Toward a Competitive Market for Reactive Power by Prof. Bhattacharya

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1206 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 4, NOVEMBER 2002

Toward a Competitive Market for Reactive PowerJin Zhong and Kankar Bhattacharya, Senior Member, IEEE

AbstractThis paper presents the design of a competitive

market for reactive power ancillary services. Generator-reactivepower-capability characteristics are used to analyze the reactivepower costs and subsequently construct a bidding framework. Thereactive power market is settled on uniform price auction, using acompromise programming approach based on a modified optimalpower-flow model. The paper examines market power issues inthese markets and identifies locations where strategic marketpower advantages that need to be removed through investments inreactive power devices are present.

Index TermsAncillary services, compromise programming,deregulation, market design, market power, reactive power.

I. INTRODUCTION

MANAGEMENT and procurement of reactive powerservices and consequent payment schemes used byindependent system operators (ISOs) differ across systems inthe way the contracts are framed and the markets operate. Inthe U.S. context, as per North American Electric ReliabilityCouncils (NERC) Operating Policy-10 [1], only reactivepower from a synchronous generator is considered to be anancillary service and can receive payment. Among the variousmarkets within United States, the New York ISO has set outclear mechanisms for payment that considers the embeddedcost of the service. It also has a provision for compensating agenerator for itslost opportunity costwhen it has to back downits real power output on an ISOs request for additional reactive

power [2]. In California, the generators are required to providereactive power in the power factor range of 0.90 lag and 0.95lead without any payment. For reactive support beyond theselimits, generators are paid, which includes a component if theyare required to reduce their real power output [3].

In Australia, payment for reactive support is admissible togenerators and synchronous condensers. The payment com-prises an availability componentfor their preparedness andto synchronous condensers, additionally, an enabling compo-nentwhich is paid when their service is activated by the ISO.Generators receive, in addition to the availability component, acompensation componentbased on their lost opportunity costwhen they have been constrained from operating according to

their market decisions [4].In the deregulated markets of Nordic countries, there is, how-

ever, no provision for payment toward reactive power services.For example, in Sweden, the responsibility for managing reac-tive power lies with regional transmission companies, with cer-

Manuscript received September 27, 2001; revised April 5, 2002. This workwas supported by Sydkraft Research Foundation of Sydkraft AB, Sweden, aspart of the research project on ancillary services.

The authors are with the Department of Electric Power Engineering,Chalmers University of Technology, Gothenburg, Sweden.

Digital Object Identifier 10.1109/TPWRS.2002.805025

tain rules from the ISO stipulating that there should be no ex-

change of reactive power over different network voltage levelsand transformers. To meet this requirement, individual entities,such as local and regional networks, make a provision for theirown reactive power [5]. A detailed review of reactive powermanagement in various deregulated electricity markets has beenpresented in [6].

From the prior discussions, we see that there has been a movetoward creating payment mechanisms for reactive power ser-vices in many systems. However, a fully competitive reactivepower market has yet to emerge. Several factors make operatingreactive power services within a competitive market frameworkvery difficult. Some of them are discussed in the folowing.

Reactive power needs to be provided locally, and hence,the worth of one megavoltampere (MVAr) of reactivepower is not the same everywhere in the system. Thus, if areactive power market is settled like a real power market,the ISO can end up with a stack of low-priced offers fromlocations that are undesirable from system considerations.Therefore, reactive power markets need a new approachthat takes into account both offer prices and location ofthe resource.

As we have noted in [6], not one of the deregulated sys-tems yet recognizes reactive power from sources otherthan generators or synchronous condensors as ancillaryservices. Changes at the policy level are necessary to in-

clude other reactive power sources such as capacitors, re-actors, FACTS devices etc., as ancillary services. Throughconventional load-flow analysis, there are market

players (i.e., reactive power providers)1 that can determinethose buses that consistently require high reactive support.A provider located at such a bus would have significant op-portunities to indulge in gaming, given the limited numberof potential players in the system and at a bus. To preventthis, we can do the following.

I fa uniform priceauction isusedto determine the re-active power market prices, the providers will haveincentives to offer their true operating and opportu-nity costs. Since each provider would receive a price

greater than its offered price, submitting an offerpriced above its costs will expose the provider to therisk that the offer is not selected, with a resulting lossof revenue. Thus, providers will have a clear incen-tive to offer prices equal to their costs and quantitiesequal to their capacity [7].

It can be argued thatnodal reactive power pricingmethods would motivate new reactive power in-

1In this paper, provider refers to synchronous generators and condenserssince these are the only recognized reactive power ancillary service providers.This is per NERC and other markets existing regulations, as discussed earlier.

0885-8950/02$17.00 2002 IEEE
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ZHONG AND BHATTACHARYA: TOWARD A COMPETITIVE MARKET FOR REACTIVE POWER 1207

vestments in high-demand areas and thereby reducemarket power concerns. However, as discussed in[8], these pricing instruments would only representa portion of the true cost of the reactive power ser-vicethat associated with fuel costs of real power.The capital and opportunity cost components ofreactive power will not be accounted for. Moreover,

with the enormous volatility of nodal prices, thistype of pricing could lead to highly unstable mar-kets.

If other reactive power sources, such as capacitorbanks, reactors, or SVCs could participate in themarket, there would be more competition. However,this requires changes in the existing policies and de-tailed studies, which we will not consider in thispaper.

A long-term contract-based reactive power marketcould prevent providers from exercising their marketpower and offer their reactive energy at higher pricesthan the cost of alternative reactive power generation

[8].The design of a reactive power market is, thus, an important

issue, and the possibilities for gaming and market power needto be eliminated so that the market functions efficiently.

In an earlier paper by these authors [9], an approach to op-timal contracting of reactive power services by the ISO was pre-sented, using the maximizationof a societal advantage function.The present work extends the issue further to the creation of acompetitive market for reactive power services and determininga possible model for market settlement and obtaining uniformreactive power prices for all providers. We also analyze thebarriers to the creation of such a competitive marketthoseexisting in the form of market power with certain serviceproviders. When these barriers are identified, the ISO can takecorrective steps to remove them and improve the efficiency ofthe reactive power market.

II. DESIGN OF AREACTIVEPOWERMARKET

To begin with, we define two terms that will be used for thedevelopment of the reactive power market.

a) Expected Payment Function (EPF):Generators providingreactive power services incur various costs depending on

their operating regime. While some of these costs are verydifficult to differentiate from other costs, some are diffi-cult to quantify. A comprehensive analysis of these costshas been provided in [10]. Under deregulation, a properfinancial mechanism must exist to compensate for thesecosts. The EPF is a mathematical formulation of costcomponents vis--vis the generators expectation of pay-ment for these components.

b) Cost of Loss:This is one of the components of EPF. Reac-tive power supplied or absorbed by a generator increasesthe real power loss in field windings. The power thuslost is a nonlinear function of reactive power [11]. Al-though this component is much smaller compared with

other losses in the system, it needs to be accounted for.This will be referred to ascost of lossin this paper.

The following assumptions are made regarding the design ofa reactive power market.

The ISO or a similar entity operates this market and is thesole contractor of reactive power services with providers.Thus, the market is monopsonic in structure. The ISO callsfor reactive power offers from the providers.

The market operates on long-term contracts so thatshort-term demand fluctuations, reserve conditions, orreal power market price spikes do not affect reactivepower offer price trends. The market is assumed to befairly perfect with rational participants [8].

The market is settled onfirst price, uniform auction. Thismeans that all selected providers receive a uniform price,which is the highest priced offer accepted. As discussed in[7]andin[12], this provides the players enough incentivesto bid their true costs.

A. Cost of Reactive Power Production From a GeneratorThe reactive power market structure is built on the providers

EPF for their services. An offer price structure was developedin [9], which is modified in this work with a more realistic rep-resentation of thecost of losscomponent and the EPF. For thesake of continuity, we discuss this issue along similar lines as in[9].

The reactive power capability curve of a generator is shownin Fig. 1 [13]. is the reactive power required by the gen-erator for its auxiliary equipment. If the operating point lies in-side the limiting curves, say, at ( , ), then the unit canincrease its reactive generation from up to withoutrequiring readjustment of . This will, however, result in in-creased losses in the windings and, hence, increase the cost ofloss.

If the generator operates on the limiting curve, anyincrease inwill require a decrease in to adhere to the winding heating

limits. Consider the operating point on the curve definedby ( , ). If more reactive power is required from the unit,say , the operating point requires shifting back along thecurve to point , where . This signifies thatthe unit has to reduce its real power output to adhere to fieldheating limits when higher reactive power is demanded. Theloss in revenue to the generator due to the reduced productionof real power is termedlost opportunity costand is a significant

issue. The two cost components of a reactive power supply froma generator are depicted in Fig. 2.Based on the information presented before, we define three

operating regions for a generator on the reactive power coordi-nate as follows:

Region-I: 0 to Reactive power produced in thisregion caters to the generators requirements to maintainits auxiliary equipment. Therefore, reactive power outputin this region should not qualify as an ancillary service,nor is the generator entitled to payments.

Region-II: ( to ) and (0 to ):When the gen-erator is injecting or absorbing reactive power within thisregion, it would incurcost of lossand, hence, can expect to
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Fig. 1. Synchronous generator capability curve.

Fig. 2. Cost incurred by a generator as a function of reactive power support.

be paid for its services. Its EPF would consist of two com-ponents in this regionan availability component and costof loss component.

EPF Availability Cost of Loss component

Region-III: to When the generator provides re-active power in this region, it is entitled to receive a pay-ment commensurate with its opportunity cost of reducedreal power production, along with the other components.The EPF can then be expressed as

EPF Availability Cost of Loss Opportunity

However, the ISO will not be in a position to estimate the EPFfor a generator in deregulated markets. An appropriate optionfor the ISO isto call for reactive offers from all generators based

on the EPF structure. A possible structure of such reactive offersis discussed next.

B. Structure of Reactive Power Offers

Based on the classification of reactive power productioncosts, a generalized EPF and, hence, an offer structure can beformulated mathematically

EPF

(1)

The coefficients in (1) represent the various components ofreactive power cost incurred by provider that need to be offeredin the market. These are explained as follows:

availability price offer in dollars;cost of loss price offer for operating in underexcitedmode (absorb reactive power), in

$/MVar-h;cost of loss price offer for operating in the regionin $/MVar-h;

opportunity price offer for operating in the regionin ($MVar-h)/MVar-h (note that

the opportunity offer is a function of reactive poweroutput, and hence, the corresponding EPF componentwill be a quadratic function of ).

The generalized EPF vis--vis the offer parameters, discussedbefore, are shown in Fig. 3. Note that the prior discussions alsohold for synchronous condensers, except for the opportunitycost component. Synchronous condensers will be assumed tooffer all components, except for the opportunity price.


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Fig. 3. Structure of reactive offers from providers.

We should note here that the availability offer typically

represents a part of the generators capital cost that goes towardproviding reactive power. This is annualized and further reducedon a days scale. Understandably, this is very difficult to sepa-rate from the total capital cost but, in any case, is a small fractiononly. The cost of loss offer represents the generators opera-tional costs in providing the service. These two components aretherefore not very different in magnitude, both being of similarorders in the model.

III. MARKETSETTLEMENT ANDPRICEFORMATION

All participating providers submit their offers to the ISO interms of the four components, as discussed in Section II-B. Asmentioned earlier, the opportunity price offer for synchronouscondensers is zero. Once these price offers are received, theISO settles the market and declares the uniform market price ofeach component separately.

We know that in real-power markets, the offers are stackedin increasing order of prices and that offer intersecting the de-mand curve determines the market price. However, withreactivepower offers, location being an important issue, a low-pricedoffer need not necessarily be attractive if the provider is locatedat a remote bus. Similarly, an expensive offer from a provider ata heavily loaded demand center may be unavoidable and needto be procured.

Therefore, settlement of a reactive power market must con-sider the system configuration and operating conditions in addi-tion to offer prices. While, on one hand, reactive power servicesshould seek to minimize the system losses, they should not re-sult in a high-payment burden for the ISO. Further, the procuredservices should also ensure that contracted real power transac-tions are met and that curtailments are kept at a minimum. TheISO is thus faced with a conflicting situation, where it has tocontract reactive power services to ensure that losses, curtail-ments, and payments are all within tolerable limits.

To achieve this, a compromise programming approach is pro-posed here to settlethe marketand determinethe uniform prices,incorporating the following considerations.

The reactive power market is settled such that the totalpayment made by the ISO is minimized.

The ISO aims to satisfy all contracted real power trades-between suppliers and customers.

The transmission losses are minimized.Four steps are necessary to arrive at the compromise solution

and, hence, the market settlements, which are discussed in Sec-

tions III-AD.

A. Market Settlement to Minimize Payment

This subsection describes reactive power market settlementwithtotal payment (2) as the objective for minimization.The total payment will depend on the market price of the fourcomponents of reactive power being offered to the providers.The principle of highest priced offer selected determining themarket price is applied with additional system constraints

(2)

Reactive power output from a provider is classified into threecomponents , , or that represent the regions ( , 0),( , ), and ( , ), respectively. Accordingly, onlyone of the binary variables , , and can be selected. In(2), is theuniform availability priceand and are theuniform cost of loss prices, whereas is theuniform opportu-nity price. If a provider is selected, will be one, and it willreceive the availability price, irrespective of its reactive poweroutput. The system constraints are as follows.

1) Load-Flow Equations:

(3)

(4)

where, index for buses;

index for generator at a bus;contracted real powergeneration at bus in perunit;actual real power transaction allowed by ISO in perunit;reactive power support at a bus in per unit;reactive power demand at a bus in per unit;reactive support from shunt capacitors at a bus inper unit;voltage at a bus in per unit;element of network admittance matrix in per unit;angle associated with in radians.

2) Reactive Power Relational Constraints and Limits:As perthe reactive power offer regions, discussed in Section II-A, a


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set of governing algebraic relations is required to ensure appro-priate allocation. These can be written as follows:

(5)

(6)

(7)

3) Determining the Market Prices:The market prices are de-termined separately for each component of reactive power. Thefollowing constraints ensure that the market price, for a givenset of offers, is the highest priced offer accepted:

(8)

(9)

(10)

(11)

(12)

4) Reactive Power-Generation Limits:

(13)

(14)

In (13), the upper limit on reactive power output from a gener-ator is (see Fig. 1), which takes into account the opportunitycomponent. in (14) is the reactive power support from otherreactive sources (e.g., capacitor banks). These are not includedin the market since they are not considered ancillary services.

5) Bus Voltage Limits:

load bus

constant bus (15)

6) Limit on Bilateral Transactions:This constraint ensuresthat all bilateral transactions are within prespecified limits. Thebilateral transactions are modeled using the method discussedin [14]

(16)

is the contracted real power transaction by a load at buswith generator . is the decision variable and denotes

the actual transaction permitted by ISO.

B. Market Settlement to Minimize Transmission Losses

This model describes the procurement of reactive power ser-vices to minimize transmission losses (17) and is similar toa classical reactive power-optimization problem. Market pricesare determinedex post. That means that after the optimal solu-tion is obtained, the highest priced offer selected determines theuniform price. The model is described as

(17)

where is the onductance of line in per unit.The constraints are as follows

1) Load Flow(3) and (4);2) Reactive power generation limits(13) and (14);3) Bus Voltage Limits(15);4) Limit on Bilateral Transactions(16).

C. Market Settlement to Minimize Deviation From ContractedTransactions

This model ensures that the procured reactive power contractsminimizedeviations from contracted transactions . There-fore, this also ensures that curtailment of power transactions isminimized. As in the case of minimizing transmission losses,the market prices are determined ex post. The model is describedbelow. represents the difference between contracted trans-actions (between generators and loads) and actual transactionspermitted by the ISO

(18)

The constraints are as follows

1) Load Flow(3), (4);2) Reactive Power Generation Limits(13) and (14);3) Bus Voltage Limits(15);4) Limit on Bilateral Transactions(16).

D. Market Settlement to Minimize the Compromise Function

It is seen that the reactive power market can be based ondifferent objective functions for the ISO. For example, inSections III-AC, we have formulated markets that 1) seekto achieve the minimum market price consumer payment

minimization, 2) minimize losses, and 3) minimize deviationsfrom contracted transactions.While each model independently seeks important targets, an

ISO would often want to achieve all of the three targets simulta-neously. To achieve that, we propose a compromise program-ming model that attains the best compromise among the con-flicting objectives [15], [16]. The three objectives can be com-bined into a compromise function (19), which, when mini-mized, will represent the ISOs requirement of meeting contra-dictory objectives simultaneously

(19)

where , , and are the respective minimum values when, , and are optimized independently. Note that while

we have used an equal weight for each conflicting component in(19), this need not necessarily be the case in actual markets. TheISO may choose to have a priority on the objectives, dependingon the market condition. For example, if the participants arewilling to pay for increased losses in order to have their transac-tions fulfilled, the weight on could be very small. Thus, thechoice of weights to be associated with the three componentsof (19) should be made by the ISO, as per its decision-makingcriteria. In this paper, we consider equal weights of unity for thethree components.
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TABLE IREACTIVE POWER OFFERS AND OPTIMAL

CONTRACTS INBASECASE

b) Amongst the contracted generators, 4011, 1013, and1022 are also contracted for their opportunity compo-nent.

c) Market prices are determined by the highest offerin each category from selected providers. Thus,we get , MV Arh, and

MV Arh, and generators 4072, 4062,and 4011 are the corresponding price setters. Theunderexcited operation market price is zero, i.e., ,since no offer is selected from this category.

It can be seen from Table I that if the ISO minimizes lossesor transaction deviations only, it would need to contract almostall the offers in the market and a significant number of themfor the opportunity component. Although losses or deviationswould be low, its financial burden would be very high. Whenthe ISO seeks to minimize total payment only, it contracts formuch less reactive support while bearing a burden of increasedlosses and transaction deviations.

In the compromise solution, the total reactive power con-tracted, and the number of contracted parties is kept at a fairlyrational level without jeopardizing the system loss or transactiondeviation standards. The total payment, losses, and deviationsachieved from the compromise optimization are fairly close to

that obtained when these are individually minimized. The uni-form prices achieved for each component, in the compromisesolution, are also close to the lowest value achievable from theindividual minimization.

2) Market Power in Reactive Power Markets: We men-tioned in the introduction that reactive power in a competitiveframework could provide strategic advantages to certain partic-

ipants by virtue of their location vis--vis the configuration ofthe system. In this subsection, we attempt to examine if suchstrategic advantages do exist with any of the providers in oursystem, whether certain providers have market power, i.e.,dothey manage to remain the price setter under all circumstances?If such situations exist, how do we identify those providers?Such information can help the ISO to handle the market forreactive power more efficiently.

Say the contracted providers from base case presume thattheir reactive support will always be necessary due to theirstrategic location in the system and load profile. Consequently,these providers seek market power by offering prices higherthan their EPF and try to increase the market price. Five gaming

scenarios of high offer prices from these providers are con-structed below (S1 to S5). In S1, all contracted providers offer20% higher prices than their base offer, in the S2 scenario, theyoffer 30% higher prices, in S3, 40% higher, in S4, 50% higher,and in S5, they offer 60% higher prices. The correspondingoptimal reactive power contracts offered by the ISO based onthe compromise programming solution are provided in Table II.

From Table II, we can make the following observations:a) Generator 4072 remains the price setter for from base

case through all the gaming scenarios.b) As in base case, continues to be zero in all scenarios.c) Generator 4062, which was the price setter of in base

case, does not remain so in the gaming scenarios. Gener-

ator 4072 becomes the price setter for this componentas well.d) Generator 4011 was the price setter of in base case.

In the gaming scenarios, 4021 becomes the price setterin S1, 1012 in S2, and 1013 in S3 to S5.

From the above observations, we can say that when all base-contracted generators simultaneously indulge in gaming, gener-ator 4072 clearly retains market power and is the price setterfor two of the price components. It is also seen that the ISOcontinues to contract generators 4072, 4011, 4012, and1013 under all gaming scenarios. However, we note that ex-cept for 4072, the others do not have the capability to setprices in asimultaneous gamingscenario. This, however, may

not be true in an individual gamingscenario and is examinedand discussed next.We now consider only one of the four generators indulging in

gaming, at a time, by increasing its offer price by 60%, whereasothers offer their true EPF. The results are shown in Table III.

From Table III, we observe the following1) When generator 4072 indulges in gaming (see column

3), we get the following.a) Generator 4072 retains itself as a price setter for

and increases its market power to become theprice setter for as well.

b) Consequently, and increase significantly frombase case.


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TABLE IIOPTIMAL CONTRACTS BY THE ISO IN

GAMINGSCENARIOS

c) Although two new generators are contracted inplace of 4062 and 1022, other base case con-tracts are still retained by the ISO. The paymentburden for ISO increases by 52% for the reactivepower services.

d) System loss and transaction deviations are main-tained at base-case levels.

e) The ISO cannot avoid contracting reactive supportin significant quantities from generator 4072.

2) When generator 4011 indulges in gaming (see column4), we get the following.

a) Generator 4011 is eliminated from the market.The ISO establishes contracts with several newproviders.

b) Prices are practically similar (if not better) as levelsin base case through contracts with a wide rangeof generators. No contract required for opportunitycomponent of reactive power, and hence, .

c) ISO pays approximately 20% more to maintainlosses and transaction deviations at same levels asthe base case.

3) When generator 4012 indulges in gaming (see column5), we get the following.

a) Generator 4012 remains in the market, contractedby the ISO. All other generators contracted in basecase also continue to retain their contracts. The

TABLE IIIOPTIMALCONTRACTSWHENONEGENERATORINDULGES INGAMING

price setters, price levels, payment, loss, and devi-ation levels also remain the same as in base case.

b) In summary, gaming by generator 4012 does not

affect the system in any way.4) When generator 1013 indulges in gaming (see column

6), we get the following.

a) Generator 1013 is eliminated from the market andis no longer contracted by the ISO. Some new re-active power contracts are brought in by ISO.

b) The price setters from base case stay as price setters.c) The price level remains almost the same as the

base-case level. Payment, losses, and deviationsare affected very little from base case.

From the analysis, we conclude that only generator 4072has the capability to influence market prices and has immense

market power. The other generators that continue to remain con-tracted under all scenarios, however, cannot exercise marketpower. If they attempt to do so, they are eliminated from thecompetition. In summary, we can say that the system under in-vestigation does provide a competitive marketplace for reac-tive power. However, the imperfection arising from the marketpower of 4072 needs to be removed.

We also note that the proposed market structure and settle-ment model implicitly negotiate market power of strategicallylocated providers. For example, if the ISO seeks only loss min-imization, it would end up contracting several providers (seeTable I). A number of them could hold market power in the longrun. On the other hand, when the ISO seeks minimum payment,


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the cheapest offers, irrespective of providers location and con-tribution to losses, are contracted. Now, most of the providerswho were located at strategic buses from the loss minimizationapproach are eliminated. The same happens with the transac-tion deviation minimization approach. Finally, after the com-promise solution is obtained, we are left with seven providerswho are essential to the system from all considerations. There-

after, we carry out analysis to determine if any of the sevenproviders holds market power by gaming. It is seen that noneof the providers except 4072 can hold market power if theyindulge in gaming. Thus, 4072 is the most critical node andneeds capital investments. Only a market design or bid-ding framework cannot handle the inefficiency existing at thisbus.

3) Note on Computational Aspects: The reactive powermarket model to minimize payments (see Section III-A) andthe composite model minimizing the compromise objective(see Section III-D) are mixed-integer nonlinear programming(MINLP) problems with the presence of nonconvexities. Themodels are solved in generalized algebraic modeling systems

(GAMS), which is a high-level programming platform, usingthe DIscrete COntinuous OPTimization (DICOPT) solver.The DICOPT solver is based on the extensions of the outerapproximation algorithm for the equality relaxation strategy. Ititeratively invokes the MINOS5 and XA10.0 solvers for non-linear (NLP) and mixed-integer-programming (MIP) solutions,respectively [18], [19].

The NLP solution is obtained by MINOS5 by extremizingan augmented Lagrangian function using the reduced gradientalgorithm. XA10.0 uses the primal/dual simplex method toobtain the linear programming solution, combined with thebranch-and-bound method to obtain the MIP solution.

Under certain circumstances, the solution obtained from

DICOPT may not be globally optimum. This can happenduring the iterative process of the NLP and MIP subproblems;MINOS5 fails to handle nonconvexities. On the other hand,the GAMS/DICOPT algorithm has built-in provisions tohandle nonconvexities, and hence, we can, with a fair degreeof confidence, rely on the GAMS/DICOPT optimal solutionsto be globally optimal. It should be mentioned, however, thatthere is lot of work ongoing in the area of global optimizationmethods [20], [21], and improved techniques (or solvers withhigher confidence levels) should appear in the literature in thecoming years.

The reactive power market models minimizing transmis-sion loss (see Section III-B) and transaction deviation (see

Section III-C) are NLP problems and are solved using theGAMS/MINOS5 solver.

Both the GAMS/DICOPT and GAMS/MINOS5 efficientlyhandle the 32-bus CIGR system that is considered. However,we should note that the computational burden would inevitablyincrease for a larger system, particularly so for the MINLPmodels. Although algorithms for the solution of MINLP prob-lems yet to reach the maturity level of NLP or LP problems,there are global optimization methods available in the literature.In this context, global search techniques based on genetic algo-rithms, simulated annealing, etc. have a very promising scopefor applications in these problems. In Table IV, we present thecomputational burden involved in order to obtain the optimal

TABLE IVCOMPUTATIONALREQUIREMENTS FORSOLVING THEMODEL

solutions for each model. The programs were solved on aPentium-II 400-MHz computer with 256-MB RAM.

V. CONCLUSIONThe design of a competitive market for reactive power ser-

vices in deregulated electricity systems has been attempted inthis paper. The market is based on offers from generators or syn-chronous condensers for four components of service. The ISO,whois the sole buyer, settles the marketusinguniform price auc-tion, using a compromise optimization approach on an optimalpower-flow-based model. The compromise market settlementattains the best possible solution, keeping various contradictoryobjectives such as total payment, system loss, and transactioncurtailment, within reasonable limits.

Anexpected payment functionhas been formulated based on

the generators reactive power capability characteristic and anoffer-price framework has been proposed. The proposed marketstructure and settlement model implicitly negotiates price set-ting with strategically located generators. In addition, the possi-bilityof marketpowerwith contracted providers has been exam-ined in detail. Through five scenarios of simultaneous gaming,it is found that generator 4072 retains immense market powerand acts as the price setter for two of the price components.Due to the nature of the system load profile and network con-figuration, the ISO is compelled to contract generators 4072,4011, 4012, and 1013under all circumstances. However,when these generators take recourse to gaming (one generatorgaming while others offer rationally), only generator 4072

holds on to its reactive power market power.Other generatorsend up with reduced contracts or complete elimination from themarket. Thus, it can be concluded that bus 4072 is one of thestrategic buses in the system where a reactive power providerwill always have immense market power.

The ISO should seek measures to remove this market powerfrom bus 4072 in order to improve the efficiency of themarket. One possible way of removing this market power atbus 4072 is by investing in more reactive support (not neces-sarily reactive power ancillary service providers, for example,capacitor banks). This will help reduce the ISOs burden ofincreased payments and reduce the risk of high-market pricesthrough gaming.
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Toward a Competitive Market for Reactive Power by Prof. Bhattacharya