 
51 below, where the level of ENS for the whole RES generation spectrum is shown. When 
the  EuroAsia  interconnector  is  not  included  in  the  grid,  there  are  loss  of  load  events 
distributed for roughly all the generation levels. The frequency and magnitude of the ENS 
hours  are  brought  to  zero  when  the  EuroAsia  interconnector  is  added  to  the  zonal 
dispatch. 

interconnector  and 

In  addition,  Figure  52  displays  the  relation  between  the  power  flow  through  two  parts  of 
the  area.  The 
the  EuroAsia 
interconnectors are used at full capacity for a consistent number of hours. The link GR03 
– CY00 sees a power flow to GR03 (Crete) for most of the time, highlighting how Crete is 
in constant need of power. Differently, the power flow for CY00 – IL00 is more distributed 
across the range of possible power flow values for the interconnector. 

the  RES  generation 

levels 

in 

Table 23 - Computed KPIs for EuroAsia interconnector, zonal model, scenario 
GA2030, climate year 2007 

GA2030, cy 2007 

ENTSO-E TYNDP data  

KPIs 

No investment 

Investment 

Benefit 

Benefit 

B1 – Socio-
economic 
welfare  – 
all market 
zones 

B2 – CO2 
emissions 
[Mton/yr]   

B3 – RES 
integration 
[GWh]  

B4 – NOx 
emissions  
[kton/yr]  

B4 – SOx 
emissions  
[ton/yr]  

B6 – 
Adequacy, 
ENS 
[GWh/yr]  

175.91 bn€ 

176.16 bn€ 

246.25 M€ 

261 – 270 M€ 

15.31 

15.76 

0.45 

0.76 - 2 

464.92 

477.11 

12.19 

0 - 22 

19.51 

18.81 

0.70 

901.67 

370.74 

530.93 

- 

- 

8.855 

0 

8.855 

0.78 – 2.96 

113 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Figure 51 - Energy not served for different RES generation levels in the EuroAsia zonal model, GA2030, climate year 2007 

Figure 52 - Power flows through two parts of the EuroAsia interconnector for different RES generation levels in the EuroAsia 
zonal model, GA2030, climate year 2007 

Table  24  shows  the  total  system  cost  for  the  EuroAsia  interconnector  when  the  inertia 
constraints are enforced for Cyprus. As expected, the case without inertia constraints but 
with the EuroAsia interconnector installed is the cheapest with respect to generation costs 
compared  to  the  other  two  cases  including  inertia  constraints.  We  observe  that  the  total 
generation  costs  increase  with  16  and  104  and  MEuro,  respectively  if  the  HVDC  link 
provides inertia or not. This means that the value of inertia provision through the HVDC is 
88 MEUR, e.g., the difference of the cost increase of both inertia constrained cases.  

The hours with low inertia can be seen in Figure 53, where we see the inertia values for 
Cyprus over all operational hours. We can clearly observe that in many hours the system 
inertia  can  drop  as  low  as  to  zero  in  the  base  case  without  inertia  constraint  (blue 
markers),  where  the  entire  demand  is  supplied  by  RES.  This  shows  the  importance  of 
including  inertia  constraints  in  the  optimal  dispatch  model,  as  such  zero  inertia  cases 
would be infeasible in real life, if no counter measures such as synchronous condensers 
or grid forming HVDC links can be used. 

When the inertia constraint is included in the optimization problem, the minimum inertia is 
constrained  by  the  inertia  limits  represented  by  the  horizontal  lines.  The  inertia  limits 

114 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

obtained through the dynamic simulations are 6250 MWs (without frequency support from 
HVDC,  assuming  max.  RoCoF  of  2Hz/s)  and  3125  MWs  (with  frequency  support  from 
HVDC (limited to 250MW) max. RoCoF of 2Hz/s). We can observe in  Figure 53 that the 
system  inertia  remains  above  the  imposed  limits  for  the  cases  without  (orange  markers) 
and with (green markers) inertia support.  

Table 24 - Total cost and comparison to the unconstrained zonal model with 
investment of the inertia-based OPF model with and without HVDC EuroAsia 
interconnector, GA2030, climate year 2007 

Case 

Total cost [bn€] 

Difference with respect to 
unconstrained model [M€] 

Unconstrained model 

Inertia constrained, no HVDC 

Inertia constrained, with HVDC 

175.911 

176.015 

175.927 

- 

104 

16 

Figure 53 - Inertia values for Cyprus with different RES generation levels for the zonal model, unconstrained and inertia-
based OPFs, with and without HVDC, GA2030, climate year 2007 

7.5.1.4. 

Frequency stability 

As in the case of the Celtic Interconnector, the frequency stability is investigated based on 
the  simplified  two-area  system  described  in  section  6.3.  For  illustrative  purposes,  the 
following simplifications/assumptions have been made: 

•  A threshold of 49 Hz has been considered, below which it is assumed that under-

frequency load shedding would take place.  

•  The  sizing  incident  would  be  the  outage  of  one  pole  of  the  HVDC  link  when 
injecting power to Cyprus. Compared to the case of Ireland though, here there is 

115 

 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

only  one  HVDC  connection  to  Cyprus,  and  the  outage  of  500  MW  would  be  too 
constraining.  In  addition,  it  is  expected  that,  in  practice,  the  power  of  the  HVDC 
injection to Cyprus would be limited below the maximum rating, namely, to allow to 
provide  frequency  reserves  in  case  of  the  outage  of  one  pole.  For  this  reason,  a 
sizing incident of 400 MW has been considered in this analysis.  

•  The  converter-based  renewable  units  (wind  and  PV),  as  well  as  the  run-on-river 

hydro units do not provide frequency support. 

Results are provided for four cases: 200 MW, 400 MW,  500 MW and 1000 MW (i.e., full 
range of one pole of the connection from maximum export to maximum import). They are 
shown in Figure 54 - Figure 58. 

Figure  54  -  Frequency  of  CY  with  maximum  200  MW  of 
HVDC support 

Figure 55 - Frequency of CY with maximum 400 MW of 
HVDC support 

Figure  56  -  frequency  of  CY  with  maximum  500  MW  of 
HVDC support 

Figure 57 - frequency of CY with maximum 1000 MW of 
HVDC support 

Similar conclusions are obtained as in the case of the Celtic Interconnector. Allowing more 
participation  by  the  HVDC,  results  in  more  operating  points  without  need  for  load 
shedding.  As  a  result,  the  cost  for  redispatch  to  account  for  reserves  is  lower  and  the 
operating  points  with  higher  generation  by  renewable  units  can  be  achieved.  It  is 
interesting to note, that high renewable penetration is usually accompanied with export of 
power from the HVDC. Hence, in such cases: 

•  The outage of the HVDC is not the sizing incident (since its outage would result in 

over-frequency which is in general more easily managed) 

116 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

• 

the  actual  range  of  the  reserves  that  can  be  provided  by  the  HVDC  is  higher  (it 
could reach twice the rating of the VSC) 

Figure  58  shows  how  the  percentage  of  load  shedding  cases  is  improved  with 
increasing  contribution  by  the  HVDC  link.  It  is  interesting  to  note  that  when 
increasing the HVDC contribution from 200 MW to 400 MW, the number of cases 
where  load  shedding  occurs  after  5  s  is  increased.  This  is  because  the  fast 
response of the HVDC allows to delay the collapse of the system. Further increase 
of  the  contribution  by  the  HVDC  has  a  positive  impact  on  the  number  of  load 
shedding either due to insufficient reserves or due to low inertia.  

Figure 58 : Percentage of operating points with risk of under frequency load shedding 

7.6. 2050 MTDC 

The 2050 multi-terminal DC grid case was selected in order to illustrate extra benefits that 
could  not  be  captured  using  the  2030  cases.  However,  based  on  the  results  of  the  four 
previous cases, we were able to show additional benefits for each study case. In fact, the 
combination  of  the  four  studied  use  cases  covers  the  configuration  of  the  2050  MTDC 
case. When investigating the 2050 MTDC use case, it was identified that a pan-European 
use  case  brings  additional  complexities  in  terms  of  computation  challenges,  need  for  a 
harmonized  dataset  and  also  for  adequate  modelling  of  the  different  layers  of  control  of 
the  MTDC.  However,  it  will  not  show  additional  benefits  that  were  not  covered  in  the 
previously studied cases. 

In future work, the methodologies developed in this work could also be applied to the 2050 
Multi-Terminal  European  backbone  system,  in  order  to  better  quantity  the  risks  through 
IBR  based  generation  and  potential  benefits  through  the  use  of  HVDC  technology. 

117 

 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

However, harmonized power system models are needed both for the zonal as well as the 
nodal network models in order to obtain meaningful results. 

Considering that such a backbone will have multiple terminals within some countries, the 
currently  available  zonal  network  model  would  need  to  be  updated,  also  based  on  the 
outcome  of  the  bidding  zone  review  currently  ongoing.  Further,  in  the  case  of  the 
backbone  system,  one  could  expect  high  benefits  through  power  flow  controllability 
considering  the  ring  structure  spanning  over  France,  Belgium  and  Germany.  This  would 
require  regional  level  redispatch  calculations,  for  which  again  reliable  and  harmonised 
nodal network models are needed. Considering the computational intensity, also network 
reduction techniques would most likely need to be applied in this case. 

7.7. Main challenges encountered during analysis of the use 

cases 

The main challenges encountered during the implementation of the use cases have been 
related  to  the  inconsistencies  and/or  incompatibilities  of  available  data.  Firstly,  the 
translation/disaggregation of the zonal TYNDP model to the nodal high voltage grid model 
requires a number of assumptions, on the distribution of the demand and the renewable 
generation  sources.  Although  the  demand  can  be  disaggregated  linearly,  as  also  done 
within this project, for the disaggregation of the generation, the type of generator needs to 
be known in the nodal model. However, for many of the provided detailed nodal models, 
the  generator  types  are  not  directly  visible,  and  heuristics  based  on  the  size  of  the 
generator, or the naming convention chosen by the TSOs need to be developed to extract 
generator types in the nodal model. Secondly, inconsistencies exist between the installed 
generation capacities in the zonal and nodal models. As such, the validation of the afore-
mentioned use of heuristics to derive the generation types of the nodal model is needed. 
For the sake  of  validation  of  both models,  in the  future,  it  will  be  essential  to  ensure  the 
consistency and compatibility of both models. 

Another  major  challenge  encountered  w.r.t.  data  was  inconsistencies  of  data  within  the 
nodal models. The aim of the nodal model is to provide a power flow solution to the non-
linear AC power flow equations. However, to be able to use this model for optimal power 
flow type of calculations, the quality of the data should be improved. Inconsistencies of the 
data often result in infeasible solutions of the optimisation problem. The main sources of 
inconsistencies encountered were: 

• 

Inconsistent power ratings in subsequent lines and circuit breakers 

•  Negative impedance values for branches 

• 

Inconsistent bounds on generators, e.g. 𝑃𝑔

𝑚𝑖𝑛 ≥ 𝑃𝑔

𝑚𝑎𝑥 

•  Non-unique node names 

•  Unrealistic  generation  and  demand  values,  often  from  injections  not  modelled 

explicitly, e.g. from interconnectors or HVDC links 

• 

Inconsistent  modelling  of  HVDC  links,  e.g.  modelling  as  equivalent  generation 
versus modelling using actual converters 

•  Unrealistic line ratings, usually on lower voltage levels, or for antenna connections  

118 

 
 
 
 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

8. Main findings and recommendations 

Summary of the work and findings 

In order to try to answer to the following question “Are the existing methodologies, models 
and tools adequate to capture all risks and benefits when planning AC/DC hybrid grid?”, 
this work proposed some improvements to the current European CBA approach used by 
ENTSO-E. Therefore, the focus is at the planning stage when the evaluation of the costs 
and benefits of a project candidate takes place.  

It was identified that commonly used CBA methods do not capture all the technical risks 
related  to  operations  of  a  system  with  high-penetration  of  IBRs.  Therefore,  operating 
conditions might not be stable and would require additional investment or redispatch to be 
viable.  

The  proposed  improvements  were  detailed  in  section  5  and  can  be  summarized  by  the 
three following aspects: 

•  More detailed power system representation, towards a network model 
• 

Integration  of  power  flow  control  and  stability  constraints  in  the  optimization 
problem 

•  Addition  of  qualitative  KPIs  regarding  system  stability  (in  particular  for 

frequency and converter-driven stability) 

These  improvements  are  to  be  added  to  the  existing  ENTSO-E  CBA  approach  which 
forms the basis of the proposed incremental approach (illustrated by the pyramid in Figure 
8). These incremental levels of complexity are proposed to better quantify some KPIs and 
also risks in systems with high-penetration of Inverter-Based Resources. The main point is 
that the zonal approach may provide optimistic benefits, in the sense that some costs can 
be “hidden” when planning system with large penetration of inverter-based RES because 
of security and operational challenges. Therefore, it is highly recommended to perform a 
CBA using the static network model and considering stability metrics such as inertia and 
SCR.  Both  inertia  and  converter-driven  stability  metrics  can  be  translated  to  KPIs  by 
assessing how many operating conditions per year are at risk of frequency or converter-
driven instability. These quantitative KPIs should be used as an indicator of the need for 
future  investment  or  for  operational  measures.  Regarding  frequency  stability,  a  cost  is 
also evaluated based on redispatch methodology (similar to current B.10 KPI of ENTSO-
E). Regarding the converter-driven stability KPI, it must be seen as a risk indicator, which 
can lead to more detailed simulations in the next stage of the project or even to additional 
investment. 

Modelling  requirements  and  guidelines  for  implementations  of  the  proposed  approach 
were  detailed  in  section  6.  In  particular,  modelling  details  focusing  on  the  HVDC 
technology are summarized in section 6 and implementation details for the CBA approach 
could be found in section 6.2 and section 6.3. 

It has been observed from the use case results that indeed the zonal CBA approach can 
lead  to  optimistic  results  in  a  system  with  high  penetration  of  RES  or  when  network 
thermal  constraints  are  reached.  It  has  also  been  identified  that  VSC  HVDC  technology 
can provide system stability services that would allow stable operation for a high number 
of operating conditions (in particular at higher penetration of IBRs). This was the case in 
particular for an HVDC link connecting two asynchronous areas and where one area had 
a  significant  share  of  IBR  penetration.  Also,  it  has  been  confirmed  from  the  use  case 
where the  HVDC  link is  embedded to the  AC  grid that  the  power  flow  control  abilities of 
HVDC  provide  additional  benefits.  In  all  studied  cases,  additional  benefits  of  the  HVDC 
technology could only be seen with the use of an inertia constraint and/or with the use of a 
nodal network model (even if there is an AC/DC interface between two zones). 

119 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

Our  methodology  is  valid  for  HVDC,  but  similar  additional  benefits  can  also  be  seen  for 
devices  participating  to  power  flow  control,  frequency  stability  or  with  grid  forming 
features. 

The  work  performed  can  be  summarized  into  the  three  following  parts  (which  are  more 
detailed in sections 5, 6 and 7). 

1. 

Updated CBA methodology and implementation guidelines 

The proposed CBA approach quantifies additional benefits and identifies potential risks for 
system  stability.  It  is  important  to  note  that  these  additional  benefits  can  only  be  seen 
when  performing  the  CBA  on  a  nodal  model  and/or  with  stability  constraints  (such  as 
inertia).  

Firstly,  an  existing  open-source  AC/DC  grid  optimal  power  flow  (OPF)  model  has  been 
used  in  order  to  determine  the  social  welfare  benefits  considering  internal  congestion  in 
the network, as opposed to using zonal models neglecting intrazonal constraints. Further, 
the OPF model has been modified to determine the additional benefits through power flow 
control  provided  by  HVDC  links  during  contingency  situations.  Using  the  modified  OPF 
formulation,  the  redispatch  costs  are  minimized  for  a  number  of  selected  critical 
contingencies. By performing two separate calculations with disabled and enabled power 
flow control, the additional benefits through power flow control are determined. The results 
show that security related redispatch costs can be significantly decreased by making use 
of such controllability. 

Moreover, the developed OPF implementation allows to include additional constraints. An 
inertia constraint has been tested for two study cases and it was clearly observed that the 
HVDC  technology  could  considerably  reduce  the  minimum  inertia  constraint,  which  by 
consequence  increase  the  number  of  stable  operating  conditions.  This  effect  is  also 
quantified  by  means  of  redispatch  cost  reduction  as  a  proxy  of  required  reserves  to 
ensure frequency stability. Further, it has been demonstrated that such inertia constraints 
can  be  included  in  detailed  nodal  optimal  power  flow  models,  and  either  inertia 
constrained dispatch or re-dispatch simulations can be performed. 

An extremely important aspect is power system stability in a system with high penetration 
of IBR. The main initial idea was to perform RMS (or EMT) simulation in order to capture 
instabilities  of  grid-following  assets  in  weak  grids  (e.g.  PLL  control).  However,  while  it  is 
generally agreed that EMT simulations are needed in order to assess stability in a weak 
grid, models with the required level of details and accuracy of the control parameters are 
typically  not  available  for  the  considered  planning  horizon.  For  this  reason,  it  is 
recommended  to  evaluate  risk  of  instabilities  (at  specific  locations  of  the  grid  and/or  at 
specific operating conditions) via calculation of simplified indicators. A simple indicator is 
the short-circuit ratio (SCR) but other indicators considering some control loop parameters 
of IBRs and their dispatch provide a more accurate view of the stability risk. The common 
philosophy of these indicators is to try to catch the relationship between a variation of the 
(grid following) converter output and the variation of voltage at the point of connection. If 
the  sensitivity  is  high,  then  the  risk  of  instability  is  higher.  These  stability  indicators  are 
translated  to  a  clear  quantitative  KPI  which  is  the  number  of  hours  per  year  of  having  a 
risk of instability. 

2. 

Technical aspects and modelling requirements 

One  part  of  the  work  (summarized  in  section  6.1)  specifically  focuses  on  the  modelling 
requirements  for  the  HVDC  technology.  A  comprehensive  review  of  the  type  of  models 
and  level  of  details  adequate  for  each  phenomenon  was  presented.  For  each 
functionality/technical aspects of HVDC systems, the modelling was specified.  

Section  6.2  and  section  6.3  detail  the  modelling  requirements  for  implementing  the 
proposed CBA approach, and outline how additional CBA KPIs can be implemented within 

120 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

steady-state optimisation models, and how steady-state and dynamic simulations can be 
combined  to  analyse  risks  of  IBR  based  generation,  as  well  as  additional  benefits  of 
HVDC  technology.  These  sections  provide  to  the  interested  reader  all  the  required 
information for implementing the proposed approach. 

3. 

Illustration on realistic use cases 

The  use  cases  provided  us  not  only  with  quantitative  results  but  also  with  a  return  of 
experience  on  the  proposed  implementation.  The  zonal  approach  has  been  easily 
implemented, however it is clear that the nodal approach has led to significant challenges, 
mainly  attributed  to  available  data.  It  has  been  shown  that  our  approach  could  be 
implemented  on  multi-country  systems  with  several  thousands  of  nodes,  lines  and 
generators.  An  important  outcome  is  also  that,  while  highly  recommended  with  an 
accurate  dataset,  conclusions  from  time-domain  power  system  simulations  should  be 
analysed with care in systems with high penetration of RES and with uncertainties on the 
control  loops.  It  is  therefore  recommended  to  start  with  indicators  based  on  the  “static” 
network model in order to identify stability risks.  

Main findings and recommendations for future improvements 

(i) 

Main Findings 

the  socio-economic  benefits  of  new 

(1)  Use  of  nodal  network  model  is  necessary:  Although  zonal  models  can 
determine 
in  a 
computationally efficient manner, they tend to underestimate these benefits as 
the internal congestion in the network is not considered. The reason therefore 
is the zonal approach underestimates the curtailment of renewable energy due 
to internal network congestion in high RES scenarios, where the added value 
of  interconnection  is  even  more  significant.  Our  study  shows  that  more 
complex  nodal  models  can  be 
feasibly  used  within  of  CBA 
methodologies despite higher computational complexity (24 hours vs. 30 min 
for yearlong calculations) and higher data requirements. 

interconnectors 

(2)  Power flow control provides significant benefits: The study shows that HVDC 
technology  provides  significant  benefits  through  power  flow  control  in 
case  of  contingencies  by  reducing  the  required  redispatch  cost. 
Especially embedded HVDC links can reduce redispatch costs in the order of 
several tens of millions of Euros per year in case of severe contingencies in the 
system. To analyse such benefits, the use of nodal models is unavoidable. 

(3)  Stability  constraints  are  necessary:  It  is  essential  to consider  stability  /  inertia 
constraints  in  long  term  planning  models  to  estimate  the  additional  risk  of 
deteriorating system inertia for determining the best mitigation options. Further, 
our  study  shows  that  inertia  provision  through  HVDC  decreases  the 
necessary  cost  for  ensuring  system  stability  in  the  order  of  several  ten 
million Euros per year.  

(4)  Stability indicator can be used to identify operational risks: Our study shows 
that  simplified  models  with  stability  and  inertia  constraints  can  provide 
acceptable  high-level  results  for  CBA  analysis.  In  terms  of  dynamic  data 
and control parameters, it is clear that the most accurate data allow to be more 
confident in the results of advanced tools. However, with currently available 
models  and  data  sets,  it  is  not  adequate  to  perform  intensive  detailed 
simulations  for  long-term  planning  studies.  We  conclude  that  detailed 
dynamic simulations should only be used in cases where detailed network and 
equipment  models  are  available  which  can  represent  different  control  loops 
and  where  control  parameters  are  known.  As  such,  potential  risks  and  de-

121 

 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

risking  actions  have  to  be  identified  but  can  be  done  later  in  the  planning 
process when detailed models are available.  

(5)  Harmonized  models  are  needed:  Our  study  shows  the  need  to  harmonize 
the network models used in the context of CBAs. Especially, to quantify the 
effects  of  congestion  and  benefits  through  power  flow  control  as  well  as  to 
better  approximate  dynamic  stability  constraints,  harmonized  models  are 
essential. 

(ii) 

Recommendations for future improvements 

(1)  Dataset  Improvement:  As  the  network  data  are  mandatory  in  our  proposed 
approach, it is extremely important to have a reliable European network model 
(static).  To  that  end,  different  data  sets  used  for  long  term  generation  and 
transmission expansion planning versus detailed grid models used to perform 
power  flow  studies  should  be  harmonized  in  order  to  obtain  accurate  results 
capturing  all  benefits.  The  modelling  section  provides  clear  requirements  in 
terms  of  the  tools  and  model  details  for  studying  each  phenomenon.  It  has 
been  shown  in  this  study  (and  also  in  the  literature)  that  control  parameters 
have  a  huge  influence  on  IBR  stability.  Therefore,  in  the  near  future  it  is 
extremely important to have a European grid model with representative control 
parameters  for  existing  IBRs.  This  will  allow  to  perform  a  better  screening  of 
the instabilities that might occur 

(2)  Need  for  high-performance  computer  infrastructure:  Although  detailed  nodal 
models  are  computationally  more  expensive,  parallelization  of  calculations, 
application  of  artificial  intelligence  methods  for  contingency  filtering,  improved 
clustering techniques for selecting a subset of representative operating points 
(both  for  steady  state  and  dynamic  analysis)  and  the  use  of  dedicated  high-
performance  computer  infrastructure  can  allow  the  implementation  of  the 
demonstrated  mathematical  models  within  state-of-the  art  tools.  Further,  the 
development  of  dedicated  open-source  tools  can  help  to  provide  transparent 
results in the context of the CBA. 

(3)  Defining power system stability in the future grid: Our study shows a particular 
approach for including stability indicators within CBA methodologies. However, 
there  are  a  variety  of  stability  indicators,  which  all  can  be  quantified  using 
different  types  of  optimisation  /  simulation  models.  As  such,  in  the  long  run  it 
will be important to define stability indicators in a harmonized way. Especially, 
in the  context  of  grid forming  and  black  start  capabilities,  clear  definitions  are 
needed based on which, indicators can be defined, and subsequently models 
can  be  developed  to  quantify  these  indicators.  We  believe  that  fundamental 
research  and  a  broad  stakeholder  involvement  are  necessary  to  achieve  this 
goal. 

122 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

9. Appendix I: stakeholder interaction 

During this project, two presentations with external stakeholders were done. 

First  a  virtual  stakeholder  workshop  took  place  on  31st  March  2022,  for  which 
approximately  75  people  registered  and  covered  OEM,  TSOs,  Consulting,  developers, 
research  centre  and  academia.  Secondly,  a  virtual  was  performed  an  IEEE  Working 
Group Meeting on “Studies for Planning of HVDC”. 

Later this year, it is also expected to present this work in a panel session “Infrastructure 
for the bulk energy transmission in high RES systems” at the 2022 IEEE Power & Energy 
Society General Meeting. While not in the scope of the initial offer, the Consortium would 
be  open  to  additional  virtual  stakeholder  interactions  if  requested  by  the  European 
Commission. 

In  addition  to  these  above-mentioned  stakeholder  meetings,  punctual  interactions  with 
ENTSO-E  are  expected,  in  particular  on  the  data  available  and  technical  details  on  the 
modelling. 

9.1. Stakeholder feedback on use case selection 

Figure 59 - Stakeholder feedback on use case selection 

9.2. Modelling requirements and cost-benefit analysis 

As shown in Figure 60, it has been confirmed during the workshop that benefits of HVDC 
are  not  well  evaluated  in  the  existing  CBA.  Also,  the  first  functionality  identified  as  most 
relevant is power flow control, which is a very important part of our work. Care should be 
taken  when  generalizing  responses  from  a  single  workshop.  However,  these  answers 
confirm  the  important  of  this  project  for  stakeholders.  The  second  ranked  functionality  is 
on black start capabilities, closely followed by grid forming functionality. Therefore, these 
points have to be analysed in detail in this project, keeping in mind that our work focuses 
at  the  planning  stage  (which  is  performed  usually  without  knowing  detail  design  and 
operational  procedures).  Participants  also  asked  whether  benefits  such  as  permitting, 
public acceptable, environmental impact and total footprint of an HVDC project should not 

123 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables – Final Report 

also  be  quantified.  It  is  however  believed  that  these  aspects  are  project  specific  and 
therefore very difficult to quantify and generalize. 

Figure 60 - Workshop question on benefits of HVDC in classical planning approach 

In terms of simulations, modelling and methodology, a meeting took place with ENTSO-E 
on  14th  March  2022.  Some  important  remarks  were  formulated,  including  the  practical 
constraints  that  ENTSO-E  face  during  the  TYNDP  process.  Therefore,  it  is  important  to 
extend the existing methodology step by step. For example, the use of simplified stability 
KPIs allowing to perform a screening of potential problem is seen as a very promising way 
forward. It will allow to clearly define for which operating conditions and at which locations, 
additional detailed simulations need to be performed. 

Another  important  question  was  asked  regarding  further  extension  of  HVDC  links  (as 
shown  in  Figure  61).  While  most  of  the  persons  responded  that  HVDCs  should  be 
“extendible”  (via  anticipation  and  standardization)  and  that  MTDC  grid  should  not  be 
considered as a single project, it is important to outline that this is technically complex and 
will most likely lead to extra-cost (with the current technology and design). Therefore, an 
extra cost-margin will be considered in this project to allow for future extension. This extra-
margin  can  include  assets  (DCCB,  measurement  devices,  DC  switchgear,  etc.), 
software/control upgrade, or simply spare space. 

124 

 
 
 AC/DC hybrid grid modelling enabling a high share of Renewables –Final Report 

Figure 61 - Workshop question on HVDC extendibility 

125 

 
 
 
10. Appendix II: use case selection 

Table 25 - Assessment of to the long list of use cases considering the economic 
indicators as defined in section 7.1.3.2 

Use case 

Voltage 
regulation 

Frequency 
regulation 

Grid forming 

Power flow 
control 

Black start 

Sum 

1. Slovenia-Italy 
link 

2. HVDC 
SuedOstLink 

3. Navarra-Landes 
Link 

4. MONITA project 

5. Celtic 
interconnector 

6. TUN.ITA. 

7. Viking DKW-GB 

8. TuNur 

9. Ultranet + A-
North 

10. EuroAsia 
interconnector 

11. MaresConnect 

12. LaSGo Link 

13. Nautilus 

14. MTDC multi-
country backbone 

15. North Sea 
Wind Power Hub 
(NSWP) 

4 

4 

4 

4 

2 

2 

2 

2 

5 

2 

2 

2 

2 

5 

5 

0 

0 

0 

0 

3 

3 

3 

2 

0 

5 

3 

3 

3 

5 

5 

2 

2 

2 

2 

3 

2 

2 

1 

2 

3 

3 

3 

2 

4 

4 

126 

3 

3 

3 

3 

2 

2 

2 

1 

4 

2 

2 

3 

3 

5 

5 

1 

1 

2 

1 

3 

3 

3 

2 

2 

5 

4 

5 

3 

5 

5 

10 

10 

11 

10 

13 

12 

12 

8 

13 

17 

14 

16 

13 

24 

24 

 
 
11. Appendix  III:  Data  sources  for  the  zonal  economic 

dispatch model  

The  installed  generation  capacities  for  each  market  zone,  planning  year,  scenario  and 
considered  climate  year  can  be  found  under:  https://2020.entsos-tyndp-scenarios.eu/wp-
content/uploads/2020/06/TYNDP-2020-Scenario-Datafile.xlsx.zip  

the  NTCs 

Further, 
the  market 
https://www.entsoe.eu/Documents/TYNDP%20documents/TYNDP2020/Reference%20Grid
%202025%20-%20TYNDP%202020.xlsx  

between 

zones 

found 

can 

be 

under: 

The  demand  time  series  for  the  different  climate  years  for  the  different  climate  years, 
scenarios and planning years can be found under: https://tyndp.entsoe.eu/maps-data   

The  hourly  capacity  factor  time  series  for  offshore  wind,  onshore  wind,  and  solar  PV 
generation 
under: 
years 
35 
https://zenodo.org/record/3702418#.YnOn7C8Rp-X  

climate 

found 

can 

for 

be 

The  detailed  ENTSO-E  network  model  for  all  European  countries  can  be  requested  under 
confidentiality 
https://www.entsoe.eu/publications/statistics-and-
data/#entso-e-on-line-application-portal-for-network-datasets 

agreement 

under: 

The  generation  cost  data  have  been  obtained  from  the  TYNDP  2020:  https://2020.entsos-
tyndp-scenarios.eu/wp-content/uploads/2020/06/Charts-and-Figures_Underlying-Data-for-
TYNDP-2020.xlsx.zip.  Approximate  costs  based  on  the  above  information  have  been 
assigned to generator types that are not presented in the above data. An overview of these 
costs is presented below (all values are given in Euro / MWh): 

"DSR" => 119, # demand side response 
"Other non-RES" => 120, 
"Offshore Wind" => 59, 
"Onshore Wind" => 25, 
"Solar PV" => 18, 
"Solar Thermal" => 89, 
"Gas CCGT new" => 89, 
"Gas CCGT old 1" => 89, 
"Gas CCGT old 2" => 89, 
"Gas CCGT present 1" => 89, 
"Gas CCGT present 2" => 89, 
"Reservoir" => 18, 
"Run-of-River" => 18, 
"Gas conventional old 1" => 120, 
"Gas conventional old 2" => 120, 
"PS Closed" => 120, 
"PS Open" => 120, 

 
 
 
  
"Lignite new" => 120, 
"Lignite old 1" => 120, 
"Lignite old 2" => 120, 
"Hard coal new" => 120, 
"Hard coal old 1" => 120, 
"Hard coal old 2" => 120, 
"Gas CCGT old 2 Bio" => 120, 
"Gas conventional old 2 Bio" => 120, 
"Hard coal new Bio" => 120, 
"Hard coal old 1 Bio" => 120, 
"Hard coal old 2 Bio" => 120, 
"Heavy oil old 1 Bio" => 120, 
"Lignite old 1 Bio" => 120, 
"Oil shale new Bio" => 120, 
"Gas OCGT new" => 89, 
"Gas OCGT old" => 120, 
"Heavy oil old 1" => 150, 
"Heavy oil old 2" => 120, 
"Nuclear" => 110, 
"Light oil" => 140, 
"Oil shale new" => 150, 
"P2G" => 120, 
"Other non-RES DE00 P" => 120, 
"Other non-RES DKE1 P" => 120, 
"Other non-RES DKW1 P" => 120, 
"Other non-RES FI00 P" => 120, 
"Other non-RES FR00 P" => 120, 
"Other non-RES MT00 P" => 120, 
"Other non-RES UK00 P" => 120, 
"Other RES" => 60, 
"Gas CCGT new CCS" => 89, 
"Gas CCGT present 1 CCS" => 60, 
"Gas CCGT present 2 CCS" => 60, 
"Battery" => 119, 
"Lignite old 2 Bio" => 120, 
"Oil shale old" => 150, 
"Gas CCGT CCS" => 89, 
"VOLL" => 10000, # value of lost load 

128 

 
 
 
 
12. References 

[1]   European Commission, “Stepping up Europe’s 2030 climate ambition,” COM(2020) 562 final, 

Brussels, 2020. 

[2]   European Commission, “An EU Strategy to harness the potential of offshore renewable energy for 

a climate,” COM(2020) 741 final, Brussels, 2020. 

[3]   ENTSO-E, “3rd Guideline for Cost-Benefit Analysis of Grid Development Projects (draft),” 2019. 
[Online]. Available: https://consultations.entsoe.eu/system-development/cba-methodology-3-
0/supporting_documents/191023_CBA3_Draft%20for%20consultation.pdf. 

[4]   WP 4.7, PROMOTioN Project Deliverable, “Preparation of cost-benefit analysis from a protection 

point of view,” 2020. [Online]. Available: https://www.promotion-
offshore.net/fileadmin/PDFs/D4.7_Preparation_of_cost-
benefit_analysis_from_a_protection_point_of_view.pdf. 

[5]   ENTSO-E, “System Needs Study - System dynamic and operational challenges,” July 2022. 

[Online]. Available: https://eepublicdownloads.blob.core.windows.net/public-cdn-container/tyndp-
documents/TYNDP2022/public/syst-dynamic-operational-challenges.pdf. 

[6]   W. Baker, D. Ramasubramanian, M. Val Escudero, E. Farantatos and A. Gaikwad, “Application of 
advanced short circuit strength metric to evaluate Ireland's high renewable penetration scenarios,” 
in The 9th Renewable Power Generation Conference (RPG Dublin Online 2021), Dublin, 2021.  

[7]   CIGRE WG C4.56 TB881, “Electromagnetic transient simulation models for large-scale system 

impact studies in power systems having a high penetration of inverter-connected generation,” 
CIGRE C4, 2022. 

[8]   N. Hatziargyriou et al., “Definition and Classification of Power System Stability – Revisited & 
Extended,” IEEE Transactions on Power Systems, vol. 36, no. 4, pp. 3271-3281, 2021.  

[9]   T. V. Cutsem, Classification of power system stability, University of Liege.  

[10]  ENTSO-E, “TYNDP 2020,” [Online]. Available: 

https://eepublicdownloads.blob.core.windows.net/public-cdn-container/tyndp-
documents/TYNDP2020/Forconsultation/TYNDP2020_Report_forconsultation.pdf. 

[11]  L. Papangelis, “Local and centralized control of multi-terminal DC grids,” ULiege, 2018. 

[12]  European Commission, COMMISSION REGULATION (EU) 2017/2196, Official Journal of the 

European Union, 2017.  

[13]  Jiang-Hafner, Ying et al., “HVDC with voltage source converters-a powerful standby black start 

facility,” in IEEE/PES T&D Conf. and Expo., 2008.  

[14]  Midtsund, T., et al., “A live black-start capability test of a voltage source HVDC converter,” in 

CIGRE Canada Conference, 2015.  

[15]  The National HVDC Centre, “Maximising HVDC Support for GB Black Start and System 

Restoration,” 2019. 

 
 
 
[16]  CIGRE WG B4.70, TB 832:Guide for electromagnetic transient studies involving VSC converters, 

2021.  

[17]  ELIA – National Control Center & Market Development, “Study on the Review of the Black Start 

Ancillary Services,” 2018. 

[18]  ENTSO-E - WGAS, “Survey on Ancillary Services Procurement, Balancing Market Design 2017,” 

2018. 

[19]  ENTSO-E, High Penetration of Power Electronic Interfaced Power Sources and the Potential 

Contribution of Grid Forming Sources, 2017.  

[20]  Z., Emin et al., “System Strength,” Cigre Science and Engineering, no. CSE 020, 2021.  

[21]  OSMOSE Project WP3, “D3.2: Overall Specifications of the Demonstrations,” 2019. 

[22]  M. Paolone, T. Gaunt, X. Guillaud, M. Liserre, S. Meliopoulos, A. Monti, T. Van Cutsem, V. Vittal 
and C. Vournas, “Fundamentals of power systems modelling in the presence of converter-
interfaced generation,” Electric Power Systems Research, 2020.  

[23]  C. Schöll and H. Lens, “Design-and simulation-based comparison of grid-forming converter 

control concepts,” in 20th International Workshop on Large-Scale Integration of Wind Power into 
Power Systems as well as on Transmission Networks for Offshore Wind Power Plants, 2021.  

[24]  P. Unruh, M. Nuschke, P. Strauß and F. Welck, “Overview on grid-forming inverter control 

methods,” Energies, 2020.  

[25]  ESIG Task Force on High Share of Inverter-Based Generation, “Grid-Forming Technology in 

Energy Systems Integration,” 2022. 

[26]  R. Rosso, X. Wang, M. Liserre, X. Lu and S. Engelken, “Grid-forming converters: control 

approaches, grid-synchronization, and future trends-A review,” IEEE Open Journal of Industry 
Applications, 2021.  

[27]  Power System Dynamic Performance Committee, “Stability definitions and characterization of 

dynamic behavior in systems with high penetration of power electronic interfaced technologies,” 
IEEE, 2020. 

[28]  ENTSO-E, “Inertia and Rate of Change of Frequency (RoCoF) - Version 17,” 2020. 

[29]  EirGrid, Soni, “Shaping our Electricity Future - Technical Report,” 2021. 

[30]  Transpower System Operator, “RMT_Specification_V9,” 2022. [Online]. Available: 

https://www.transpower.co.nz/sites/default/files/bulk-
upload/documents/RMT_Specification_V9_issue.pdf. 

[31]  NERC, “Odessa Disturbance - Texas Events: May 9, 2021 and June 26, 2021 Joint NERC and 

Texas RE Staff Report,” 2021. 

[32]  AEMO, System strength in the NEM explained, 2020.  

[33]  W. Wenzong, M. H. Garng, R. Deepak and F. Evangelos, “Transient stability analysis and stability 

margin evaluation of phase-locked loop synchronised converter-based generators,” IET 
Generation, Transmission & Distribution , vol. 14, no. 22, 2020.  

130 

 
 
[34]  ENTSO-E, ““One Vision 2030” Roadmap towards PE-Dominated Power Systems (incl. HVDC)”. 

[35]  D. Ramasubramanian et al., “Positive sequence voltage source converter,” IET Generation, 

Transmission & Distribution, vol. 14, no. 1, pp. 87-97, 2020.  

[36]  P. Borowski, “Zonal and Nodal Models of Energy Market in European Union,” Energies, vol. 13, 

no. 10.3390/en13164182, p. 4182, 2020.  

[37]  ENTSO-E, “System dynamic and operational challenges - Final version after ACER opinion,” 
August 2021. [Online]. Available: https://eepublicdownloads.blob.core.windows.net/public-cdn-
container/tyndp-documents/TYNDP2020/FINAL/entso-
e_TYNDP2020_IoSN_Systemdynamicandoperationalchallenges_2108.pdf. 

[38]  B. Badrzadeh, Z. Emin, S. Goyal, S. Grogan, A. Haddadi, A. Halley, A. Louis, T. Lund, J. 

Matevosyan, T. Morton, D. Premm, S. Sproul, “System strength,” 2021.  

[39]  A. Hoke, V. Gevorgian, S. Shah, P. Koralewicz, R. Kenyon and B. Kroposki, “Island power 

systems with high levels of inverter-based resources: Stability and reliability challenges,” IEEE 
Electrification Magazine, 2021.  

[40]  ENTSO-E, Overview: Operational Limits and Conditions for Frequency Coupling, 2018.  

[41]  ENTSO-E, “Research, Development and Innovation Roadmap 2020-2030,” 2022. [Online]. 

Available: https://eepublicdownloads.azureedge.net/clean-
documents/Publications/RDC%20publications/entso-e-rdi_roadmap-2020-2030.pdf. 

[42]  ENTSO-E, “Grid-Forming Capabilities: Towards System Level Integration,” 31 March 2021. 

[Online]. Available: https://eepublicdownloads.entsoe.eu/clean-
documents/RDC%20documents/210331_Grid%20Forming%20Capabilities.pdf. 

[43]  ENTSO-E, “System Needs Study - Opportunities for a more efficient European power system in 

2030 and 2040,” July 2022. [Online]. Available: 
https://eepublicdownloads.blob.core.windows.net/public-cdn-container/tyndp-
documents/TYNDP2022/public/system-needs-report.pdf. 

 
 
 
 
 
 
 
GETTING IN TOUCH WITH THE EU 

In person 

All over the European Union there are hundreds of Europe Direct information centres. You can find the 
address of the centre nearest you at: https://europa.eu/european-union/contact_en 

On the phone or by email 

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, or  

– by email via: https://europa.eu/european-union/contact_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 at: https://europa.eu/european-union/index_en 

EU publications 

You can download or order free and priced EU publications from: https://op.europa.eu/en/publications. 
Multiple copies of free publications may be obtained by contacting Europe Direct or your local 
information centre (see https://europa.eu/european-union/contact_en). 

EU law and related documents 

For access to legal information from the EU, including all EU law since 1952 in all the official language 
versions, go to EUR-Lex at: http://eur-lex.europa.eu 

Open data from the EU 

The EU Open Data Portal (http://data.europa.eu/euodp/en) provides access to datasets from the EU. 
Data can be downloaded and reused for free, for both commercial and non-commercial purposes. 

132 

 
 
 
 
M
J
-
0
5
-
2
2
-
4
2
6
-
E
N
N

-

ISBN 978-92-76-60277-4