Flexible Optimal Operation of Battery Storage Systems for Energy Supply Networks

2788 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013

Flexible Optimal Operation of Battery StorageSystems for Energy Supply Networks

Aouss Gabash, Member, IEEE, and Pu Li

Abstract—Active-reactive optimal power flow (A-R-OPF) in dis-tribution networks (DNs) with embedded wind generation and bat-tery storage systems (BSSs) was proposed recently. The solutionwas based on a fixed length in the charge and discharge cycle fordaily operations of BSSs. This can lead to a low profit when the pro-files of renewable generators, demand and prices vary from day today. In this paper, we extend the A-R-OPFmethod by developing aflexible battery management system (FBMS). This is accomplishedby optimizing the lengths (hours) of charge and discharge periodsof BSSs for each day, leading to a complex mixed-integer nonlinearprogram (MINLP). An iterative two-stage framework is proposedto address this problem. In the upper stage, the integer variables(i.e., hours of charge and discharge periods) are optimized and de-livered to the lower stage. In the lower stage the A-R-OPF problemis solved by a NLP solver and the resulting objective function valueis brought to the upper stage for the next iteration. It can be shownthrough a case study that a flexible operation strategy will achievea considerably higher profit than by a fixed operation strategy ofBSSs.

Index Terms—Distributed power generation, flexible batterymanagement system (FBMS), optimal power flow, optimizationmethods.

I. INTRODUCTION

T HE dynamic behavior of the generation from renewableenergy sources (e.g., wind and solar), demand, and en-

ergy prices leads to a complex process which needs adaptivestrategies to deal with. Energy storage systems (ESSs) such asbattery storage systems (BSSs) [1] could help in many aspectsif their integration with the energy supply networks is economi-cally feasible. A method based on genetic algorithms (GAs) wasapplied to evaluate the impact of energy storage costs on eco-nomic performance of a distribution substation [2]. Other algo-rithms have been reviewed in literature for analysis of both tech-nical and economical parameters for storage systems [3]. Manyenergy storage technologies were examined in [4] for three ap-plication categories [bulk energy storage, distributed genera-tion (DG), and power quality] with significant variations in dis-charge time and storage capacity.

Manuscript received May 24, 2012; revised September 04, 2012; acceptedNovember 21, 2012. Date of publication December 20, 2012; date of currentversion July 18, 2013. This work was supported by the Ministry of Higher Ed-ucation of the Syrian Arab Republic. Paper no. TPWRS-00562-2012.The authors are with the Department of Simulation and Optimal Processes,

Institute of Automation and Systems Engineering, Ilmenau University ofTechnology, Ilmenau 98684, Germany (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.2012.2230277

Based on [4], a cost analysis considering life-cycle of grid-connected electric energy storage was made in [5]. It was shownthat the length of discharge cycle [not the depth of discharge(DoD)] has an impact on the cost added to the electricity cost.This analysis was also used in [6] for sizing and allocating anESS in a distribution network (DN) with a high penetration ofwind energy. It was shown that the only economically feasibleBSS technology is Zn/Br. It is suggested to reduce the numberof charge/discharge cycles a BSS in order to prolong its life-time and thus one charge/discharge cycle per day was proposedin [6]. An optimization method based on a trade-off betweendifferent objectives for siting and sizing BSSs in DNs was pro-posed in [7]. It was shown that installing more BSSs wouldlower the probability of voltage violation. The authors in [7]proposed a techno-economical model for BSSs in [8]. The workin [8] was partially based on [3] where a depreciation cost ofcycling a BSS was used. However, in [3], [7] and [8] the op-portunity cost of reactive power during cycling a BSS was notincluded. Recently, active and reactive power control within thecircular constraints of converters of BSSs [9] and inverter rating(the apparent power) of renewable energy generators [10] hasbeen investigated. A modeling of storage devices is proposed inthe OPF framework to take the transmission network (TN) intoconsideration [11]. It is to note that in [11] the problem is for-mulated using a lossless DC OPF model, and therefore, losses,voltage, and reactive power are not considered.In [12], the reactive power capability of a wind-battery

station in electricity market was investigated. Based on [6]and [12], a combined problem formulation for active-reactiveoptimal power flow (A-R-OPF) in DNs with embedded windgeneration and BSSs was proposed in [13], with which a hugereduction in both energy losses and reactive energy can beachieved. In the work of [6] and [13], however, the lengthsof charge and discharge periods for BSSs were fixed in dailyoperations. Such a fixed battery operation strategy will lead tolow profit, since the profiles of renewable penetration, demandand energy prices vary from day to day. Therefore, a flexibleoperation strategy for BSSs is considered in this paper toadapt to these variations. The lengths (hours) of charge anddischarge periods in each day will be optimized based on theactual information on the renewable generation, demand andenergy prices. This, together with the A-R-OPF formulation,leads to a complex mixed-integer nonlinear programming(MINLP) problem which cannot be readily solved by availableapproaches. There are only a very limited number of funda-mental studies related to storage in grids: design, dimension,location, operation planning and control of BSSs. The focus inthis work is on developing optimal and flexible strategies for

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GABASH AND LI: FLEXIBLE OPTIMAL OPERATION OF BATTERY STORAGE SYSTEMS FOR ENERGY SUPPLY NETWORKS 2789

operating BSSs. The developed model here can handle not onlythe continuous decision variables but also integer variables.Developed by Holland [14] and Goldberg [15], GA has been

successfully applied in solving many optimization problems inpower systems, especially when both integer and continuousvariables are present. In [16], GA was applied to solve unitcommitment problems. Additional schemes like intelligentand problem-oriented permutation mechanisms were addedto improve the GA search [17]. The authors in [16] and [17]presented an enhanced GA [18] for the solution of OPF withboth continuous and discrete control variables. Kennedy andEberhart [19] presented a method for optimization of contin-uous nonlinear functions using particle swarm optimization.They extended their method to handle binary variables [20].Such a method is applied in reactive power and voltage controlformulated as a MINLP problem [21]. Other search methodssuch as machine learning [22] and motion estimation [23], [24]were also used in solving optimization problems with integervariables.Since all these methods treat the continuous and integer vari-

ables simultaneously, they are not suitable to be used for ourlarge-scale complex MINLP problem. We propose a two-stageframework to decompose the optimization problem. The integervariables (hours of charge and discharge periods) will be opti-mized with an efficient search method in the upper stage, whilethe continuous variables are handled by a NLP solver in thelower stage. The profit improvement through flexible operationsof BSSs is shown by a case study.The paper is organized as follows: The problem of operating

BSSs with varying demand, generation and price profiles is de-scribed in Section II. In Section III, the optimization problem isformulated and a solution framework proposed. Optimizationresults from the case study are presented as well as discussionsare drawn in Section IV. The paper is concluded with Section V.

II. PROBLEM DESCRIPTION

To clearly describe our concern, we consider operations of aDN shown in Fig. 1. It consists of 5 BSSs, 3 wind parks and avariety of demands at different nodes. It is necessary to developan optimal strategy which will lead to a maximum profit and afeasible operation. Themajor difficulty comes from the dynamicbehavior of demand, wind power generation and energy prices.This difficulty can be well addressed by the available BSSs.Unfortunately, their capacity is restricted.

A. Varying Demand, Generation, and Price Profiles

It is a well-recognized fact that demand and wind powerprofiles are different from day to day. Following the IEEE-RTSseason’s days [6], two typical demand profiles in differentseason’s days, denoted by (winter) and (spring),are shown in Fig. 2. Wind power profiles can be representedby day-ahead forecasted scenarios. Two different wind powerprofiles, denoted by and , are also shown in Fig. 2.Here, wind generation profiles are generated based on real windspeed data from a city in Germany.The mathematical model used for transforming wind speed to

output power is taken from [25], while wind speed parameters

Fig. 1. Distribution system for the case study.

Fig. 2. Daily wind/demand power profiles, where and stand for dif-ferent wind/demand power profiles at different days.

(i.e., rated, cut-in and cut-out wind speed) are taken from [6]. Itis to note that a curtailment factor is introducedat each wind park to reduce wind power generation if systemconstraints will be violated [13].Time-of-use (TOU) pricing is usually used by utilities for

charging different rates throughout the day [26], [27]. It meansthat active energy prices are low during low demand and highduring high demand. This is depicted in Fig. 3, whereis the active energy price during hour . In this work, threedifferent price models for active energy prices, as shown inFig. 3, are used to analyze their effect on the operation, where

, , and denote the two-/three-/and 24-hour-tariffprice model, respectively. Here, , , and stand forthe durations of low, medium and high prices for the firsttwo price models, respectively, while different hourly pricesare assumed to follow the demand in winter and spring forthe third price model. In addition, reactive energy prices areapplicable in certain countries based on the measured reactiveenergy (Mvarh) [28] (e.g., in Germany), or based on the costsof providing reactive power, including additional costs dueto energy losses incurred by running at a non-unity powerfactor and costs of running the generation units as synchronouscondensers if requested by the independent electricity systemoperator (IESO) [29] (e.g., in Ontario). It is suggested in [28]and [29] that reactive energy prices can be assumed in the rangeof . In this paper, a fixed reactive energy price

, as seen in Fig. 3, is considered for comparison purposes.All of these profiles are important to the operation of the

distribution system. They are time dependent and different from


Fig. 3. Daily active and reactive energy price models. Here, , , andstand for a two-/three-/24-hour-tariff price model of active energy, respectively,while the fixed line (dashed) stands for a fixed-tariff price model of reactiveenergy.

day to day. Therefore, operation strategies for BSSs shouldbe flexible and adaptive to the variations of these profilesso as to always ensure the system in an optimal and reliableperformance.It should be noted that the above mentioned wind power and

demand profiles are assumed to be forecasted in the time frameof optimization as shown later. The inaccuracies in these fore-casts are not considered in this study.

B. Operational Constraints of BSSs

ABSS consists mainly of a power conditioning system (PCS)and a storage unit. The BSS can be either charged or dischargedat the same time and its PCS is capable of independent and rapidcontrol of active and reactive power. During a charge/dischargeprocess power losses can be determined by charge and dischargeefficiencies. Detailed relationships between the active powercharge/discharge (P-PCS), reactive powers dispatch (Q-PCS),energy level (E) and efficiencies ( and ) of a BSS aregiven in [13].It was shown in [1] and [5] that the lifetime of a battery

storage depends on a fixed number of charge/discharge cyclesand DoD. This can be represented by a replacement period inyears as follows [5]:

(1)

where is the total number of charge/discharge cycles in thelifetime, is the annual operation days, and is the numberof charge/discharge cycles per day. Therefore, to prolong the

Fig. 4. Illustration for one charge/discharge cycle every day with two differentdecisions. Here, and stand for fixed/flexible operations, respectively.

lifetime for BSSs only one cycle charge/discharge per day istypically chosen for optimal planning [6] and operation [13].In our model [13] and the model proposed in [6], although the

charging and discharging power is flexible, the charging and dis-charging time in each day (24 hours) is fixed. This was realizedby predefining an integer variable in each hour for each BSS,namely 1 for charging and 0 for discharging. In other words,P-PCS-ch for , while P-PCS-dis for

.However, when renewable energies as well as other parame-

ters vary from day to day this restriction should be released, i.e.,these integer variables should be optimized. Briefly, the cycleof charge is determined by two integer variables representingthe time periods (hours) of charge ( and ). The cycle of dis-charge is defined by one integer variable representing the hoursof discharge , as depicted in Fig. 4, where the notation 1means charging period and 0 discharging period. Two operationstrategies are shown: the upper part shows a fixed strategy, i.e.,stringent decisions, and the lower part a flexible strategy, i.e.,free decisions. In this work, we also consider one charge/dis-charge cycle every day, but the lengths of the charge and dis-charge cycles will be optimized based on the day-to-day pro-files discussed above. The three integer variables in a cycle areconstrained by

(2)

(3)

where and are the minimum and maximum bounds onthe variables, respectively. Since we consider a daily operationof BSSs, there should be and . It is usefulto know that two procedures A and B are used in this work as in[13]. In procedure A, the problem has a daily horizon

and is solved four times for the four individual days. Inprocedure B, the time horizon is defined as four days

and the problem is solved only once. In both procedures,the final storage level is equal to the initial in the time horizon.

C. Market Strategies

The same simple market strategy defined in [13] is consid-ered in this paper to make a clear comparison. In addition, three


Fig. 5. Input-output scheme for the combined A-R-OPF with a searchalgorithm.

different energy price models, as shown in Fig. 3, are used andcorresponding results compared in this paper. Here, we considera DN with distributed wind parks and BSSs. The network isbeing operated by a distribution system operator (DSO) who isresponsible for operating the system with a high quality. TheDSO tends to maximize the benefits from the system operationand meanwhile to minimize the total costs. For a clear analysisfollowing considerations are taken in the mathematical model.• The integration of a BSS in a DN with high penetration ofDG units is economically feasible.

• The DG units, BSSs embedded in a DN, reverse activeenergy to the TN and active energy losses are paid for orcharged by the same price model, i.e., the two-/three-/24-hour-tariff price model.

• The reactive energy import/export from/to the TN is paidfor or charged by the same price model, i.e., the fixed re-active energy price.

• Both active and reactive reverse power flow to the TN isallowed without any rejection.

III. PROBLEM FORMULATION AND SOLUTION FRAMEWORK

A. Problem Formulation

The optimization problem, as shown in Fig. 5, has three in-teger variables in addition to the continuous control variables(i.e., three control variables for each BSS and one for each windpark). The time step is 1 hour for each continuous variable.A general formulation of an A-R-OPF problem can be ex-

pressed as follows:

(4)

(5)

(6)

(7)

where the objective function to be maximized is the totalrevenue from wind power and BSSs minus the total cost ofenergy losses (the nonlinear term in the objective function in-cludes the cost of active energy losses in the grid [13]), is thevector of state variables (real and imaginary component of com-plex voltage at PQ buses, active and reactive power injected at

slack bus and energy level in BSSs), is the vector of contin-uous control variables including active power charge/dischargeof BSSs, reactive power dispatch of BSSs and curtailment fac-tors of wind power at wind parks, is the vector of the integercontrol variables, i.e., the number of charge/discharge hours perday. In (5), represents equality constraints including activeand reactive power flow equations (they are nonlinear terms). Inaddition, energy balance equations for BSSs are also included.The inequality constraints in (6) and (7) include voltage bounds,active and reactive bounds at the slack bus, and main feederbounds. The bounds of the curtailment factors and the opera-tional constraints (2) and (3) are also included to the inequalityconstraints; see details in [13].

B. Two-Stage Solution Framework

To solve the MINLP problem formulated above we proposean iterative two-stage framework scheme, as shown in Fig. 5.We decompose the whole optimization problem into two sub-problems. In each iteration, the upper stage solves the followingproblem:

(8)

subject to (2) and (3), where only the integer variables aresearch variables. With values delivered from the upper stage,the lower stage solves the following NLP problem:

(9)

(10)

and (6) and (7) as inequality constraints, where only continuousvariables are present. The solution of the lower stage providesthe objective function value for the upper stage where an updateof will be made for the next iteration. This procedure willconverge when the number of iterations is reached as describedbelow.The influence of energy prices, wind power generation and

demand profiles is dealt with in the lower stage. Thus the lowerstage solves the A-R-OPF problem with given charge/dischargehours provided from the upper stage. A unique feature of thelower stage is that the operational constraints (6) and (7) willbe ensured for any charge/discharge lengths, due to the intro-duction of curtailment factors. Therefore the lower stage can beconsidered as a black-box solver for the upper stage.Here, the upper stage is implemented in MATLAB [30]

while the lower stage in GAMS [31]. The framework shown inFig. 5 is realized by using GDXMRW for interfacing GAMSand MATLAB. The computation is carried out on a desktopwith Intel XEON X5690. 3.47 GHz (6-core) 32.00 GB RAM.

C. Search Method for the Upper Stage Problem

Due to the constraints of the three integer variables describedby (2) and (3), the search space can be illustrated with Fig. 6(a),where each point represents a possible combination of thevariables. Thus the total number of combinations is 325. Notethat formulating the problem with more than one cycle per dayor with smaller time steps will increase the complexity of theproblem by increasing the search scales. Since an exhaustive


Fig. 6. (a) Illustration of the search space. (b) String-structure.

search or enumeration will cause much computation time, weuse a more efficient search method described as follows.Goldberg pointed out in [15] that a G-bit improvement is a

canonical method of local search which could be hybridizedwith GAs. This method can be summarized by a bit-by-bitsweeping process in a given string; see Fig. 6(b). In contrast,Adby and Dempster [23] presented a simple technique ina two-variable optimization case (see an application of thismethod in [24]), in which only one variable is adjusted at atime with the other fixed. Thus it is called one-at-a-time search(OTS). Since there are three variables instead of two in ourcase and they should satisfy (2) and (3), we modify OTS anduse it in the upper stage, including the following steps:1) Choose a feasible initial string (including 24-bit, either 0or 1, where 1 stands for charge and 0 for discharge). Forexample, which is depicted inFig. 6(a) and (b).

2) Provide this initial string to the lower stage to evaluatethe objective function value. Then record this fitness in aregister.

3) Sweep bit by bit (the search step is taken to be 1 bitwhich represents the smallest step) in the forward as well asbackward direction, as shown in Fig. 6(b), with a specificdepth (8 bit which represents the maximum depth when

). Note that is still fixed at thissweep process, while is being changed depending on thechange in . For example: , , andafter two sweeps in the forward direction. Note that aftereach sweep the produced string is evaluated in step 2.

4) Sort the fitness of the successive evaluated strings in as-cending order and retain the best of them (if two or morestrings have the same fitness, the algorithm preserves the

TABLE IDATA OF WIND TURBINES, PCSS CAPABILITIES, AND BSSS CAPACITIES

original ordering of the fitnesses). This gives the best po-sition of and related to .

5) Fix at its best position and begin to sweep and evaluatethe produced strings in a similar way as in steps 3 and 4.The total number of evaluations needed to find a convergedsolution is 33, given the parameters (initial point, depth andstep) as shown in Fig. 6.

6) The best string found and its fitness represents the optimaloperations for a specific day.

It should be noted that any sweep which violates the con-straints (2) and (3) will be refused. In the integer search methodthe optimization horizon is set to one day (24 hours) which isthen repeated. Since the modified OTS method is a local searchscheme, a large number of scenarios were tested in the casestudy (see Section IV) to show the impact of initialization, depthand step of the search. From the computed scenarios followingcan be observed:• Local hills can be obtained when a bad initialization isused, e.g., starting from corners of the search space.

• If the search step is more than one bit maximum hills couldbe prevented.

• The parameters (initial point, depth and step) are logicallyrelated. It means if the initialization is the center, there isno need to set the depth of search higher than 8 bit. Forother initial points, many sweeps will be refused.

• The best initial point found is the center whichmostly leadsto the global maximum for all scenarios tested. However,if one wants to guarantee the global solution with any se-lected initial point as well as input scenarios, we refer to[15].

• Different values of the integer variables can lead to approx-imately the same objective function value when no curtail-ments are present and/or with slight differences in energyprices. For example, , , and (fixedmethod) and , , and (OTSmethod) can have a very slight difference in the objectivefunction value, as shown in the case study.

Here, we summarize some advantages of our solution approachas follows:1) The treatment of charging/discharging periods in theupper-stage makes the solution procedure highly effective.

2) Each iteration of the upper-stage is feasible, since all con-straints are satisfied in the lower-stage.

3) Due to the limited search space of the upper-stage thenumber of iterations to reach the optimal solution will below.

IV. CASE STUDY

The network considered for the case study is taken from[13]. It is a typical rural distribution network with 41 buses


Fig. 7. Trajectories by flexible and fixed A-R-OPF based on the two-tariff price model (left column) and three-tariff price model (right column). (a) Total windpower generation (solid-blue) and total demand power (dashed-black). (b) Total active power charge/discharge. (c) Total reactive power dispatch. (d) Total curtail-ment factor. (e) Slack bus active power. (f) Slack bus reactive power. (g) Total energy level. Note: from (b) to (g) the lines (dashed-red) for fixed and (solid-blue)for flexible A-R-OPF.

and 27.6 kV. The maximum feeder capacity is 14.3 MVA. TheDN, as shown in Fig. 1, has 3 embedded wind parks connected

to buses 19, 28, and 40, respectively. In addition, 5 BSSs areconnected to buses 4, 9, 28, 39 and 40, which were also consid-


Fig. 8. Trajectories by flexible and fixed A-R-OPF based on the 24-hour-tariffprice model. (a) Total wind power generation (solid-blue) and total demandpower (dashed-black). (b) Total active power charge/discharge. (c) Total reac-tive power dispatch. (d) Total curtailment factor. (e) Slack bus active power. (f)Slack bus reactive power. (g) Total energy level. Note: from (b) to (g) the lines(dashed-red) for fixed and (solid-blue) for flexible A-R-OPF.

ered in [6] and [13]. The data used for the case study are givenin Table I, where is the rated power of each wind park,

is the upper bound of apparent power of each BSS

TABLE IIACTIVE ENERGY PRICES FOR 24-HOUR-TARIFF PRICE MODEL IN WINTER

(WINT.) AND SPRING (SPRI.)

station, and is the installed capacity of each BSS station.Values in per unit system are given on 10-MVA base, otherwisespecified. The charge and discharge efficiencies are with avalue of . The lower and upper bounds of thestorage units are 20% and 90% of their capacity, respectively.Bus 1 is considered as the slack bus, whereas the other buses

are considered as PQ buses. The demand data is taken from[13]. The on-, mid- and off-peak active energy prices are 117$/MWh, 100$/MWh, and 65$/MWh from [27], respectively. Ifthe DSO takes hourly spot market prices instead of the fixed tar-iffs, hour-by-hour prices can be adopted and used to show howthe effects if such prices are taken [32]. Generally, based on theTOU pricing, two to three price periods each day correspondwith a good fit to hour-by-hour prices as shown in [32] and[33]. This feature is relevant, since it is simpler for consumersto treat three prices than 24 different hourly prices each day.However, it can be desirable to update 24 different hourly pricestracking the expected spot prices [33] and gaining additionaladvantages. Therefore, a further hour-by-hour tariff is adaptedaround the fixed tariffs to show the impact of such prices on theperformance of the system. Hourly prices assumed in winter andspring are given in Table II. The fixed reactive energy price isassumed to be 12$/Mvarh [28], [29]. The total wind power anddemand scenarios in 4 different days considered for the opti-mization are shown in Figs. 7 and 8.The optimization results listed in Tables III–V show the total

revenue obtained by three methods for different wind/demandscenarios in 4 different days (see Figs. 7 and 8). The threemethods include the modified OTS as well as enumeration tosearch for a flexible operation strategy for charge and dischargehours of the BSSs, and the fixed operation strategy for theBSSs. The results in Tables III–V are from the two-tariff,three-tariff, and 24-hour-tariff price model, respectively.Using themodifiedOTSmethodwemostly obtained the same

maximum as by enumeration, but it took much less computationtime. However, a suitable initialization is required by the OTSto avoid local hills. It is clearly seen from Tables III–V that thetotal revenue based on the three-tariff and 24-hour-tariff pricemodels are lower than that based on the two-tariff model. Thisis because the prices considered for the two-tariff price modelare higher than the others, as shown in Fig. 3. It should be notedthat the results here obtained are based on the condition of onecycle per day for the BSSs.


TABLE IIIOBJECTIVE FUNCTION VALUE AND COMPUTATION TIME FOR DIFFERENT DAYS IN THREE METHODS USING THE TWO-TARIFF PRICE MODEL

TABLE IVOBJECTIVE FUNCTION VALUE AND COMPUTATION TIME FOR DIFFERENT DAYS IN THREE METHODS USING THE THREE-TARIFF PRICE MODEL

TABLE VOBJECTIVE FUNCTION VALUE AND COMPUTATION TIME FOR DIFFERENT DAYS IN THREE METHODS USING THE 24-HOUR-TARIFF PRICE MODEL

There is a very slight difference, i.e., 5647.144244 ($/day) (fixed), 5647.145829 ($/day) (enumeration), and 5647.144248 ($/day) (OTS).The modified OTS finds a local solution, while the global maximum found by the enumeration method is 18285 $/day at .

By comparing the revenue differences between the flexibleand fixed operation strategies, it can be seen that considerablymore revenues can be gained in each day when high wind powergeneration occurs during midday hours. This takes place in thefirst, third, and fourth day, respectively. In contrast, no differ-ence can be seen in the second day, because the wind powergeneration occurs mostly during night hours. It is also noted thatthe integer variable does not change in all scenarios of thetwo-/three-tariff price model, because the energy prices are al-ways low and constant during the first 7 hours of the four daysunder consideration. Note that the integer variable changeseven with high energy prices before 21h due to high wind powergeneration and possible curtailments. Moreover, changes, asgiven in Table V, when hourly prices are taken. This reflects thefact that the flexible strategy can achieve more profit under dif-ferent price models. In addition, there is either no or with a verysmall difference (0.06%, see the third day in Table V) betweenthe enumeration method and the modified OTS.It was shown in [13] that a longer optimization horizon

(with deterministic wind and demand power profiles) leads tomore benefits not only economically but also in the sense ofa smoothing operation. However, with a longer optimizationperiod, uncertainty due to wind-power production and demandincreases. Therefore, we solve the optimization problem for thefour days with two different time horizons, namely 24h (proce-dure A) and 96h (procedure B), based on the three price models,respectively. The optimal trajectories are shown in Figs. 7 and

TABLE VIOBJECTIVE FUNCTION VALUE USING THE TWO-/THREE-/24-HOUR-TARIFF

PRICE MODEL FOR PROCEDURE B IN TWO METHODS

8, while the total revenue is given in Table VI. It is also seen thatthe revenue differences in procedure B are also considerable. Inour previous study, no reactive energy costs have been consid-ered in the formulation of the A-R-OPF [13]. Now, to show theimpact of the flexible operation strategy on the reactive energyimport as well as cost from the connecting TN, we calculate thereactive energy cost by . Here,is the reactive power injected at slack bus in Mvar during hour.It is shown in Table VII that the flexible operation strategy

leads mostly to a higher cost compared with the fixed A-R-OPF.By comparing both differences, namely Diff.(P) and Diff.(Q), itcan be clearly seen that the total gain from the flexible strategydominates the total loss from the fixed strategy. Another pointto note is that when using the three-/24-hour-tariff price modelthis impact will be either negligible (in the three-tariff) or even


TABLE VIITOTAL COST OF REACTIVE ENERGY IMPORT USING THE TWO-/THREE-/24-HOUR-TARIFF PRICE MODEL FOR PROCEDURE B IN TWO METHODS

TABLE VIIITOTAL REVENUE FROM WIND POWER AND BSSS USING THE

TWO-/THREE-/24-HOUR-TARIFF PRICE MODEL FORPROCEDURE B IN TWO METHODS

TABLE IXTOTAL COST OF ENERGY LOSSES USING THE TWO-/THREE-/24-HOUR-TARIFF

PRICE MODEL FOR PROCEDURE B IN TWO METHODS

in the opposite direction (in the 24-hour-tariff). This is becausethe fixed strategy follows the energy prices during the charge/discharge process and has less attention on the reactive power.This can be clearly seen by comparing the differences duringthe third and fourth day in Figs. 7(b)–(g) and 8(b)–(g).Since the objective function in this paper has two main terms,

it is useful to show their values separately. The first term is thetotal revenue fromwind power and BSSs, as given in Table VIII.It is clearly seen that this term is in accordance with the re-sults in Table VI for the two-/three-/24-hour-tariff price model.This is because the major saving comes from avoiding windpower curtailments through the flexible strategy. The secondterm is the total cost of energy losses, as given in Table IX.This term is in accordance with the results in Table VII forthe two-/three-/24-hour-tariff price model. This reflects the re-lationship between the power losses and reactive power flowin the network. We can conclude from these findings that moreprofits can be obtained from the flexible A-R-OPF even withhigher power losses.Fig. 7(b)–(g) (left column) shows the optimal profiles caused

by the flexible (solid) and fixed A-R-OPF (dashed) obtainedfrom procedure B using the two-tariff price model. It can be seenfrom Fig. 7(b) and (c) (left column) that the flexible strategy

shifts the optimal control profiles of active power charge (posi-tive part)/discharge (negative part) and reactive power dispatch.This leads to less wind power curtailments as seen in Fig. 7(d)(left column), which can be clearly seen in the first, third, andfourth day. Since there are three wind parks in the case study,the total curtailment factor axis has a range 2.2–3. In contrast,no curtailments are present in the second day due to low windpower generation. Fig. 7(e) and (f) (left column) shows the ac-tive and reactive power exchange at the slack bus. It can be seenthat the flexible strategy leads to more active energy export orless energy import. However, the reactive energy import is seenin an opposite direction in comparison to the slack active power.This is because the active power charge/discharge of BSSs dom-inates the reactive power capability of the BSSs. Fig. 7(g) (leftcolumn) shows large differences in the total energy level in theBSSs (i.e., the sum of the energy content of all 5 BSSs), es-pecially in days when a high penetration of wind power genera-tion is present. Similarly, Fig. 7(b)–(g) (right column) shows theoptimal trajectories of the flexible (solid) and fixed A-R-OPF(dashed) obtained from procedure B using the three-tariff pricemodel. The same discussions presented above for the two-tariffprice model are true for the three-tariff price model. However, inthis case the flexible operation of BSSs avoids more wind powercurtailments [see Fig. 7(d) (right column)], comparing that bythe two-tariff price model.Fig. 8(b)–(g) shows the impact if hourly prices are used in-

stead of the fixed price models. Since the difference betweenthe highest and lowest active energy prices of , as shownin Fig. 3, is lower than those used in the two-/three-tariff pricemodels, this leads to make more charge from wind power thanfrom importing energy from the TN. This can be clearly seenin the first day where no charge occurs in the first 11 hours incomparison to the same period in Fig. 7(b). It means that thecharge/discharge cycle is not always full-load, but it dependson input scenarios. However, as a rule for many practical appli-cations, a cycle is considered to be full-load even if the storagesystem is not always used with its full capacity [34].It is worth mentioning to note here that a price difference is

required before arbitrage is performed for active power charge/discharge. For example, if there is no wind power generation inthe considered four days, and the off-peak price is 65$/MWh inthe two-tariff price model, the on-peak price should be at least107$/MWh for the BSSs to begin to response for active powercharge and discharge (see Fig. 3). Another important aspect isthat the BSSs response always to reactive power dispatch ofBSSs, even if the on-peak price is equal to off-peak price.

V. CONCLUSIONS

In this paper we have proposed a FBMS for the operationsof DNs with renewable penetration. In particular, the optimallengths of charge/discharge cycle of BSSs for daily operationsor even multiple days can lead to a considerably higher profitin comparison to that from a fixed operation strategy. In addi-tion, three different energy price models have been used andtheir impacts on the flexible operation compared. To solve thecomplex MINLP problem, we have proposed to separately treatthe integer and continuous optimization variables, leading to atwo-stage framework.


A real DN including dispersed wind parks, BSSs, and de-mands has been used as a case study. The effectiveness of theproposed FBMS is demonstrated through applying and testingdifferent daily scenarios. It can be concluded that the proposedflexible and adaptive operation strategy will be promising foroperating energy storage systems in the future energy networks.Note that our algorithm, in this paper, does not allow cyclingBSSsmore than one time per day. Allowing the storages to cyclefor more cycles could be considered in a future study.

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Aouss Gabash (S’11–A’12–M’12) received theM.Eng. degree from Aleppo University, Aleppo,Syria, in 2008. He is currently working towardthe Ph.D. degree at the Institute of Automationand Systems Engineering, Ilmenau University ofTechnology, Ilmenau, Germany.His current research interests include power

system planning, analysis, operation, optimizationtechniques, artificial intelligence, and distributedgeneration and storage.

Pu Li received the M.Eng. degree from ZhejiangUniversity, Hangzhou, China, in 1989 and the Ph.D.degree from the Technical University of Berlin,Berlin, Germany, in 1998.He was a senior researcher at TU Berlin from 1998

to 2005. Since 2005, he has been a full professor atthe Ilmenau University of Technology, Ilmenau, Ger-many. His research interest is process systems engi-neering, i.e., modeling, simulation, optimization, andcontrol of industrial processes.

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Flexible Optimal Operation of Battery Storage Systems for Energy Supply Networks

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