wang, wang & wu - operational reserve model in the power market

IEEE TRANSACTIONS ON POWER SYSTEMS 1

Operating Reserve Model in the Power MarketJianxue Wang, Xifan Wang, Senior Member, IEEE, and Yang Wu, Student Member, IEEE

AbstractMost of the current research on operating reservemarkets assumes that the required capacity is predetermined,which means that the demand of operating reserve capacity isinelastic. This paper considers that operating reserve capacityin a power system is flexible and that one should optimize it bycost-benefit analysis. Based on the reliability evaluation of the gen-eration system, a clearing model of the operating reserve market isproposed to determine the optimal reserve capacity and simulta-neously clear the operating reserve market. The model is discussedon both uniform-price and pay-as-bid auction mechanisms. Byusing a heuristic method, we suggest an efficient algorithm tosolve the model. Case studies for reliability test system (RTS96)demonstrate the usefulness and efficiency of the proposed model.

Index TermsCost-benefit analysis, operating reserve capacity,power market, reliability.

I. INTRODUCTION

I N power systems, it is very important to maintain a cer-tain amount of operating reserve capacity to avoid powershortage due to generator random outages, load fluctuations, etc.In most research and practices, the amount of operating reservecapacity is determined by dispatch rules that require operatingreserve is greater than the capacity of the largest generator and afraction of the peak load. Although this approach is easy to im-plement, it cannot maximize the social welfare of the operatingreserve in an unbundled power market.

In power markets, the operating reserve capacity is a com-modity like electricity. How to purchase operating reserve aswell as electricity is a hot topic on which many researchers areworking. A model on coordinated scheduling of reserves, con-tracts, and supplemental energy is proposed in [1]. The sug-gestion that all reserve markets are cleared together is given in[2]. A price-based adaptive requirement model of spinning re-serve based on the Lagrange relaxation approach is presented in[3]. Combining the reliability calculation with the unit commit-ment (UC), paper [4] brings forward a novel model on optimalscheduling of the spinning reserve. In this research, system op-erators are supposed to buy predetermined reserve capacity. Weargue that operating reserve capacity should be optimized in thepower market circumstance according to benefits and cost anal-ysis. Obviously, the more expensive the operating reserve ca-pacity, the less operating reserve capacity should be purchased;the bigger the interrupted energy assessment rate (or the value

Manuscript received October 9, 2003; revised July 21, 2004. This work wassupported by the National Science Foundation of China under Key Project59937150. Paper no. TPWRS-006342003.

J. Wang and X. Wang are with Xian Jiaotong University,Xian, Shaanxi 710049, China (e-mail: [email protected];[email protected]).

Y. Wu is with Texas A&M University, College Station, TX 77843-3128 USA(e-mail: [email protected]).

Digital Object Identifier 10.1109/TPWRS.2004.841232

of lost load), the more operating reserve capacity should be pur-chased. Thus, the proper operating reserve capacity varies withits cost and the benefit. We call this varied operating reserve ca-pacity flexible reserve. A novel model of flexible reserve andrelative algorithm is discussed in the paper.

The reserve benefit can be evaluated by reduction of EnergyExpectation Not Served (EENS). EENS is a very important andwidely used reliability index in power system planning, whichcan be calculated by a reliability evaluation or probabilistic pro-duction simulation algorithm [5]. Reserve cost depends on thepayment mode. There are two kinds of payment modes: the uni-form-price mode and the pay-as-bid (PAB) mode. Generatorsare paid by uniform market-clearing prices in the uniform-pricemode and paid by bid prices in the PAB mode. Reference [6]points out that the principle of the uniform price is the equalbidding price criteria and the principle of the pay as bid origi-nates from the equal incremental cost criteria. The comparisonof the two payment modes has been discussed in [7][10]. Thispaper proposes the flexible reserve model based on both pay-ment modes. The comparison of the two modes in operating re-serve market is given in the case study.

The structure of this paper is as follows: Section II proposesa clearing model of the operating reserve market. In SectionIII, a very efficient algorithm to solve the above model is sug-gested. The algorithm is demonstrated by a standard test systemin Section IV. Section V contains some conclusions and the em-phasis of further research.

II. CLEARING MODEL OF FLEXIBLE OPERATING RESERVE

As mentioned before, a clearing model of an operating re-serve market should optimize reserve capacity as well as clearthe market. First, we introduce the model of the flexible oper-ating reserve market.

A. Flexible Operating Reserve ModelWithout predetermined reserve capacity, the most important

aspect of the flexible reserve is to find out the optimal operatingreserve capacity that maximizes the social benefit or mini-mizes the social cost . The objective can be, respectively, ex-pressed as

(1a)

(1b)

where is the operating reserve capacity to be optimized.is the decrease of the interruption loss, and is

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

the interruption loss when the system has reserve capacity .They can be, respectively, measured by

(2a)or

(2b)

Here, is the EENS before purchasing operating reserve,and is the systems EENS after purchasing operatingreserve capacity . Coefficient is the Interrupted EnergyAssessment Rates (IEAR) in North America or Value of LostLoad (VOLL) in the U.K. VOLL/IEAR varies with differentcustomer categories, usage time, etc. [11]. In this paper, sinceoutages due to shortage of generation capacity affect the systemas a whole, it is assumed to be the same for all customers at alltimes. As IEAR is an approximate value, the benefit of the op-erating reserve is difficult to be evaluated accurately. The pre-cision of (2) would be improved with further research on theIEAR.

The cost function in (1a) and (1b) depends on differentpayment modes. Suppose the bid price of unit is and theclearing price of operating reserve market is . repre-sents the set of selected reserve units. According to PAB mode,the purchase cost can be expressed as

(3)

The purchase cost on uniform-price mode can be definedas

(4)

The constraints include

(5)(6)

wheremaximum reserve capacity of unit ;minimum reserve capacity of unit ;required time of the operating reserve;ramp speed of unit (in Megawatts per minute).

Equation (5) is the operating reserve capacity constraint ofunit . The ramp speed is considered in (6) to ensure that theoperating reserve capacity can hold on in required time (forexample, for spinning and nonspinning reserve is tenminutes).

It must be pointed out that the model above is based on marketstructure in which the operating reserve market is independentfrom other markets and is cleared right after the energy market.The correlation among hours in the unit commitment problemhas been solved in the energy market. Hence, in the operatingreserve market, there is no correlation among hours.

B. Condition of Optimal Reserve CapacityThe same condition of optimal reserve capacity can be de-

duced from (1a) and (1b). The following deduction is based on

Fig. 1. Optimal capacity condition for pay-as-bid mode.

(1b). Taking the partial derivative of (1b), we obtain the neces-sary condition of optimal reserve capacity

(7)

Because is not a continuous variable in the purchasingprocess, we use the difference equation to replace the aboveequation

(8)or

(9)where is the incremental cost of , and is theEENS change that is usually a negative due to increasing oper-ating reserve . Whether or not to purchase can be de-termined by (9). When the following inequality holds for in-creasing

or

(10)purchasing is favorable, because the benefit due to de-creasing interruption loss is larger thanthe cost of . Otherwise, one should stop purchasing

.

The principle of clearing operating reserve capacity under thePAB mode can be illustrated by Fig. 1. First, we sort the biddingprices reported by suppliers into a merit order, assuming

From (3), the cost of under the PAB mode can be repre-sented by

Thus, we can establish the supply curve , as shown inFig. 1. and in thefigure are the cumulative operating reserve capacity and the cu-mulative cost after purchasing .

WANG et al.: OPERATING RESERVE MODEL IN THE POWER MARKET 3

Another curve in Fig. 1 is the interruption loss curve .At the beginning of the clearing process, the operating reservecapacity of the system is zero. By generation system reliabilityevaluation, we can obtain the respective EENS of the system

and the interruption loss , as shown inFig. 1. If purchasing , the EENS of the system decreased to

; the benefit is

As shown in the figure, is larger than the cost of

Therefore, purchasing is favorable. Next, we will determineif should be purchased. At this point, the system already hasreserve . If purchasing , the reserve becomes

Evaluating system reliability under the condition of reserve ca-pacity , we obtain the EENS of the system . Thus,the benefit of is

When the benefit is larger than the cost of

purchasing is favorable.Continuing this process until

and becomes the optimal operating reserve capacity. Asshown in Fig. 1, the curve is continuously decreasing untilthe above inequality holds when , where reaches itsminimum.

III. ALGORITHM OF OPERATING RESERVE MODELA heuristic algorithm based on the merit-order method is em-

ployed to solve the above operating reserve model. The solutionprocess of the model for PAB mode is shown in Fig. 2.

In the main loop of the algorithm, the reserve capacity is pur-chased one unit by one unit according to the merit order.and are the systems EENS before and after purchasingoperating reserve of unit . Thus, the decrease of EENS dueto increasing reserve is

(11)

For the pay-as-bid mode, (9) can be rewritten as

(12)

Fig. 2. Flowchart of operating reserve clearing process.

and for the uniform-price mode, (9) can be rewritten as

(13)

Now, we will briefly introduce the solution process in Fig. 2with the following.

1) Form the merit order according to bidding price.2) Calculate by running a reliability evaluation pro-

gram under the condition that the reserve capacity of thesystem is zero.

3) Set initial values.4) Select reserve with the lowest bidding price among the

residual units.5) Check whether constraints are satisfied; if not satisfied, go

to (9), and select the next unit.6) Increase to system reserve , and calculate .7) Calculate the decrease of the social cost.8) Check whether the purchasing condition (10) is satisfied.


Fig. 3. Test system load curve for a 24-hr period.

9) When the purchasing condition (10) is satisfied, select thenext unit, and go back to step (4).

10)When (10) is not satisfied, purchasing is not favorable;stop purchasing and obtain the optimal reserve capacity.

The main difference between the solution processes of thetwo market modes lies in the formulas used to obtain the pur-chase cost. The incremental social benefit cost in pay-as-bidmode is calculated by (12), while that in uniform-price modeis calculated by (13). Thus, replacing (12) with (13) in Fig. 2,we get the flowchart for the uniform-price mode.

IV. CASE STUDIES

The IEEE test systemRTS96is employed to demonstratethe proposed operating reserve model. The system has threeareas, and each area has six hydro units, 24 thermal units, andtwo nuclear units [12]. The total installed is 10 215 MW. Thepeak load is 5860 MW at 10 a.m., and the base load is 3398 MWat 3 a.m. The unit information (including type, size, bidding, andselected capacity in energy market) is shown in the Appendix.

The load curve for a 24-hr period is shown in Fig. 3. IEAR isassumed to be $1/kWh. The spinning reserve market is clearedby cost-benefit analysis in every period, and the spinning reservecapacities of 24-hr are given in Fig. 4.

Fig. 4 shows that the spinning reserve curves in two modesboth have the flexible characteristic, i.e., spinning reserve ca-pacities are determined by social benefit analysis in every periodrather than the predefined deterministic criteria. This methodcan maximize the social benefit. The shape of SR in Fig. 4 issimilar to the load shape in Fig. 3. It indicates that the peakcapacity of spinning reserve corresponds with the peak load.The result is reasonable, and the system reliability can be wellguaranteed.

The unit order is fixed in the uniform-price mode, and theselected unit has the lowest bidding price in the residual capaci-ties. The clearing capacities may vary with the load situation andsometimes fluctuate abnormally. In the PAB mode, an additionalloop could be introduced in the algorithm, as shown in Fig. 2, toimprove the operating reserve selection strategy. In every loop,

Fig. 4. System spinning capacities.

Fig. 5. Comparison of reserve ratios.

the social benefit of all residual reserve units is calculated, andthe unit with maximum social benefit in the current loop is se-lected. In this way, the unit order is not fixed with the biddingprice but is dynamically adjusted according to their social ben-efit in each loop. In this approach, the selected unit always hasthe highest social benefit, which enhances the stability of theclearing process.

In order to analyze the feasibility of the flexible reserve, theratios of the spinning reserve over the load obtained by the sug-gested flexible spinning reserve model are compared with thoseof the traditional model in other papers. As is shown in Fig. 5,the scheduled reserve of the traditional model has a smaller ratioat peak load and larger ratio at base load, while the flexible re-serve has a higher ratio at peak load and lower ratio at base load.Obviously, the clearing capacity of the flexible reserve is morereasonable.

The optimal spinning reserve capacity is affected by the valueof IEAR. Fig. 6 shows the clearing capacity of the spinning re-serve market with different values of IEAR. It can be observedfrom these curves that the optimal spinning reserve capacityvaries significantly with the value of IEAR. When the IEAR


Fig. 6. System spinning capacities with different values of IEAR.

Fig. 7. Social benefit of reserve.

increases, the spinning reserve benefit becomes larger, and thesystem should buy more spinning reserve capacity.

In the view of flexible reserve, the social benefit should bemaximized in each period. The social benefit of two modesduring the peak load is shown in Fig. 7 under the same bids.The maximum social benefits and optimal spinning reserve ca-pacities are marked in the figure.

Fig. 7 shows that the social benefit increases until reachingthe maximum value, and then, it slowly decreases. In the wholeclearing process, the social benefit in the PAB mode is higherthan that in the uniform-price mode.

It should be pointed out that the advantage of operating re-serve flexibility is embodied on the basis of enough capacity.Under the condition of insufficient capacity, some reserve unitswith a high bid are still selected. The clearing process may notreach the maximum social benefit. So, the flexible operating re-serve model is more suitable for large markets.

When the generators of the system are more reliable [theyhave lower forced outage ratios (FORs)], less operating reserve

Fig. 8. System spinning capacities versus different values of FOR.

Fig. 9. Clearing capacity when all plants raise price together.

should be required. This adjustment can be automatically real-ized in the presented model. The required spinning reserve ca-pacities are shown in Fig. 8 for different FORs of the generators.

Comparing with traditional dispatch, the proposed operatingreserve model is more flexible because the information aboutthe generators robustness can be used in determining optimaloperating reserve capacity. The system with less-robust genera-tors should buy more capacity and vice versa. This will optimizethe usage of our resources.

Furthermore, flexible reserve can also reduce the marketpower on the basis of the bidding information in the market.Consider the worst case when all independent power producers(IPPs) raise bidding prices together. Under traditional dispatchrules, all the predetermined reserve capacity should be bought.In the flexible reserve model, the market could buy less capacityas countermeasures against rising prices. In order to explain thiseffect on the spinning reserve market, Fig. 9 gives the clearingcapacity of spinning reserve as a function of markup rates.

From Fig. 9, we can see that the higher the bidding price,the less spinning reserve capacity the market should buy. In


TABLE IU100 ENERGY BID

TABLE IISPINNING RESERVE CAPACITY DURING PEAK LOAD OF AREA 1

the flexible reserve model, the adjustment can be carried outautomatically.

V. CONCLUSIONBased on cost-benefit analysis, this paper proposes a novel

operating reserve model. This model makes full use of the

TABLE IIISPINNING RESERVE BID

market information and system reliability information whenpurchasing the operating capacity. According to the model,more operating reserve capacity should be purchased when thesystem is less reliable, the value of IEAR is higher, and thebidding price is lower in the power market, and vice versa.Because the operating reserve capacity of a power system isnot predetermined, the proposed model not only can maximizesocial benefit but also can reduce the market power. From theresults of case studies, it seems that PAB mode is superior to theuniform-price mode in reducing market power and smoothingthe cost for the operating reserve market.

In order to realize the flexible operating reserve market, thecharacteristic of IEAR and a specific market structure shouldbe carefully considered. The PAB and the uniform-price modeneed to be further investigated to judge which is preferable.

APPENDIX

The algorithm was demonstrated on the test system RTS96.The energy market adopts simple patterns since the emphasisof this paper is the operating reserve market. The cost of eachunit could be seen in paper [12]. Units submit four-block bidsand keep the bidding curves fixed all day. The bidding curvescontain the following four blocks: The first-block bid is lowerthan the cost so that the unit will be chosen to serve. The secondand third block bids are equal to the costs. The fourth bid, whichis higher than the cost, is submitted to game for more benefit.The energy bid of U100 is given in Table I as an example.

Table II gives the clearing results in the energy market andthe spinning reserve capacities during the period of peak load inArea 1. The data of Areas 2 and 3 are similar with that of Area1. The SR capacity is subject to the residual capacity and theramp rate simultaneously.

The bid curves of the spinning reserve are founded on the en-ergy bids and the capacities that units can provide in ten minutes,assuming that the bid is 50% of the energy bid. As an example,the spinning reserve bid of U100 is given in Table III.

REFERENCES[1] X. Wang, Y.-H. Song, and Q. Lu, A coordinated real-time optimal dis-

patch method for unbundled electricity markets, IEEE Trans. PowerSyst., vol. 17, no. 2, pp. 482490, May 2002.

[2] J. M. Arroyo and A. J. Conejo, Optimal response of a power generatorto energy, AGC, and reserve pool-based markets, IEEE Trans. PowerSyst., vol. 17, no. 2, pp. 404410, May 2002.

[3] H. B. Gooi et al., Optimal scheduling of spinning reserve, IEEE Trans.Power Syst., vol. 14, no. 4, pp. 14851492, Nov. 1999.

[4] C.-L. Tseng et al., Price-based adaptive spinning reserve requirementsin power system scheduling, Elect. Power Energy Syst., vol. 21, pp.137145, 1999.


[5] X. Wang, Equivalent energy function approach to power system prob-abilistic modeling, IEEE Trans. Power Syst., vol. 3, no. 3, pp. 823829,Aug. 1988.

[6] E. Yu, J. Zhou, and X. Zhang, Bidding model and bidding principle forpower markets, Automat. Elect. Power Syst., vol. 25, no. 1, pp. 2427,2001.

[7] C. Vzquez, M. Rivier, and I. J. Prez-Arriaga, If pay-as-bid auctionsare not a solution for California, then why not a reliability market?,Elect. J., vol. 14, no. 4, pp. 4148, 2001.

[8] A. E. Kahn, P. C. Cramton, and R. H. Porter, Uniform pricing orpay-as-bid pricing: A dilemma for California and beyond, Elect. J.,vol. 14, no. 6, pp. 7079, 2001.

[9] T. Mount, Market power and price volatility in restructured markets forelectricity, Decision Support Syst., vol. 30, pp. 311325, 2001.

[10] N. Fabra, N.-H. von der Fehr, and D. Harbord, Modeling electricityauction, Elect. J., vol. 15, no. 7, pp. 7281, 2002.

[11] K. K. Kariuki and R. N. Allan, Factors affecting customer outage costsdue to electric service interruptions, Proc. Inst. Elect. Eng. Gener.Transm. Distrib., vol. 143, no. 6, pp. 521528, 1996.

[12] C. Grigg, P. Wong, P. Albrecht, R. Allan, M. Bhavaraju, R. Billinton, Q.Chen, C. Fong, S. Haddad, S. Kuruganty, W. Li, R. Mukerji, D. Patton,N. Rau, D. Reppen, A. Schneider, M. Shahidehpour, and C. Singh, TheIEEE reliability test system-1996. A report prepared by the ReliabilityTest System Task Force of the Application of Probability Methods Sub-committee, IEEE Trans. Power Syst., vol. 14, no. 3, pp. 10101020,Aug. 1999.

Jianxue Wang received the B.S. and M.S. degrees in electrical engineering fromXian Jiaotong University, Xian, China, in 1999 and 2002, respectively. Cur-rently, he is pursuing the Ph.D. degree at Xian Jiaotong University.

His major research interests include power market and system reliability.

Xifan Wang (SM86) received the B.S. degree from Xian Jiaotong University,Xian, China, in 1957.

He is a Professor in the Department of the Electrical Power Engineering atXian Jiaotong University. His major research fields include power market, re-liability evaluation, generation planning, system contingence analysis, and sta-bility analysis.

Yang Wu (S05) received the B.S. and M.S. degrees in electrical engineeringfrom Xian Jiaotong University, Xian, China, in 1999 and 2002, respectively.Currently, he is pursuing the Ph.D. degree at Texas A&M University, CollegeStation, TX.

His major research interests include protective relaying and substationautomation.

tocOperating Reserve Model in the Power MarketJianxue Wang, Xifan Wang, Senior Member, IEEE, and Yang Wu, StudI. I NTRODUCTIONII. C LEARING M ODEL OF F LEXIBLE O PERATING R ESERVEA. Flexible Operating Reserve ModelB. Condition of Optimal Reserve Capacity

Fig.1. Optimal capacity condition for pay-as-bid mode.III. A LGORITHM OF O PERATING R ESERVE M ODEL

Fig.2. Flowchart of operating reserve clearing process.Fig.3. Test system load curve for a 24-hr period.IV. C ASE S TUDIES

Fig.4. System spinning capacities.Fig.5. Comparison of reserve ratios.Fig.6. System spinning capacities with different values of IEARFig.7. Social benefit of reserve.

Fig.8. System spinning capacities versus different values of FOFig.9. Clearing capacity when all plants raise price together.TABLE I U100 E NERGY B IDTABLE II S PINNING R ESERVE C APACITY D URING P EAK L OAD OF A RV. C ONCLUSION

TABLE III S PINNING R ESERVE B IDX. Wang, Y.-H. Song, and Q. Lu, A coordinated real-time optimal J. M. Arroyo and A. J. Conejo, Optimal response of a power generH. B. Gooi et al., Optimal scheduling of spinning reserve, IEEE C.-L. Tseng et al., Price-based adaptive spinning reserve requirX. Wang, Equivalent energy function approach to power system proE. Yu, J. Zhou, and X. Zhang, Bidding model and bidding principlC. Vzquez, M. Rivier, and I. J. Prez-Arriaga, If pay-as-bid auA. E. Kahn, P. C. Cramton, and R. H. Porter, Uniform pricing or T. Mount, Market power and price volatility in restructured markN. Fabra, N.-H. von der Fehr, and D. Harbord, Modeling electriciK. K. Kariuki and R. N. Allan, Factors affecting customer outageC. Grigg, P. Wong, P. Albrecht, R. Allan, M. Bhavaraju, R. Billi

wang, wang & wu - operational reserve model in the power market

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