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IEEE TRANSACTIONS ON POWER SYSTEMS 1

Stochastic Simulation of Utility-Scale StorageResources in Power Systems With Integrated

Renewable ResourcesYannick Degeilh and George Gross, Fellow, IEEE

Abstract—We report on the extension of a general stochasticsimulation approach for power systems with integrated renewableresources to also incorporate the representation of utility-scalestorage resources. The extended approach deploys models of theenergy storage resources to emulate their scheduling and opera-tions in the transmission-constrained hourly day-ahead markets.To this end, we formulate a scheduling optimization problem todetermine the operational schedule of the controllable storage re-sources in coordination with the demands and the various supplyresources, including the conventional and renewable resources.The incorporation of the scheduling optimization problem intothe Monte Carlo simulation framework takes full advantage ofthe structural characteristics in the construction of the so-calledsample paths for the stochastic simulation approach and to ensureits numerical tractability. The extended methodology has thecapability to quantify the power system economics, emissions andreliability variable effects over longer-term periods for powersystems with the storage resources. Applications of the approachinclude planning and investment studies and the formulation andanalysis of policy. We illustrate the capabilities and effectivenessof the simulation approach on representative study cases on mod-ified IEEE 118 and WECC 240-bus systems. These results providevaluable insights into the impacts of energy storage resources onthe performance of power systems with integrated wind resources.

Index Terms—Discrete random processes, emissions, energystorage resources, Monte Carlo/stochastic simulation, productioncosting, reliability, renewable resource integration, sample paths,transmission-constrained day-ahead markets.

I. INTRODUCTION

S TORAGE devices offer substantial benefits to system op-erations by providing the flexibility to mitigate the effects

of variable renewable energy sources and the ability to supplyenergy and capacity-based ancillary services [1]–[4]. Effectivestorage deployment can, moreover, obviate or defer the need

Manuscript received February 03, 2014; revisedMay 07, 2014, June 11, 2014,and June 22, 2014; accepted June 23, 2014. This work was supported in partby the U.S. Department of Energy through “The Future Grid to Enable Sus-tainable Energy Systems”, an initiative of the Power Systems Engineering Re-search Center (PSERC), the Stanford University Global Climate and EnergyProject (GCEP) and the PSERC funding for the Project S-40 “Integration ofStorage Devices into Power Systems with Renewable Energy Sources”. Paperno. TPWRS-00161-2014.The authors are with the Department of Electrical and Computer Engineering,

University of Illinois at Urbana-Champaign, Urbana, IL 61821 USA (e-mail:[email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2014.2339226

for specific transmission improvements and/or addition of newgeneration resources. The ability to exploit the increased flex-ibility imparted by storage applications to the power systemhinges on the development of appropriate models, methodolo-gies and tools, and the formulation of effective policy initia-tives. A particularly acute need is a practical simulation tool thatcan emulate, with good fidelity, the expected variable effectsin transmission-constrained systems with integrated renewableand utility-scale energy storage resources (ESRs).We report on the extension of a Monte Carlo simulation

approach [5] to represent the impacts on the hourly transmis-sion-constrained day-ahead market (DAM) outcomes of theoperations of multiple integrated ESRs interacting with thedemands and renewable/conventional resource outputs. Weconsider MWweek-scale ESRs that are, typically, scheduledover horizons ranging from a few days to a week. Examplesof such utility-scale ESRs include pumped-hydro storage,compressed-air energy storage (CAES) and some types ofbattery technologies, such as sodium sulfur (NaS) and flowbatteries [1, p. 39]. Moreover, we assume that the ESRs aredeployed as a system resource by the Independent SystemOperator (ISO). In such a context, the ESR outputs are notoffered into the market, as is the case for speculative sellers;rather, the ESRs are ISO-controlled and operated in such a wayas to bring maximum economic benefits to the side-by-sidepower system and DAM operations over the specified timeperiod. To this end, the DAM clearing mechanism must beadapted to recognize and exploit arbitrage opportunities inthe operations of ESR in coordination with the clearing of thedemands and conventional/renewable resource outputs. Bycontrast, ESRs that are operated for-profit by a speculativeseller have their outputs offered into the DAMs. In such a case,the scheduling of the ESR is the responsibility of the specu-lative seller, who specifies the offer quantity and price (bidquantity and willingness-to-pay, when it comes to purchasingenergy from the market to charge the storage resource) of theESR with the objective to maximize his own profit over thespecified time-period. We point out that, once the offering/bid-ding strategy of the speculative seller is known, for-profit ESRparticipation in the DAM is represented by its offer quantityand price (bid quantity and willingness-to-pay), similarly tothat of a conventional generation resource (load). Therefore,our approach is in contrast to the large body of literature thatinvestigates the operations and impacts of hybrid wind-storagesystems [6]–[9] and the participation of ESRs in the markets

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

as for-profit, independent resources [10]–[13]. Our work fallsin a different thread of research, that for which the ESRs areassumed to be controlled by a central entity—the ISO forexample. Most papers in that area primarily seek to develop op-timal strategies for storage resource operations in the short run,with an evident operational planning perspective [14]–[17].The stochastic programming frameworks used in these works,while very well detailed, require extensive computations andas such, do not lend themselves to the simulation of powersystem with integrated renewable and storage resources overextended periods of time. Our approach adopts a longer-termplanning perspective and is developed with the objective toevaluate the impacts on the variable effects of MWweek-scaleESRs deployed as system resources1 in power systems withintegrated renewable resources. More specifically, the deploy-ment of the proposed extended stochastic simulation approachis to assess, over longer duration periods, the ESR impacts onpower grid variable effects in terms of economics, reliabilityand emissions. The paper explicitly considers ESRs and theirinteractions with the other resources, including the variablerenewable resources and time-varying demand. Moreover, thevarious sources of uncertainty under which the power systemsoperate in the competitive electricity market environment withfull consideration of grid constraints, are explicitly represented.The extended stochastic simulation approach retains the in-

frastructure and the core aspects of the methodology in [5] andincorporates the steps to appropriately represent the ESR op-erations, which strongly depend on the loads and the outputsof the conventional and renewable resources. Specifically, weretain the representation of the demands and supply-resourceswith discrete-time random processes (r.p.s). Such models ac-count for not only the uncertain and time-dependent behaviorof the demands/resource outputs, but also the spatial correla-tions among the various load/resource sites as well as their tem-poral correlations. Our simulation methodology uses systematicsampling mechanisms based on Monte Carlo simulation tech-niques to generate the realizations—the so-called sample paths(s.p.s)—of the various r.p.s that represent the sources of un-certainty in the demands/resource outputs [5]. Based on suchs.p.s, we determine the offers and demands to be used as in-puts into the hourly DAMs in a simulation period of one-weekduration. The incorporation of ESRs requires that we scheduletheir operations over multiple time periods so as to adequatelyrepresent their charge/discharge cycles. Such a requirement en-tails modifications in the Monte Carlo simulation methodologyin [5] which emulates the solution to a sequence of 168 sep-arate OPFs to represent the clearing of the 168 hourly DAMsin a weekly simulation period, as part of a so-called simulationrun. In this work, we construct the so-called scheduling opti-mization problem (SOP) and deploy it as the basic mechanismin the extension of the stochastic simulation framework in [5]to represent the impacts of ESRs on the DAM outcomes over aweek-long period. We formulate the SOP as a multi-period op-timization able to take advantage of arbitrage opportunities inthe operations of each ESR so as to meet the demand together

1We note that our approach is still able to represent the impacts of for-profitESRs, so long as the offering strategies of the associated speculative sellers areknown.

with the set of conventional and renewable resources, and withthe intertemporal ESR operational constraints fully considered.Conceptually, absent the representation of the ESRs and theiroperational intertemporal constraints, the SOP, defined over the168 periods of a weekly simulation period, solves the identicalproblem as that solved by the 168 separate OPFs that clear thehourly DAMs in [5]. As such, the SOP formulation is used toemulate both the DAM outcomes and the ESR schedules overthe weekly simulation period. In the extended simulation frame-work, we use the SOP to map the s.p.s of the input r.p.s—thedemands, renewable resource outputs at various sites and theconventional generation available capacities—into the s.p.s ofthe market outcome r.p.s, including the ESR operations, loca-tional marginal prices (LMPs), congestion rents, supply-siderevenues, wholesale purchase payments and the emissions, aswell as the contributions to the LOLP and EUE indices. Themarket outcomes serve to compute the performance metrics ofinterest, analogously to the scheme presented in [5]. In fact, inthis manner we also obtain the hourly expected stored energy ofeach ESR and the associated discharge output/load charge loadover the week-long simulation period.The extended methodology is therefore able to evaluate the

impacts of storage integration into a grid with renewable re-sources, taking explicitly into account various sources of uncer-tainty, renewable variability and intermittency and the impactsof the transmission constraints on the deliverability of the elec-tricity to the loads. The effective deployment of the SOP is crit-ical in the quantification of the variable effects of large-scalepower systems with storage and variable renewable resourcesoperating in a market environment in terms of economics, re-liability and emissions. There is a broad range of applicationsof the simulation methodology to planning, investment, trans-mission utilization and policy formulation and analysis studiesfor systems with integrated storage and variable energy sources.In addition, the methodology is very useful in the quantitativestudy of a broad array of what if questions.The remainder of the paper consists of three sections. In

Section II, we discuss the modeling of the ESRs and statethe mathematical formulation of the SOP. In Section III, webriefly summarize the salient aspects of the approach in [5]and describe the steps taken in its extension to incorporate therepresentation of the ESRs. We also provide some details on theimplementational aspects of the extended simulation approach.In Section IV, we illustrate the capabilities of the methodologywith representative case studies that focus on the economic,reliability and environmental impacts of ESR in systems withintegrated wind resources. We also present a case study on theeconomic impacts of ESR siting. We conclude in Section Vwith a summary.

II. ESR MODELING AND SOP FORMULATION

We devote this section to describe the modeling of the utility-scale ESRs and the formulation of themathematical statement ofthe SOP that is solved to determine the hourly ESR operations.We discretize the time axis so as to adopt the granularity usedin most North American DAMs, i.e., we adopt an hour as theshortest indecomposable period of time. As such, all the vari-ables/parameters in the ESR models are indexed by the hour,


DEGEILH AND GROSS: STOCHASTIC SIMULATION OF UTILITY-SCALE STORAGE RESOURCES 3

and the ESR operations are scheduled on an hourly basis. Wedenote by the variable in hour and use the notationgiven in the Appendix.

A. Modeling of the ESRs

We consider the set of ESRs. EachESR acts either as a load in hours during which it charges,or as a generation resource in hours during which it discharges.In other hours, it remains idle with no impact on the side-by-sidepower system and market operations. We assume that the opera-tional state—discharge, charge or idle—of ESR , together withits associated MW discharge output (charging load ),remain unchanged over the duration of a particular hour . Weintroduce the binary variables , to specifythe operational state of ESR in hour . Binary variable

takes value 1 if ESR discharges (charges) during hour, 0 otherwise. We enforce the physical fact that an ESR cannotboth charge and discharge at the same time, that is, and

cannot be both equal to 1, by requiring that for each hour, . ESR is said to be idle when it nei-ther discharges nor charges, i.e., . We alsodenote by the maximum discharge (charge) ca-pacity of ESR and by the minimum discharge(charge) capacity. We refer to and

as the effective lower and upperlimits on the output (load) of ESR such that, in any hour ,for any ESR , and

.Let be the stored energy in resource at the close

of hour , or, equivalently, at the start of hour . This en-ergy must satisfy the specified minimum and maximum storedenergy MWh limits, and , respectively, of ESR .We also represent the discharge (charge) efficiency of ESRby the factor . For each hour thatESR supplies MW (charges MW) to (from) thegrid at its node, its stored energy level decreases (increases) by

MWh .

B. SOP Formulation

The economic deployment of utility-scale ESRs aims to takeadvantage of arbitrage opportunities by charging the resourceswhen electricity market prices are low and discharging theirstored energy to displace electricity generated by higher-pricedand, typically, polluting resources, with the overall efficienciesof the charge-discharge cycle explicitly taken into account. Inthis paper, we assume that each integrated ESR is controlledby the Independent System Operator (ISO), whose objective isto maximize the total system social surplus over all the hours.The ISO, therefore, ensures that the ESRs are deployed so as toenhance the economic performance of the side-by-side powersystem andDAM operations. A direct consequence of such ESRdeployment policy is that the ESRs also contribute to avert un-economical scarcity events, thereby improving the system re-liability. The maximization of the system social surplus mustbe performed over multiple hours so as to fully take advantageof the ESRs’ ability to shift significant amounts of energy over

time. We formulate the scheduling optimization problem (SOP)to determine the most economic operational trajectory for theESRs considering the variations in the demands and the outputsof the renewable resources and the available capacity of eachconventional resource over the time horizon of interest. The so-lution of this optimization problem determines the optimal loadand supply-resource dispatch, including that of the ESRs, foreach hour of the optimization period .The SOP is formulated as a multi-period OPF with the ex-plicit representation of the inter-hour constraints in storage op-erations, demands and supply-resource outputs, as well as thetopology of the transmission network in each hour . Inthe formulation of the SOP, we make explicit use of the loss-lessness assumption typically deployed in the linearized powerflow model, which is the practice in today’s ISO-run markets[18, p. 534].We present the mathematical statement of the SOP using the

notation in the Appendix. For the development here, we limitthe renewable resources to wind so as to simplify the presen-tation. The decision variables of the SOP are the withdrawals

due to each demand , the outputs of the varioussupply resources , the operational state binary variables

and , the withdrawals , the outputs and thestored energy level of each ESR in , as well as thephase angles . The SOP co-opti-mizes the withdrawal/output of each load/resource—includingthose of the ESRs—over each hour with the objective tomaximize the total system social surplus:

(1)

to maximize the sum of the hourly social surpluses over thehours in . The hour social surplus is expressed as the differ-ence between the total social benefits andthe total supply costs of the conventional and wind resources,

. We further assumethat the cost (benefit) functions

are piecewise linear, as is the case in theOPF-based market clearing mechanisms, typically, used bythe ISOs. We explicitly exclude the benefits/costs for thestorage resources in the objective function (1) as those areindirectly accounted for in terms of the ESR impacts on thesystem supply-resource dispatch costs. Indeed, in the ex-pression for the nodal power balance equations, the term

explicitly representsthe net power injection of the storage resources connected atnode in hour ( and cannot be both strictlypositive in the same hour , as per their effective lower andupper limits and the requirement that ):

(2)

(3)



Each ESR , whose stored energy at the end ofhour exceeds its minimum capability , may actas a generation resource and displace higher-priced supply re-sources in hour . In such cases, the output of each dis-placed supply resource is reduced commensurately, as are theirassociated costs in the objective function (1), re-sulting in a corresponding increase in the social surplus (1) forthat hour. For an optimal trajectory, the storage resources dis-charge, typically, in the peak hours so as to displace the out-puts of the higher-priced supply resources and maximize theresulting increases in the objective function (1). On the otherhand, when an ESR acts as a load to charge energy in hour , itmakes use of energy generated by both conventional and renew-able resources, resulting in additional generation costs for thathour. The solution of the SOP takes advantage of arbitrage op-portunities so that the charging hours for the storage resourcesare in the periods of low prices—typically, the low-load hours.The optimal solution that maximizes the total social surplusover all the hours in ensures that the ESRs are utilized onlywhen the value of the energy they displace exceeds the costs in-curred in their charging, with the efficiencies of the charge/dis-charge cycle fully taken into account. Furthermore, the opti-mization scheme takes advantage of the potential synergy be-tween storage and wind resources. In the absence of storageresources, the ISO may be forced to “spill” wind energy dueto the insufficiency of the load demand in the low-load hours.The charging of the ESRs may be scheduled to be carried outin such hours of high supply and low demand, when the gen-eration costs are, typically, low. The additional demand createdby ESR charging may be supplied, in some cases, by the windenergy that would have otherwise been “spilled”. In that sense,the storage resources provide the ability to shift the wind energyproduced during the low load hours to the peak load hours, whenit can be used to displace the outputs of polluting and more ex-pensive conventional resources.The SOP formulation explicitly incorporates transmission

constraints to ensure that the line flows do not violate thethermal limits of the transmission lines:

(4)

We represent of the ESR intertemporal operational constraintsthat relate the charge/discharge decisions to the stored energyin an ESR, with the discharge/charge efficiencies explicitly con-sidered:

(5)

The stored energy in each hour is a critically important decisionvariable, even though it is not explicitly represented in (1). Thepresence of the constraints in (5) introduces an intertemporalcoupling in the multi-hour optimization, resulting in a system ofinterdependent OPFs. These equalities serve to ensure that thestorage resources accumulate energy during the lower-pricedhours so as to discharge energy in subsequent, higher-pricedhours. The discharge (charge) efficiency coefficient

, strongly influence the storage resource operations. Themore efficient the ESRs, the higher their utilization since the

optimization tries to minimize the energy losses incurred witheach charge/discharge cycle so as to lower the overall supplycosts.We also include the constraints to specify the capacity ranges

within which an ESR may discharge or charge, respectively:

(6)

(7)

We note that the minimum and maximum discharge (charge) ca-pacities are both multiplied by the operational state status vari-able . So, whenever ESR discharges (charges) inhour , the associated status variable is 0, resultingin the discharge output (charge withdrawal ) being0. This formulation preserves the linearity of the constraints,which helps with the computational tractability.Further, we represent constraints to ensure that an ESR may

not both discharge and charge in the same hour since

(8)

(9)

Also, we represent the constraints on the physical limits on theenergy that can be stored in ESR by

(10)

with the initial stored energy is given by

(11)

The consideration of the limits on the demand/output of all eachload and each supply resource results in the constraints:

(12)

(13)

(14)

The resulting SOP in (1)–(14) is a large-scale mixed-integerlinear program (MILP). We use the superscript to denote theoptimal value of the decision variables that solve the SOP. Forexample, the values provide the ESR dis-patch results . We note that the solution to theSOP determines not only the operations of the ESRs, but alsothe load and resource dispatch for each hour in the optimizationperiod. Similarly, at the optimum, the dual variables (shadowprices) of the power balance constraints (2) and (3) are inter-preted as the locational marginal prices (LMPs) for each hour

. As such, we view the dispatch and shadow prices deter-mined by the SOP solution to be those of a DAM with the ex-plicit representation of the impacts of the ESRs on the nodal netpower injections, and consequently, on the DAM outcomes. Wemake use of this fact in the extension of the stochastic simula-tion approach of [5] to represent the impacts of the utility-scalestorage resources on the side-by-side power system and marketoperations. We also note that, absent the representation of theESRs and their associated intertemporal coupling constraints(5), the SOP consists of separate OPF problems that maythen be independently solved. Each suchOPF is identical to the



hourly DAM clearing model discussed in the Appendix in [5].Thus, the SOP can be seen as the “time-coupled”, generalizedstatement of the DAM clearing problem formulated in [5].In the next section, we discuss the SOP deployment in the ex-

tended simulation approach to determine not only the schedulebut to also emulate the clearing of the DAMs with integratedstorage resources.

III. EXTENDED STOCHASTIC SIMULATION APPROACH

We devote this section to the discussion of the steps under-taken to incorporate the representation of the utility-scale ESRsinto the stochastic simulation approach for power systems withintegrated renewable resources presented in [5].We use the sim-ulation we developed to emulate the side-by-side power systemand transmission-constrained DAM operations with the objec-tive to quantify the impacts of integrated renewable resourceson the power system variable effects over longer duration pe-riods. We briefly review such stochastic simulation approach inthe first subsection, then discuss in the second subsection its ex-tension to incorporate the representation of ESRs.

A. Fundamentals of the Stochastic Simulation Approach

The simulation study period is decomposed into the non-overlapping weekly simulation periods ’s with ,

. We assume the system resource mix and unitcommitment, the transmission grid, the operational policies, themarket structure and the seasonality effects are fixed over theduration of each simulation period . Each simulation periodconsists of 168 hourly subperiods, whose set is denoted by

, and where each subperiod is thesmallest indecomposable unit of time in the representation ofany phenomena of interest.For the explicit consideration of uncertainty associated with

the time-varying loads, the highly variable renewable resourcesand the available capacities of the conventional resources, weuse discrete-time random processes (r.p.s) indexed by the 168hours of the simulation period. Each conventional resource ismodeled as a multi-state unit with two or more states—outaged,various partially derated capacities and full capacity.We assumethat each conventional resource is statistically independent ofany other generation resource, and use a discrete-event drivenMarkov Process model with the appropriate stochastic event-times distributions to represent the underlying r.p. governingthe available capacity of each conventional resource [19]. Themodeling of the multi-site wind speed and demand share somesimilarities: we make use of time-synchronized mesoscale datato construct the wind speed (power output) and demand inputr.p.s.2 More specifically, we gather weeks of simultaneously-measured hourly wind speeds at multiple sites buyer demands(at multiple buses) from time-synchronized mesoscale histor-ical data. We use these data to build the sample spaces of windspeed and demand random processes and capture, as a result, thespatial and time correlations among the hourly wind speeds (de-mands) at multiple sites (load buses). In particular, the multi-site

2We note that any statement on the wind speed r.p. applies equally well to astatement on its associated wind power output r.p. due to the fact that the windpower output is modeled as a piece-wise polynomial function of the wind speed.

wind speed (nodal buyer demand) random process is a collec-tion of time-indexed random vectors, with each random vectorcontaining the ordered collection of the wind speed (buyer de-mand) random variables at the multiple sites (load buses) foreach value of the time index, i.e., a particular sub-period of thesimulation. We note that, by construction from the time-syn-chronized mesoscale data, the random variables that are the ele-ments of the time-indexed random vectors in the collection thatrepresents the random process of interest, be it the nodal de-mand or multi-site wind speed random process, are intrinsicallycorrelated. The random process representation, therefore, cap-tures the time dependent behavior of the wind speeds (wind re-source outputs) at the various locations and that of the nodal de-mands. Under this representation, in a system with low windsduring peak load periods for example, the expected high de-mand in a peak hour is associated with low expected valuesin the wind power outputs in that same hour . In this way, ourapproach represents the misalignment of the wind power out-puts and the demand in such a peak hour . We use the simpli-fying assumption that the random variable that represents thewind speed at site in hour and the random variable thatrepresents the nodal buyer demand in hour are statisticallyindependent. This assumption, in effect, indicates that the be-havior of buyer demand in hour has no impact on the be-havior of the site wind speed (power output) in that hour andin all the other hours and vice-versa. In terms of the misalignedwind power outputs and loads during peak hour example dis-cussed above, the statistical independence assumption impliesthat the deviations of the wind power outputs from their lowexpected values in peak hour are independent from the devi-ations of the demands from their high expected values in thatsame peak hour . In some other hours, both the wind and de-mand may be low—and this will be correctly represented byour approach since the expected values of the wind and de-mand random variables in those hours will be low—yet theirdeviations around their expected values will be independent.We note that this statistical independence assumption is reason-able in light of the primary purpose of our simulation approach:to evaluate, over longer-term periods, the expected variable ef-fects of large-scale power systems with integrated renewableand storage resources. As such, our methodology does not rep-resent the more extreme and exceptional weather events suchas storms, for example, that may strongly impact—albeit overrelatively short-term periods—both demand and wind patterns.Furthermore, in the study of large scale systems, we note that thewind resources are often located at considerable distance fromthe load centers. Under such conditions, the hourly wind speedvariations at a remote wind farm are unrelated to the hourly vari-ations in the demands, and so the correlations among demandsand wind speeds, or, equivalently, power outputs are, virtually,0. Thus, for such simulations, it is reasonable to assume that thedemands behave independently from the wind speeds (poweroutputs).In the analytical framework of the approach, we view the

hourly transmission-constrainedDAM outcomes as themappingof the “input” r.p.s via the OPF solution of the market clearing.Consequently, the DAM outcomes are also r.p.s indexed by the168 hours of the simulation period. For convenience, we refer to



them as the “output” r.p.s. The approach’s use of Monte Carlosimulation techniques systematically samples the various r.p.sto generate the so-called sample paths (s.p.s) that contain thehourly realizations of the random variables (r.v.s) constitutingthe r.p.s. The thrust of the Monte Carlo simulation approach isthe emulation of the 168 hourly DAM outcomes in each simu-lation period. The s.p.s of the input r.p.s provide the basis forthe formulation of the offers and bids into the 168 DAMs of thesimulation period. The clearing of the 168 DAMs in the simula-tion period results in the construction of the s.p.s of the outputr.p.s. We refer to the evaluation of the hourlyDAM outcomes forthe 168 hours in the simulation period as a simulation run. Thebasic idea of the independentMonte Carlo simulation [20, p. 10]is to execute multiple statistically independent simulation runsin such a way as to construct for each “output” r.p. of interest acollection of output s.p.s which are used to estimate the perfor-mance metrics. Such performance metrics are selected to be theexpected values of the time-indexed r.v.s constituting the outputr.p.s of interest.3 We perform a sufficient number of simulationruns to obtain the specified statistical reliability requirement forthe sample mean estimators of the market outcomes of interest[21, pp. 82 and 451].

B. Extension of the Approach To Represent the ESRs

We now detail the steps taken to extend the base stochasticsimulation framework summarized in Section III-A to incorpo-rate the representation of the utility-scale ESRs. With the in-tertemporal coupling introduced by the representation of theESR operations, we can no longer solve, as part of a simula-tion run, a sequence of 168 independent hourly OPFs to clearthe hourly DAMs over the week-long simulation period. Bycontrast, we now solve a sequence of 7 SOPs, one for eachday of the week. In such a context, each SOP serves two pur-poses: to emulate, for a given day in the simulation period ,the clearing of its 24 hourly DAMs, and to schedule the ESRoperations over a week-long period whose first day is the daywhose DAM clearing results are obtained. For clarity in the pre-sentation, we will refer to such a day as day in the simula-tion period , with . We regard the solutionsof the SOP for the 24 hours of day to be the outcomes ofthe corresponding hourly DAM. These day outcomes serve toconstruct the output s.p.s whose values we use to quantify theperformance metrics of interest. The SOP optimization period

must also include additional hoursthat immediately follow the 24 hours of day to ensure that theESRs are scheduled in such a way as to reflect their continuedoperations beyond the simulated day . Such additional periodis required so that the ESRs are not discharged by the last hourof day , an unrealistic outcome as the ESRs are operated on abroader horizon than a day. To avoid complications with a lim-ited scheduling horizon, we solve each SOP over a week-periodand so for a given simulation period . The solu-tion of each SOP for the hours beyond those of the simulatedday are not used in the construction of the output s.p.s; theyserve simply to represent the continued operations of the ESRs

3Other metrics, such as the variances of said r.v.s, may be defined along sim-ilar lines.

Fig. 1. Role of the SOP in the emulation of the DAMs of a simulation period.

beyond day . The stored energy of each ESR at the end of thelast hour of day is recorded to be used as the initial storedenergy of each ESR in the formulation of the SOP for the day

. For the purposes of this discussion, we assume that theinitial stored energy level of each ESR in the first hourof day 1 is given. For each hour in day , the so-called cost(benefit) functionsin the SOP objective (1) are the offer (bid) functions submittedby each seller (buyer) for the 24 DAMs of day . The upperbounds on the demands in (12) and the supply-resource out-puts in (13) and (14) are set by the hourly realizations of thes.p.s of the corresponding input r.p.s, as is the case discussed in[5]. The sampling procedure we use to construct such s.p.s fromthe joint cumulative distribution functions of the correspondinginput r.p.s is identical to that in [5]. For each hour beyondthe 24 hours of day , the offer (bid) functions, as well as theupper bounds on the demands and supply-resource outputs areobtained differently to reflect the fact that, in the real world, themarket players only submit their bids and offers for the “cur-rent” day and any supplementary information about the hoursfollowing day must be estimated by the ISO. Thus, we assumethat the demands are fixed and the sellers offer at a predeter-mined price in all hours following day ; furthermore, we makeuse of the expected values for the loads and wind power outputs,coupled with the assumption that a conventional generation re-source keeps running at full capacity (potentially after recov-ering from a forced outage state) to determine the upper boundson the demands and supply-resource outputs in these hours. Weillustrate in Fig. 1 the overall procedure for the execution of agiven simulation run.In terms of the stochastic simulation framework, the ESR’s

operating outputs are represented by a discrete-time r.p., alongthe lines used to represent the uncertain and time-varying de-mands or multi-site wind speeds in [5]. As such, the ESR op-eration r.p. is a collection of time-indexed random vectors for

, where each random vector in a given hour containsthe r.v.s that represent the output of each ESR in . Such model



Fig. 2. Conceptual structure of the simulation approach with the incorporatedutility-scale storage resources.

captures the cross-correlations among the operations of the var-ious ESR in as well as the correlations over time that char-acterize the strongly time-dependent behaviors of storage re-sources. Within the framework of our extended simulation ap-proach, the storage operation r.p. constitutes an output r.p. thatis obtained from the mapping of the input r.p.s—the buyer de-mand, the multi-site wind speed and the conventional genera-tion resource available capacity r.p.s—by the sequence of the 7SOP solutions. As shown in Fig. 2, the other output r.p.s are thesame as in [5].We also discuss the use of a relaxed version of the SOP in

(1)–(14) for improved tractability in the Monte Carlo simu-lations. We relax the highly-computationally-intensive MILPinto the more tractable linear program (LP) we next describe.The proposed relaxation only involves the modification ofconstraints (6) and (7): we assume that the ESR minimumcharge and discharge capacities are 0, with allthe binary variables and equal to 1. We note that theoutcomes of the resulting LP cannot reflect the impacts of theESR minimum discharge/charge capacities. In actual simula-tions, the discharge outputs (charge loads) that fall below theminimum charge (discharge ) capacities can beapproximated by simply rounding them to either 0 (in whichcase, such ESRs would be considered idle) or said minimumdischarge (charge) capacities, whichever is closer. We foundthat the proposed relaxation proved effective in the case studiesreported in Section IV, as there were very few hours for whichsuch rounding was necessary.In the next section, we illustrate the broad capabilities of

the extended stochastic simulation approach with a variety ofcase studies aimed at investigating the economic, reliability andemission impacts of integrated ESR in power systems with in-tegrated wind resources.

IV. REPRESENTATIVE SIMULATION RESULTS

We performed extensive testing of the simulation approach onvarious test systems to study a broad range of applications, in-cluding resource planning, production costing issues, transmis-sion planning, environmental assessments, reliability and policyanalysis. We illustrate the application of the approach with threerepresentative studies performed onmodified IEEE 118 [22] and

Fig. 3. Expected hourly storage operation and SMPs.

WECC 240-bus systems [23]. We refer the reader to [24] and[5] for the detailed description of the modified IEEE 118 andWECC 240-bus systems, respectively. In all the case studies,we run a unit commitment for each simulation period to deter-mine the set of conventional generators that are committed, andso, the sellers that participate in the DAMs, and ensure a 15%reserve margin (unless otherwise specified), measured with re-spect to the simulation period peak load. In such cases whereESRs are part of the resource mix, we assume that each ESRreserve capability is equal to its installed capacity, in light ofthe ability of ESRs to discharge and thereby provide capacityduring the peak hours. As a result, each MW of installed ESRcapacity replaces a MW of conventional generation capacity tomeet the 15% reserves requirements in systems with ESRs in theresource mix. We note, however, that were a co-optimized en-ergy/ancillary service market implemented, such an assumptionwould no longer be necessarily valid since the market clearingwould determine which resources are to provide capacity for thepurpose to meet the 15% reserves requirements.We also assumethat each buyer bids his load as a fixed demand in each hourlyDAM. Since wind power has no fuel costs, we assume that allwind power outputs are offered at 0 $/MWh in each hourlyDAMthroughout the simulation period. In each study, we limit ouranalysis to a single year in order to focus on the insights intothe nature of the results obtained. Thus, all chronological plotsare done over the “average week of the year”, for which thehourly values are averaged over all the representative weeks ofthe year [5], with weights equal to the number of actual weeksrepresented by each represented week.In the first case study, we examine the impacts of integrated

ESRs on the modified WECC 240-bus system under deepeningwind penetration: from 0 MW total wind nameplate capacity inthe base case to 13 600MW, in 3400 MW increments. The totalwind nameplate capacity is allocated in equal quantities among4 wind farms at distinct locations. To gain insights into the im-pacts of the integrated ESRs on the variable effects, we evaluateeach wind penetration case with and without the ESRs. In theno storage cases, the supply-side resources consist of the systemconventional generation units and the 4 wind farms, while op-erations use a 15% reserves margin provided solely by the con-ventional units. In the storage cases, the system sports, in ad-dition to the resource mix of the no storage cases, 5 identicalstorage units, each with 400 MW capacity, 4000 MWh storagecapability and a round-trip efficiency of 0.9. In such cases, the



Fig. 4. Expected hourly total wholesale purchase payments and emis-sions; all values are averages over the hours of the year.

Fig. 5. Annual reliability metrics.

15% reserves margin is provided by a combination of conven-tional and storage resources. We provide in Fig. 3 plots of theexpected hourly storage charge load/discharge output for oneof the ESRs, as well as the expected hourly values of what wecall, for convenience, the system marginal prices (SMPs)—theweighted averages of the LMPs over all the system nodes, withweights equal to the cleared demands.The results indicate that the ESRs tend to charge (discharge)

during the low-load (peak-load) hours when the electricityprices are low (high). The SMP plots further show that theESRs not only favorably impact the peak-load hour prices,they also reinforce the benefits brought about by integratedwind resources. We note from the plots in Fig. 4 that, as thewind penetration deepens, the expected hourly total wholesalepurchase payments and emissions are reduced. Significantimprovements in the system reliability indices are shown inFig. 5. These plots also make plainly clear that these reductionsand improvements are characterized by diminishing returns asthe wind penetration deepens. Such results are representativeof the ability of the ESRs to attenuate, to some extent, suchdiminishing returns. Overall, storage works in synergy withwind to drive down further wholesale purchase payments andimprove system reliability. On the other hand, emissionsare insignificantly affected by the integration of a storage unit.We attribute this result to the fact that, in a system where thenameplate wind capacity does not exceed the system base load,

emissions depend largely on the relative utilization of thevarious fossil-fuel fired units, as affected by the charge/dis-charge cycles of the ESRs. In this particular case, the reductions

Fig. 6. Annual LOLP and EUE versus system reserves margins.

in emissions caused by the ESR displacement of pollutingconventional resources during the peak-load hours are about thesame as the increases in emissions due to ESR chargingduring the low-load hours.In the second case study, we investigate the extent to which

a combination of wind and ESRs may replace conventionalresources from a purely system reliability perspective in theWECC 240-bus system. For reference, we also provide theresults of the same case study with no ESRs. The base casewith no wind and no ESRs evaluates the system LOLP andEUE with a 15% system reserves margin. In all the other cases,the conventional resource mix is supplemented by 4 windfarms—with a total nameplate capacity of 13 600 MW, i.e.,about 16% of the annual 81 731MW peak load - and 5 identicalstorage units as in the first study set. In these cases, the reservesare provided by the conventional and ESRs (where applicable)and we examine the impacts of progressively retiring someconventional resources, thus decreasing reserves margin levels.We provide in Fig. 6 the annual LOLP and EUE values as afunction of the system reserves margin levels.The sensitivity results without ESRs indicate that the 13 600

MW of installed wind capacity can replace roughly 4% of theweekly peak loads, on average over the year, in terms of re-tired conventional generation capacity, that is about 3000 MW.With the integrated ESRs, and all other conditions unchanged,the LOLP results indicate that another half percent can be re-placed, which corresponds to an additional 400 MW of retiredconventional generation capacity. We note that, as the reservesare provided by the conventional and ESRs, these additional 400MW represent the added benefits, from a purely reliability per-spective, of combining wind and storage resources. While thewind resources by themselves had a firm capacity of about 22%of their total nameplate capacity, the integration of 2000MW ofstorage capacity raised the wind resource firm capacity by anadditional 3% of the total wind nameplate capacity. This resultindicates that wind and ESRs can work synergystically to im-prove system reliability.The third case study pinpoints the ability of the simulation

approach to study congestion impacts. We examine the impactsof ESR siting on transmission utilization and the economics ofnode 59, the most heavily loaded bus in our modified IEEE118-bus test system. We present sensitivity cases that involvethe siting of 4 identical ESRs—each with 200 MW capacity,2000 MWh storage capability and a round-trip efficiency of



Fig. 7. Expected hourly total congestion rents (a) and transmission path con-gestion (b).

Fig. 8. Expected hourly at bus 59 before (a) and after doubling the trans-mission capacity of the path (b).

0.9—as the ESRs are successively further removed from bus59. The total ESR capacity accounts for about 10% of theannual peak load. For reference, we provide a base case with nointegrated ESRs. In the first subcase, all the 4 ESRs are locatedat bus 59. In each subsequent subcase, the ESRs are sited onemore node removed from bus 59, such that in the 4th subcase,all ESRs are 3 nodes away from bus 59. We provide in Fig. 7plots of the expected hourly total congestion rents as well aswhat we have identified to be a congested transmission path,from a major generation source node with 2 nuclear 400 MWunits to the major load center at bus 59.The congestion rent plots in Fig. 7(a) indicate that ESR opera-

tions cause congestion during the low-load hours, especially sothe closer to bus 59 the ESRs are sited. We provide in Fig. 8(a)plots of the expected hourly LMPs at bus 59 that incorporate theimpacts of such congestion. For each siting subcase, the conges-tion rents are clearly reflected in the bus 59 LMP and particu-larly so during the low-load hours. These plots further indicatethe influence of siting the ESRs on the decreases (increases) ofbus 59 LMP during the high-load (low-load) hours due to ESRdischarge to displace more expensive conventional resources(charge). The observed congestion leads to an examination ofeffective steps to reduce the congestion rents. For example, theincrease of the total transmission capacity of the path (depictedin Fig. 7(b)) by 100% results in the elimination of the conges-tion and in virtually identical LMPs for each siting subcase, asshown in Fig. 8(b). The results also indicate that, in this partic-ular case study, it is best to locate the ESRs 3 nodes away frombus 59 in order to avert the transmission path congestion and theresulting raise in bus 59 LMP. Indeed, the curves in Fig. 8(b) are

essentially the same as the curve in Fig. 8(a) representing theevolution of bus 59 LMP before the reinforcement of the trans-mission path and when the ESRs are 3 nodes removed from bus59. Overall, this third case study suggests that the siting of ESRcan have significant impact on the network congestion patternsand, consequently, on the LMPs.

V. CONCLUSION

In this paper, we report on the extension of a stochastic simu-lation approach for power system with integrated renewable re-sources to incorporate the representation of utility-scale energystorage resources. We develop models for the energy storageresources and deploy the scheduling optimization problem toschedule their operations over multiple time periods, in con-junction with the demands and the conventional/renewable re-sources and with the explicit consideration of the transmissionconstraints. The seamless incorporation of the energy storageresource representation into the stochastic simulation approachallows us to retain the detailed use of discrete-time randomprocesses in the adaptation of Monte Carlo simulation tech-niques to explicitly represent the various sources of uncertaintyin the demands, the available capacity of conventional genera-tion resources and the time-varying renewable resources, withtheir temporal and spatial correlations. In such a framework,the energy storage resource operations are themselves repre-sented by a discrete-time random process, as their operations di-rectly depend on the interactions among the demands and othersupply-resources. The extended simulation approach thus sportsthe ability to quantify the impacts of integrated renewable andstorage resources on the power system economics, reliabilityand emissions.The representative results we present from the extensive

studies performed demonstrate effectively the strong capabil-ities of the simulation approach. The results of these studieson modified IEEE 118 and WECC 240-bus systems, clearlyindicate that energy storage and wind resources tend to com-plement each other and this symbiosis reduces wholesale costsand improves system reliability. In addition, we observe thatemission impacts with energy storage depend on the resourcemix characteristics. An important finding is that storage seemsto attenuate the “diminishing returns” associated with increasedpenetration of wind generation. The limited ability of integratedstorage resources to enhance the wind resource capability tosubstitute for conventional resources from purely a systemreliability perspective is evidenced in the studies presented.Some useful insights into the siting of storage resources areobtained and they indicate the potentially significant impactsof such decisions on the network congestion patterns and,consequently, on the LMPs.The development of the approach provides the first compre-

hensive implementation for the simulation of large-scale powersystems with integrated renewable and storage resources. Thestochastic simulation approach has a broad range of applicationsto various issues in planning, operational analysis, investmentevaluation, policy formulation and analysis and provides quan-titative answers to various what if questions.



APPENDIXNotation:

Discrete time variable(hour).

Optimization period of theSOP.

Set of network buses withbus 0 as the slack bus.We consider the networkconsists of buses.

Set of transmission lines.

Reduced branch to nodeincidence matrix.

Branch susceptance matrix.

Reduced nodal susceptancematrix.

Column vector of thenodal susceptance matrixcorresponding to bus .

Vector of power angle(excluding the slack buspower angle which is takenas 0).

Vector of line flows.

Vector of transmission linethermal rating.

Vector of transmissionline thermal rating in theopposite flow direction.

Set of wind farms thatparticipate in the DAM.

Set of conventionalgeneration resources thatparticipate in the DAM.

Offer price of seller .

Seller resource output(decision variable).

Available capacity of sellergeneration resource.

Available power output ofseller wind farm.

Minimum capacity of sellergeneration resource.

Power injection at nodedue to conventional resourcegeneration.

Power injection at nodedue to wind farm generation.

Set of buyers in the DAM.

Buyer willingness-to-buy.

Buyer demand (decisionvariable).

Power consumption at nodedue to loads.

Set of ESRs beingconsidered.

ESR output (decisionvariable).

net power injection atnode due to ESRgeneration/consumption.

ESR discharge status(binary) variable.

ESR charge status (binary)variable.

Maximum dischargecapacity of ESR .

Minimum dischargecapacity of ESR .

Discharge efficiency ofESR .

ESR stored energy at theend of hour .

ESR demand (decisionvariable).

Maximum charge capacityof ESR .

Minimum charge capacityof ESR .

Charge efficiency of ESR .

Round-trip efficiency ofESR .

Optimal value of decisionvariable in the SOP.

Study period.

ith simulation period.

Set of subperiods , i.e.,smallest indecomposibleunit of time, in a simulationperiod ; in the proposedapplication of the approach,a subperiod is of durationone hour and .



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Yannick Degeilh has recently defended his Ph.Dthesis in power system engineering at the Universityof Illinois at Urbana-Champaign and is currentlyserving as a consultant for Energy ExemplarLLC—the developers of the Energy Market Mod-eling software PLEXOS—in Roseville, California.Yannick also holds a M.Sc. degree from Texas A&MUniversity in the same area of expertise and receivedhis French engineer degree in Mechanical/ElectricalEngineering from the Ecole Spéciale des TravauxPublics (ESTP), Paris, France. His research interests

include power system analysis, planning and operations, energy markets,renewable resource integration as well as stochastic modeling, simulation andoptimization.

George Gross (F’88) is Professor of Electrical andComputer Engineering and Professor, Institute ofGovernment and Public Affairs, at the Universityof Illinois at Urbana-Champaign. His current re-search and teaching activities are in the areas ofpower system analysis, planning, economics andoperations, utility regulatory policy and industryrestructuring. In the 1999–2000 academic year,he was a Visiting Professor at a number of Italianinstitutions of higher learning, including Universityof Pavia, Politecnico di Milano and Politecnico di

Torino. His undergraduate work was completed at McGill University, and heearned his graduate degrees from the University of California, Berkeley. Hewas formerly with the Pacific Gas and Electric Company, where Dr. Grossfounded the company’s Management Science Department and held other keymanagement, technical and policy positions. During 1992–93, Dr. Gross wasat the Electric Research Power Institute to develop research directions on openaccess transmission. George Gross is a co-founder of POWERWORLD andserved on its Board of Directors from 1996–2001. Dr. Gross won the FranzEdelman Management Science Achievement Award in 1985 and is the recipientof several prize paper awards from IEEE and HICSS.Prof. Gross has consulted on electricity issues with utilities, government or-

ganizations and research institutions in North America, Europe, South America,Australia and Asia. He has lectured widely and has given numerous invited pre-sentations at leading universities and research institutions throughout the world.His numerous publications have appeared in the leading journals in the field andhis research results have been presented at a wide array of international confer-ences. He has made a broad range of contributions in various areas of powersystem planning, operations, analysis and control. His work on smart grid is-sues has focused on both the technical and the regulatory aspects. The principalareas of involvement include the design of AMI architectures to ensure cyber se-curity, the deployment of AMR for demand response, the integration of demandresponse, renewable and storage resources into the grid and the economics ofsmart grid implementation.