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NIST GCR 14-978

Electricity storage in buildings for 

residential sector demand response: 

Control algorithms and economic 

viability evaluation

Menglian Zheng

Christoph J. Meinrenken

Klaus S. Lackner

Lenfest Center for Sustainable Energy, Earth Institute

Department of Earth and Environmental Engineering, Columbia University

http://dx.doi.org/10.6028/NIST.GCR.14-978
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NIST GCR 14-978

Electricity storage in buildings for residential sector demand 

response: Control algorithms and economic viability evaluation

Prepared for

U.S. Department of Commerce

Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

By

Menglian Zheng

Christoph J. Meinrenken

Klaus S. Lackner

Lenfest Center for Sustainable Energy, Earth Institute

Department of Earth and Environmental Engineering, Columbia University

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.GCR.14-978

June 2014

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Willie May, Acting Under Secretary of Commerce for Standards and Technology and Acting Director
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iii

Any opinions, findings, conclusions, or recommendations expressed in this publication do not necessarily 

reflect the views of the National Institute of Standards and Technology (NIST). Additionally, neither NIST 

nor any of its employees make any warranty, expressed or implied, nor assume any legal liability or 

responsibility for the accuracy, completeness, or usefulness of any information, product, or process 

included in this publication. 

This report was prepared under Contract number grant 60NANB11D192 between the National Institute 

of Standards and Technology and Columbia University. The statements and conclusions contained in this 

report are those of the authors and do not imply recommendations or endorsements by the National 

Institute of Standards and Technology.

Abstract

“Smart grid”-enabled demand response (DR) provides significant opportunities to improve today’s 

electricity grids’ reliability, efficiency, affordability and security. In contrast to conventional DR, 

electricity storage in buildings (residential or commercial) can provide essential, flexible and reliable DR 

service without requiring consumers to operate their appliances on shifted or reduced schedules. With a 

number of DR tariffs and DR-enabling technologies available (e.g., storage technologies and two-wayinverters), one of the key current barriers for higher penetration of DR is consumers’ understanding of the 

cost-benefit issue. To address this question, and focusing on the residential sector, we (i) devised an 

agent-based appliance-level stochastic model to simulate the electricity demand of an average U.S. 

household; (ii) developed control strategies to shift loads from the peak periods to the off-peak periods 

(i.e., loadshifting strategy) and to shed the peaks of the power demand loads (i.e., peak reduction strategy); 

(iii) suggested the potential profits for the consumers, i.e., the reduced electricity cost of the modified 

demand with realistic tariffs (Con Edison, New York) minus storage costs. We optimized DR operation 

for the above two DR strategies to maximize the profits for consumers and determined the economic

viabilities for a range of traditional and advanced storage technologies. We concluded that annual profits 

range from $61 to $1365 per year per household by utilizing the loadshifting strategy and from $161 to 

$1058 per year per household by using the peak reduction strategy. These profits can be achieved without 

changing the actual consumption patterns of appliances. Of the two DR strategies, the peak reduction 

strategy can render more storage technologies economically viable.

Keywords

Demand response; Smartgrid; Electricity storage; Agent-based modeling; Arbitrage; Peak shedding
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iv

Table of contents

Abstract.......................................................................................................................................................iii

Keywords....................................................................................................................................................iii

Table of figures............................................................................................................................................v

Table of tables ............................................................................................................................................vi

Glossary .....................................................................................................................................................vii

1 Introduction.........................................................................................................................................1

1.1 Background...................................................................................................................................1

1.2 Residential DR and residential demand profile modeling ............................................................1

1.3 Existing DR optimization research ...............................................................................................2

1.4 Motivations and objectives of present study.................................................................................2

1.5 DR scheme overview ....................................................................................................................3

2 DR tariffs.............................................................................................................................................4

2.1 TOU kWh tariff.............................................................................................................................5

2.2 TOU kW tariff...............................................................................................................................7

3 Electricity storage technologies, framework of storage cost model and scenarios........................9

3.1 Electricity flow model and definitions..........................................................................................9

3.2 Uncertainties, financing cost model and scenarios.....................................................................10

4 Agent-based stochastic residential demand model ........................................................................11

4.1 Presentation of data and steps to build up the demand model ....................................................12

4.1.1 Approach to air conditioning ..............................................................................................14

4.1.2 Approach to lighting ...........................................................................................................14

4.1.3 Other appliances..................................................................................................................14

4.1.4 Calibration (all appliances).................................................................................................14

4.2 Testing.........................................................................................................................................17

4.2.1 Individual appliance level and model convergence ............................................................18

4.2.2 Household level...................................................................................................................21

5 Storage dispatch strategy, operating optimization and economic viability evaluation results 

(loadshifting)..............................................................................................................................................23

5.1 Storage dispatch strategy (loadshifting strategy) ..............................................................................23

5.1 Operation optimization and economic viability evaluation model .............................................25

5.2 Results.........................................................................................................................................25

5.2.1 Base case (no storage): Composition of electricity bill and seasonal effects......................25

5.2.2 Optimal effective storage size.............................................................................................26

5.2.3 Economic viability ..............................................................................................................28

5.3 Analytic approach to optimal size of storage..............................................................................28

6 Storage dispatch strategy, operating optimization and economic viability evaluation results 

(peak reduction) ........................................................................................................................................30

6.1 Storage dispatch strategy (peak reduction strategy)....................................................................30

6.2 Operating optimization and economic viability evaluation model .............................................31

6.3 Results.........................................................................................................................................32

6.3.1 Base case (no storage): Composition of electricity bill and seasonal effects......................32

6.3.2 Optimal effective storage size and optimal operating upper limit ......................................33
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v

6.3.3 Economic viability ..............................................................................................................39

7 Discussion ..........................................................................................................................................40

7.1 Demand tariffs versus energy tariffs...........................................................................................40

7.2 Technological improvement and storage cost reduction.............................................................41

7.3 Lowering installation costs .........................................................................................................42

7.4 Impact of interest rates................................................................................................................42

7.5 Technological viability of PHS and CAES.................................................................................42

8 Conclusions........................................................................................................................................42

Acknowledgements ...................................................................................................................................43

References (main document)....................................................................................................................44

Appendix A. Operating characteristics of storage technologies and cost estimations........................49

Appendix B. Demand profile model testing results ...............................................................................54

Table of figures

Figure 1. DR scheme and flows of relevant data and electricity..................................................................4

Figure 2. Con Edison rate structure (summarized from [45, 46])................................................................4

Figure 3. Daily electricity charge rates (supply and delivery, excluding monthly service fees). ................5

Figure 4. Illustration of the electricity flow ...............................................................................................10

Figure 5. Illustration of the stochastic demand profile model....................................................................12

Figure 6. Flow chart of agent-based logic in the appliance demand profile model. ..................................16

Figure 7. An example of one household demand profile generated by aggregating appliances demand 

profiles........................................................................................................................................................17

Figure 8. Mean load curve from simulations and in-use probability profile from ATUS [57]..................19

Figure 9. Mean load curve from simulations and in-use probability profile for air-conditioning. ............20

Figure 10. Mean load curve from simulations and flat in-use probability profile .....................................20

Figure 11. Mean load curve from simulations and respondents being at home and awake probability 

profile..........................................................................................................................................................21

Figure 12. Pie chart comparison between RECS 2005 data and simulation results...................................22

Figure 13. Mean load curve from simulations versus aggregated demand curves reproduced from 

EMET[60]...................................................................................................................................................22

Figure 14. Data traces generated by the loadshifting strategy ...................................................................24

Figure 15. Annual payments breakdowns (under the kWh tariff)..............................................................26

Figure 16. Annual payments for various storage technologies and capacities (loadshifting). Error bars 

represent one standard deviation above and below the mean. ....................................................................27

Figure 17. Data traces generated by the peak reduction strategy...............................................................31

Figure 18. Annual payments breakdowns (under the kW tariff). ...............................................................33

Figure 19. Surface plot of annual payments with varying ECs and varying ULs (peak reduction)...........34

Figure 20. Annual payments variations at controlled ECs or controlled ULs (peak reduction).................34

Figure 21. Demand profile simulations and storage (dis) charging patterns by implementing different 

operating ULs (EC = 4.6 kWh)...................................................................................................................35

Figure 22. Demand profile simulations and storage (dis)charging patterns by implementing different 

operating ULs (EC = 23.7 kWh).................................................................................................................36
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vi

Figure 23. Optimal ECs for a variety of storage costs in the average-case scenario (peak reduction). Error 

bars represent one standard deviation above and below the mean..............................................................38

Figure 24. Annual payments and optimal ULs for a variety of storage options in the average case scenario 

(peak reduction). Error bars represent one standard deviation above and below the mean. .......................38

Table of tables

Table 1. Electric rates for residential customers initial requirements less than 10 kW................................6

Table 2. Electric rates for residential customers with initial requirements in excess of 10 kW...................8

Table 3. Cashflows [$] for a $1,000 upfront for equipment with a life time of 5 years.............................11

Table 4. List of FCRs (10% interest rate) used in the study.......................................................................11

Table 5. Parameters of storage operating characteristics and purchase cost..............................................11

Table 6. Operating characteristics of typical electric appliances in the residential sector in the U.S. .......13

Table 7. Optimal effective capacity and maximum profits for two scenarios (loadshifting).....................28

Table 8. Optimal EC, optimal UL and maximum profits for the average-case scenario (peak reduction) 39

Table 9. Optimal EC, optimal UL and maximum profits for the best-case scenario (peak reduction) ......40

Table 10. Economic evaluation results comparison between two strategies..............................................41
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vii

Glossary

ATUS American Time Use Survey

CAES Compressed Air Energy Storage

CF Calibration factor

DADRP Day Ahead Demand Reduction Program

DoD Healthy depth of discharge

DOE U.S. Department of Energy

DR Demand response

DSASP Demand Side Ancillary Service Program

EC Effective capacity

EDRP Emergency Demand Response Program

EPRI Electric Power Research Institute

ES Shifted electricity

FCR Financing cost rate

FERC Federal Energy Regulatory Commission

GHG Green House Gas

MAC Monthly Adjustment Clause

MFC Merchant Function Charge

MSC Market Supply Charge

NaS Sodium Sulfur batteries

NiCd Nickel Cadmium batteries

NiZn Nickel Zinc batteries

NYISO New York Independence System Operator

Pb-acid Lead-acid batteries

PEV Plug-in Electric Vehicle

PHS Pumped Hydro Storage

RECS Residential Energy Consumption Survey

RSEM Relative standard deviation of the mean

SETIS Strategic Energy Technology Information System

SMES Superconducting Magnetic Energy Storage

SoC State of charge

TOU Time of use

UL Upper limit

VRB Vanadium Redox Batteries

ZEBRA Sodium nickel chloride batteries

ZnBr Znic Bromide batteries

ZnMnO2 Znic Manganese Dioxide batteries
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1

1 Introduction

1.1 Background 

Facing time-varying and overall increasing demand, today’s electricity grid is struggling to balance 

supply and demand on a moment-to-moment basis reliably. Even in the relatively modern grid in the U.S., 

black-outs and brown-outs still occur and cost $500 per person per year [1]. Typical and traditional grids 

employ peak generating capacities, frequency regulation, and (some) grid-based storage [2-4] to follow a 

time-varying demand profile. Sitting idle during off-peak periods, peak generators typically increase 

overall cost as well as life cycle greenhouse gas(GHG) emissions per unit of consumed electricity [1, 5]. 

The novel “smart grid” provides significant opportunities for improving the grid’s reliability, efficiency, 

affordability and security. One of the core characteristics of a “smart grid” is two-way flow of electricity 

and information between the supply side and the demand side [1]. In this context, rather than approaching 

the supply-demand mismatch from the supply side only, the demand side also plays an essential role in 

the future electricity grids. This set of solutions is broadly referred to as demand side management or 

simply demand response (DR). DR attempts to smoothen (in time) the electricity demand profiles 

themselves and thus enable the near-instantaneous balance of supply and demand at the device level. A 

large variety of DR approaches exist [6], which can be loosely categorized into incentive- or time-based 

schemes [7]. Potential benefits include reducing electricity prices, resolving transmission line congestion, 

and enhancing grid reliability [8]. Given appropriate incentives via DR tariffs, DR can also facilitate 

integrating higher percentages of intermittent capacity such as from solar and wind into the grid [9, 10]. A 

variety of DR programs are now available in different electricity markets to achieve the above benefits

[11]. Two common ones are to shift load from peak periods to off peak periods (often referred to as 

loadshifting) [12, 13] and to reduce the peak power demand (often referred to as peak reduction) (e.g., 

[14]). Other DR approaches include loadfollowing in the real time market or the day-ahead market, 

providing regulation services or spinning reserves in the ancillary service market (e.g., [15]). 

Conventional DR, typically employed in commercial/industrial buildings, involves temporally 

interrupting or delaying a building’s various appliances to adjust their overall loads in response to 

incentive- or time-based DR signals. This however creates the challenge of having to balance DR benefits 

to the grid with a level of service commensurate with customer expectation [16]. If instead, buildings 

(whether commercial or residential) employ electricity storage, the demand side can provide DR vis-à-vis 

the grid without requiring a change in actual consumption patterns in the building. 

1.2 Residential DR and residential demand profile modeling

In contrast to commercial or grid based storage, DR via many, small residential consumers can be more 

manageable than via fewer, larger consumers because failure of a single consumer will not substantially 

disrupt the overall DR response. In addition, since residential consumers are typically more 

homogenously distributed spatially than industrial consumers, residential-based (as well as other 

geographically distributed) storage can respond to spatial contingencies more precisely [16]. Similarly, 

availability of residential-based storage would facilitate integration of building-based (rather than gridbased) decentralized renewables (not the focus of this study). Finally, residential storage schemes could 

also create synergies with plug-in electric vehicles (PEV). For example, Denholm and Short concluded 
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2

that with proper charging schedules and coordination between PEVs, their batteries could improve the 

quality of electricity supply rather than burden it by imposing higher peak loads [17, 18]. However, a 

possible adoption barrier resulting from more frequent charging/discharging of the vehicles compared to 

driving alone and thus accelerated battery degradation would have to be carefully evaluated (e.g., [19]).

Finally, in the US, about 38% of total electricity consumption is by residential consumers [20]. If a large 

portion of these were to engage in DR, this could smoothen the total load profiles substantially. 

Since there are above benefits by installing storage devices in the residential sector, understanding 

residential load profiles will be required to conduct DR optimization work for the residential sector. 

Wright and Firth suggested measurements with 1 or 2 minute resolution in order to capture the peaks of 

individual households [21]. However, such appliance-level, high time resolution, measured residential 

demand data for individual households in the U.S. are largely unavailable. An exception is the recent data 

set made available by the Pecan Street Research Institute (www.pecanstreet.org). Bottom-up modeling 

was therefore proposed to complement the costly data collection process [22]. Such studies often use 

survey data of household activities (e.g., when do residential consumers cook, wash, watch television, etc.)

[23, 24]. Richardson et al. then extended such mapping to a high-resolution stochastic model to simulate 

domestic demand profiles and compared the aggregated appliance demand profiles with measured 

residential sector demand profiles [25, 26]. 

1.3 Existing DR optimization research

A large body of DR optimization research exists throughout the world. Alongside the growing body of 

research on pertinent tariffs (e.g., [27]), more DR programs have been offered in electricity markets [11]. 

When optimizing electricity cost under relatively straight forward time-of-use (TOU) tariffs (which 

typically provides different rates per kWh for different periods of the day), one key question in optimizing 

the overall system is how to size the storage so as to maximize the profits to consumers. And variations in 

consumption (from one day to the next or between seasons) make it more difficult to predict the optimal 

size of storage [28]. Another approach to DR is to reduce the peak power demand (in kW) specifically 

(rather than total kWh drawn during times of high kWh prices). This is relevant for tariffs, already 

available in the U.S. and other countries, that charge customers based on a combination of kW and kWh 

drawn from the grid [29, 30].

Other control schemes focus on arbitrage through real-time, day-ahead markets, or ancillary service 

markets (or combinations). For example, Byrne and Silva-Monroy estimated the maximum potential 

revenues in California via a linear programming approach [31]. Where linear programming was deemed 

too inflexible (e.g., because it typically does not capture the stochastic nature of load profiles), dynamic 

programming was deployed in order to capture uncertainties of electricity prices and load profiles [15, 32-

34]. 

1.4 Motivations and objectives of present study

Over the past decades, economics and operating performance of electricity storage technologies have

improved [35-41]. However, in the U.S., today's existing DR programs represent less than 25% of the 

total market potential for DR [42, 43]and barriers to wider use of these technologies for DR in residential 

settings remain: For example, Mokrian and Stephen pointed out that storage technologies still lack 

practical control strategies and deeper understanding of cost-effectiveness [15]. Dunn et al. also raised the 
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3

issue of economic viability [36]. Provided consumers will act based on economic criteria [44], the 

question arises whether the additional cost of installing storage (and the necessary inverters and 

controllers) in someone’s house will be lower than the potential savings available via participating in DRaimed tariffs. Analysis to answer this question is expected to lead to deeper understanding of costeffectiveness and, where proven economically viable, wider adoption of storage-based DR.

Few of the above mentioned studies involve the use of storage, and fewer yet are applicable to storagebased DR schemes in the residential sector. However, recognizing the overall promise and possible 

benefits of such schemes, we set out to investigate whether consumers interested in such schemes could 

install DR systems that are both technologically feasible and economically viable under currently 

available tariffs. Here, we define economically viable specifically as meaning that the cost of battery and 

control systems, including financing, maintenance, and operating expenses, is smaller than electricity bill 

savings via arbitrage that the storage can enable over the lifetime of the storage system. And if such 

break-even can be achieved, which storage technology on one hand and dispatch strategy on the other 

hand (i.e., when and how to discharge/charge the storage) creates the lowest overall cost to the residential 

consumer?

To answer this question, we developed an agent-based stochastic demand model to randomly generate 

demand profiles for a single, representative household in the U.S. We developed two dispatch strategies 

for two currently available DR tariffs from Consolidated Edison Company of New York, Inc. (henceforth 

"Con Edison") respectively. We then evaluated the economic viability of various available storage 

technologies using a simulation-based approach. Finally, we further validated and understood the 

simulation results based on given load profiles. 

1.5 DR scheme overview

In the above context, a basic scheme to exercise DR is illustrated in Figure 1. As shown in the figure, the 

control unit supplies electricity to the appliances as required, however this electricity can be taken from 

the grid, the battery (discharging mode), or both. In addition, the unit passes electricity from the grid to 

the battery (charging mode). Note that although we only investigated two DR tariffs in this report, the 

term “tariff” in Figure 1 denotes tariffs more generally as other DR tariffs can be adopted within the 

scheme illustrated in Figure 1. We first explained the specific tariffs used in this work (Sec. 2), then

overviewed electricity storage technologies, built up the framework of the cost model and scenarios (Sec.

3), followed by the agent-based stochastic bottom-up demand model (Sec. 0). Then in Sec. 5, we 

introduced the chosen dispatch strategy and rationale for the kWh tariff, explained how the model was

used to determine optimal storage capacities and displayed results. In Sec. 6, the dispatch strategy and 

results based on the kW tariff were written. Finally, discussions and conclusions were addressed in Sec. 7

and Sec. 8 respectively. 
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4

Figure 1. DR scheme and flows of relevant data and electricity. 

2 DR tariffs

In contrast to other electricity storage analyses which are based on more general tariffs (e.g., [35]), we 

based our economic viability analysis on actual DR-relevant tariffs available from Con Edison. As typical 

in the U.S. electricity pricing, the monthly cost to residential consumers comprises (i) supply charges, (ii) 

delivery charges and (iii) taxes and other fees. Dependent on the specification class (SC), supply charges 

and delivery charges can charge in $ per kWh drawn from the grid (kWh tariff) or in both $ per monthly 

peak demand (maximum demand during one billing month) and $ per kWh drawn from the grid (kW 

tariff). The structure of the electric bill is illustrated in Figure 2. 

Figure 2. Con Edison rate structure (summarized from [45, 46]) Bills

Supply charges 

(by kWh OR kW&kWh)

Market supply charge

(MSC)

Adjustment factors

Merchant function 

charge (MFC)

Delivery charges (by 

kWh OR kW&kWh)

Customer charge

Energy or capacity (if 

applicable) delivery 

charges

Additional delivery 

charges and 

adjustments

Taxes and other fees

Appliance 

1

Appliance 

2

Appliance 

3

...

Storage unit

(incl. 2-way AC:DC 

inverter)

Grid Control unit 

(incl. storage dispatch)

Tariff

State of charge 

(SoC) and 

operating 

characteristics

Relevant data

Electricity flow
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5

A number of demand response tariffs are available from Con Edison. Among them, Emergency Demand 

Response Program (EDRP), Day Ahead Demand Reduction program (DADRP) and Demand Side 

Ancillary Service Program (DSASP) are incentivized by New York Independent System Operator 

(NYISO). Besides these programs, time-of-use tariffs (based on the kWh tariff or the kW tariff), 

distribution load relief program, commercial system relief program and curtailable electric service are 

also available for Con Edison’s customers on a voluntary or mandatory basis. More information can be 

found on the NYISO website (http://www.nyiso.com) and Con Edison website (http://www.coned.com/).

In this study, actual TOU tariffs available from Con Edison were investigated. 

2.1 TOU kWh tariff

For residential consumers with less than 10 kW peak demand monthly, SC1 is the specific classification 

assigned by Con Edison. Under SC1, both delivery charges and supply charges are charged in $ per kWh. 

Two rates are available for SC1 customers: Rate I (basic, Con Edison Rate I; Page 387-388 in [45]) and 

Rate II (TOU, Con Edison Rate II; Page 389 in [45]). The TOU kWh tariff charges differing rates for 

peak periods (Monday to Friday, 10 am-10 pm) and off-peak (all other hours). Rates further differ 

between summer (June to September) and other months. For comparison, the time-invariant "basic tariff", 

which charges the same $ per kWh rate irrespective of the time of day but varied by season, was also 

incorporated in the model. 

Table 1 gives a full list of the charge items and the corresponding charge rates. Note that rates listed 

below don’t reflect changes made by Con Edison after 02/25/2013. The relevant electric rate documents 

and definitions can be found on the Con Edison website: http://www.coned.com/rates/elec.asp. The 

market supply charge calculator (https://apps1.coned.com/csol/msc_cc.asp) was used to obtain historical 

market supply charge rates for each month. Charges for metering services are not included. Assume lowvoltage services. MSC adjustment factor, MFC, Monthly Adjustment Clause (MAC) and MAC 

adjustment factor vary between months but variations are small. Therefore, for the sake of simplicity, 

average values over one year (02/2012-01/2013) was used for each charge rate mentioned above. 

Figure 3. Daily electricity charge rates (supply and delivery, excluding monthly service fees). 

Figure 3 depicts the values of charge rates for both TOU and basic kWh tariff. Solid lines represent rates 

under the TOU tariff while dashed lines represent rates under the basic tariff. Summer months (June to 

0E+00

1E-04

2E-04

3E-04

4E-04

5E-04

6E-04

7E-04

8E-04

9E-04

1E-03

Supply and delievery charge rates 

12 AM 6 AM 12 PM 6 PM

(cents/Wmin)

Time of day

TOU tariff in June to September TOU tariff in other months

Basic tariff in June to September Basic tariff in other months
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6

September, heavy lines) are different from other months (light lines). Basic service charges ($15.76 per 

month for the basic tariff and $24.30 per month for the TOU kWh tariff) are only a small portion of the 

total electricity bill (Figure 15) and not plotted in Figure 3 .

During summer months, the TOU kWh tariff provides a lower charge rate during off peak hours while a 

much higher charge rate is observed during peak hours in comparison with the basic tariff. In other 

months, the charge rate increase during peak hours under the TOU kWh tariff, however is less than the 

charge rate decrease during off-peak hours. There is a slight increase in the charge rate under the basic 

tariff in summer months, but not significantly. Complete details are shown in Table 1.

Table 1. Electric rates for residential customers initial requirements less than 10 kW

SC1-Rate I (basic kWh tariff)

Supply 

charges 

MSC See peak/off peak prices below

MSC adjustment factor -0.4341 ¢/kWh Averaged

MFC 0.5659 ¢/kWh Averaged

Delivery 

charges

Basic service charge (customer charge) 15.76 $ per month

Energy delivery charge See peak/off peak prices below

MAC 1.7123 ¢/kWh Averaged

Adjustment factor-MAC 0.2013 ¢/kWh Averaged

System benefits charge 0.34 ¢/kWh

Renewable portfolio standard program 0.23 ¢/kWh

Surcharge to collect PSL 18-a 

assessments 0.4674 ¢/kWh

Revenue decoupling mechanism 

adjustment 0.2150 ¢/kWh

Summary (excl. basic service charge)

Total

Energy delivery 

charge MSC

Jun-Sep First 250 kWh 21.542 ¢/kWh 8.899 ¢/kWh 9.3455 ¢/kWh Over 250 kWh 22.867 ¢/kWh 10.224 ¢/kWh

Other 

months All kWh 19.692 ¢/kWh 8.899 ¢/kWh 7.4948 ¢/kWh

SC1-Rate II Voluntary time-of-use (TOU kWh tariff)

Supply 

charges 

MSC

See peak/off peak prices 

below

MSC adjustment factor -0.4341 ¢/kWh Averaged

MFC 0.5659 ¢/kWh Averaged

Delivery 

charges

Basic service charge (customer charge) 24.30 $ per month

Energy delivery charge See peak/off peak prices below

MAC 1.712 ¢/kWh Averaged

Adjustment factor-MAC 0.2013 ¢/kWh Averaged

System benefits charge 0.34 ¢/kWh

Renewable portfolio standard program 0.23 ¢/kWh

Surcharge to collect PSL 18-a assessments 0.4674 ¢/kWh

Revenue decoupling mechanism adjustment 0.2150 ¢/kWh

Summary (excl. basic service charge)

Total MSC

Energy delivery 

charge

Jun-Sep Mon-Fri 10AM-10PM 51.60 ¢/kWh 18.0313 ¢/kWh 30.27 ¢/kWh

All other hours 8.52 ¢/kWh 4.0660 ¢/kWh 1.16 ¢/kWh

Other 

months Mon-Fri 10AM-10PM 26.97 ¢/kWh 12.6878 ¢/kWh 10.98 ¢/kWh

All other hours 8.74 ¢/kWh 4.2838 ¢/kWh 1.16 ¢/kWh
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7

2.2 TOU kW tariff

If residential customer’s initial requirements1are expected to be in excess of 10 kW, SC8 will be assigned 

to these customers instead of SC1. Under SC8, delivery and supply charges are charged in both $ per 

kWh energy usage and $ per kW peak demand2(i.e. maximum demand during one billing period). Three 

rates are available for SC8 customers: Rate I (basic), Rate II (mandatory TOU) and Rate III (voluntary 

TOU). In this study, customers are assumed to select tariffs on a voluntary basis. Therefore, the 

mandatory TOU kW tariff is outside the scope of this study. In this kW tariff set, electricity bills consist

of the cost of energy (charged in $ per kWh energy use) and the cost of demand (charged in $ per kW 

peak demand). For summer months, the TOU kW tariff records three maximum demands (i.e. three peaks) 

in three time periods: Monday to Friday, 8 am-6 pm; Monday to Friday, 8 am-10 pm; all hours of all days. 

For the remaining months, the tariff records only two peaks: Monday to Friday, 8 am-10 pm and all hours 

of all days. Different peaks are assessed different charge rates, and the monthly demand cost is the sum of 

these three (two) demand costs. The energy cost part charges differing rates for peak periods (Monday to 

Friday, 10 am-10 pm) and off-peak periods (all other hours). Both energy charge rates and demand charge 

rates further differ between summer months (June to September) and other months. In comparison, the

time-invariant basic kW tariff charges the same $ per kWh rate and $ per kW rate, irrespective of the time 

of day but varied by season. One further difference between the basic kW tariff and the TOU one is that, 

according to [45] “the minimum charge for any monthly billing period shall be the charge for 10 kW of 

demand” under the basic kW tariff while there is no such “10 kW rule” embedded in the TOU one. The 

details of the charging rates are given by Table 2. The same sources and methods used to obtain kWh 

tariff details were used here too. 

To illustrate how the TOU kW tariff works, one household whose maximum demand in June is 15 kW 

occurring at 12 am was employed as an example. By using the rates in Table 2, the demand cost charged 

by the TOU kW tariff would be:

15 × 7.58 + 15 × 17.92 + 15 × 24.84 = $755.1

If the consumer could wait till 9 pm to use appliances with high power ratings, the maximum demand (or 

peak demand) would be reduced to 9 kW during 8 am – 6 pm and 15 kW during 8 am -10 pm. The 

demand cost would be:

9 × 7.58 + 15 × 17.92 + 15 × 24.84 = $709.62

If the peak demand could be further postponed to occur after 10 pm, the peaks could be: 9 kW during 8 

am-6 pm, 10 kW during 8 am -10 pm and 15 kW during all the hours. In other word, the peak of 15 kW 

occurs before 8 am or after 10 pm. The demand cost could be further decreased to:

9 × 7.58 + 10 × 17.92 + 15 × 24.84 = $620.02

From the above simple example, one’s bill can be reduced by postponing the usage of high power rated 

appliances to off-peak periods under the TOU kW tariff. Alternatively, one can reduce the peaks (e.g., not 

 

1 According to personal communications with representatives from Con Edison, the initial requirements are 

determined by installing demand meters. 

2 Demand charges are measured and billed according to 30-minute increments according to Con Edison.
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8

using high power rated appliances simultaneously) or smooth his/her demand profile to achieve a lower 

electricity bill under either the basic kW tariff or the TOU kW tariff. 

Table 2. Electric rates for residential customers with initial requirements in excess of 10 kW

SC8-Rate I (basic kW tariff)

Supply 

charges 

MSC

Demand supply charge(capacity) 8.33 $/kW

MSC adjustment factor -0.4341 ¢/kWh Averaged

MFC 0.1626 ¢/kWh Averaged

Delivery 

charges

Demand delivery charge See prices below.

Energy delivery charge 1.76 ¢/kWh

MAC 1.7123 ¢/kWh Averaged

Adjustment factor-MAC 0.2013 ¢/kWh Averaged

System benefits charge 0.34 ¢/kWh

Charge for renewable portfolio 

standard program 0.23 ¢/kWh

Surcharge to collect PSL 18-a 

assessments 0.3304 ¢/kWh

Revenue decoupling mechanism 

adjustment -0.7920 ¢/kWh

Summary

Demand delivery 

charge

Subtotal (demand 

charges) MSC

Subtotal

(energy 

charges)

Jun-Sep 27.14 $/kW 35.47 $/kW 5.010 ¢/kWh 8.52 ¢/kWh

Other months 20.98 $/kW 29.31 $/kW 4.901 ¢/kWh 8.41 ¢/kWh

Minimum charge: The minimum delivery charge for any monthly billing period shall be the charge for 10 kW of demand.

SC8-Rate III Voluntary time-of-use (TOU kW tariff)

Supply 

charges 

MSC See peak/off peak prices below

Demand supply 

charge(capacity) 8.33 $/kW

MSC adjustment factor

-

0.4341 ¢/kWh Averaged

MFC 0.1626 ¢/kWh Averaged

Delivery 

charges

Demand delivery charge See peak/off peak prices below

Energy delivery charge 0.82 ¢/kWh

MAC 1.7123 ¢/kWh Averaged

Adjustment factor-MAC 0.2013 ¢/kWh Averaged

System benefits charge 0.34 ¢/kWh

Charge for renewable 

portfolio standard program 0.23 ¢/kWh

Surcharge to collect PSL 

18-a assessments 0.3304 ¢/kWh

Revenue decoupling 

mechanism adjustment

-

0.7920 ¢/kWh

Summary 

Demand 

delivery charge Subtotal($/kW)

MSC(excl. demand 

supply charge)

Subtotal(excl. 

demand charges)

Jun-Sep

Mon-Fri 8AM-6PM 7.58 $/kW 7.58 $/kW 6.3976 ¢/kWh 8.9682 ¢/kWh Mon-Fri 8AM-10PM 17.92 $/kW 17.92 $/kW

All hours of all days 16.51 $/kW 24.84 $/kW 3.93 ¢/kWh 6.5006 ¢/kWh

Other 

months

Mon-Fri 8AM-10PM 13.27 $/kW 13.27 $/kW 5.6230 ¢/kWh 8.1936 ¢/kWh

All hours of all days 5.33 $/kW 13.66 $/kW 4.2249 ¢/kWh 6.7954 ¢/kWh
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9

3 Electricity storage technologies, framework of storage cost model and scenarios

A variety of currently available technologies were investigated in this study, ranging from the 

conventional ones, e.g., Lead-acid (Pb-acid) batteries to relatively advanced ones, e.g., the novel Zinc 

Manganese dioxide (ZnMnO2) batteries developed by City College of New York (CUNY). Some 

operating parameters and cost parameters are essential to perform a detailed comparison of the storage 

options and to incorporate the storage devices in the model. The general definitions are available in the 

following cost model. The main sources used here include the Electric Power Research Institute (EPRI) 

report [35], reports from Sandia National Laboratories [37, 38], European Commission’s Strategic Energy 

Technologies Information System (SETIS) report [47], and study by Chen et al. [40]. The complete list of 

the operating characteristics, cost estimations of storage options are detailed in Table A.1. Note that 

technical properties and cost estimations of the devices can be different from one source to another and 

also depends on the specific applications and the angle of the analysis. The uncertainties of the data will 

be addressed in the financing model. Additionally, two scenarios were analyzed to address the inherent 

data uncertainties.

3.1 Electricity flow model and definitions 

Figure 4 illustrated the electricity flow starting from the grid to the storage and finally being discharged to 

appliance(s) along with losses during power conversion (PCS1 and PCS2, involving inverter and/or 

converter) and charging/discharging processes (CH1 and CH2). 

Some definitions of the operating parameters are also useful in the model:

 EffG to S is defined as the ratio of electricity stored to electricity drawn from the grid, reflecting 

both loss through the first power conversion unit (PS1 in Figure 4) and charging process.

 EffS to A is defined as the efficiency of energy stored to electricity consumption by appliances, 

reflecting discharging loss and loss through the second power conversion unit (PS2 in Figure 4).

In our model, EffG to S and EffS to A are equal in value.

 DoD is healthy depth of discharge.

The concept “power density" (kW/kWh) was used when the data collected from literature were converted 

to specific parameters used in the model (detailed values are listed in Table A.1). Power density is the 

maximum continuous (dis)charging power for a storage module of one kWh nominal capacity. In this 

report, sometimes, another similar term is used: “charging at, e.g., 1C”, meaning, 1 kW per kWh nominal 

capacity. Certain storage can withstand pulse discharging, i.e. discharging at as several times the power of

its nominal power rating. In this study, only the continuous (dis)charging power (i.e. nominal power 

rating at the normal (dis)charging mode) was considered in the model. 

Figure 4 illustrates the concept of "effective capacity" (EC) as used throughout our analysis: EC reflects 

the maximum amount of electricity stored that can be withdrawn and used by appliances after discharging 

(CH2) and power conversion loss (PC2). We thus used cost for a given kWh effective capacity (per year) 

to provide a useful metric to levelize the costs of technologies of different lifespans and/or dis(charging) 

efficiencies: 
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10

Figure 4. Illustration of the electricity flow 

3.2 Uncertainties, financing cost model and scenarios 

Financing costs, here referring to the principal and 10% interest payments for the storage and control unit 

combined over their lifetime, were broken down into two parts: One part scales proportional to the 

storage capacity (kWh). The other, a one-time home installation fee, is (approximately) independent of 

the storage size (here assumed to be $2,000). To account for price variations by vendor as well as possible 

future price reductions and/or improvements in storage life time, we used ranges (low, high) of financing 

costs. Some uncertainties in storage cost and lifetime are due to their level of technological maturity. For 

example, the limited operational field experience for newer storage technologies, such as flow batteries 

and Li-ion batteries, make it difficult to obtain accurate cost values from current literature. In contrast, 

cost uncertainties for e.g., Pb-acid batteries and sodium sulfur (NaS) batteries, both more proven 

technologies [48], are smaller. Because of the inherent uncertainties in financing costs, relatively smaller 

operational and maintenance costs were not treated separately, but rather considered already included in 

the financing costs.

Cost = ( PC ∙

EC

EffS to A ∙ DoD + IC) ∙ FCR (1)

Where PC denotes the purchase cost of storage per kWh nominal capacity (excl. installation),

EC denotes the effective capacity of storage,

IC denotes the installation fee (assumed to be $2,000),

FCR denotes the annual finance cost rate (principal repayment plus 10% interest, see

Table 3).

Financing cost (interest rate and principal repayment) over the lifespan of the storage equipment (storage 

unit (costs incl. control unit) and installation cost) was calculated with an assumption of 10% interest rate. 

For the sake of simplicity, storage technologies were roughly categorized into four lifespans: The average 

lifespans of each storage technology were rounded to generally 5, 10, 15, or 20 years by assuming one 

cycle per day (one cycle includes charging and discharging storage once).

Effective

capacity 

(EC)

 

Healthy 

depth of 

discharge

(DoD)

Effective 

capacity 

PCS1 PCS2 (EC)

PCS1 loss

PCS2 loss

CH2 loss

CH1 loss

Storage

CH1 CH2

Nominal 

capacity of 

storage

Grid

EffG to S EffS to A

Appliances
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11

Example cashflows for equipment of 5-year life time and an initial $1,000 investment are listed in Table 3.

Financing cost rates (FCRs) for any given interest rate and lifetime are given by equation 2 and the 

specific values used in the model are listed in Table 4.

FCR =

r(1 + r)

k

(1 + r)

k − 1

(2)

Where r denotes the interest rate,

k denotes the number of annual payments (e.g., for a life time of 5 years, k=5).

Table 3. Cashflows [$] for a $1,000 upfront for equipment with a life time of 5 years

Year ("stock" values are end of year) 0 1 2 3 4 5

Interest -100 -84 -66 -46 -24

Repayment of principala-164 -180 -198 -218 -240

Total financing cost 264 264 264 264 264

Annual FCR (% of upfront) 26.4% 26.4% 26.4% 26.4% 26.4%

Remaining debt -1000 -836 -656 -458 -240 0

a Repayment of principal = -Initial investment*FCR-Accumulated interest. FCR is solved by setting zero remaining debt at the 

end of the fifth year. 

Table 4. List of FCRs (10% interest rate) used in the study

FCR [% of upfront cost] per year per day

5 years 26.4% 0.072%

10 years 16.3% 0.045%

15 years 13.1% 0.036%

20 years 11.7% 0.032%

Table 5. Parameters of storage operating characteristics and purchase cost 

Purchase cost of 

storage

($/kWh-capacity) DoD

Roundtrip 

efficiencya Life time (cycles)

Power conversion 

system efficiency

Bestcase 

scenario

Average 

(geometric 

mean)

Average 

(arithmetic 

mean)

Average 

(arithmetic 

mean)

Average 

(arithmetic 

mean) (year) PS1 PS2

Flywheel 1,000 2236 88% 90% 30,000 20

95% 95%

Conventional 

batteries

Metal air battery 10 40 100% 45% 800 5

Lead-acid (Pb-acid) 106 489 75% 78% 2,350 10

Nickel-cadmium (NiCd) 600 949 75% 76% 2,000 10

Advanced 

batteries

Lithium-ion (Li-ion) 500 1342 80% 88% 5,500 15

Sodium sulfur (NaS) 250 826 80% 81% 3,250 10

NaNiCl ZEBRA 100 141 80% 90% 2,500 10

Flow 

batteries

Zinc bromine (ZnBr) 150 541 100% 68% 6,000 15

Vanadium redox (VRB) 150 433 100% 75% 10,000 20

Nickel zinc 700 700 90% 80% 7,000 15

ZnMnO2 100 141 90% 80% 4,000 15

Super capacitor 500 707 100% 95% 5E+07 20

CAES 2 29 70% 55% 12,500 20

PHS 5 22 100% 80% 35,000 20

SMES 1,000 3162 100% 95% 55,000 20

a The round-trip efficiency takes into account the charging loss through CH1 and the discharging loss through CH2. 

Recognizing above parameter ranges, we analyzed economic viability under two scenarios: 1) Best-case; 

and 2) average-case. The best-case scenario uses the lowest cost cited in the literature for a specific 
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12

storage technology. The average-case uses the average (geometric mean) of lowest and highest costs in 

the literature. For all other parameters such as lifetime (here specifically number of daily cycles), 

(dis)charging efficiencies, and DoD, we used arithmetic means of low and high literature values (same in 

both scenarios). Scenarios with low storage cost and long lifetime were not considered. Since cost often 

correlates with performance-related parameters such as lifetime or efficiency, such scenarios are much 

less realistic. The operating characteristics and cost estimations for storage options under two scenarios 

are summarized in Table 5.

4 Agent-based stochastic residential demand model 

An agent-based, appliance-level demand model to randomly generate demand profiles (1 minute time 

resolution) for a typical household in the U.S. was devised based on the scheme illustrated in Figure 5.

Figure 5. Illustration of the stochastic demand profile model. 

Simulating one year of minute-by-minute demand, storage dispatch, and resulting electricity cost takes 

about 8 minutes on a laptop computer with 2.5 GHz Intel Core i5-2520M CPU and 4 GB RAM). The 

model generally follows the approach introduced by Widén [24]. The strategy of mapping time-use data 

Step 6: Aggregate all the 

appliances selected in Step 1

Step 5: Turn appliance i OFF when 

CLL = 0

Goal 3: Capture 

stochastic nature of 

appliance demand

Step 4: If Probi(t)*CFi < Rnd(), 

START appliance i:

CLL (cycle length left) = CLi

CFi = Calibration factor

Goal 2: Reflect 

time-preference of 

using appliances

Goal 1: 

Reproduce 

average U.S. 

household

Step 1: Household configuration

Step 2: Appliance operating 

characteristics Pi, CLi, Ci

Pi = Power rating; CL= Cycle length

Ci = Cycles per day

Step 3: Mapping corresponding 

activity profile to appliance i

CFi

Appliances 1 2 ... i
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13

of activities to corresponding appliances was explained and validated by Capasso et al. [22]. The 

simulated demand profiles, of each appliance individually as well as the household in aggregate, were 

subjected to various tests to confirm the fidelity of the model.

4.1 Presentation of data and steps to build up the demand model

Step 1: Household configuration and Step 2: Appliance operating characteristics

We selected appliances according to two rules: 1) Match the total electricity consumption (in kWh) and 

demand profile (in kW) of a typical U.S. household; 2) match the consumption make-up from various 

appliance types (e.g., air conditioning vs. lights vs. heating, etc.). 

For each appliance, typical power rating, cycle length, and cycles per year were selected and slightly 

adjusted simultaneously within ranges cited in the literature (mostly from the Department of Energy 

(DOE) 2011 Building Energy Data Book, Table 2.1.16 [49] and the DOE Energy Saver [50], see Table 6

for details) so as to render the corresponding annual usage (in kWh) consistent with literature sources 

(mostly from the Residential Energy Consumption Survey (RECS) , see Table 6 for details). 

Table 6. Operating characteristics of typical electric appliances in the residential sector in the U.S.

Appliance Power 

draw

Electricity 

consumption 

per cycle per 

household

Annual 

usage per 

household 

(calculated

Annual 

usage per 

household 

(lookup)

ON 

time Cycles

Calibrati

on factor

(CF) Activity codea Sources

(W) (kWh) (kWh) (kWh) (min)

(n/yea

r) (min-1)

Dishwasherb 1,457 0.69 253 120-512 54 365 4.12547 020203 [24, 49-52]

Microwave oven 1,500 0.15 170 131-209 6 1133 3.71951 020201 [49-52]

Toaster oven 1,400 0.47 52 50-54 20 111 0.36182 020201 [49-51, 53]

Refrigerator 250 0.08 1007 660-1359 20 12089

c 0.04085 [49, 50, 52, 54-56]

Freezer 155 0.05 1120 470-1150 20 21681 0.19075 [49, 51, 52, 56]

Lighting-Bathroom 317 0.16 162

940

31 989 2.23461 010201 [51, 57, 58]

Lighting-Bedroom 200 0.20 124 60 621 0.74326 TEWHERE=1 [51, 58]

Lighting-Living 

Room 256 0.26 215 60 840 1.03289 TEWHERE=1 [51, 58]

Lighting-Dining 

Room 235 0.12 163 30 1387 3.07522 110101 [51, 57, 58]

Lighting-Hallways 207 0.05 91 15 1752 2.04803 TEWHERE=1 [51, 58]

Lighting-Kitchen 250 0.13 228 32 1711 6.17806 020201 [51, 57, 58]

Clothes dryer

2895 2.90 1039 1000-1079 60 359 3.33162 020102 [24, 49-52]

Clothes washerd 2150 0.77 303 110-420 48 392 3.61809 020102 [24, 49-52]

Television 185 0.35 267 222-313 115 752 1.85108 120303 [24, 49-52, 57]

Air conditioning 3500 0.58 3220 2822 10 5520e 96 [50, 54]

Space heater 1,447 1.45 2136 2136 60 1476 0.01639 [49, 50, 54]

Vacuum 1,440 0.84 53 55 35 63 0.56724 020101 [24, 49, 50, 57]

Computers and 

others 100 2.4 876 810 1440 365 1 [49]

a Activity code in the above table is coded by 2011 American Time Use Survey 2011 [57]. Descriptions can be found in the 

coding document. http://www.bls.gov/tus/lexicons.htm

b Dishwasher operated in 4 stages: P1=1457 W, P2=220 W, P3=1457 W, P4=220 W; T1=18 min, T2=18 min, T3=6 min, T4=12 min.

c All 14 and 16 cu. ft. (TBX/CTX models vs. TBF models of past) will have an average run time of between 40 and 52% as do 

compact models,(TA2,4,6). Chest & Upright freezers run 75% to 90% of the time [56].

d Clothes washer is operated on three stages: P1=2150 W, P2=210 W, P3=450 W; T1=18 min, T2=24 min, T3=6 min.

e Assume space heater runs 12 hours per day and mean cycle length is 60 minutes. In use during the winter, i.e. in November, 

December, January and February.
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14

Step 3: Mapping corresponding activity profiles to appliances

For activity profiles, we used 2011 American Time Use Survey (ATUS) data reported by 13,260 

respondents [57]. Each appliance was linked to a corresponding activity with an activity code in Table 6. 

The column of activity codes were obtained from the ATUS. The full lexicons can be found in 

http://www.bls.gov/tus/lexicons.htm. Those with blank activity codes are discussed below. Activity 

probability profiles are displayed in

Figure 8-11. To smooth out artificial spikes, a rolling window of 11 minutes was applied.

4.1.1 Approach to air conditioning

No suitable ATUS activity profile could be found for air-conditioning. Instead, a starting probability 

profile of air-conditioning was reproduced from Reddy, T. A., Figure.1 [59]. Note that the reproduced 

profile is not a starting probability profile but rather an in-use probability profile (while for all the other 

appliances, starting probability profiles are available from ATUS). Without time-varying air-conditioning 

demand profile, the aggregated demand profile for one whole household would have two (Figure 13(a)) 

instead of one (Figure 13(b)) peak over the course of one day. In other words, we cannot map a flat 

starting probability profile to air-conditioning because the time-variance of using air-conditioning is 

significant. Therefore, the in-use probability profile reproduced from Ref. [59] was assigned to airconditioning as an approximation. 

4.1.2 Approach to lighting

A similar difficulty occurs with respect to lighting for which finding a directly related ATUS activity is 

difficult. Addressing lighting in bedroom, living room and hallways, the starting probability profile of 

occupancy being at home and awake (coded as TEWHERE =1) was used as an approximation. Unlike airconditioning, the underlying assumption is that the load demanded by lighting will not contribute to 

shaping the demand profile of one whole household to a large degree. 

4.1.3 Other appliances 

Uniform probability profiles were assigned to refrigerator, freezer and space heater under the assumption 

that using these three appliances is not occupancy related. They do however stochastically turn on and off, 

adding significant noise to the aggregate household profile (see Figure 7). Since power ratings of 

computer and some other rechargeable electronic devices such as mobile phone chargers are all relatively 

low, they will not contribute to a peak during the day but only contribute some base-load 24 hours a day. 

Therefore, in this model, computer and other typical electronic devices were grouped into a single 

appliance. The minimum ON time was set to 1440 minutes making it a base load without ever turning off.

Step 4 & Step 5: Calibration and programming

4.1.4 Calibration (all appliances)

Since parameters where drawn from multiple sources, it is necessary to calibrate (or normalize) the on 

probability profiles to render the total starting probabilities over one year consistent with typical total 
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15

annual cycle times for each appliance. Average number of cycles per day and duration of each cycle, for 

each appliance separately, were calibrated to follow data from the Buildings Energy Data Book (Table 

2.1.16; [49]) and the RECS report [51].

Starting Probi

(t) =

Ni,home(t)

13260

In − use Probi

(t) =

Mi,home(t)

13260

(3)

(4)

Where Ni,home(t) denotes #respondents to START activity i (at home/yard) at time step t, 

Mi,home(t) denotes #respondents to DO activity i (at home/yard) at time step t,

13260 is the total number of participants in the survey.

CFi =

CYCi

1440−(CLi−1)×CYCi

1440

∑ Starting Probi

(t)

t=1440

t=1

(5)

Where CFi denotes the calibration factor of appliance i,

CYCi denotes reference cycles per day for appliance i,

CLi denotes the cycle length of appliance i. 

The flow chart in Figure 6 is used to illustrate the agent-based logic to randomly generate a demand 

profile for one household. 
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16

Figure 6

3

. Flow chart of agent-based logic in the appliance demand profile model. 

 

3 Continues until the total set time T (e.g., 525,600 minutes for one year or 1440 minutes for one day) is reached.

StatusFlag = 0

START Appliance

StatusFlag = 1

CycleTimeLeft = MeanCycleLength 

-1

Power = 

GetPowerUsage(CycleTimeLeft)

 Minute = Minute + 1 

Rnd() < CF*

ActivityProbability

Minute = T

 Appliance = Appliance+ 1

Appliance = n

YES

YES

CycleTimeLeft = 0

Switch OFF Appliance

StatusFlag = 0

CycleTimeLeft =

CycleTimeLeft - 1

NO

YES

NO

YES

NO

NO

 Appliance = 1

Minute = 1

HasAppliance = 1 NO

YES
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Step 6: Aggregate appliances demand profiles to form household demand profiles

Figure 7 shows an example how appliances demand profiles are aggregated to form the demand profile 

for one typical household in the U.S. in one random summer day. 

Figure 7. An example of one household demand profile generated by aggregating appliances demand profiles

4.2 Testing

For individual appliances, we tested (i) on/off cycling; (ii) power and electricity draw, cycles per year, 

and total electricity consumption per year; and (iii) the average daily demand time profile. For the 

household aggregate demand, we tested (iv) average demand time profile (differentiated by season); (v) 

total kWh draw per year; and (vi) % contribution of appliance types to total annual kWh consumption (air 

conditioning vs. lighting vs. heating, etc.). The model was found to capture above features (i)-(vi) 

adequately.

Three groups of tests were performed. (1) On individual appliance level (Sec. 4.2.1), simulations for a 

large number of days should yield, for each appliance, the same average cycles per year and the average 

daily electricity consumption as the input parameters listed in Table 6. In addition, the average daily load 

profiles for each appliance were compared with the corresponding in-use probability profiles from ATUS

(

Figure 8-11). (2) On household level (Sec. 4.2.2), the simulated average daily electricity usage profile 

(simulated over hundreds of days and thus reflecting the aggregate profiles of hundreds of households on 

a single day) was compared to RECS [54] (Figure 12) as well as sector-level daily demand profiles 

reproduced from EMET Consultants Pty Ltd, Figure 4.1 and Figure 4.2 [60] (Figure 13). (3) Finally, 

cycle lengths observed for a subset of appliances available from the Pecan Street Research Institute [61]

were compared with the corresponding simulated cycle lengths. The comparison results confirmed that 

the simulated cycle lengths are within the measured ranges (not shown).

0

1000

2000

3000

4000

5000

6000

7000

8000

12 AM 6 AM 12 PM 6 PM

(W)

Time of day

Air conditioning

Television

Clothes washer

Clothes dryer

Lighting-Kitchen

Lighting-Hallways

Lighting-Dining Room

Lighting-Living Room

Lighting-Bedroom

Lighting-Bedroom

Freezer

Refrigerator

Toaster oven

Microwave oven

Dishwasher
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4.2.1 Individual appliance level and model convergence 

As shown in Table B.1 individual appliance demand loads were averaged over a large number of days to 

yield the results on a “converged” day. For each minute individually, the relative standard deviation of the 

mean (RSEM) power draw is less than 5%. Generally, the shapes of modeled mean curve loads for each 

appliance are in agreement with the shapes of in-use probability profiles from ATUS (

Figure 8). Peaks are reproduced well. Figure 9 for air-conditioning is of particular interest here. Instead of 

the starting probability profile, in-use probability profile was used as an approximation. The simulated 

mean load curve displays a slight right-shift in comparison to its in-use probability profile. Still, the 

overall time-preference is captured well. One methodological source of the small mismatches visible e.g., 

in Figure 10 is the CF. The current way to calculates CFs involves an approximation made for available 

minutes in Eq.(5). However, instead incorporating accurate minute-by-minute CFs would be too timeconsuming computationally. Lastly, the resulting mean load curves for lighting in the bedroom, living 

room, and hallways were compared to the probability profile reflecting when occupants were at home and 

awake. Due to the mismatch between appliance cycle lengths (no more than 1 hour for these three 

appliances, see Table 6 and the activity (being at home and awake) lengths (commonly more than 1 hour), 

the simulated curves and the comparison curves display mismatches in Figure 11. This mismatch however 

does not substantially affect our results and conclusions because the kW draw of lighting appliances is 

small in comparison to overall power demand.

In summary, the model is able to capture the time-preferences well and the daily electricity consumption 

value from literatures (see Table B.1) is reproduced well. Possible future refinement lies in the 

improvement of starting probability profiles. Other sources of starting probability profiles for airconditioning and lightings are desirable. A model to generate lighting load curve based on the indoor 

luminance may be included in the model in the future. 

(a) Dishwasher (b) Microwave oven

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

12 AM 6 AM 12 PM 6 PM

[kW]

Time of Day
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19

 (c) Toaster (d) Lighting in the bathroom

(e) Lighting in the diningroom (f) Lighting in the kitchen

(g) Clothes washer (h) Clothes dryer

(i) Television (j) Vacuum cleaner

Figure 8

4

. Mean load curve from simulations and in-use probability profile from ATUS [57]. 

 

4 The probability profiles are plotted on the secondary axis. The solid lines represent the mean load curves from 

simulations while the long-dashed lines represent the in-use probabilities. 
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20

Figure 9

5

. Mean load curve from simulations and in-use probability profile for air-conditioning. 

(a) Refrigerator (b) Space heater 

 (c) Freezer (d) Computers and other rechargable electronic devices

Figure 106. Mean load curve from simulations and flat in-use probability profile

 

5 The in-use probability profile was reproduced from Reddy, T. A., Figure 1 [59] Reddy TA. Statistical analyses of electricity use 

during the hottest and coolest days of summer for groups of residences with and without air-conditioning. Energy. 1990;15:45-61.

6 No ATUS [57] US Bureau of Labor Statistics. 2012 American Time Use Survey. United Department of Labor; 2013. data are 

available for the appliances in Figure 8. Therefore, flat starting probability profiles were created. For these appliances, the in-use 

probability profile is also flat. For an average demand profile, the impact from these appliances are small because demands from 

them are not time-variant and thus will not change the shape of the demand profile a lot. For one single day, these appliances 

compromise a large portion of the single household daily electricity consumption.
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21

(a) Lighting in the bedroom (b) Lighting in the livingroom 

 (c) Lighting in the hallways 

Figure 117. Mean load curve from simulations and respondents being at home and awake probability profile.

4.2.2 Household level

The main purpose here was to test the aggregate appliance demand profiles in comparison with the RECS 

data for per average household in U.S. (Table CE 2.1 [62]). From Table B.1, the average daily electricity 

consumption per household is 30.6 kWh which is only 1% less than data given by 2009 RECS data (31 

kWh). The pie chart in Figure 12 also displays a good agreement between 2005 RECS results (Table 

US14 [54]) and simulation results from the model. Numbers are portions of total annual electricity 

consumption in the residential sector. 2009 RECS data were only partly available in 2012 when the 

comparison was conducted. Therefore 2005 RECS data were used instead where 2009 RECS data were

not available. 

 

7 No ATUS data are available. Here, probability profiles simply reflects the likelihood of respondents being at home and awake. 

Mismatches exist but lighting only compromise a small portion of the daily electricity consumption per household (see Table 6).
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22

(a) RECS 2005 (b) Simulation results

Figure 12. Pie chart comparison between RECS 2005 data and simulation results

In Figure 13, average demand profile from simulations are plotted vis-à-vis with EMET reported 

aggregated demand curves [60] for summer days and winter days, respectively. Note that the simulation 

model correctly predicts two demand peaks per day during non-summer months (Figure 13 (b)) while the 

additional air conditioning during the summer results in only one obvious peak (Figure 13 (a)). 

(a) Summer

(b) Winter

Figure 13.

8 Mean load curve from simulations versus aggregated demand curves reproduced from EMET[60]. 

 

8 Solid lines represent the yielded mean load curves while the long-dashed lines represent the reference demand 

curves. 

Space 

heating

14%

Air 

conditioning

16%

Water 

heating

19%

Refrigerator

10%

Other 

appliances 

and lighting

41%

Space 

heating

15%

Air 

conditioning

19%

Water 

heating

21%

Refrigerator

7%

Other 

appliances 

and lighting

38%

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0

0.5

1

1.5

2

2.5

12 AM 3 AM 6 AM 9 AM 12 PM 3 PM 6 PM 9 PM

[kW] [MW]

Time of day
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23

5 Storage dispatch strategy, operating optimization and economic viability evaluation results

(loadshifting)

9

5.1 Storage dispatch strategy (loadshifting strategy)

Figure 14 shows examples (example for Li-ion battery with 15kWh EC, 80% DoD) of simulated data 

traces for two randomly chosen days. Solid lines represent a random spring summer day while dashed 

lines represent a random spring day. Dotted lines in Figure 14 (b) indicate max. (dis)charging rate (1C for 

Li-ion battery). Implementing a straight forward arbitrage strategy, storage charging commences at 10pm 

(indicated by " A " in Figure 14; all letter markers are for solid lines), at the lowest possible charge rate 

such that storage reaches full capacity by 10am (see B ) without however causing unnecessary burden on 

the grid (Eq.(2)). From 10am onwards, any appliance – e.g., demand at 12 pm (see C ) reflects the 

aggregate demand of the air conditioning, freezer, and clothes washer (other appliances are off) – is first 

supplied by discharging storage (see D ), thus minimizing purchase of costlier electricity from the grid. 

Whenever the maximum discharge rate (1C, i.e. 1kW per kWh nominal capacity) is reached (not in

Figure 14) or the storage's state of charge (SoC, Eq. (3)) reaches DoD (see E ), the control unit 

supplements electricity from the grid (see F ). Breaching either maximum discharge rates or DoD have 

been demonstrated to lead to early degradation (e.g., [63]) and are thus avoided.

Charge rate =

EC

EffS to A ∙ EffA to S

12

SoC(t) = SoC(t − 1) −

DischE(t)

EffS to A

EC ≥ DoD

(6)

(7)

Where EC denotes the effective capacity of storage (see section 3.1),

EffG to S denotes the ratio of electricity stored versus drawn from grid, 

EffS to A denotes the efficiency of energy stored to consumption by appliances,

DoD denotes the healthy depth of discharge,

SoC(t) denotes the state of charge of storage at time step t,

DischE(t) denotes the amount of electricity discharged at time step t.

 

9

In Sec.5, the basic and TOU tariff mentioned are both kWh tariff if not stated otherwise. 
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24

Figure 14. Data traces generated by the loadshifting strategy

0

1

2

3

4

5

6

7

12 AM 6 AM 12 PM 6 PM

(a) Power draw from 

appliances [kW]

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

-16

-12

-8

-4

0

4

8

12

16

12 AM 6 AM 12 PM 6 PM

(b) (Dis)Charging 

[kW]

SOC(t) 

Charging at 1C

Discharging at 1C

Charging/discharging

SoC

DoD

A 

0

1

2

3

4

5

6

7

12 AM 6 AM 12 PM 6 PM

(c) Power draw from 

grid (net of storage) 

[kW]

0

0.01

0.02

0.03

0.04

0.05

0.06

12 AM 6 AM 12 PM 6 PM

(d) Electricity 

charges [$/time]

one random spring day one random summer day

B

C

D

E

F
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25

5.1 Operation optimization and economic viability evaluation model

Using the above model, the storage capacity was varied to maximize profit to the consumer:

Max profit = Electricity billbasic w/o S − (Cost + Electricity billDR with S

) (8)

Where Electricity billDR tariff with S denotes electricity bill for 1 year under the DR tariff (with storage),

Electricity billbasic w/o S denotes electricity bill for 1 year under the basic tariff (without storage),

Cost denotes the financing costs of storage (see Sec. 3.1).

The maximum profit was determined simply by stepwise increasing the effective storage capacity from 

zero to two times the average electricity consumption during peak periods (Epeak). At each increase (10% 

of Epeak), annual payment (=storage cost plus electricity bill) was recorded by the model. Two baselines 

(i.e., cost without storage) were used: (a) Electricity bill for one whole year under the basic tariff before 

installing storage (Electricity billbasic w/o S, shown in Eq.(8)); (b) electricity bill for one whole year under 

the TOU tariff (also without storage) (Electricity billDR w/o S, not shown in Eq.(8)).The rationale for 

considering two baselines is the fact that consumers, even before installing storage, could be on either the 

basic tariff or the TOU tariff. Under certain circumstances such as the specific appliance configuration in 

our model, simply switching from the basic to the TOU tariff (before installing storage) can significantly 

increase the electricity bill (in our case due to much higher day time electricity use from using air 

conditioning in the summer months, see Figure 15). One could argue that for such circumstances the 

savings from arbitrage must be high enough to offset not only the installation and cost of storage but also 

the electricity bill increase that results from switching to the TOU tariff that enables the arbitrage savings 

in the first place. We therefore present economic viability results for both baselines.

5.2 Results

The "typical residential household" devised in our model consumes 11,164 kWh electricity per year, with 

an average daily consumption (all seasons over one year) of 31 kWh (50 kWh/day during summer 

months). We first investigated the cost composition for the two baselines, then optimized the size of 

storage, followed by evaluating the economic viabilities of different storage options. Finally, an analytic 

approach was developed to identify the optimal capacity size and analytic results were compared with the 

empirical results. 

5.2.1 Base case (no storage): Composition of electricity bill and seasonal effects

We first broke down annual electricity bill into eight parts: 1) Cost during peak periods in summer; 2) offpeak periods in summer; 3) peak periods in winter; 4) off-peak periods in winter; 5) peak periods in other 

months (no space heater or air-conditioning is used); 6) off-peak periods in other months; 7) basic 

monthly service charges; and finally 8) financing costs of storage system (including installation).

Figure 15 uses the example of ZnMnO2 battery with 30kWh EC, average-case scenario) to show annual 

payments without storage (the first and second columns); the third column shows payments when buying 

and operating storage. Figure 15 shows a net increase of ~$650 in annual payments (from $2,523, or 26%) 

when switching from basic to TOU tariff (no storage yet installed). The increase is mostly due to raised 

electricity bills for peak periods in the summer. For other months, there is no significant increase or 
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26

decrease in the electricity bill under the two tariffs. In the summer, peak consumption under TOU is 

~$800 higher than those charged under the basic tariff while the less expensive off peak consumption 

under TOU only results in a ~$250 decrease. Higher basic service charges for TOU contribute the 

remaining $100 to the net $650. Generally, basic service charges contribute only a small portion to total 

electricity cost; therefore consumption and load shifting patterns and the supply and delivery portions of 

each tariff are crucial drivers of overall cost and potential arbitrage savings.

Figure 15 also shows a TOU cost structure when using (profit optimized) 30 kWh EC of ZnMnO2

batteries that can supply the entire daily electricity consumption during peak hours in non-summer 

months (and a portion during summer months). This leads to annual arbitrage savings of ~$700 compared 

to the TOU base case ($20 for the basic tariff base case). Since during summer months only a portion of 

peak-consumption can be loadshifted to off-peak times, installing more EC than 30 kWh would decrease 

the annual electricity cost. However, since such additional capacity would essentially remain idle during

non-summer months (no return on investment), annual profit would decrease. Therefore, 30 kWh EC, for 

this particular battery technology, (dis)charging losses and DoD, is the optimal size. This is illustrated 

further in Sec. 5.2.2. 

Figure 15. Annual payments breakdowns (under the kWh tariff) 

5.2.2 Optimal effective storage size

Figure 16 shows the impact of increasing EC on annual payments (best-case scenario) for a selection of 

storage technologies. Payments include financing for storage purchase (best-case scenario) and 

installation as well as electricity bills. Error bars indicate residual uncertainty of the stochastic simulation 

(standard error of the mean). See Sec. 5.2.3 for other storage technologies not displayed in the figure.

615

1,428

69

406

156

464

429

588

0

381

169

431

284

449

0

220

95

264

189

292

292

982

0

500

1000

1500

2000

2500

3000

3500

Basic tariff without

storage

TOU tariff without

storage

TOU tariff with storage

Annual payments ($/year)

Storage and installation cost

Basic service charges

Spring and fall off peak periods

Spring and fall peak periods

Winter off peak periods

Winter peak periods

Summer off peak period

Summer peak periods

∑=$2,523

∑ = $3,175

∑ = $2,502
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27

Li-ion batteries exhibit a continuous increase in annual payments while NaS batteries, after a stepincrease in annual payments (due to installation costs), exhibit a small decrease, followed again by an 

increase. For ZnBr, ZEBRA (NaNiCl batteries), Metal air and ZnMnO2 batteries, significant decreases in 

annual payments can be achieved. NiCd batteries, flywheel, Superconducting Magnetic Energy Storage 

(SMES) and NiZn batteries (not shown in Figure 16) exhibit payments higher than Li-ion batteries. The 

super capacitor option shows trends similar to NaS batteries. Payments simulated for Pb-acid batteries are 

almost identical to those for ZnBr batteries. For Compressed Air Energy Storage (CAES), see Sec.7.4.

Figure 16 suggests three broad classes of storage technologies when determining the optimal storage size 

to achieve lowest costs: (1) Li-ion or NaS batteries do not provide any economic benefits (even in the best 

case scenario). (2) For Pumped Hydro Storage (PHS) and Metal air batteries, the exact size is not crucial: 

As seen in Figure 16, an increase in EC from 30 kWh to 50 kWh leads to only minor increases in annual 

payments (see explanation in Sec. 5.3). (3) For the remaining storage technologies, sizing should be 

conducted accurately. For example, increasing EC of ZnBr batteries from 30 kWh to 50 kWh would cause 

~$800 additional annual payments.

Figure 16. Annual payments for various storage technologies and capacities (loadshifting). Error bars represent one standard 

deviation above and below the mean.

2200

2300

2400

2500

2600

2700

2800

2900

3000

20 25 30 35

Annual payments ($)

EC (kWh)

ZnBr

Metal air

ZEBRA

ZnMnO2

(b)

1000

2000

3000

4000

5000

6000

7000

0 10 20 30 40 50 60

Annual payments ($)

EC (kWh)

Basic tariff baseline

Li-ion

TOU tariff baseline

(a)

NaS

ZnBr

ZEBRA

Metal air

ZnMnO2

PHS

2700

2800

2900

3000

3100

3200

3300

3400

3500

3600

3700

0 5 10

Annual payments ($)

EC (kWh)

Li-ion

Metal air

NaS

ZnBr

ZEBRA

ZnMnO2

PHS

(c)
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28

5.2.3 Economic viability

Table 7 summarizes the optimization results for best-case and average-case scenarios for all storage 

technologies. Profits from arbitrage savings versus the basic tariff and the TOU tariff baselines are also 

shown. Optimal effective storage capacity span a wide range depending on the storage technology, 

12 kWh~37 kWh in the best-case scenario and 7~35 kWh in the average-case scenario. For economically 

viable technologies, annual profits range from as low as $8 for the super capacitor (0.3% of annual 

electricity cost without storage, TOU baseline) to $1,465 for PHS (46%). Because of the additional cost 

increase when first switching from the basic to the TOU tariff (before installing storage, Sec. 5.2.1), more 

technology options are economically viable when assuming the TOU baseline versus the basic tariff 

baseline. Only PHS and CAES are economically viable in both scenarios and both baselines. This raises 

the question of their technological viability for residential settings (see Sec. 7.5). Finally, flywheel, SMES, 

NiZn, NiCd, NaS and Li-ion batteries are not economically viable for either scenario or baseline, and the 

aforementioned $8 profit for super capacitors is below the accuracy of the stochastic simulation (see 

Figure 16). We thus concluded that – for the average U.S. household consumption profile and Con Edison 

tariffs used in this study – short-term storage technologies (flywheel, super capacitor, and SMES) as well 

as some emerging batteries are not economically viable.

Table 7. Optimal effective capacity and maximum profits for two scenarios (loadshifting)

Best-case scenarioa Average-case scenariob

Optimal 

capacityc

(kWh)

Annual 

payment

($/year)

Profitd 

($/year)

Profite

($/year)

Optimal 

capacityc

(kWh)

Annual 

payment

($/year)

Profitd 

($/year)

Profite

($/year)

Flywheel - 3542 -1013 -344 - 3847 -1315 -664

Conventional batteries

 Metal air 33 2742 -213 456 30 3121 -590 61

 Lead-acid (Pb-acid) 28 2690 -161 509 - 3590 -1058 -407

 Nickel-cadmium (NiCd) - 3661 -1132 -462 - 3805 -1273 -622

Advanced batteries

 Lithium-ion (Li-ion) - 3474 -945 -275 - 3729 -1198 -546

 Sodium sulfur (NaS) 12 3302 -774 -104 - 3707 -1176 -525

 Sodium nickel chloride (NaNiCl ZEBRA) 30 2442 87 757 28 2704 -172 479

Flow batteries

 Zinc bromine (ZnBr) 28 2677 -149 521 - 3476 -945 -294

 Vanadium redox (VRB) 30 2450 79 749 10 3261 -729 -78

 Nickel zinc (NiZn) - 3529 -1000 -330 - 3513 -982 -330

 Zinc manganese dioxide (ZnMnO2) 30 2303 226 896 30 2510 22 673

Super capacitor 12 3191 -662 8 7 3412 -880 -229

CAES 37 2073 456 1126 33 2292 239 890

PHS 37 1733 796 1465 35 1818 713 1365

SMES - 3500 -971 -302 - 3974 -1442 -791

a The best-case scenario uses the lowest cost available in the literature.

b The average-case scenario uses the average (geometric mean) of lowest and highest costs in the literature.

c 

‘-‘indicates optimal storage is zero because any storage would only increase overall cost. Optimal storage size above zero but 

negative profits indicate cases where larger storage means lower cost, however not low enough to offset cost from change in 

tariff and installation. 

d Compared with the payment charged by the basic tariff without installing storage. Positive values of profit indicate the 

evaluated storage option is economically viable and vice versa. 

e Compared with the payment charged by the TOU tariff without installing storage.

5.3 Analytic approach to optimal size of storage

The above model determines the economic viability and optimal EC via a trial-and-error approach. To 

understand the underlying effects more fundamentally we derived an analytical formula that can predict 
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29

optimal EC directly, based on statistical parameters obtained from simulating only the demand profile 

(without also simulating storage dispatch and electricity cost).

Within the above scheme, the number of kWh shifted (ES), which drive cost savings via arbitrage, cannot 

exceed the effective capacity (EC), which drives financing costs for storage. Therefore, optimal EC can 

be expected to be approximately equal to the daily-average consumption during peak times Epeak

(~30kWh, see Table 1). Crucially, however, Epeak varies stochastically from one day to the next and 

systematically between seasons. Optimal EC, therefore, is driven by the trade-off between gaining more 

arbitrage savings during days with relatively high Epeak and wasting idle capacity during days with low 

Epeak. Now assume a set E comprised of N days’ Epeak (across all seasons) and let yet-to-be-determined 

optimal EC be denoted by E

m

peak. m indicates the m-th Epeak in the set when sorted from smallest to largest. 

This means that for m days of the set, EC can shift 100% of the Epeak to off-peak hours. For the remaining 

(N-m) days, only a portion of Epeak can be shifted. If EC is increased to E

m

peak+ΔE, then additional (N-m)

days in the set can shift an additional portion of their Epeak, namely ΔE, from peak to off-peak hours. 

Resulting incremental arbitrage savings are (N-m)·S*·ΔE. Resulting incremental storage costs are 

N·C*·ΔE, where S* and C*, both in $/kWh, are given by:

S

∗ = Ppeak −

Poff−peak

EffS to A ∙ EffG to S

(9)

C

∗ =

PC ∙ FCR

EffS to A ∙ DoD (10)

Where Ppeak and Poff-peak denote the costs per kWh during peak and off-peak hours, respectively,

EffG to S denotes the ratio of the amount of electricity stored over the amount of electricity 

drawn from the grid (see Figure 4 for more details), 

EffS to A denotes the efficiency of converting energy from storage to appliances,

DoD denotes the healthy depth of discharge,

PC denotes the purchase cost of storage per kWh nominal capacity (excl. installation),

FCR denotes the annual finance cost rate (principal repayment plus 10% interest, see Sec.

3.2).

Now recognizing that profit can be increased so long as additional arbitrage savings for any incremental 

ΔE are higher than additional storage costs, we find the optimal EC by requiring: 

F(Epeak

m ) = 1 −

C

∗

S

∗

(11)

Where F(E) denotes the portion of Epeak in set E that are smaller than E

m

peak.

E

m

peak can be solved by referring to the m-th Epeak in the sample ranking from smallest to largest when

m = N ∙ (1 −

C

∗

S

∗

)

(12)

The value of C* varies substantially across storage technologies, due to varying costs and operating 

characteristics. In contrast, S* does not vary much across storage technologies. For example, Metal air 

batteries (C*= 0.011 in best-case scenario) and PHS (C* = 0.002) exhibit nearly flat cost after EC reaches 
This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.GCR.14-978

30

30 kWh (Figure 16). For comparison, C* for ZnBr batteries is 0.069 (best-case scenario), leading to a 

marked rise in annual payments once EC is increased beyond the optimal capacity (Figure 16). Generally, 

higher ratios of C* to S* will lead to smaller optimal EC (Eq.(11)). Note that storage size is optimized 

across one year. Tradeoffs occur between different seasons because demand profiles and tariffs are 

different. For NaS batteries for example, optimal EC in the summer is 31 kWh (in best-case scenario). But 

in other seasons S* is smaller and therefore any EC increase in seasons other than summer will lead to 

smaller profits. As a result of this tradeoff, the optimal EC for NaS batteries, across the full year, is 

12 kWh (Table 7). 

In summary, optimal EC can be determined as a function of the histogram of Epeak, the operating 

characteristics and cost of storage, and the peak versus off-peak kWh charges. In contrast, installation cost 

and fixed monthly electricity fees affect the achievable profit (Eq.(8)) but not optimal EC.

6 Storage dispatch strategy, operating optimization and economic viability evaluation results

(peak reduction)10

6.1 Storage dispatch strategy (peak reduction strategy)

Figure 17 illustrates the storage dispatch strategy for the kW tariff (example for ZnMnO2 battery with 10 

kWh EC, 90% DoD, the upper limit (UL) is set as 2.5 kW) The long dashed line in Figure 17(a) indicates 

the UL. In Figure 17(b), the short dashed lines indicate max. (dis)charging (1C for ZnMnO2 battery. In 

Figure 17(c), the dotted line is measured on the basis of 1 minute while the solid line is averaged on the 

basis of 30 minutes. 

The goal is to reduce the peak demands for each month to the pre-assigned UL by utilizing storage. When 

the aggregate demand from the appliances exceeds the UL (e.g., at A in In Figure 17; all letter markers 

are for solid lines), the grid only supplies it with the power equaling the UL (see C); the remaining 

demand is supplied by discharging storage (see B). On the contrary, when the aggregate demand from 

appliances is below the UL (e.g., at D), storage (if not full) is charged at the dynamically calculated 

charging rate (see E): The combined power draw from the storage charging and the appliances demands 

could not exceed the UL (see F). Whenever the maximum discharge rate (1C i.e. 1 kW per kWh nominal 

capacity) is reached (not in Figure 17) or the storage’s state of charge reaches DoD (see G), the control 

unit supplements electricity from the grid. In the end, the measured synthetic demand from appliances and 

storage is averaged over a 30-minute window as specified by Con Edison (see H; the dashed line is the 

minute-by-minute demand profile while the solid line the averaged demand profile). 

 

10 In Sec. 6, both the basic and the TOU tariff are kW tariff, unless stated otherwise.
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31

Figure 17. Data traces generated by the peak reduction strategy.

6.2 Operating optimization and economic viability evaluation model

In contrast to the loadshifting control strategy which works only in the context of the TOU tariff, this 

specific peak reduction control strategy is not time-of-use constrained and can possibly reduce the peak 

demands, thus reducing the electricity bills under both the TOU tariff and the basic tariff. However, note 

that there is the “10 kW rule” specified by the basic tariff: The minimum peak demand during the billing 

period is 10 kW. Consider that monthly peak demands (averaged every 30 minutes) simulated by our 

model are less than 10 kW. The peak demand reduction will not lead to a reduction in the electricity bill 

charged under the basic kW tariff, still charged for 10 kW. On the contrary, since there is no such “10 kW 

0

1

2

3

4

5

6

7

8

9

10

12 AM 6 AM 12 PM 6 PM

(a) L(t): Power draw 

from appliances 

[kW]

Upper limit 

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

-15

-10

-5

0

5

10

15

12 AM 6 AM 12 PM 6 PM

SOC(t) (b) (Dis)Charging 

[kW]

SOC

Charging/discharging

Charging at 1C

Discharging at 1C

0

1

2

3

4

5

6

7

8

9

10

12 AM 6 AM 12 PM 6 PM

(c) L'(t): Power draw 

from grid (net of 

storage) [kW]

A 

D 

F B 

H 

G 

C 

E 
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32

rule” in the TOU tariff, for a typical U.S. household as modeled in this study, the peak reduction control 

strategy is used under the TOU tariff only. 

Using the above agent-based demand model and control strategy, the storage EC and the operating UL

were varied separately to maximize profit (Eq. (8)) to the consumer under the TOU tariff. The maximum 

profit was determined by stepwise increasing the effective storage capacity geometrically from zero to the 

average daily electricity consumption (20% increase at each step) and adjusting the UL geometrically 

from 2 kW to 6.3 kW (10% increase at each step) for each EC. The steps were selected based on the 

preliminary results. For each case, annual payments were recorded and compared with two baselines: (a) 

The electricity bill for one whole year under the basic tariff before installing storage (b) the electricity bill

for one whole year under the TOU tariff before installing storage. 

6.3 Results

The "typical residential household" devised in our model consumes 11,164 kWh electricity per year, with 

the average peak demand (averaged over 30 minutes) of 6.511 kW (during summer months) and 5.7 kW 

(during the remaining months). We first investigated the cost composition for the two baselines, then 

optimized the size of storage and the operating UL, followed by evaluating the economic viabilities of 

different storage options. 

6.3.1 Base case (no storage): Composition of electricity bill and seasonal effects

Similar to what we have done for the loadshifting model, we broke down two baselines into seven parts to 

investigate their cost composition: 1) Demand cost in summer; 2) energy cost in summer; 3) demand cost 

in winter; 4) energy cost in winter; 5) demand cost in other months; 6) energy cost in other months; 7) 

financing costs of storage system (incl. installation cost).

In Figure 18, the first and second column show payments without storage. The third column shows 

annual payments when buying and operating storage under the TOU tariff (by using peak reduction 

strategy described in Sec. 6.1). Figure 18 shows a decrease of ~$1,500 when one switches from the basic 

tariff to the TOU tariff with no storage installed. The difference mainly comes from the ~$560 decrease in 

the demand cost in winter and the ~$800 decrease in the demand cost in spring and fall months. This big 

difference may be partly due to the “10 kW rule” embedded in the basic tariff. Rather than seeing a 

decrease under the TOU tariff, the summer demand costs remain almost unchanged. For summer months, 

the average peak demand is still less than 10 kW (averaged over the course of 30 minutes), indicating that 

that the 10 kW rule’s impact should still remain but be offset by the costlier summer TOU tariff, without 

storage being installed or the consumer’s electricity consumption habits being altered. 

Unlike the TOU kWh tariff, which incurs an increase in the annual payments when a consumer switches 

from the basic kWh tariff and no storage is installed, the TOU kW tariff costs less in terms of energy cost 

throughout the year. Nevertheless, the reduction in the annual energy consumption cost is only $81 in 

total for one whole year. 

 

11 Although the simulated peak demand for one household is less than 10 kW, SC 8 is still considered to be available 

for the modeled household because two or more households can choose to hold one single account, which is 

possibly eligible to use SC 8. 
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33

Figure 18. Annual payments breakdowns (under the kW tariff).

The third column in Figure 18 is based on the ZnMnO2 battery of 10 kWh EC with an UL of 2.5 kW. By 

utilizing this storage and the control algorithm elaborated above, we expect a ~$700 reduction in the 

annual payments per year: The summer demand cost is expected to be reduced by ~$600 and followed by 

a ~$320 reduction for winter months, then a $300 reduction for spring/fall months. Energy charges are 

slightly increased ($20) compared with those charged under the TOU tariff before storage is used. 

6.3.2 Optimal effective storage size and optimal operating upper limit

The surface plot of Figure 19 shows an example of the varying annual payments by installing ZnMnO2

batteries with varying EC and UL. The EC geometrically increases from 0.1 kWh to 34 kWh at 20% 

increase at each step. The UL geometrically increases from 2 kW to 6.5 kW at 10% increase at each step. 

The optimal EC and the optimal operating UL were identified by the lowest point on the surface. Figure 

20 plots a selection of lines (obtained from Figure 19) at controlled ECs or controlled ULs. 

1,064 1,017

408

386 361

371

1,172

608

291

339

303

309

1,527

727

427

210

190

194

521

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Basic tariff without

storage

TOU tariff without

storage

TOU tariff with storage

Annual payments ($/year)

Storage financing cost

Spring and fall energy charge

Spring and fall demand charge

Winter energy charge

Winter demand charge

Summer energy charge

Summer demand charge

∑=$4,698

∑=$3,207

∑=$2,519
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34

Figure 19. Surface plot of annual payments with varying ECs and varying ULs (peak reduction).

Figure 20(a) shows how the annual payments change with the UL on the horizontal axis. In the figure, 

each line represents one case with one specific EC. A general trend can be found that the annual 

payments first decrease, followed by increases when the UL increases gradually from 2 kW to 6.5 kW. 

This can be explained by looking into how the demand profiles would respond by implementing different 

ULs (Figure 21and Figure 22). 

Figure 20. Annual payments variations at controlled ECs or controlled ULs (peak reduction)

When ECs are small (e.g., EC = 0.3 or 0.4 kWh in Figure 20(a)), the annual payments are reduced by 

installing small size storage operated at the UL around 4 kW. When EC is moderate (e.g., EC = 2.7, 4.6, 

6.6 kWh in Figure 20 (a)), on certain days, lower UL (e.g., 2 kW) may lead to lower peaks during the day, 

2

2.4

2.9

3.5

4.3

5.2

6.3

2500

2700

2900

3100

3300

3500

3700

3900

4100

4300

UL(kW)

Annual payments ($/year)

EC(kWh)

4100-4300

3900-4100

3700-3900

3500-3700

3300-3500

3100-3300

2900-3100

2700-2900

2500-2700

2 2.7 3.5 4.7 6.3

2500

2700

2900

3100

3300

3500

3700

3900

4100

4300

UL(kW)

Annual payments ($/year)

2000

2500

3000

3500

4000

4500

1 2 3 4 5 6 7

Annual payments ($/year)

UL(kW)

EC 0.1 EC 0.3 EC 0.4

EC 0.9 EC 1.3 EC 2.7

EC 4.6 EC 6.6 EC 13.7

EC 23.7 EC 34.2

(a)

2500

2700

2900

3100

3300

3500

3700

3900

4100

4300

Annual payments ($/year)

EC(kWh)

2000

2500

3000

3500

4000

4500

0.1 1 10

Annual payments ($/year)

EC (log10 kWh)

UL 2

UL 2.4

UL 2.7

UL 2.9

UL 3.5

UL 4.3

UL 5.2

UL 6.3

(b)
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35

but the capacity constraint prevents it from lowering the peaks for other days during the month: The 

monthly peak demand to be charged will still remain the same. For example, Figure 21displays the 

measured loads by using ZnMnO2 battery sized at the EC equaling 4.6 kWh but implementing different 

ULs (2 kW, 3.2 kW and 6.3 kW). For the purpose of comparison, the original minute-by-minute 

aggregate appliances demand profile (solid grey line) and the averaged one (dashed black line) without 

using storage are also plotted. Around 5 PM – 6 PM, however, the 2 kW UL results in a demand of 4 kW 

due to the insufficient available capacity of storage. In contrast, with batteries that have not yet been 

dumped, the case with the UL of 3.2 kW successfully reduces the peak to 3.2 kW. In this case, the higher 

UL results in lower peaks in comparison to those that result from a lower UL. However, when the UL is 

higher than the optimal one, the ruled demand is higher (e.g., when UL is 6.3 kW (green line) in Figure 21

(a)), thus the electricity bills increase. 

Note that instead of reducing the daily peak demands, a high UL (e.g., 6.3 kW) may result in a load higher 

than the original load without using storage (see the green line in Figure 21(a)), when the original load is 

below the UL. During that time slot (30 minutes before 12 AM in Figure 21(a)), the grid refills the storage 

which had been discharged previously. In addition, some extra electricity goes into losses during the 

(dis)charging processes. 

Figure 21. Demand profile simulations and storage (dis) charging patterns by implementing different operating ULs (EC = 4.6 

kWh).

0

1

2

3

4

5

6

7

8

12 AM 6 AM 12 PM 6 PM

Power draw from the grid (kW)

Time of day

UL 2

UL 3.2

UL 6.3

No storage (averaged)

No storage

(a)

-6

-5

-4

-3

-2

-1

0

1

2

3

4

12 AM 6 AM 12 PM 6 PM

Charging/discharging (kW)

Time of day

UL 2

UL 3.2

UL 6.3

(b)
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36

When the EC is higher (e.g., EC = 23.7, 34.2 kWh in Figure 22), the optimal ULs are reduced with 

increased ECs. However, although the EC is as high as 23.7 kWh, the 2 kW UL target is not yet fulfilled

(see Figure 22). In both Figure 21 and Figure 22, the demand loads are equaling or above 2 kW most of 

the time in both cases, indicating that when the UL is as low as 2 kW, the storage has taken every chance 

to get charged. Further reducing the loads requires a much higher capacity which stays idle for most of 

time because no available time slots can be found to re-charge this amount of capacity. 

Figure 22. Demand profile simulations and storage (dis)charging patterns by implementing different operating ULs (EC = 23.7 

kWh)

Looking into the plots with the axis of EC (Figure 20(b)), each line represents a case with a certain UL. 

The annual payments first decrease, then increase. As discussed above, the higher capacity can effectively 

reduce the peaks during days and months, thus resulting in lower peaks, which comes with a penalty of 

the higher storage cost. Note that although in Figure 20(a), optimal UL generally decreases with higher 

EC, optimal EC does not always increase with lower UL (see Figure 20(b), blue versus red trace). As 

explained above, in order to further reduce the loads to remain below 2 kW from 2.42 kW, possibly much 

more capacity is needed. By weighing the largely incurred financing cost of storage against the relatively 

small potential electricity bill reduction, the model determines that a smaller capacity which is insufficient 

to get the loads below or closer to the UL is the optimal solution. 

In the end, the energy cost can decrease or increase the annual payments in two ways: It can 1) increase 

the annual payments due to the additional cost for the energy losses during the storage 

0

1

2

3

4

5

6

7

8

12 AM 6 AM 12 PM 6 PM

Power draw from the grid( kW)

Time of day

UL 2

UL 2.42

UL 6.3

No storage (averaged)

No storage

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

12 AM 6 AM 12 PM 6 PM

Charging/discharging (kW)

Time of day

UL 2

UL 2.42

UL 6.3
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37

charging/discharging processes, or 2) possibly decrease the annual payments due to the arbitrage savings 

from loadshifting. For the latter, the peak reduction control algorithm possibly reduces the loads and the 

electricity consumption during peak periods simultaneously. However, the potential of the arbitrage 

savings is limited: Under the TOU kW tariff, the difference between the peak energy charge rate and the 

off peak charge rate is only 2.5 cents per kWh shifted electricity in summer months, and 1.4 cents per 

kWh shifted electricity in other months (Table 2). Assuming storage of 30 kWh EC, the maximum 

potential for arbitrage savings under the TOU kW tariff is:

2.5 × 30 × 92 + 1.4 × 18 × 120 + 1.4 × 9 × 153 = 11851.8 cents/year = $118.5/year12

$118.5 per year is considerably smaller than the annual payments (more than $2000 per year). In terms of 

energy losses, the energy cost is between 6 to 8 cents per kWh electricity consumption (Table 2), which 

should be paid attention to when the storage has low efficiencies. Seen from Figure 21(b), when the EC is 

4.6 kWh the lower UL tends to result in more frequent charging/discharging, thus more energy losses. 

However, when the EC is 23.7 kWh in Figure 22(b), the optimal UL (2.42 kW) leads to higher energy 

losses in comparison with the UL of 2 kW. Besides, by comparing Figure 21(b) and Figure 22(b), more 

energy losses occur when EC is larger. 

In summary, with higher storage EC, the loads can be smoothed effectively with lower optimal UL. 

However, to further reduce the loads, the EC should be increased exponentially. Otherwise, given an 

insufficient storage capacity (e.g., Figure 22), lowering the UL would result in higher loads after the 

storage reaches its DoD in comparison with loads measured by implementing a higher UL. The optimal 

EC and the optimal UL are thus determined by weighing the reduced electricity bills coming with higher 

EC and potentially lower optimal UL against the increased financing cost of storage. The optimal annual 

payments are thus a function of the charging/discharging efficiencies, the financing cost of storage (Eq. 

(1)) and the demand profiles. Table 8 and Table 9 summarize the optimal EC, the optimal UL and the 

minimum annual payments for a variety of storage options in the average-case scenario (Table 8) and in 

the best-case scenario (Table 9), respectively. 

Figure 23 shows the impact of the rising financing cost on the corresponding optimal EC for various 

storage options (average-case scenario). Each marker represents one storage option. Detailed financing 

costs are given in Table 5. An exponential reduction trend can be seen in that decreasing financing costs 

leads to increasing optimal ECs. When the financing costs are less than $50 per kWh per year, the optimal 

ECs are more than 5 kWh. With small financing costs, CAES and PHS are optimized at ECs of more than 

20 kWh. The exponential trend observed can be explained that with low financing costs, the model 

determines that the marginal savings from lowering UL and enlarging EC exceed the marginal financing 

cost of storage. Above, we have explained that in order to get down to a low optimal UL, e.g., 2 kW, the 

increase in EC is remarkable and exponential. On the other hand, after the financing costs grow into more 

than $50 kWh per year, the variations of the optimal ECs with increasing financing costs become less 

obvious.

 

12 According to the testing results of our agent-based demand profile model (see Table B.1), the average electricity 

consumption during peak periods (i.e. the maximum amount of electricity that can be shifted for the purpose of 

arbitrage savings) is 30 kWh for summer days (92 days out of one year), 18 kWh for winter days (120 days out of 

one year) and 9 kWh for the remaining days.
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38

Figure 23. Optimal ECs for a variety of storage costs in the average-case scenario (peak reduction). Error bars represent one 

standard deviation above and below the mean.

Figure 24. Annual payments and optimal ULs for a variety of storage options in the average case scenario (peak reduction). Error 

bars represent one standard deviation above and below the mean.

Figure 24 shows the impact of increasing EC on the corresponding optimal operating ULs and the annual 

payments (average-case scenario) yielded by installing a variety of storage options. As discussed above, 

generally, the higher optimal EC comes with a lower UL, except for metal air batteries (circled points in

Figure 24). Note that according to Table 5, the round-trip efficiency of metal air batteries is 45%, the 

lowest one on the list. It is shown above that when the optimal EC is of a moderate amount, a higher UL

would lead to less electricity getting into/out of storage, and thus also to fewer (dis)charging losses. In 

this sense, the model determines a higher UL for metal air batteries to reduce the energy losses in 

comparison to the expected UL following the trend. 

The minimal annual payments also exhibit a decreasing trend with higher optimal ECs in Figure 24, 

except for the point representing metal air batteries. It is possibly due to the low lifetime of metal air 

batteries (5 years, see Table 5). The low lifetime would result in the high annualized installation fee, 

which makes the annual payments of metal air batteries become higher than the points on the left side. 

When the annualized installation fee is subtracted from the annual payments, the annual payments of 

metal air batteries drop remarkably. 

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400 450

Optimal EC (kWh)

Financing cost of storage ($/kWh-effective*yr) 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25 30 35

Optimal UL (kW)

Annual payments ($/year)

Optimal EC (kWh)

Annual payments (excl. installation fee)

Annual payments (incl. installation fee)

Upper limit

metal air batteries
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39

In summary, the decreasing financing cost of storage leads to the optimal EC increasing. When the 

financing cost is less than $50 per effective kWh per year, the optimal EC increases exponentially. 

Generally, for the optimal UL, a larger optimal EC comes with a lower optimal UL, but exceptions exist 

due to the impact of interactions between energy losses and the operating UL. In the end, the lower annual 

payments can be approached by the lower financing cost of storage (thus the higher optimal EC) and the 

lower optimal UL. 

6.3.3 Economic viability

Table 8 summarizes the optimization results for the average-case scenario for all storage technologies. 

Optimal ECs span a wide range depending on the storage technology, 0.38 kWh – 26.84 kWh in the 

average-case scenario. The optimal ULs range from 2.4 to 4.1 kW in the average-case scenario. As shown 

in Figure 18, the TOU kW tariff costs less compared to the basic kW tariff for the typical consumer 

modeled in this study. Assume that the SC8 consumers would select the kW tariff, which costs less, as 

their base tariff. The modeled minimal annual payments therefore are compared against the TOU kW 

tariff baseline: Storage yielding negative profit against the TOU kW tariff baseline is determined as “not 

economically viable”. Table 8 shows that for economically viable technologies, annual profits (also 

determined by using the TOU kW tariff baseline) range from $161 for the Pb-acid batteries (5% of annual 

electricity cost without storage ,TOU baseline) to $1058 for PHS (33%). Flywheel, SMES, NiCd, Li-ion 

and NaS batteries, all sized at small ECs (0.38 kWh – 2.6 kWh), are not economically viable in the 

average-case scenario. Nevertheless, the gaps are all below $200/year. In the end, though PHS and CAES 

are determined as economically viable storage options, their technological viabilities for residential 

settings are discussed in Sec. 7.

Table 8. Optimal EC, optimal UL and maximum profits for the average-case scenario (peak reduction)

Annual 

payments

($/year) SEMa

Optim

al EC 

(kWh) SEM

Optim

al UL

(kW) SEM

Basic 

w/o 

storag

e SEM

Profitb

($/yea

r)

TOU 

w/o 

storag

e SEM

Profitc

($/year

)

Flywheel 3406 23.16 0.778 0.15 3.724 0.08 4692 2.54 1287 3248 17.30 -158

Conventional 

batteries

Metal air 

battery 2852 20.94 11.63 1.09 2.934 0.06 4692 2.54 1840 3248 17.30 396

Pb-acid 3087 23.64 3.065 0.17 3.511 0.03 4692 2.54 1606 3248 17.30 161

NiCd 3394 26.10 1.819 0.18 3.482 0.07 4692 2.54 1299 3248 17.30 -146

Advanced 

batteries

Li-ion 3320 26.67 1.900 0.20 3.418 0.07 4692 2.54 1372 3248 17.30 -72

NaS 3273 25.87 2.571 0.17 3.546 0.05 4692 2.54 1419 3248 17.30 -25

ZEBRA 2666 16.66 9.271 0.70 2.827 0.07 4692 2.54 2026 3248 17.30 582

Flow batteries

ZnBr 2922 20.10 3.550 0.21 3.479 0.04 4692 2.54 1770 3248 17.30 326

VRB 2769 16.17 4.069 0.30 3.382 0.05 4692 2.54 1924 3248 17.30 479

ZnNi 2999 22.36 3.129 0.18 3.479 0.04 4692 2.54 1694 3248 17.30 249

ZnMnO2 2550 18.20 10.23 0.83 2.779 0.09 4692 2.54 2142 3248 17.30 698

Super capacitor 2842 20.43 3.625 0.22 3.350 0.05 4692 2.54 1850 3248 17.30 406

CAES 2376 13.75 20.79 2.19 2.616 0.05 4692 2.54 2316 3248 17.30 872

PHS 2190 9.18 26.84 2.12 2.398 0.02 4692 2.54 2502 3248 17.30 1058

SMES 3438 21.19 0.380 0.06 4.082 0.19 4692 2.54 1255 3248 17.30 -190

a Standard deviation of the mean.

b Compared with the payment charged by the basic kW tariff without installing storage. 

c Compared with the payment charged by the TOU kW tariff without installing storage. Positive values of profit indicate the 

evaluated storage option is economically viable and vice versa.

In the best-case scenario, all storage technologies are economically viable (see Table 9). The optimal ECs 

range from 2.636 kWh to 27.744 kWh depending on the storage technology in the best-case scenario. The 
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40

optimal ULs range from 2.4 to 3.6 kW, which are generally lower than the corresponding ones in the 

average-case scenario. In the best-case scenario, annual profits range from $63 for NiCd to $1,119 for 

PHS (TOU baseline).

Table 9. Optimal EC, optimal UL and maximum profits for the best-case scenario (peak reduction)

Annual 

paymen

ts

($/year) SEMa

Optimal

EC 

(kWh) SEM

Optim

al UL

(kW) SEM

Basic 

w/o 

storag

e SEM

Profitb

($/yea

r)

TOU 

w/o 

storag

e SEM

Profitc

($/year

)

Flywheel 3052 29.13 2.968 0.18 3.450 0.07 4692 2.54 1641 3248 17.30 197

Conventional 

batteries

Metal air 

battery 2663 11.35 23.494 2.23 2.662 0.00 4692 2.54 2029 3248 17.30 585

Pb-acid 2670 22.14 9.520 0.80 2.885 0.09 4692 2.54 2022 3248 17.30 578

NiCd 3185 28.34 2.636 0.11 3.582 0.06 4692 2.54 1507 3248 17.30 63

Advanced 

batteries

Li-ion 2903 27.32 3.525 0.14 3.382 0.05 4692 2.54 1789 3248 17.30 345

NaS 2850 24.28 4.356 0.29 3.318 0.05 4692 2.54 1842 3248 17.30 398

ZEBRA 2588 22.87 11.791 0.58 2.693 0.06 4692 2.54 2104 3248 17.30 660

Flow batteries

ZnBr 2607 22.06 9.689 0.82 2.907 0.06 4692 2.54 2085 3248 17.30 641

VRB 2523 21.93 11.594 0.59 2.776 0.08 4692 2.54 2170 3248 17.30 725

ZnNi 3011 27.49 3.012 0.17 3.514 0.06 4692 2.54 1681 3248 17.30 237

ZnMnO2 2485 23.18 12.760 0.79 2.693 0.06 4692 2.54 2208 3248 17.30 763

Super capacitor 2753 25.82 4.230 0.34 3.288 0.06 4692 2.54 1940 3248 17.30 495

CAES 2227 15.07 24.655 2.17 2.565 0.04 4692 2.54 2466 3248 17.30 1021

PHS 2129 8.93 27.744 2.08 2.398 0.02 4692 2.54 2563 3248 17.30 1119

SMES 2979 27.92 3.227 0.15 3.382 0.05 4692 2.54 1713 3248 17.30 269

a Standard deviation of the mean.

b Compared with the payment charged by the basic kW tariff without installing storage. 

c Compared with the payment charged by the TOU kW tariff without installing storage. Positive values of profit indicate the 

evaluated storage option is economically viable and vice versa.

7 Discussion

In this section, we first compare results from two DR strategies devised in this study: Loadshifting 

strategy and peak reduction strategy (Sec. 7.1). The a variety of options were discussed that could render 

DR via residential storage (even) more economically attractive, gain wider adoption, and thus provide 

more benefits to the grid as a whole (Sec. 7.2-7.4). Finally, the technological viabilities of installing PHS 

and CAES in residential buildings are addressed in Sec. 7.5. 

7.1 Demand tariffs versus energy tariffs

The Con Edison tariff used in our analyses charge both the delivery and the supply portion of monthly 

electricity bills according to the kWh drawn from the grid (Sec. 2.1). For residential customers with at 

least 10kW peak demand (over any 30min window, at least once a month), Con Edison offers another 

TOU kW tariff (SC8-Rate II; see Sec. 2.2) that charges both by demand (kW) and by energy consumption 

(kWh). The results for these two tariffs (and two strategies) are compared in Table 10 in terms of 

economic viabilities of storage options. 

As seen in Table 10, the TOU kW tariff can render more storage technologies economically viable: Not 

economically viable under the TOU kWh tariff and by using the loadshifting strategy (see Sec. 5.1), a 

number of batteries, incl. metal air, Pb-acid, ZEBRA, ZnBr, VRB and ZnNi batteries, and super capacitor 

become economically viable by implementing the peak reduction strategy (see Sec. 6.1) in the averagecase scenario. However, “short term” technologies such as flywheels and SMES are not economically 
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41

viable (average-case scenario); their cost per kWh capacity is simply too high. In the best-case scenario, 

all the storage technologies can generate positive profits by using the peak reduction strategy while only 

five storage technologies are economically viable by using the loadshifting strategy. 

Another tariff model, participating in the frequency regulation market (likely via aggregating multiple 

residences into a single contractor), may generate alternative or additional savings also (future work, not 

in this study) [15, 18].

Table 10. Economic evaluation results comparison between two strategies

TOU kWh tariffa TOU kW tariffb

Average-case 

scenario

Best-case 

scenario

Average-case 

scenario

Best-case 

scenario

Flywheel NO NO NO YES

Conventional 

batteries

Metal air battery NO YES YES YES

Pb-acid NO NO YES YES

NiCd NO NO NO YES

Advanced 

batteries

Li-ion NO NO NO YES

NaS NO NO NO YES

ZEBRA NO YES YES YES

Flow batteries

ZnBr NO NO YES YES

VRB NO NO YES YES

ZnNi NO NO YES YES

ZnMnO2 YES YES YES YES

Super capacitor NO NO YES YES

CAES YES YES YES YES

PHS YES YES YES YES

SMES NO NO NO YES

a Determined by comparing the minimum annual payments by implementing the loadshifting strategy (see Sec.5.1) to the basic 

kWh tariff baseline (see Table 7).

b Determined by comparing the minimum annual payments by implementing the peak reduction strategy (see Sec. 6.1) to the 

TOU kW tariff baseline (see Table 8).

7.2 Technological improvement and storage cost reduction

Roundtrip efficiencies reported in various literature on metal-air batteries, ZnBr batteries and Vanadium 

Redox Batteries (VRB) are relatively low (45% for metal-air, 60%-75% for ZnBr, 65%-85% for VRB, 

see Table 5). However, research is underway to improve efficiencies of metal-air and flow batteries [41, 

64].This would significantly increase achievable profits for residential customers. For example for metalair batteries, assuming a doubling of roundtrip efficiency from 45% to 90% (achievable in the future [65]),

annual profits could be increased by 22% (average-case scenario, loadshifting strategy).

In contrast, the efficiencies of flywheel storage and SMES are already high (see Table 5). With high 

power rating but low energy capacity (and thus short discharge duration), device costs of flywheel and 

SMES are expensive (per kWh capacity). For these devices, potential cost reductions to consumers would 

result from manufacturing cost reductions rather than efficiency increases.

For not yet fully matured battery technologies, future manufacturing cost reduction (and/or life time 

improvement) may be achieved in the coming years due to the modularity and scalability of battery 

systems and technology breakthroughs, for example the use of less costly Na as an alternative to Li in Liion batteries [36]. In contrast, Pb-acid batteries have been cost-competitive in the market for a long time. 

Instead of manufacturing cost, the main limiting factor for Pb-acid batteries is the relatively limited 

lifetime (number of cycles). Another common disadvantage of Pb-acid batteries, their low-energy density 
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42

[48], will likely not constitute material issue for residential use. For Pb-acid batteries sized at 45 kWh 

(optimal nominal capacity for Pb-acid (best-case scenario, loadshifting strategy) in this study), the 

required volume is 0.38-0.9 m3(energy density of 50-120 Wh/l, Table A.1). Even when including 

additional space for the control unit, this can be easily fit into a single family home. 

7.3 Lowering installation costs

Besides the storage manufacturing cost (Sec. 4.2), lowering the fixed one-time home installation costs 

also has potential to improve economic viability. Some storage technologies and scenarios, while not 

economically viable in our model, are so close to break-even that a reduction in installation costs would 

render them economically viable. For example, as can be seen from Table 7, the best-case scenario for 

super capacitors has a gap to break-even of only $149 per year (loadshifting strategy). With assumed 

installation cost reduction of 50%, the super capacitor would become economically viable. Still, by using 

the loadshifting strategy, for flywheel, Li-ion batteries, NiCd batteries, NiZn batteries, and SMES, storage 

manufacturing costs and/or (dis)charging losses are so high that gaps to provide profit are more than $900 

per year, i.e. higher than the savings possible from lowered installation costs. In the contrast, the breakeven gaps yielded by utilizing the peak reduction strategy are all below $190 per year (Table 8, averagecase scenario), indicating that they are likely to become economically viable or get closer to be breakeven if the assumed installation cost would be reduced by 50%. 

7.4 Impact of interest rates

Considering 5% instead of 10% interest rate would result in 27% lower total financing costs of the storage 

system (interest and principal repayments). Conversely, a more conservative 15% instead of 10% would 

increase financing costs by 50% (for examples for 15 years lifetime). However, considering average 

instead of best case storage costs leads to much higher cost increases (between 41% (super capacitor) and 

362% (Pb-acid batteries)). In other words, the sensitivity of economic viability to the exact interest rate is 

low compared to the large uncertainty in storage manufacturing costs themselves. Varying interest rates 

are therefore not further considered in this study.

7.5 Technological viability of PHS and CAES

With regards to economic viability, PHS and CAES show the highest possible profit (Table 1). However, 

from a practical perspective, applications of PHS and CAES will be limited by site conditions. Although 

emerging PHS and CAES technologies have been proposed or demonstrated to work as compact systems

[66], their low energy density still poses obstacles: For PHS, the optimal EC of 12kWh (average-case 

scenario, loadshifting strategy) would require 488m3(~500 tons) of water stored in two separate tanks at 

10m altitude difference. This will be possible only for select residential buildings and specific architecture. 

For CAES, however, recent commercially available systems have been shown to be suitable for 

installation e.g., in the basement of single-family homes [66].

8 Conclusions and future work

We found that, when choosing suitable storage technologies and carefully sizing capacity, typical U.S.

households can achieve considerable profits when load-shifting their electricity consumption or reduce 

their peak power demands. The annual profits range from $61 to $1365 per year per household by 
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43

utilizing the load-shifting strategy and from $161 to $1058 per year per household by using the peak 

reduction strategy. These profits can be achieved without changing the actual consumption patterns of 

appliances. The peak reduction strategy can render more storage technologies economically viable than 

the loadshifting strategy. Note that the demand model represents the U.S. average household (see test 

results in Sec. 4.2). For other households – with different appliance configuration (e.g., a second 

television or air conditioning unit) or tariffs other than the specific Con Edison tariff used here – profits 

may change.

An important further investigation into the benefits of DR would be a quantification of possible 

greenhouse gas emissions savings (on a lifecycle bases, [67-70]). Further optimized or new dispatch 

strategies may be found by analyzing patterns of demand profiles in the frequency rather than the time 

domain [71].

Acknowledgements

The work presented herein was supported by the National Institute of Standards and Technology (NIST) 

Grant No 60NANB11D192. Parts have been published elsewhere [72, 73].
This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.GCR.14-978

44

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Appendix A. Operating characteristics of storage technologies and cost estimations

Table A. 1. Characteristics of storage technologies and cost estimations, incl. data sources

Description

Power density 

(kW/kWh) 1 Healthy 

depth of 

discharge 

(%)

Roundtrip 

efficiency

(%)

Energy density

Operating 

temperature

Selfdischarge 

(%/day)

Cost

Life time 

(cycles)

Commercial 

availability Continuously 

discharging

power

Pulse

power

(Wh/kg) (Wh/l) Capital cost 

($ /kWh)

Conventional batteries

Metal air

Anode: Metals with high energy density like Al 

or Zn

Cathode: A porous carbon structure or a metal 

mesh covered with proper catalysts

Electrolytes: Good OH-ion conductor

0-102 NA 1003 40-504 110-

4205 2003 NA small 10-6021603

100-3002

~1,5003

Mature in 

conventional 

generation

Demo to 

increase 

lifetime and 

efficiency

Lead acid

(Pb-acid)6

Anode: Pb+SO42-↔PbSO4+2eCathode: PbO2+SO42-+4H+++2e-

↔PbSO4+2H2O

0.05-3.4 11.2-15 70-80 75-80 30-50 50-

1207

(-20) - 50°C7 0.1-0.3

106-400

950-2260 

for 

advanced 

batteries

200-1000

4500 for 

advanced 

batteries

Mature

Nickel

cadmium 

(NiCd)8

2NiO(OH)+Cd+2H2O↔2Ni(OH)2+Cd(OH)2 0.05-2.77 30 NA 60-91 40-75 171.6 NA 0.2-0.6 600-1500 1000-3000 Mature

Advanced batteries

Lithium-ion 

(Li-ion)9

0.12-6.17 0.3-

15.64 8010 75-100 50-200 100-500

-20-

+45/60°C

0.1-0.3 500-3600 1000-6000

>10,00011

Mature 

portable 

market

Sodium sulfur 

(NaS)12 2Na+4S↔Na2S4 0.03-0.14 NA NA 70-92 150-240 150-

370 300-350°C 20

250-555

1100-

273013

2000-4500

Mature in 

Japan; Demo 

in USA

Sodium nickel 

chloride 

(NaNiCl 

ZEBRA)14

2NaCl+Ni↔NiCl2+2Na NA NA NA 90 100-120 150-

180 -40-+70°C 15 100-200 2500 Demo and trial

Flow batteries (additional electrolyte is stored externally, which is usually pumped through the cell (or cells) of the reactor)

Zinc bromine 

(ZnBr)15

Positive electrode: 2Br-↔ Br2(aq)+2eNegative electrode: Zn2+ +2e- ↔ Zn 0.2-0.5 NA 100 60-75 30-85 30-60 -30 -+50°C 1150-1000

725-1950

2000

5000

10,000

Mature?

Vanadium 

redox (VRB)16

Negative electrode: V2+/V3+

Positive electrode: V4+/V5+

Electrolyte: Mild sulphuric acid solutions

0.25-0.33 NA 100 65-85 4-33 10-30

Ambient 

conditions

Small 150-1250 10,000+

Immature, a 

few 

examples 

worldwide

Nickel zinc17

Water-based flow-assisted batteries.

2.78 NA 90 80 31.49 28.6 Low 700 5000

Zinc manganese dioxide17 90 80 Low 100-200 3000-5000
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50

Table A.1. (continued) Characteristics of storage technologies and cost estimations, incl. data sources

Description

Power density 

(kW/kWh) Healthy 

depth of 

discharge

(%)

Roundtrip 

efficiency

(%)

Energy density

Operating 

temperature

Selfdischarge 

(%/day)

Cost

Life time 

(cycles)

Commercial 

availability Continuously 

discharging

power

Pulse

power

(Wh/kg) (Wh/l) Capital cost 

($ /kWh)

Flywheel18

To store energy mechanically in the form of 

kinetic energy by rotating a mass around an 

axis. In charging periods, the mass speeds up 

by electricity transformed by the motor. When 

discharging, the flywheel slows down.

4

56-16019 117 75-10020 85-95 3-3021 10-

8021

-20 ~ +40°C 20-100 1000-

500022

10,000-

25,000

Demo, few 

plants under 

construction

Super 

capacitor23

Make use of high surface area actived carbons 

as electrolyte solutions between two solid 

conductors

70-220 1524-

2454 100 95 0.05-15 2-10 -40~+85°C 2-40 500-100030,000 10E4-10E8 

Developing 

in transport 

applications

Compressed 

air energy 

storage 

(CAES)24

The energy is stored as the compressed air in 

tanks or underground geologic formations. 

When the demand turns to peak, the 

compressed air is released into a gas-fired 

turbine generator system. 

0.002-1

- 70 42-54

65-9525 30-60 3-6 - 0 2-43026 5,000~20,000

Mature in 

conventional 

generation

demo to 

increase 

efficiency 

and decrease 

size

Pumped hydro 

storage 

(PHS)27

To store energy by means of two reservoirs 

located at different elevations 75-85 0.5-1.5 0.5-1.5 - 0 5-100 20,000-50,000 Mature

Superconducti

ng magnetic 

energy storage 

(SMES) 27

Energy is to be stored in the magnetic field 

created by injecting a DC electric current into a 

superconducting coil

95 0.5-5 0.2-2.5 1.8-4.1K 10-15 1,000-

10,000

10,000-

100,000

Immature, 

few power 

quality 

applications

 

1 Certain storage technologies can withstand so called pulse discharge modes at peak discharging power which is considerably higher than its normal (dis)charging power. Continuous discharging 

power here refers to the maximum continuously discharging power.

2 Taken from Chen, et al. [1].
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51

 

3 Taken from EOS Energy Storage [2].

4 Taken from Edberg and Naish [3].

5 Usually referred to the weight at the charged state (oxygen included). Taken from Naish, et al. [4].

6 Summarized from Chen, et al. [1,5-8], unless stated otherwise.

7 Taken from Naish, et al. [4].

8 Summarized from Chen, et al. [1, 5, 7, 9], unless stated otherwise.

9 Summarized from Chen, et al. [1, 5-7, 9-12], unless stated otherwise.

10 Available sources indicate that the healthy DoD is 80% for Li-ion batteries with one exception of 60%.

11 The enlarged life cycles are achieved at 50% DoD and by strictly controlling (dis)charging processes.

12 Summarized from Chen, et al. [1, 5-7, 12, 13], unless stated otherwise.

13 $1100-2700/kWh is indicated by the NGK company. According to the NAS battery cost projection by NGK, the cost is expected to be reduced to $140/kWh if massively produced (1600 

MWh/year).

14 Summarized from Chen, et al. [1, 5].

15 Summarized from Chen, et al. [1, 5-7, 14, 15].

16 Summarized from Chen, et al. [1, 4-7, 12, 16, 17].

17 Personal communication, CUNY Energy Institute, NY.

18 Summarized from Chen, et al. [1, 4-7, 12, 18-21], unless stated otherwise.

19 The range reflects different flywheel models. The latest generation of flywheels using magnetic bearings and the ring, which increases the energy capacity of flywheel thus reduces the relative 

power density (kW/kWh). On the other hand, the model of the high power rating and the low energy capacity reflects the first generation of flywheels, which can be applied in the power quality 

regulation market.

20 Conventional flywheels are limited to drop 59% of the maximum rator speed due to the industrial “fail-safe” standard, while the new generation can dump 100% of the maximum rator speed [22].

21 The high end in the range takes into account the integrated power conversion system, cooling system and pumped vacuum system while the low end reflects the energy density of the rator only.

22 A high speed flywheel costs as high as five times the manufacturing cost of a low speed flywheel.

23 Summarized from Chen, et al. [1, 5, 7, 23].

24 Summarized from Chen, et al. [1, 5, 7, 24].

25 The round-trip efficiencies of CAES from literatures vary due to the different definitions used for the CAES round-trip efficiency. On the condition that the waste energy utilization is taken into 

account, the round-trip efficiency of CAES could be increased. The emerging CAES technology is claimed to be able to increase the efficiency from 40% to 70%. According to Ref. [24], the 

advanced CAES could be materialized by 2015.

26 The costs of CAES system varies with different scales or kW capacities.

27 Summarized from Chen, et al. [1, 5].
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52

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This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.GCR.14-978

54

Appendix B. Demand profile model testing results

Table B.1. Testing results of the appliance demand profile model

Single day Converged day

Operating parameters

RS

E

M

28

Duty cycles per year

Daily electricity 

consumption

RSE

M29

Power draw on first/last 

minute Overall 

shape of the 

demand 

profile

Max. 

power

Min. 

power

Cycle 

length

From 

simulat

ions

Expec

ted Relativ

e error

From 

simul

ations

Expec

ted Relativ

e error

Epeak

Eoff

peak

Epeak

/Eoff 

peak

P(1) P(14

40) Relative 

error

(W) (W) (min) (Wh) (Wh) (Wh) (Wh) (W) (W)

Individ

ual 

applian

ce

Dishwasher 1457 0 54 OK 5% 344 365 -5.81% 653 692.8 -5.81% 497 156 3.20 12% 5.5 6.6 -17.86% OK

Microwave oven 1500 0 6 OK 5% 1171 1133 3.30% 481 466 3.30% 314 168 1.87 50% 0.3 0.5 -42.86% OK

Toaster oven 1400 0 20 OK 5% 112 111 1.16% 144 142 1.16% 90 54 1.67 100% 0.1 0.1 0% OK

Refrigerator 250 0 20 OK 2% 12087 12089 -0.02% 2760 2760 -0.01% 1393 1367 1.02 5% 115 108 6% OK

Freezer 155 0 20 OK 0% 21699 21681 0.08% 3072 3069 0.09% 1538 1534 1.00 5% 122 129 -5% OK

Lighting-Bathroom 317 0 31 OK 5% 920 989 -7.00% 413 444 -7.00% 185 227 0.81 6% 10.1 10.5 -4% OK

Lighting-Bedroom 200 0 60 OK 5% 623 621 0.35% 341 340 0.35% 190 151 1.26 7% 4.5 4.5 -1% NOT YET

Lighting-Living room 256 0 60 OK 5% 816 840 -2.75% 573 589 -2.75% 328 244 1.35 5% 8.4 8.5 -1% NOT YET

Lighting-Dining room 235 0 30 OK 5% 1336 1387 -3.68% 430 447 -3.68% 295 135 2.18 12% 1.7 1.7 1% OK

Lighting-Hallways 207 0 15 OK 5% 1705 1752 -2.71% 242 248 -2.71% 136 105 1.30 11% 1.8 1.8 0% NOT YET

Lighting-Kitchen 250 0 32 OK 5% 1650 1711 -3.57% 603 625 -3.57% 391 211 1.85 14% 1.3 1.3 -2% OK

Clothes dryer 2895 0 60 OK 5% 353 359 -1.60% 2802 2847 -1.60% 1775 1026 1.73 13% 16.2 16.5 -2% OK

Clothes washer 2150 0 48 OK 5% 388 392 -1.09% 822 831 -1.09% 500 322 1.55 21% 4.1 4.5 -9% OK

Television 185 0 115 OK 5% 704 752 -6.30% 684 730 -6.30% 489 195 2.51 5% 21.9 22.3 -2% OK

Air conditioning 3500 0 10 OK 1% 5270 5520 -4.53% 33414 30667 8.96% 20879 12535 1.67 5% 1335 1405 -5% OK?

Space heater 1447 0 60 OK 2% 1465 1476 -0.71% 17432 17364 0.39% 8757 8676 1.01 5% 683 677 1% OK

Vacuum 1440 0 35 OK 5% 63 63 -0.12% 146 146 -0.12% 89 57 1.55 19% 1.3 0.6 132% OK

Computers and other 

rechargeable electronic 

devices 100 100 1440 OK 0% 365 365 0.00% 2400 2400 0.00% 1200 1200 1.00 0% 100 100 0% OK

Whole 

househ

old

Summer 12207 100 - OK 2% - 50306

57392

30 30235 20071 1.51 5% 1829 1797 2%

Winter 9003 100 - OK 2% - 33705 - 17862 15843 1.13 5% 1111 1115 0%

Spring or fall 8242 100 - OK 3% - 16259 - 9348 6911 1.35 5% 419 420 0% NA

Average day - 30586

31011

31

-1% 17408

 

28 RSEM denotes the relative standard deviation of the mean. Here, the RSEM is the maximum RSEM among RESMs of fully cycles per year, daily electricity consumption, electricity consumption 

during peak hours and electricity consumption during off-peak hours.

29 Here, RSEM is the larger one between RSEM of the power draw at the first minute of the day and RSEM of the power draw at the last minute of the day.

30 The average daily electricity consumption for summer days is obtained from Pecan Street Research Institute, http://www.pecanstreet.org/. [accessed 5/13/2013].

31 The average daily electricity consumption per household in U.S. is obtained from U.S. Energy Information Administration, 2009 Residential Energy Consumption Survey (RECS) Data Table 

CE2.1 Fuel Consumption Totals and Averages, U.S. Homes, U.S. Energy Information Administration. http://www.eia.gov/consumption/residential/data/2009/index.cfm?view=consumption#fuelconsumption. [accessed 1/22/2014].