optimal operation strategy of energy storage system for grid-connected wind power plants

Optimal Operation Strategy of Energy Storage Systemfor Grid-Connected Wind Power PlantsZhen Shu, Student Member, IEEE, and Panida Jirutitijaroen, Senior Member, IEEE

Abstract—This paper proposes an adaptive optimal policy forhourly operation of an energy storage system (ESS) in a grid-connected wind power company. The purpose is to time shift windenergy to maximize the expected daily profit following uncertaintiesin wind generation and electricity price. A stochastic dynamicprogramming (SDP) framework is adopted to formulate this prob-lem, and an objective function approximation method is applied toimprove the SDP computational efficiency. Case studies on theElectric Reliability Council of Texas demonstrate that the resultantprofits from SDP-based operation policy are considerably higherthan those from deterministic policy, and comparable to those fromtheperfect informationmodel. It is concluded that the presentedSDPapproach can provide operation policy highly adaptive to uncer-tainties arising from wind and price. The proposed framework canhelp the wind company optimally manage its generation with ESS.

Index Terms—Energy storage system (ESS), optimization,stochastic dynamic programming (SDP), storage operation, windgeneration.

NOMENCLATURE

Indices:Time index.Terminal time index.

Sets:Convex set of continuous feasible decisions.Set of operation policies.Set of the entire admissible policies.

Parameters:Operating cost of storage ($/MWh).Transmission capacity (MW).Initial and final energy levels of storage (MWh).Energy capacity of storage (MWh).Power capacity of storage (MW).Ratio of total generated energy to the energyconsumed from compressed air.Energy conversion efficiency of charging.Energy conversion efficiency of discharging.

Variables:Random wind power output at time (MW).Random electricity price at time ($/MWh).Energy level of storage at time (MWh).

Charging ( > ) or discharging energy( < ) of storage during hour (MWh).Discarded power during hour (MW).

I. INTRODUCTION

I NTEGRATION of large-scale renewable energy sourcesbrings new challenges to power system operation due to

their high intermittency. The energy storage system (ESS) is aviable option to mitigate variability of renewable generation[1]–[3]. System operators use ESS for reliability improvement[4], ancillary services [5], and transmission congestion relief [6].Renewable energy producers apply ESS for capacity firmingand energy time shifting [2], [7]–[9]. For wind power plants,using ESS for energy time shifting may result in higher profitsthus making wind integration more attractive [2]. In the ElectricReliability Council of Texas (ERCOT), the wind power outputis usually high at night and low during daytime, whereas theelectricity load and price are usually low at night and becomehigher during daytime. If wind energy is stored during low-priceperiods and discharged back to the grid during high-priceperiods, higher profit can be achieved and peak load can alsobe reduced to help alleviate transmission congestions.

For wind power companies, the operation strategy of ESS isvery important in achieving optimal tradeoff between operationcost and revenue growth. This operation problem is challengingdue to stochastic behaviors of wind power and market prices.The issue of coupling wind power plants with ESS for energytime shifting has been studied in some literature in both planningand operation aspects [8]–[14]. However, these techniques areneither optimal [10]–[12] nor applicable to a large number ofwind and price scenarios [9], [10], [12].

In [12], a number of sample paths for uncertain price needto be obtained beforehand. A profit maximization problem isformulated and separately solved to find optimal daily operationfor each path. An operation strategy is then found from anenvelope of those daily operations, which provides a preferableoperation outline, but can neither indicate operations accuratelyunder various scenarios nor guarantee optimality. Moreover, asthe number of random variables grows or time horizon increases,the size of scenarios will grow substantially, which makes theproblem computationally intractable. The objective of [13] is tominimize the cost from thermal generator operation as well asESS installation without considering ESS operating cost. Theoperation policies are over-optimistic since future uncertaintiesare assumed known,which is not valid in practice. ESSoperationsare found as functions of system states with dynamic program-ming [9], [14]; however, a deterministic model in [9] is not

Manuscript receivedMarch 22, 2013; revised July 13, 2013; accepted August10, 2013. Date of publication September 30, 2013; date of current versionDecember 12, 2013. This work was supported by Ministry of EducationAcademic Research Fund, Grant R-263-000-691-112.

The authors are with the Department of Electrical and Computer Engineering,National University of Singapore, 119077, Singapore (e-mail: [email protected]; [email protected]).

Color versions of one ormore of the figures in this paper are available online athttp://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSTE.2013.2278406

190 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 1, JANUARY 2014

1949-3029 © 2013 IEEE

suitable for decision making under uncertainties. Although un-certainties are included by forecasted paths in [14], parametricanalysis under different forecast accuracies is still not capable ofrevealing the impact of uncertainties on hourly ESS operation.

The main challenge of ESS operation is to take a sequentialand adaptive action according to hour-by-hour realization ofwind and market price. Stochastic dynamic programming (SDP)is one of the mathematical tools that can be used to find suchhourly policy [16]–[18]. The SDP technique has already beenutilized in optimal powerflow control [19], long-term schedulingof hydrothermal generation [20], [21], as well as predictivecontrol of electric vehicles [22], [23]. Its application to storagemanagement has been discussed in some literature [24]–[26].Their applicability to the actual systems is limited due to severalsimplifications of storage systemmodeling, such as relaxation ofcharging/discharging ramp rate [26], neglecting of ESS operat-ing cost as well as energy conversion efficiency [24], [25].Without ramp rate constraint, sharp charging and dischargingcan severely damage ESS and are not allowed in practice [27].It should be noted that these simplifications may lead to aconsiderable overestimation of optimal profit, and therefore,mislead the ESS investment.

In this paper, an SDP framework is proposed to achieve theoptimal operation of ESS for wind energy time shifting. Thehour-by-hour uncertainties from wind and energy prices, as wellas realistic storage characteristics are considered. The casestudies demonstrate that the hourly optimal policy allows plantoperators to obtain considerably higher profits than those fromdeterministic policy and comparable profits to the perfect infor-mation (PI) model. The contribution of this paper is twofold.First, the SDP-based ESS operation policy adapting to hourlyinformation ofwind and price is developed. TheESS formulationincludes operation cost, charging/discharging ramp rate, as wellas energy conversion efficiency. The second contribution is toapply objective function approximation (OFA) for computingthe formulated SDP problem.Computational results demonstratethat the OFA method can be applied to a considerably largenumber of scenarios with acceptable computing efficiency; seeSection III for more details.

This paper is organized as follows. Section II presents problemformulation; Section III presents the solution method of OFA;SectionIVdescribessolutionvalidationandcomparison;SectionVshows case study results; and Section VI draws conclusions.

II. PROBLEM FORMULATION

A. Background

To construct a theoretically tractable problem, there are twoassumptionsmade in advance. 1)Acompressed air energy storage(CAES) is used as a storage option for a grid-connected windpower plant with an installed capacity between 50 and 100 MW[28]. The CAES provides capacity output in a range of severalhours and response time less than 0.5 h [2], [27], [29]. 2) Thegenerationcompanyoperating thiswindpowerplant is consideredas a price taker in the energy market. Assume that its wind powerproduction is considerably smaller than the total market capacityand will not have any significant impact on the energy price. This

is a common assumption found in similar studies [26], [31]–[33].Note that it might not hold for companies operating several large-scale wind plants. In such a case, the effect of wind production onmarket price will need to be considered according to a combina-tion of factors such as wind production, system load demand, andpower-dispatch rule [11], [34]–[36].

The ESS is used to control hourly power output from thepower plant according to uncertainties in wind production andmarket price. The SDP technique is applied to model theseuncertainties and to yield sequential and adaptive optimal deci-sions on a charging/discharging level.

B. SDP Framework

The SDP algorithm decomposes a sequential decision-makingproblem into several subproblems based on decision time inter-vals called stages. Uncertainties from stage to stage are incorpo-rated into subproblems. Solutions are determined based oninformation that is completely available at the current stage.

A decision process under the SDP framework is shown inFig. 1. On the finite horizon [ ], the decision stages are

. At each stage, the ESS levels (states) can beobserved. After random information of wind output and energyprice arrives at the beginning of each stage, the decision to chargeor discharge ESS is made using current realization. Consequent-ly, the storage level is adjusted from the current state to a newstate of the next stage (the next time interval). The decision ofeach stage is fully dependent on its revealed information. Thisproperty allows the operator a flexibility to adjust the storagelevel accurately according to real-time information. Note thatthe storage levels at the initial and final time are set to be equal.This is to ensure continuity of energy level over each horizon.

ThemaincomponentsofSDPframeworkare introducedbelow.1) Decision stages: The analysis is focused on the daily

operation over a horizon of 24 h. Each hour is defined as adecision stage , where , and the end ofhorizon is .

2) State variables: Two state variables are defined at time :ESS energy level , and two-dimensional discrete randomvariable . is described by joint probabilitydistribution of random wind and price . Assume that therandom information becomes available at time

before the decision for stage is made, and that the

Fig. 1. Decision process of ESS operation.

SHU AND JIRUTITIJAROEN: OPTIMAL OPERATION STRATEGY OF ENERGY STORAGE SYSTEM 191

values of state variables are consistent at each stage. A time-inhomogeneous Markov model is used to incorporate theuncertainties of hourly wind and price. Since wind power andelectric price, by nature, are both strongly dependent on thetime of day, their transition probabilities can be considered asfunctions of time. A time-inhomogeneous model would enablethese stochastic characteristics to be captured adequately.Stochasticity and correlations of random variables are modeledwith probability transition matrix , where is theprobability of transition from state at time to state attime , .

3) Decision variables: Two decision variables are defined ateach stage: charging or discharging energy amount , anddiscarded power . Assume that during a short interval ,the output power is , and that functions andare mappings from states to decisions and ,respectively.

C. Application of SDP to Storage Operation Problem

1) State transition function:Using CAES characteristics in [8]and [27], the storage energy level is described in the following:

where energy level at time is equal to its level at timeplus net energy. With input energy in charge mode, the netenergy is . With output energy in dischargemode, the net energy is . Note that CAESdischarges by burning natural gas to expand compressedair [8] and [27]. The ratio of total generated energy to theenergy consumed by compressed air is expressed by a factor

.2) Objective Function: The objective is to maximize expected

daily profit as seen in the following:

Hourly profit consists of two components: revenue from outputenergy in MWh, and operating cost fromconsuming natural gas in dischargemode. The set denotes theentire feasible decisions, given a state of .

It is impractical to directly compute function (2), since a hugenumber of daily scenariosmight be involved. The SDP algorithmis used to transform this problem into (3), which consists of a setof smaller subproblems. Each subproblem is a backward recur-sion function, and each value function expresses the relation-ship between current states and optimal profits earned in asubsequent period , as follows:

With random information available at the beginning of eachstage , (3) is further written into (4), where istransition probabilities of random variable. For simplicity, a term

in (5) is used to represent the objective, and it becomes afunction of states and decisions if isreplaced using (1). As seen in (6), an optimal operation policycan be generated as a sequence of functions that mapstates into decisions. This policy is chosen from a set includingthe entire admissible policies seen in (7), as follows:

3) Constraints: The problem constraints are shown in thefollowing:

Constraint (8) restricts energy level within ESS energy capacity,(9) and (10) ensure the continuity of energy level over each dayby imposing a constant for initial and final time points,(11) limits charging/discharging rate within ESS powercapacity, (12) restricts output power of this plant withinits transmission capacity, and (13) sets discarded power to bepositive. Here the time interval is set as .

4) Initial Value Function:The value function , as seen in (5),is computed from an objective , which includes two parts:profit of current stage and expectation of profit in futureperiod . At final stage , the length of period

is zero, which implies that achievable profit in thesubsequent period is also zero. The value function is henceinitialized in the following:

Note that when computation reaches stage 0, the term willpresent expected profit that is maximized for the entire horizon.

D. Challenges of SDP Approach

1) Closed-Form Solutions: Ideally, one would hope to deriveclosed-form solutions of SDP; however, they are rarely available


for most problems because functions in real settings are not instandard forms that can lead to analytical expressions [17]. In theproblem under discussion, difficulty in expressing probabilitydistributions of time-varying randomvariablesmakes the closed-form solutions impractical. As an alternative, numericalsolutions are employed.

A typical numerical method is discretization, which modelscontinuous variables as discrete values, and evaluates valuefunction with a rounding process as seen in the following:

At current state and decision , the next state found from

its discrete set is a value closest to the one deter-mined by transition function . Since the rounding process

implicitly takes any value between and as either

or , the continuous objectives are approximated as stepfunctions, which introduce some errors. A larger number ofdiscrete states can help to reduce this error [18].

2) Dimensionality: In the aforementioned discretizationapproach, a large number of states are required for eachcontinuous variable to achieve high solution accuracy, and thesize of state space grows exponentially with the number ofvariables. This “curse of dimensionality” problem bringscomputational challenge to SDP problems. Alternativeapproaches can be considered to alleviate this challenge. Forexample, objective functions can be calculated as continuousones if they are properly approximated with linear interpolationor polynomial interpolation approach [37], [38]. In this problem,ESS levels and operations have a nature of continuity such thatobjective functions are continuous on them. To preserve thiscontinuity, the objective functions are approximated withpiecewise linear interpolation and each subproblem is thensolved as a linear programming (LP) model. This approachenables SDP to achieve acceptable solution accuracy withreduced state size and computational time. Details will begiven in Section III.

III. OBJECTIVE FUNCTION APPROXIMATION

The proposed method of OFA is implemented in Fig. 2.First, probability transition matrixes are constructed, where thenumber of scenarios of random variable is , and a scenariocorresponding to index is . In initializa-tion, a set of ESS levels is specified in (16) as approximatedstates (nodes), as follows:

It has uniformly spaced values within ESS capacity limits.Two procedures are used at each stage: procedure (I) generatesfeasible states and (II) computes objective functions.

A. Procedure (I)

As seen in Fig. 2, for stage , afixed level is known. Forstages , their possible ESS energy states by thetransitions from time to time are identified as follows:

1) Given a set ofESS energy levels for timewith aminimum andmaximum , the extreme

values of a set for time are found in (17) and (18) withbackward recursion. In (17), themaximum state is restrictedby power capacity and ESS upper limit . In (18),the minimum state is restricted by power capacity ,wind generation, and ESS lower limit 0, as follows:

2) From the state set containing allpossible energy levels, find the values inthe range , and obtain a set for energy levelsat as

B. Procedure (II)

It can be proved that the objective functions are concave.Procedure (II) utilizes concavity property of the objective func-tions in computing subproblems. There are two activities (a) and

Fig. 2. Flowchart of OFA implementation procedures.


(b) under this procedure. Algorithm of activity (a) is presented inthe following steps.

1) For each ESS energy level , find a set

of possible transitions using (1). Each element isfound as

2) The objective function can be written in (21), where theterm , in (22), is an unknown function of decision .Based on the current scenario denoted as , set randomparameters as . Substitute pairs

and transition probabilitiesinto (22), and find a set of discrete points onfunction , as follows:

3) With points and known, use piece-wise linear interpolation to construct a function thatapproximates the unknown . As given in (23),consists of several segments, and their slopes and inter-cepts are found in (24) and (25), respectively,

The approximate objective is then written as

Algorithm of activity (b) is presented in the following steps.

1) Using the concavity property of function , an approxi-mate function is found in the following:

where is expressed as an infimum of linear functionsobtained in the previous activity (a).

2) For the original subproblem , construct an equivalentLP problem with decision variables ( ) in thefollowing:

where (30) ensures the feasibility of next state , and(31)–(33) are according to (11)–(13).

3) Solve this LP problem with CPLEX optimizer. Saveoptimal solution and objective profit

.

IV. SOLUTION VALIDATION AND COMPARISON

A. Validating OFA Solutions with State Enumeration

To validate the solutions of the OFA method, the stateenumeration approach is utilized, where all feasible decisionpairs are enumerated from their discrete sets, and theone that gives the best objective value will be simply chosen.

The comparison of state enumeration and OFA is illustratedin Fig. 3. The dotted curve represents an unknown concavemapping , where the function is to be maximized inorder to maximize , according to (21)–(22). Assume that sixstates are known to obtain values and thatthe feasible interval of is [ ], where

. The optimal point can be visibly observed as anintersection of function and function .

With state enumeration, within feasible decisions

, a maximum objective value is at . InOFA, an approximate function in solid line is found to preservethe continuity, monotonicity, and concavity of an unknown .

consists of five segments , where

and . On interval [ ], attains its maximumat . The fact indicates that OFA canachieve solutions and thus value functions more accuratelythan state enumeration. Higher accuracy in function willsubsequently increase solution quality at stage .

Fig. 3. Illustrative example comparing state enumeration and OFA.


B. Comparing SDP Model to Other Models

To demonstrate the performance of the SDP model, simula-tions are performed to compare the SDP model with two othermodels—the deterministic price (DET) model and the PI model.The paths of 24-h wind and price are sampled out based on theirprobability transition matrixes. Expected daily profit is thenestimated in the following:

where is a profit of sample day , and is thetotal number of sample days. Next, each model is explicitlydescribed.

1) SDPModel: For each known state including ESS leveland a random realization at hour of sample day , thecorresponding operations in the simulation environment,denoted by a decision vector , can be

found from a predetermined SDP solution array. Specifically,a sample is identified in the scenario set to give a solution set

associatedwith the knownESS state set .Then for a certain ESS level , its operations are found with

linear interpolation from two states ( , ) and their

associated solutions in (35). These

two states, satisfying , are found as the

adjacent points of from ESS state set . Withcurrent energy level and decision known, a level

at next hour is found sequentially. The profit of asample day , based on a daily sequence of operations, iscalculated in (36), as follows:

�; ;

; ;

2) DET Model: The DET model is an SDP model withoutprice uncertainties. While the wind is included stochasticallyby random variable , the price is considereddeterministically using its mean . Note that ideally adeterministic problem might be analyzed using mean valuesof both wind and price. However, optimal solutions based onmean values of wind may not be applicable, because chargingpower ( ) in constraint (12) is restricted to be no largerthan wind power. If the wind parameter is fixed at its mean ,an optimal decision satisfying may violate

for a sampled wind value .3) PI Model: This model represents an ideal case where future

information is assessable. This means that daily operationaldecisions are made after randomness of 24-h wind and priceis completely known. Given perfect information (a sample

path of wind and price) of each day , an independentproblem of maximizing daily profit is computed to obtain anoptimal profit .

V. CASE STUDIES

Case studies are conducted on a wind power plant withERCOT data in year 2008, where the peak wind output is45.87 MW with an installed capacity of 81.11 MW. Marketprices of wind resource in a rich-wind western zone are applied.Using parameters in [8], we set energy capacity

, power capacity , and initial level. The conversion efficiency of CAES is set as

[1], [27]. Note that the initial level is set compa-rably low, which gives enough space to store energy during earlyhours of a day when wind energy is sufficient. As the pricevariability is found considerably higher than wind variability,3 and 15 levels (scenarios) are used to represent randomwind andprice at each hour, respectively. The stochastic characteristics,including joint probabilities and transition probabilities, areextracted from the ERCOT historical dataset. Assume that thehistorical properties ofwind and price are representative enough toreflect their actual stochastic behaviors in the future; hence, theprediction error in the estimated stochastic characteristics is notconsidered in case analysis. The computation is performed foreach season based on its own patterns of wind and price.

A. Result Validation of SDP Model

Assume that sufficient solution accuracy is achieved by stateenumeration with 10 000 discrete states. The results obtainedfrom this approach are hence used as benchmark solutions.The expected daily profit is calculated in (37) with respectto random variable that depends on wind and price level atbeginning time , as follows:

The resultant profits are shown in Table I, where profits withoutESS as well as percentages of profit growth are also given.

Table I shows that significant profit growth can be achievedwith integration of ESS. Higher profit growths exist inwinter andspring because of the higher level of wind generation. Duringthese seasons, there exist very low or negative prices, signalingthe wind company to reduce its excess injection to stabilizethe grid [31]. The use of ESS for wind energy time shifting ismore beneficial when the low price of wind energy happensmore frequently.

The computing time of 10 000 states is around 20 h for eachseason,whichmakes SDP computationally expensive. To reducecomputational cost, the state size needs to be smaller. We start

TABLE IRESULTS WITHOUT ESS AND RESULTS WITH ESS USING SDP


with a small number of states, and increase it until sufficientaccuracy is reached. Solution accuracy is measured by percent-age error in the following:

where is seasonal index, and are profits with statesize and benchmark solutions, respectively. The computationis stopped when the condition is satisfied,where a small threshold is set as . The SDP results areshown in Tables II and III for state enumeration and OFA,respectively, where the error values are given in the bracketsbelow profits.

Tables II and III show that when the state size increases,optimal profits from both approaches become higher and closerto benchmark values. Compared with state enumeration, theOFA method uses a much lower number of states and time toreach convergence because it uses function continuity to findsolutions closer to optimal solutions. This comparison demon-strates the earlier analysis shown in Fig. 3. It is observed fromTable III that good-quality solutions are achieved with a smallstate size of 40, and this reflects that the dimensionality problemis alleviated with the use of OFA.

B. Optimal Operation Strategy of SDP Model

To analyze ESS operation strategy under various scenarios, asample of optimal operations during winter is shown in Table IV.To give compact results under space limitation, the horizon isclassified into four periods based on fluctuating patterns of windand price: hour 0–hour 5, hour 6–hour 12, hour 13–hour 19, andhour 20–hour 23. Peak wind normally exists in period 1 and peakpricenormallyexists inperiod3.Foreachperiod, anhour ischosento give a good representative of ESS operation. The hourly windand price are simply divided into three levels—high (H), medium(M),andlow(L); theoperationsareclassifiedinto“charge,”“idle,”

and “discharge,” where the term “N.A.” denotes a nonexistentscenario. The operations are determined by comparing ESS level“ ” to some threshold conditions (%). For example, at wind level“L” and price level “H,” the optimal operation at hour 9 is “charge( < ), idle ( < ), discharge ( )”. Thismeans that if ESS level is below 13%, optimal policy is to chargeESS. If it is between 13% and 34%, then leave ESS idle, and ifit is higher than 34%, then discharge ESS.

We first observe operations from hour to hour. At hour 2,chargingis thebeststrategyformostscenariosdueto thelowprice,high wind, and low initial storage level at that time. At hour 9,as price rises and wind power drops, the ESS is occasionallyused for power supply. At hour 18, as peak price arrives, dischar-ging becomes more frequent. At hour 22, the main strategy isto adjust the energy level back to its initial level of 25%.

Next, we observe operations from scenario to scenario. Athour 2 and hour 22, price level affects operations more signifi-cantly than wind level. Specifically, wind power is discarded ifvery low price exists at night (hour 22). At hours 9 and 18, windand price both affect operations to a considerable degree and in asimilar trend. At a certain level , either a higher price level orwind level can bring a storage status from “charge” to “idle” andeven to “discharge.” In periods 2 and 3, a higher wind levelcreates more incentives for discharging because it implies ahigher wind level in subsequent hours, which can providesufficient compensation for energy discharged in early hours.

C. Comparison of Simulation Results for Different Models

Monte Carlo simulations are run to evaluate scenario-basedresults from different models. For each season, 10 independentbatches of daily paths are sampled, each of size . Thepaths are used to find profits from the SDP, DET, and PI models.For the SDP and DET models, solutions from OFA using a statesize 40 are applied. We find the expected profit of each batch in(34), and obtain a two-sided 95% confidence interval for 10estimates from 10 batches. Results are shown in Table V, whereconfidence intervals ( ) are shown below mean values.

Table V shows that the confidence interval is tight, whichindicates that sample size is large enough to reflect the actualobjective value. Profits from the SDP model are very close to theconverged values in Table III. This demonstrates that the SDPpolicy successfully achieves the desired profits in the simulatedenvironment. Compared with the SDP model, the PI modelproduces slightly higher profits due to its ideal assumption,i.e., current decisions are made with complete knowledge offuture outcomes. On the other hand, the DET model producesobviously lower profits since the price randomness has not beenproperly incorporated. Profit gap between the SDP and PImodels, as well as a gap between the DET and SDP models,clearly reflects the increase in the value of information. The gapbetween the DET and SDP models is comparably high in winterand spring due to the higher uncertainty levels of price.

The daily profits from four seasons are combined to show theirdistributions in Fig. 4, where distribution of profits without ESSis also shown. Without ESS, the company has a much higherprobability of encountering loss due to negative prices imposedon excess wind energy. Using ESS, the distribution has been

TABLE IIRESULTS FROM SDP WITH STATE ENUMERATION METHOD

TABLE IIIRESULTS FROM SDP WITH OFA METHOD


altered by the three models. Compared with the DET model, theSDP model avoids loss much better and greatly increases theprobability of high profits. Distribution of the SDP model isclose to the one of the PI model. Negative profits are completelyavoided in the PI model. This is because when the future pricesare perfectly known to the operator, one can avoid such loss atleast through discarding all wind energy without using storage.

Fig. 5 shows typical trajectories in winter and spring for eachmodel, where the wind path is shown as a solid line and the pricepath as a dotted line. The price level is found to greatly impactoperating decisions such that ESS charges at a valley point anddischargesatapeakpoint.Windfluctuation,ontheotherhand,willimpact the amount of shifted energy. For example, in the SDP andPImodels of Fig. 5(a), highwind generation during hour 0–hour 8leads to high storage levels at hour 9 as ESS keeps charging.

Compared with the DET model, ESS trajectories in the SDPmodel are closer to those in the PI model. This shows that theSDP model can accurately adjust decisions through repeatedlyupdating observed information of wind and price. ConsiderFig. 5(b), for example: ESS stops absorbing energy at hour 4since it realizes that the price, instead of staying low, becomeshigher and higher. At hour 6, ESS discharges to cope with highprice at that time, and then stays idle soon after the price

stabilizes. Later during hours 18–19, a high price exists againand ESS begins to discharge. Compared to the PI model, thisdischarging is not that deep, because wind power afterwards isuncertain and ESS could not go back to its initial level if windgeneration is not enough.

VI. CONCLUSION

This paper has investigated an optimal operation problem ofESS in a grid-connected wind power plant. An SDP approachwas proposed to model the problem and achieve optimal opera-tion policy. The SDPpolicy enables ESS operation to be adaptiveto hourly wind and electricity price, and as a result, the windpower producer would be able to gain considerably greater profitas compared to a fixed policy. This advantage of SDP policy has

TABLE IVSAMPLE OF OPTIMAL OPERATIONS IN WINTER

TABLE VSIMULATION RESULTS USING SOLUTIONS OF VARIOUS MODELS

Fig. 4. Distributions of daily profits based on various models.


been demonstrated using ERCOT data. Comparison also showsthat the SDP model performs slightly worse than the PI model.It should be noted that a PI model requires uncertainties of 24-hwind and price to be completely known with 0% error, whichcould hardly be achieved in the actual operation.

One of the main challenges of applying sequential decision-making tools is the curse of dimensionality. An OFA method isproposed to improve the SDP computational efficiency. Theobjective function is approximated by a piece-wise linear func-tion so that each subproblem of SDP can be solved with LP. ThisOFA approach is shown to be effective in solving a large numberof wind and price scenarios. It is worth noting that the SDPcomputational time would grow exponentially with the increasein dimensions of random variables. For cases involving a high-dimensional random vector, the SDP computation may need tobe further explored.

As CAES has a cavern requirement, for plant owners it mightbeworthwhile to consider other options aswell, such as batteries.With minor modification on ESS characteristics, the proposedformulation can be applied to other storage options. It is alsonoted that for wind farms with lower installed capacities, smaller

ESS would be required to achieve good balance between costand revenue [1], [8]. In particular, for very small farms (e.g., inseveral kilowatts), the profit growth from wind energy timeshifting may be insignificant. Alternatively, ESS such as batter-ies and flywheel, with rapid response time, would be suitablefor other applications such as frequency regulation [39]–[41].The study on ESS operation for these issues will be one of theimportant directions of future work.

In addition, the focus in this paper is on a single wind powerplant with an assumption that its output power will not impactmarket prices. This assumption will hold as long as the plantcapacity is small compared to the total market capacity. For awind generation company owning several large plants, its impacton prices might need to be considered [34], [35], [42].

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Zhen Shu (S’09) received the B.Eng. degree from Huazhong University ofScience and Technology, China, in 2006, and the M.Sc. degree from NationalUniversity of Singapore, in 2009. She is currently pursuing the Ph.D. degree inelectrical and computer engineering at the National University of Singapore.

Panida Jirutitijaroen (S’05–M’07–SM’12) received the B.Eng. degree (Hon.)from Chulalongkorn University, Bangkok, Thailand, in 2002, and the Ph.D.degree in electrical engineering from Texas A&M University in August 2007.She is currently an Assistant Professor with the Department of Electrical and

Computer Engineering, National University of Singapore. Her research interestsare power system reliability and optimization.


optimal operation strategy of energy storage system for grid-connected wind power plants

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