DOI: 10.1002/ente.201700549

A Simple Metric for Predicting Revenue from ElectricPeak-Shaving and Optimal Battery SizingMichael Fisher,* Jay Whitacre, and Jay Apt[a]

Introduction

Commercial and industrial behind-the-meter (BTM) electric-ity storage is growing rapidly[1] as a way for customers tooffset utility demand charges and for utilities to procure dis-tributed capacity resources.[2] As storage costs fall anddemand increases, utilities and other third-party storage pro-viders marketing to retail customers face a familiar problem:which customers benefit most from BTM storage and howare these cases identified?[3] The optimization models re-quired to answer these questions necessitate sophisticatedsoftware and in-house expertise which many organizationsmay not have. Here we present a metric called the “thresh-old ratio”, which can be used in a univariate econometricmodel to predict peak-shaving revenue for individual cus-tomers and the corresponding profit-maximizing battery size.The metric is derived exclusively from the customerQs loadshape and no optimization model is required. The economet-ric model distills much of the complexity of an optimizationmodel into a simple non-linear equation with one variable.

A wide body of work has investigated the use of energystorage to reduce energy costs in current markets or plausi-ble future scenarios. For example, research has been conduct-ed on wholesale market participation,[4–6] energy storagepaired with renewable generation,[7–9] and electric cars.[10, 11]

Much of this work relies on mathematical programmingmodels to calculate the change in energy costs when instal-ling storage. In this study, we develop an alternative to math-ematical programs that can be used by non-experts to calcu-late potential revenue from storage under one particular use-case (demand charge reduction).

The literature concerning predictive metrics for the eco-nomics of a BTM peak-shaving battery is generally focusedon analyses of regional demand charges[12–16] rather than onthe characteristics of load shape that drive economics. An as-sessment of demand charges can indicate which regions may

be appropriate for BTM storage, but cannot identify promis-ing individual customers. There is previously published re-search on the optimal sizing of storage that explores themathematical programming methods by which one could sizeenergy storage. Prior work has explored optimal sizing forgrid load-leveling,[4,17–20] hybrid renewable/storage installa-tions,[21–23] and BTM storage for peak shaving. Mathematicalprogramming methods are useful and accurate, but can re-quire significant expertise and computational time. For ex-ample, Oudalov et al.[24] investigated optimal battery sizingfor peak shaving, but their exhaustive search algorithm re-quires the computation of net battery profits using an optimi-zation model at multiple discrete battery sizes to find theglobal optimum. Oh and Son[25] designed a gradient searchalgorithm for optimal sizing, but this still requires an optimi-zation model to compute net battery profits at each iterationof battery size. Neither method quantitatively characterizesthe trade-off between battery size (cost) and potential profit.Though understanding these methods is useful, this literaturedoes not identify the underlying characteristics of buildingload shapes that drive battery economics, and it does notallow for non-expert stakeholders to calculate potential reve-nue or properly size storage resources.

Wu et al.[26] formulated an analytical solution to the opti-mal sizing problem that does not rely on mathematical pro-gramming. However, they make use of a restrictive assump-

A major use case for behind-the-meter (BTM) electricitystorage is peak-shaving for commercial and industrial cus-tomers who must pay peak-demand charges. Quantifying thevalue proposition for individual customers currently requiresan optimization model, the development of which can becostly in human and computing resources. We disclose here asimple econometric model to predict revenue from retailpeak-shaving. Geared toward electric utilities, third-partystorage providers, and consumers, this model eliminates the

need to formulate a model in specialized optimization soft-ware. The model is based on a predictive metric that is de-rived from the buildingQs load profile. During model fitting,we discovered that the revenue estimates generated are inde-pendent of the power capacity of the battery if the maximumpower-to-energy ratio of the storage is held constant. Thiseffect can be used to calculate the profit-maximizing storagesize, which we explore in a case study.

[a] M. Fisher, Prof. J. Whitacre, Prof. J. AptDepartment of Engineering and Public PolicyCarnegie Mellon University5000 Forbes Ave. , Pittsburgh, PA 15213 (USA)E-mail: mjfisher@cmu.edu

Supporting Information and the ORCID identification number(s) for theauthor(s) of this article can be found under https://doi.org/10.1002/ente.201700549.

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tion that may not be satisfied in practice. Their solution as-sumes that the building load profile monotonically increasesfrom valley to peak and back to valley again. Of the hun-dreds of metered building load profiles used in our work,none satisfies this condition. While we do not have an analyt-ical solution, we have developed a more general approachthat makes use of empirical data.

Our model constitutes a tool for practitioners and incorpo-rates load shape and demand charges in predicting revenuefor individual customers. In this study, we explore the rela-tionship between our new metric, the threshold ratio, andannual revenue from peak shaving, where peak shaving reve-nue is calculated using a battery optimization model de-signed to minimize the total energy cost. We quantitativelydetermine this relationship for many battery duration/demand charge scenarios by fitting an exponential curve,which leads to an easy-to-use econometric model for storageproviders. By calculating the threshold ratio for each custom-er and mapping it onto the appropriate curve, storage pro-viders can quickly understand which customers have suffi-cient revenue potential over the accepted return-on-invest-ment period to justify the installation cost of a batterysystem. Paired with knowledge of local installation costs,storage providers can also use this information to find theprofit-maximizing battery size. To demonstrate this, we pro-vide a case study showing the use of the threshold ratio inboth revenue prediction and optimal sizing.

New Metric Development: The Threshold Ratio

Our proposed metric for storage revenue prediction (thethreshold ratio) is based on two observations. First, the eco-nomics of customer-side storage are largely determined byavoiding charges for peak demand. Second, a batteryQs abilityto reduce demand charges is a function of the total energyconsumed during the largest load spike per billing period rel-ative to the total energy capacity of the battery. While thereare other factors (e.g., recharge period) that contribute tothis effect, we ignore them in favor of a simpler model. Thethreshold ratio allows a storage provider to use a simplecharacteristic of the customer load shape to size the batterysystem.

In this section, for pedagogical reasons we first discuss anintermediate metric called the “spike-to-battery” ratio thatrelates the energies in the load spike and battery. This metricdoes not fully capture how load shape contributes to demandcharge reduction potential, so a “threshold” ratio is derivedfrom the spike-to-battery ratio to provide this information.The threshold ratio alone is ultimately used for revenue pre-diction.

We characterize a battery in terms of power (kW) andenergy (kWh) capacity. The ratio of energy capacity topower capacity gives the batteryQs duration of discharge atfull power. For example, a 20 kWh/10 kW-rated batterywould have a minimum discharge duration of 2 hours, pro-vided that the battery is able to deliver its full energy at thenecessary current level.

An intermediate metric: the spike-to-battery ratio

We begin by finding the largest energy spike (in kWh) abovea target load [Eqn. (2)]. The target load (kW) is set equal tothe maximum building load (kW) minus the battery powercapacity (kW) in Equation (1). We do this for each monthand building in the dataset. Battery power capacity, and thusthe target load, is treated parametrically in this analysis.Each time the building load exceeds the target, the totalkWh consumed above the target load is calculated until thespike ends as the load drops below the target. We presumethat the battery can be recharged as needed during timeswhen the actual load is below the load target. Figure 1 pro-vides a hypothetical example of this routine, where there arefour load spikes above the target load (in solid black). Wenote the number of kWh in the largest spike for that billingperiod (in our case, one calendar month) for future calcula-tions. No other information is retained.

Target ¼ maxt2T

Loadtð Þ@ kWBat ð1Þ

MaxSpike ¼ maxS

Xt2Si

Loadt @ Target½ A=4

!ð2Þ

T represents all time segments t in the billing period, kWBat isthe rated power of the battery, S is the set of all spikes Si. Aspike is defined as a contiguous period where building loadis greater than the target load (Loadt+Target). The Max-Spike formula is divided by 4 to convert power to energy for15-minute intervals.

A single normalized ratio for each building is calculatedby taking the median energy spike value of the 12 monthlyvalues and dividing it by the battery energy capacity[Eqn. (3)]. This provides a convenient unitless ratio to de-scribe the size of the maximum load spike (a ratio of 1 indi-cates that the typical maximum load spike in a billing periodis the same size as the battery). Calculating the mean insteadof the median does not significantly affect the resultingmodel fit.

Figure 1. Example calculation of the energy consumed above the load target.There are four spikes above the load target. Only the number of kWh fromthe largest spike is recorded.

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Spike@ to@ Battery ¼median

m2MMaxSpikemð Þ

kWhBat

ð3Þ

M is the set of all months m and kWhBat is the energy capaci-ty of the battery.

Spike-to-battery ratio behavior

We will now explain a few examples in detail to demonstratehow this spike-to-battery ratio behaves under different loadshapes to provide context for the introduction of the thresh-old ratio. For this discussion, we display the time series loaddata (kW) as a step function to accurately display the areaunder the graph, given the time resolution of the data. Weuse 15-minute energy consumption data to calculate the aver-age power in each 15-minute interval.

Figure 2 illustrates how the spike-to-battery ratio behavesunder two different hypothetical load shapes (shown in Fig-

ure 2 a). Battery power capacity is treated parametricallyfrom 0.5 to 10 kW in increments of 0.5 kW (horizontal axisof Figure 2 b). A 1 h battery duration is assumed throughoutthis example.

As the maximum battery power rating increases from 0.5to 2.5 kW, the ratio remains constant. The vertical walls ofthe load spike in this initial load region mean that loadenergy and battery energy increase such that their ratio re-mains constant. From 2.5 to 4.5 kW of power capacity, theratio increases as the base of our spike grows wider. Theratio remains the same for both the single- and double-spikeexamples because the second spike (t=4 h) is not included inthe ratio calculation. Only the largest spike above the targetload is included, and the original spike (t=2.5 h) remains thelargest spike.

As the power capacity increases above 4.5 kW, we now seea difference in the spike-to-battery ratio. The target load isnow below the base of the second spike, and it is thereforetreated as part of the same spike as the original. This largedifference in spike energy, while keeping battery energy ca-pacity the same, is what accounts for the difference in spike-to-battery ratio between the two profiles.

As the battery power capacity increases above 6 kW, wesee that both profiles have spike-to-battery ratios greaterthan 1. This means that the battery energy capacity is notlarge enough to eliminate the entire spike (in other words,the battery cannot reduce the net building load to the targetload). In the next section we will explore how differences inbuilding load shape affect the depth of load reduction forspike-to-battery ratios greater than 1.

Threshold ratio

For those spikes that are larger than the energy capacity ofthe battery (i.e., the spike-to-energy ratio is greater than 1),the time profile of the power spike will determine the magni-tude of demand charge reductions because the batterycannot provide the entire needed energy; this is why we in-troduce an additional metric to capture the relationship be-tween load shape and peak demand reduction. For example,Figure 3 highlights how demand charge reduction is realizedunder hypothetical “thin” and “wide” spikes (Figure 3a, b).Both spikes have the same total energy (17 kWh) and weassume the same size of battery in both scenarios (10 kWmax power; the duration is fixed at 0.5 hours at max power).We plot the resulting spike-to-battery ratio for many inter-mediate power levels below the maximum-rated power inFigure 3 c. These intermediate power levels are hypotheti-cal—they have no relation to the physical characteristics ofthe battery and act only as data points to aid in the calcula-tion of the threshold ratio. As both spikes embody the sameamount of total energy, and the battery is assumed to be thesame size for both spikes, the spike-to-battery ratio at themaximum power (10 kW) will be the same for both spikes.However, the demand charge reduction will be different foreach spike. A thin spike has less energy in the top of thespike than a wide spike, and therefore the peak demand re-

Figure 2. Behavior of the spike-to-battery ratio. Panel (a) shows the two exam-ple load shapes and (b) the resulting ratio at many levels of battery power ca-pacity. The example assumes a 1 h storage discharge duration.

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duction is more effective in this scenario. In our example, a5 kWh battery will reduce the peak demand by 7.5 kW and5.8 kW for the thin and wide spikes, respectively. The spike-to-battery ratio is unable to capture this behavior, and wetherefore need an additional metric.

We define the threshold ratio as a unitless ratio of powercapacity levels. The numerator is the intermediate powerlevel at which the spike-to-battery ratio crosses the thresholdof 1 (i.e. , when the battery is no longer large enough to ser-vice the entire load spike). The denominator is the maxi-mum-rated battery power. Again, a single annual metric foreach building is calculated as the median of the 12 monthlyvalues. This calculation is summarized in Table 1. In our ex-ample of a maximum 10 kW rated battery power, the thinspike has a threshold ratio of approximately 0.7, whereas thewide spike has a threshold ratio of approximately 0.1. Hence,the threshold ratio captures the intended relationship be-tween load shape and demand reduction potential for agiven battery energy capacity. The higher the threshold ratio,the greater the economic benefit to be realized per unit ofenergy stored in the battery. For those buildings that havespike-to-battery ratios less than 1 at the maximum ratedpower, we set the threshold ratio at 1.0.

In addition to the shape of the largest spike, anotherfactor that could affect demand reduction capability is theshape of the recovery period between the two load spikes; ifthe load “valley” between two spikes is not sufficient indepth or length, the battery may not be able to shave thesecond peak because a complete recharge would not yethave occurred. We found that including a measure for theshape of this valley in our model can reduce the unexplainedvariance, but the predictive accuracy gains are not sufficientto warrant the extra complexity.

Data and Optimization Model

A storage provider will likely have an estimate of the electricload profile of target customers. To develop our model, weuse metered energy consumption data from 665 commercialand industrial buildings in North and South Carolina (USA)to populate an optimization model from which we developthe predictive metric. The data have a 15-minute sample ratefor one calendar year (2013). In the Supporting Information,we compare the results from this Carolina dataset to thosefrom 100 geographically diverse buildings provided by Ener-NOC, finding good agreement. The optimization model is alinear program to minimize retail energy costs to the batteryowner, and it also considers battery degradation in makingdecisions. We assume perfect foresight of building load,which will somewhat overestimate the revenue to the battery.In reality, building load forecasts would be used in the bat-tery optimization. Short-term building load forecasting algo-rithms are an active area of research, and average forecasterrors of 5–10 % are routinely feasible.[27,28] Hence, we do notbelieve the perfect foresight assumption distorts our conclu-sions. Detailed information about the optimization model ispresented in the Supporting Information. The battery canperform peak-shifting (reduce demand charges) or energy ar-bitrage, though we found that retail energy arbitrage is large-ly uneconomic even with time-of-use rates. Our metric thusemphasizes predicting demand charge reduction.

Figure 3. Illustration of the threshold ratio for thin and wide load spikes. To find ratio values at a particular target load, read horizontally across from the build-ing load to the final panel. Note the reverse vertical scale in (c); it allows for ease of comparison to (a) because the target load is the maximum load minus thepower capacity.

Table 1. Summary of the threshold ratio calculation

Step Calculation

Numerator1 For each month, calculate the Spike-to-Battery Ratio at many inter-

mediate power capacities up to the full power capacity of the bat-tery.

2 Find the lowest intermediate power capacity for which the Spike-to-Battery Ratio is greater than or equal to 1.

Denominator1 Max rated power output of the battery.

Final Ratio1 Divide numerator by denominator for each month. The final thresh-

old ratio is the median of the monthly values.

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We assume a lithium-ion phosphate chemistry in ourmodel with an 83 % round-trip efficiency.[29] The battery cancharge and discharge at the maximum rated power for theentire rated duration; both power and duration are treatedparametrically in our analysis. The average monthly depth ofdischarge for any of the scenarios we ran does not exceed50 %. The treatment of capacity degradation from batteryuse is discussed in the Supporting Information.

In this work, we investigate only tariffs with demandcharges that do not change within a given day (no intradaypeak or off-peak periods) or seasonally (summer/winter). Wealso assume a constant energy charge. Our findings are stillvalid for locations that have seasonal demand charges(though the model parameters must be scaled) because inter-seasonal load shifting cannot be performed at scale. Build-ings can, however, shift load intraday even in the absence ofstorage, and therefore our findings may not apply to regionswith variable intraday demand charges.

Data cleaning

A utility in North and South Carolina provided energy con-sumption data from approximately 1000 commercial and in-dustrial meters. The utility provided data from a subset oftheir entire commercial and industrial population. The subsetincluded those customers who had interval meters and a suf-ficiently long history for this study.

Meters covering loads unsuitable for this study were re-moved according to usage characteristics. This included anymeters with maximum power draw less than 25 kW, averagepower draw less than 13 kW, or any meter missing a total ofmore than 2 days of data within 2013. Data gaps for meterswith less than 2 days of missing data were filled with an aver-age profile from two surrounding days of the same type(weekday/weekend). 270 meters were removed during thisstep. A subsequent visual inspection of each meterQs loadprofile identified meters that were attached to specific piecesof equipment (e.g., switching between 2 discrete load valuesthroughout the year). 59 meters were removed during thisstep. This left the 665 buildings used for our analysis.

Revenue Prediction

After investigating a number of model forms, we found thatthe threshold ratio alone is sufficient to predict peak shavingrevenue with relatively low error. A non-linear model was fitusing Equation (1).

Rev ¼ a ? eb?Thresh þ c ð4Þ

in which parameters a, b, and c are fit by nonlinear leastsquares, Rev is the annual revenue per kWh of installedenergy capacity, and Thresh is the threshold ratio. Parame-ters a and c can be thought of as scaling factors that adjustthe vertical position of the fit, and b adjusts the concavity ofthe fit. Figure 4 shows the model fit across battery power ca-

pacity scenarios with associated confidence and predictionintervals. The results shown here assume a $ 20 kW@1 demandcharge and 1 h duration, though the results are similar forother input assumptions. The duration is held constant acrossscenarios, so that as the power capacity increases, the totalenergy capacity increases as well.

The relationship between the threshold ratio and annualnormalized revenue ($ per kWh of installed capacity) doesnot change significantly across battery power capacities (Fig-ure 4 e); the prediction and confidence intervals are quitesimilar. To be clear, the total revenue will increase as thepower and energy capacities increase, but revenue per unitof installed energy capacity remains the same across thresh-old ratios. Our modelQs coefficient estimates are also similaracross power capacities. Figures S2–S6 (Supporting Informa-tion) show coefficient estimates and confidence intervalsacross battery capacities, including a combined scenariowhere data are aggregated across the four battery power ca-pacities before model fitting. The coefficient estimates arestatistically indistinguishable between power capacity scenar-ios. We extended our analysis to include power capacitiesfrom 10 % to 35 % of the maximum building load and deter-mined that this relationship held. Therefore, we will assumethat normalized revenue as a function of threshold ratio is in-dependent of power capacity for a given discharge durationat maximum power; in other words, the same fundamentallink between the normalized revenue and load shape governsacross power capacity scenarios. This is a powerful insightthat allows the selection of the optimal battery size by deter-mining the profit maximizing threshold ratio (an example isprovided in the next section). The coefficient and error esti-mates provided in the Supporting Information are the com-bined estimates derived from aggregating data across thefour battery power capacity scenarios. This information canbe used to recreate the prediction curves for any duration ortariff scenario.

The resulting curve and prediction intervals can be com-pared to estimates of battery installation cost to find break-even and maximum profit levels as a function of thresholdratio, and therefore as a function of battery power capacity.

One way of validating the model is to determine if the re-sults of the more accurate optimization model follow theshape of the simplified modelQs prediction curve. That is, doreductions in battery power capacity (increases in thresholdratio) lead to gains in normalized revenue as predicted byour model? In Figure 5, we use the results from our optimi-zation model to plot the path of two individual buildings asthey reduce the maximum battery power capacity (from30 % to 15 % of the maximum building load), finding thatthe results from the optimization model confirm the shape ofthe prediction curve. While this is true for many of the build-ings, a few buildings exhibited some deviation from the pre-dicted trend. This example also assumed a $ 20 kW@1 demandcharge and 1 h battery duration, though the results were thesame for other input assumptions.

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Sensitivity to battery and economic parameters

Figure 6 shows that our modelQs parameters change in a pre-dictable way as demand charges and duration change. In Fig-ure 6 a model curvature, captured by parameter b, does notchange as demand charges increase, but the scaling parame-ters a and c change at a linear rate to reflect a steepening ofthe curve. In Figure 6 b, all parameters except for the curva-ture parameter b follow exponential decay as the battery du-ration increases. Figure S2 (Supporting Information) showsthat changes in round-trip efficiency do not significantlyaffect the coefficient estimates. The lack of change in the cur-vature of our predictions across demand charges, duration,and efficiency lends support to our choice of mathematicalmodel.

Figure 4. Plot of annual revenue per unit of installed energy capacity as a function of the threshold ratio across a number of battery power capacities. Eachpoint represents a building. Subplots (a)–(d) represent 15 % to 30% battery capacity as a percentage of the building’s maximum load. The red dashed linesshow the 95 % confidence interval for the fit ; black dashed lines show the 95 % prediction interval for the data. Subplot (e) shows all fits on the same plot. Theassumptions are: $ 20kW@1 demand charge, 1 h duration, and 83% round-trip efficiency. The duration is held constant across all scenarios, so that as powercapacity increases, the total energy capacity increases as well.

Figure 5. Plot of the annual normalized revenue versus threshold ratio for allbuildings and battery power capacity scenarios. Two buildings are highlightedin red, showing the path taken as the maximum battery power capacity is re-duced from 30% to 15 % of the building maximum load (while holding dura-tion constant). Each circle represents the results from a battery optimizationmodel. The solid black line represents our econometric model, with the asso-ciated 95 % prediction intervals shown in dotted black lines.

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Example Analysis

We will now outline an example of how this information canbe used to predict revenue across many battery sizes and de-termine the profit-maximizing size for an individual building.The first step is to calculate the spike-to-battery ratio formany different battery power capacities. If the desired dura-tion is also unknown, then this step will be repeated for dif-ferent durations. We can then calculate the threshold ratio ateach of these power capacities, as shown in Figure 7.

We now have the relationship between the threshold ratioand battery power capacity for this building. In Figure 8, weswitch the axes to plot power capacity as a function ofthreshold ratio in Figure 8 a. Then, we overlay the predictedrevenue as a function of the threshold ratio. All coefficientand error information necessary to recreate the revenue pre-

diction curve is supplied in the Supporting Information. Theprevious section details how we derived the revenue predic-tion curves.

We can convert power capacity to energy capacity by mul-tiplying by our chosen duration. Multiplying energy capacityand normalized revenue yields the total revenue versusthreshold ratio in Figure 8 b. The total cost is also plotted inthis panel, assuming an installation capital cost of $ 750 perkWh amortized over 10 years at a 10 % discount rate, thoughin practice this assumption should be replaced with costsbased on local conditions (installation costs are expected tobe significantly lower in coming years[30]). The total profitcurve as a function of threshold ratio is then calculated asthe difference between the total revenue and cost in Fig-ure 8 b. Finally, we determine the profit maximizing batterypower capacity for the selected duration by plotting theprofit against the power capacity in Figure 8 c.

The profit-maximizing power capacity is highly sensitive tothe shape of the assumed cost function. The accuracy of thisstep relies upon a good understanding of local installationcosts. In reality, the cost as a function of battery power ca-pacity is not linear. Inverter sizes are not continuous—as bat-tery capacity is increased, larger inverters, or a greaternumber of inverters, will need to be installed, which will in-crease costs in a nonlinear manner. However, given an accu-rate cost function, the methods in the above example stilllead to the profit-maximizing power capacity.

Conclusions

We have proposed the threshold ratio as a new metric de-rived directly from a buildingQs load profile that generallycharacterizes the power spikes encountered in aggregateover a year at that site, which can be used to analytically pre-dict revenue from retail peak-shifting across different batteryand tariff scenarios. Commonly available spreadsheet soft-ware can be used to perform the calculations. This methodtrades a decrease in accuracy for a vast reduction in thehuman and computing resources required for model develop-ment. Our key findings include:

Figure 6. Comparison of the parameters across demand charges (a) and du-ration (b). The shape parameter (coefficient b) does not change acrossdemand charge levels or duration. Scaling parameters a and c change linearlyin demand charges to reflect a steepening of the curve. Scaling parameters aand c change exponentially in duration to reflect a flattening of the curve.

Figure 7. Example plot of the spike-to-battery and threshold ratios as a func-tion of battery power capacity. The threshold ratio is a simple ratio of the bat-tery power capacities—the power capacity currently being investigated divid-ed by the power capacity at which the spike-to-battery ratio equals 1. Thespike-to-battery ratio (black curve) is not smooth because it reflects the varia-bility of the building’s load shape.

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· The threshold ratio incorporates load shape and magni-tude information to predict peak-shaving revenue for indi-vidual customers.

· Our model provides an easily reproducible revenue-pre-diction curve based on three parameters (provided in theSupporting Information).

· The regression-based model allows for explicit calcula-tions of uncertainty.

· Model parameters are independent of battery power ca-pacity given a fixed discharge duration (power capacitiesof 10–35 % of the building maximum load examined inthis work).

Future work could investigate if this analysis applies to tar-iffs that have intraday changes in demand charges (e.g.,many utilities in California and Consolidated Edison in NewYork). Our algorithm could be changed to find only thosespikes in load above the target during the hours of highestdemand charges. However, this still may not adequately cap-ture the batteryQs load shifting decision between demandcharge periods. Such research may be necessary if BTM bat-teries become more prevalent, and more utilities shift awayfrom flat-rate demand charges to reflect the time-varyingnature of capacity supply costs.

Acknowledgements

This research was supported by the Carnegie Mellon Electrici-ty Industry Center. M.F. received partial support from Carne-

gie MellonQs Pugh Fellowship. J.A. received partial supportfrom the Carnegie Mellon Climate and Energy DecisionMaking Center (CEDM), formed through a cooperativeagreement between the National Science Foundation andCMU (SES-0949710). We also thank an anonymous utility forproviding the load dataset.

Conflict of interest

The authors declare no conflict of interest.

Keywords: batteries · energy storage · peak shifting ·revenue prediction · techno-economic analysis

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Manuscript received: August 9, 2017Revised manuscript received: September 20, 2017

Accepted manuscript online: October 10, 2017Version of record online: February 5, 2018

Energy Technol. 2018, 6, 649 – 657 T 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 657