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Assessing the Economics of Customer-Sited Multi-Use Energy Storage Wuhua Hu, Ping Wang, and Hoay Beng Gooi Abstract—This paper presents an approach to assess the eco- realistic aging model for the ESSs. When the storage is made nomicsofcustomer-sitedenergystoragesystems(ESSs)whichare of Li-ion batteries, the aging model characterizes the battery owned and operated by a customer. The ESSs can participate in aging cost interms of its instant charge/dischargerate and the frequencyregulationandspinningreservemarkets,andareused duration, which was experimentally established in [5]. to help the customer consume available renewable energy and reduce electricity bill. A rolling-horizon approach is developed to optimize the service schedule, and the resulting costs and II. MODELINGTHEESSSANDTHEIRSERVICES revenuesareusedtoassesseconomicsoftheESSs.Theeconomic assessment approach is illustrated with case studies, from which We use N to denote the set of ESSs. The time is dis- 7 weobtainsomenewobservationsonprofitabilityofthecustomer- cretized into slots, each with a duration of Ts. The charge sited multi-use ESSs. and discharge of ESSs are scheduled periodically to support 1 0 self-consumption of renewable energy, frequency regulation, 2 spinning reserve, and TOU electric bill reduction. The math- I. INTRODUCTION ematical models of the ESSs and the four supported services n Energy storage systems (ESSs) are a promising ingredient a are developed in this section. J forreliableintegrationofrenewableenergiesintofuturepower grids.ESSsarehowevercostlyatthepresentstage,andrecent 0 A. Modeling the ESSs 3 studies showed that they are unlikely to generate a net profit if ESSs are used to provide a single service. This motivates We assume that a customer owes and operates multiple ] the use of ESSs for multiple service provision [1]. ESSs, each of which follows a generic model used in [6]. C When ESSs are scheduled for multiple services concur- Let the charge and discharge rates of ESS i be scheduled as O rently, potential conflicts occur due to the limited power and pc and pd for time slot t, respectively. And let vc indicate i,t i,t i,t . h energy capacities available. An ideal scheduling approach the working mode of the ESS i, which is 1 (or 0) if it is not t needs to address the conflicts in an optimal way, such that discharged (or not charged). These variables satisfy a m the net profit is maximized subject to operational and service 0≤pc ≤vc pc , 0≤pd ≤(1−vc )pd , (1) constraints. So far, only a few studies have been conducted, i,t i,t i,max i,t i,t i,max [ partiallyaddressingtheencounteredchallenges.Amongthem, where pci,max and pdi,max are the corresponding upper bounds. 1 [2] presents a coarse framework to investigate the net profit, The two constraints ensure that charge and discharge comply v butleavesthenontrivialmodelingoftheoptimizationobjective with the rate limits and do not happen in the same time slot. 2 7 and constraints to readers for specific applications. Reference After charge/discharge, the state of charge (SOC) of the ESS 4 [3]developsamixed-integerlinearprogrammingmodelfocus- i, denoted by s , renews into i,t 8 ing on maximizing the revenue without considering the costs 0 of ESSs. More recently, [4] presents a concrete optimization si,t =si,t−1+Ts(ηicpci,t−pdi,t/ηid)/Eicap, (2) . 1 formulation in a rolling-horizon framework. However, the where ηc,ηd ∈ (0,1) are the energy conversion coefficients, 0 formulationdoesnotappropriatelycapturetheoperatingcosts and Ecaip isithe energy capacity of ESS i. The SOC must be 7 of ESSs which are dependent on their varying charge and i 1 maintained within certain limits in order to protect the ESSs, discharge rates [5]. : and this will be discussed later in Section II-F. v This work considers customer-sited ESSs which provide Bothchargeanddischargeincuranagingcost,whichisthe Xi multiple services. The ESSs are used to participate in reg- money loss of the initial investment. Let the cost be estimated ulation and spinning reserve markets, and help the customer r as Cc(pc ) and Cd(pd ) for charging and discharging ESS i a consume available renewable energy and reduce time-of-use i i,t i i,t attheratesofpc andpd foronehour,respectively.Thecost (TOU)electricitybill.Wedevelopacomprehensivescheduling i,t i,t of operating ESS i in time slot t is then given by model which captures the dynamics of ESSs and associated aging costs, the supported services and associated revenues, C (pc ,pd )=T Cc(pc )+T Cd(pd ). i i,t i,t s i i,t s i i,t and all major service and operational constraints. By opti- If the ESSs use Li-ion batteries, the cost can be approxi- mizing the schedule using a rolling-horizon approach, we matedbyapiece-wiselinearfunctionwhichisfurtherobtained are able to assess profitability of the ESSs. Different from by solving the following linear program [5], [6]: aforementioned literature [2], [3], [4], we include the support of self-consumption of renewable energy and embed a more α T C (pc ,pd )≈ i s minζESS, This work was supported in part by the Energy Innovation Programme i i,t i,t 0.8Eicap ζiE,StS i,t Office(EIPO)throughtheNationalResearchFoundationandSingaporeEco- s.t., γ ηc[1000×aESS(pc )2+n bESSpc ]+ 1−γi (3) nomicDevelopmentBoard.W.HuiswiththeSignalProcessingDepartment, i i k i,t i k i,t ηd i Institute for Infocomm Research, A*STAR, Singapore. P. Wang is with the ×[1000×aESS(pd )2+n bESSpd ]≤ζESS, ∀k∈K , School of Computer Engineering and H. B. Gooi is with the School of k i,t i k i,t i,t ESS Electrical and Electronic Engineering, Nanyang Technological University, where α is the unit capital cost ($/Wh) to purchase ESS i; Singapore. E-mails: [email protected], {wangping, i ehbgooi}@ntu.edu.sg. ζiE,tSS is an auxiliary variable; γi is the fraction of a single cyclic aging cost incurred by fully charging the battery from CapacityClearingPrice(RMCCP)isdenotedbycRMCCP,and t empty; n (cid:44) Ecap/0.0081, which is the number of battery the Regulation Market Performance Clearing Price (RMPCP) i i modules that form the ESS i, each with a capacity of 0.0081 is denoted by cRMPCP. Both prices are updated at a period of t kW; and {aESS,bESS} are the coefficients associated T . k k k∈KESS s with the linear segments as indicated by a certain set K . The revenue of the regulation service is then computed as ESS B. Service for self-consumption of renewable energy Rfr(pftr)=Tsρftrpftr(cRtMCCP+cRtMPCPµftr)+Tscpt (cid:88)(pifr,t,d−pfir,t,c), i∈N The customer has installed renewable energy generators. where the first term owes to the service provided, and the The aggregate generation power for time slot t is denoted secondtermaccountsfortherevenueobtainedfromtheenergy as pre. For time slot t, let the customer be scheduled to charged/discharged to/from the ESSs. t consume the renewable energy at a rate of pre,sc, and the t surplus renewable energy be charged to ESS i at a rate of D. Service as spinning reserve pre,c, and the remaining renewable energy be exported to the mia,trket at a rate of pre,s. These power variables satisfy Consider a spinning reserve market which periodically t publishes a reserve availability price, denoted by csr. The t 0≤prte,sc ≤dt, 0≤pri,et,c ≤pci,max, 0≤prte,s ≤psmax, minimum participation power is required to be psmrin, and prte,sc+prte,s+(cid:88)pri,et,c ≤prte, (4) the minimum commission time is Tmsrin. The ESSs may be scheduledtosupportthisservice,whichisdictatedbyabinary i∈N variable vsr, 1 for participation and 0 otherwise. Let psr,d where d is the load demand of the customer, and ps is t i,t t max be the power reserved by ESS i, which is the commissioned the maximum power that can be injected to the grid. The last maximum discharge rate under contingencies. The reserved inequalityadmitscurtailmentofsurplusrenewablegeneration, power satisfies if any. Giventheelectricitypurchasepricecpt andsalepricecst,we 0≤pis,rt,d ≤vtsrpdi,max, (cid:88)pis,rt,d ≥vtsrpsmrin. (6) cancomputetherevenueofconsumingrenewableenergywith i∈N the help of ESSs as The minimum support time will be enforced via constraint Rsc(prte,sc,prte,s,{pri,et,c}i∈N)=Tscpt(prte,sc+ (cid:88)pri,et,c)+Tscstprte,s, (10) ahead. The revenue for this service is calculated by i∈N (cid:88) R ({psr,d} )=csrT psr,d. of which the first part owes to the avoided purchase of energy sr i,t i∈N t s i,t from the market, and the second part owes to the surplus i∈N renewable energy exported to the market. E. Service for TOU electricity bill reduction and preparation for future services C. Service for frequency regulation WithTOUelectricitypricinginformation,theESSsmaybe Frequency regulation aims at stabilizing the grid frequency used to reduce the electricity bill by charging and discharging at a desired value. Let ufr,up be an indicator which is 1 for t the storage appropriately. At the meantime, the ESSs may ramp up regulation and 0 otherwise. The minimum power to be charged/discharged to prepare for future services. Let participateintheregulationmarketisrequiredtobepfr .The min the aggregate charge and discharge rates of ESS i for such ESSs may participate in the market or not, as indicated by vtfr purposes be scheduled as pfs,c and pbr+fs,d for time slot i,t i,t equal to 1 and 0, respectively. Let ESS i charge at a rate of t, respectively. The revenue obtained from the charged and pfr,c ifufr,up =0anddischargeatarateofpfr,d ifufr,up =1. i,t t i,t t discharged energy is computed as The power variables satisfy R ({pbr+fs,d,pfs,c} )=T cp(cid:88)(pbr+fs,d−pfs,c), 0≤pfr,d ≤vfrufr,uppd , ∀i∈N, br i,t i,t i∈N s t i,t i,t i,t t t i,max i∈N 0≤pfr,c ≤vfr(1−ufr,up)pc ∀i∈N, whichowestotheavoidedordesiredpurchaseofenergyfrom i,t t t i,max (5) (cid:88) the market. The charge and discharge rates satisfy pfr (cid:44) (1−ufr,up)pfr,c+ufr,uppfr,d ≥vfrpfr , t t i,t t i,t t min 0≤pbr+fs,d ≤pd , 0≤pfs,c ≤pc . (7) i∈N i,t i,max i,t i,max where the first two inequalities ensure that charge and discharge for the regulation service do not happen concurrently. F. Feasibility constraints to support the multiple services ConsiderthepaymentschemeimplementedbyPJMinUSA To support the four services above, we must have [7],[8].Theregulationserviceispaidbythecommittedpower capacity (denoted by pfr) and the regulation performance pri,et,c+pfir,t,c+pifs,t,c =pci,t ≤vic,tpci,max, (8) t (dictated by the performance score ρfr and the regulation pfr,d+pbr+fs,d =pd ≤(1−vc )(pd −psr,d), (9) t i,t i,t i,t i,t i,max i,t mileage ratio µftr). The performance score (ρftr) is computed s +psr,dTsr /Ecap ≤s ≤s , (10) basedontheregulationperformanceinthepastperiod;andthe i,min i,t min i i,t i,max mileage ratio (µfr) is the mileage of the fast regulation signal for each i ∈ N. Constraints (8) and (9) are related to t dividedbythemileageoftheslow(orconventional)regulation the aggregate charge rate and discharge rate for multiple signal, both in the past service period. The Regulation Market services, respectively. Constraint (10) imposes SOC limits 2 to protect the ESSs from being over charged or discharged, TABLE I: PARAMETERS OF THE ESSS. THE POWER IS IN in which s ,s ∈ (0,1) are the required limits and UNITOFKWANDTHEENERGYISINUNITOFKWH. i,min i,max pis,rt,dTmsrin is the energy committed as spinning reserve. The Type Eicap si,min si,max pci,max pdi,max ηic ηid three constraints link up the four services provided by the 1 480 0.2 0.9 102 74 0.82 0.88 ESSs,throughwhichtheconflictsinbetweenwillberesolved 2 720 0.2 0.9 148 113 0.85 0.90 via optimization. Consequently, the ESS management problem is defined as The right hand side of the inequality in (9) contains a term vc psr,d, which is bilinear in the two decision variables. It P0: min−TNP(t) i,t i,t is desirable to reformulate this term into a linear equivalent subject to, (1)−(7), (10)−(13), ∀i∈N,τ ∈Ht form. Introduce an auxiliary variable z . Then, z is equal i,t i,t wherethesubscriptτ insteadoftisusedinallconstraints,and to vc psr,d if it satisfies the following constraints: i,t i,t constraint (3) refers only to the inequalities. In P0, the power variables are pc , pre,c and pfr,c for charge and pd , pfr,d 0≤z ≤pd vc , i,τ i,τ i,τ i,τ i,τ i,t i,max i,t (11) and psr,d for discharge of each ESS i ∈ N in each time slot psi,rt,d+pdi,max(vic,t−1)≤zi,t ≤psi,rt,d, τ ∈Hi,tτ, and prτe,sc and prτe,s for the customer to self-consume and sell available renewable energy in each time slot τ ∈H . The equivalence is easy to verify with the McCormick lin- t earizationmethod[9].Therefore,wecanreplacevc psr,d with Theauxiliaryvariablesarebinaryvariables{vic,τ}i∈N,vτfr and i,t i,t vsr for all τ ∈H , and real variables {ζESS} and z for z subjectedtotheaboveconstraints,whichmakesconstraint τ t i,τ i∈N i,τ i,t all τ ∈H . (9) completely linear in the variables. t The objective and constraints of P0 are linear in the variables, except constraint (3) which is quadratic in the decision III. THESTORAGEMANAGEMENTOPTIMIZATION variables {pc ,pd } for each i ∈ N and τ ∈ H . Therefore, i,τ i,τ t PROBLEMANDITSSOLUTION theproblemisamixed-integerquadraticprogram(MIQP)and can be solved by standard MIQP solvers. Once an optimal Thestoragemanagementoptimizationproblemisdefinedto solution is obtained, only the part for the first time slot t will maximize the total net profit (namely, minimize the total net be implemented to dispatch the ESSs. The schedule for the loss)overarollinghorizonsubjecttoservicerequirementsand futuretimeslot(t+1)willbedeterminedinasimilarwayby operationalconstraints.Givenadecisiontimepointt,thetime shiftingthetimehorizonforwardbyoneslotandthensolving slots within a look-ahead horizon for a size of H are denoted the new optimization problem. by the set H . The optimization will be performed using the t forecast data over the horizon. Thetotalnetprofit(TNP)overthehorizonsumsuptherev- IV. CASESTUDY enues earned from the four services minus the operating cost This section assesses the economics of multi-use ESSs incurredtotheESSs.WiththestorageagingcostC (pc ,pd ) based on the scheduling approach developed above. i i,t i,t computedfromthelinearprogram(3),theTNPcanbeshown to have the following specific form: A. Simulation setup and input data  Rsc(pτre,sc,ptre,s,{pir,eτ,c}i∈N)  The demand is scaled historical hourly electricity demand TNP(t)=τ(cid:88)∈Ht +Rfr({p+ifr,R,τ−cb,(cid:80)rp(if{r,i,τp∈dbiN},rτi+∈CfNsi,(d)p,+cip,τfiRs,,,τcps}rdi(,iτ{∈)pNsi,r)τ,d}i∈N)  oPdfeVmagacneondlel,ergiasetiosinnca,Clweadhliifhcohirsnthoiaarisfcoaarlpaheosauukmrleymqeugraelnweteoreakt6io0[n1%0p]o.ofTwtheheresfpooelraarka-  cppre,sc+cspre,s+ρfrpfr(cRMCCP+cRMPCPµfr)  =Tsτ(cid:88)∈Ht τ+τ(cid:80)i∈Nττ+ccsτrpτp(sipτ,rdiτ,,dττ−−mτpciin,τζiE+,SτS2pα0ir,e.iτ8,τζcEiE),icSτaSp τ  sEduiSsmSchmsaewrgrietwhaegseipnkegciicnfiocsBatstriuoasnrseselesgsitvi[m1en1a]t.iendTTbhyaeb(lc3eu)s,It.ionmTwheehriircdhecphthlaoerygmseotadwneodl parameters are set the same as those in [6]. which is subject to the constraints in (3). We have used Thehourlyregulationsignalandassociatedmarketclearing the revenue and cost expressions introduced in the previous price are from the real operational records of PJM [12]. So subsections and also the equalities in constraints (8) and (9) arethehourlyspinningreserveprices.Thepriceofpurchasing to deduce the TPN. Since the decision variables {pbr+fs,d,pfs,c} do electricityfromthemarketisobtainedfromPG&E[6],which i,τ i,τ i∈N,τ∈Ht consists of peak, mid-peak and off-peak prices for different not appear in TNP(t), we can eliminate these redundant vari- periods of a day. The price of selling electricity to the market ables and simplify constraints (8) and (9) into the following: is 60% of the purchase price. The purchase and sale powers pre,c+pfr,c ≤pc ≤vc pc , (12) are unrestricted in our study. i,t i,t i,t i,t i,max pfr,d ≤pd ≤(1−vc )pd −psr,d+z , (13) i,t i,t i,t i,max i,t i,t B. Profitability of the multi-use ESSs for each i ∈ N. Here the variable zi,t is an equivalent of When the input data within the horizon is perfectly known, vic,tpsi,rt,d, satisfying constraint (11). By minimizing TNP(t) the total net profit obtained is shown in Fig. 1(a). The with the new constraints, the solution of (pbr+fs,d,pfs,c) can profit decreases with the storage purchase price, and vanishes i,τ i,τ then be recovered from (8) and (9). once the purchase price is higher than 300 $/kWh. On the 3 Profit owing to solar energy & ESSs ($)4455660505050000000000000 H50=1 100H=1520 20H0=4250 (aH)30=08fiProtowingtoESSs($)11225050500000000000H0=12 50 100 150 200 250 (b3)00 ffDi.relativetoFig.1(a)($)-----32211-050505050 H=501 100H=2150 2H00=4 250 H=3080 ffDi.relativetoFig.1(b)($)H---211-050505=012 50 100 150 200 250 300 Storagepurchaseprice($\kWh) Storagepurchaseprice($\kWh) Storagepurchaseprice($/kWh) Storagepurchaseprice($/kWh) Fig. 1: Net profit vs. the rolling (look-ahead) horizon size. Fig. 3: Profit differences relative to the profits in Fig. 1. 150H=2 0.3 forecast horizon. Further the forecast is capped within 80% W)100 ESS1 ESS2 of the minimum and 120% of the maximum true values. The (k 50 0.25 hargerate-1-05000 SOC0.01.52 d1i(faf)e-r(ebn)ceasreofshthoewnresiunltiFnigg.ne3t.pArosfiotsbrseelravteivde, ttohethdoisfefeirnenFciegs. C-150 0.1 are mostly negative (it can be positive as rolling-horizon 0 24 48 72 96 120 144 168 0 24 48 72 96 120 144 168 Hourlyrevenue($)1105500000 24H=482 72 H96=4120 144 168fiAccumulatedprot($)1234500000000000000000 24 48 72 96 120 144 168 oltirohnopsedbtsiiummecssataitzegotaosnftiitftophounrardoetefimcsttahasaseytrceeeabcruseormsonesraoudslmb.lb-rioyecplaattihtsmiesveaesflostoimrnetechtnahetsetraelpeofrpenrrrogoernasrcc.uhenN)pie,srvoisenfiordttmishc.eeaTlhteiohsnwisgs, 150H=4 hargerate(kW)-11-005500000 ESS1 ESS2 SOC0000....2345 proTahcihs ptoapsecrheddevuelelopVceu.dsCtoaOmNreoCr-lLlsiiUntegSd-IhOoNErSSizSosn fooprtimmiuzlatit-isoenrvaicpe- C-150 provision. The operating cost and yielded revenues were used 0 24 48 72 96 120 144 168 0 24 48 72 96 120 144 168 Time(h) Time(h) to assess the economics of the ESSs. The effectiveness of the Fig. 2: Battery dynamics and the resulting revenues and profits. proposed approach was illustrated with case studies. Future research will investigate the impact of storage energy and other hand, the profit increases with the horizon size H, but power capacities on the economics of multi-use ESSs. the marginal benefit decreases and becomes small once the horizon size is larger than 4. REFERENCES The above profit contains the contribution of solar energy whichisassumedfreehere.Togetridofthiscontributionand [1] Fitzgerald,Garrett,J.Mandel,J.Morris,andH.Touati,“Theeconomics of battery energy storage: How multi-use, customer-sited batteries de- obtain the value solely for the use of ESSs, we subtract the liver the most services and value to customers and the grid.” Rocky above profit with the one obtained without having any ESSs. MountainInstitute,Tech.Rep.,Sep2015. This yields the reduced profits shown in Fig. 1(b). [2] S. You, C. Træholt, and B. 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