congestion management

886 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 2, MAY 2011

Influence of Price Responsive Demand ShiftingBidding on Congestion and LMP in Pool-Based

Day-Ahead Electricity MarketsKanwardeep Singh, Narayana Prasad Padhy, Senior Member, IEEE, and Jaydev Sharma

Abstract—This paper investigates the influence of price re-sponsive demand shifting bidding on congestion and locationalmarginal prices in pool-based day-ahead electricity markets. Themarket dispatch problem of the pool-based day-ahead electricitymarket is formulated as to maximize the social welfare of marketparticipants subject to operational constraints given by real andreactive power balance equations, and security constraints inthe form of apparent power flow limits over the congested lines.The social welfare objective function of the day-ahead marketdispatch problem maximizes the benefit of distribution compa-nies and other bulk consumers based on their price responsivedemand shifting bids and minimizes the real and reactive powergeneration cost of generation companies. The price responsivedemand shifting bidding mechanism, which has been recentlyintroduced in the literature, is able to shift the price responsivedemand from the periods of high price to the periods of lowprice in day-ahead electricity markets. The comparisons of theprice responsive demand shifting bids with conventional priceresponsive and price taking bids are presented by solving hourlymarket dispatch problems on five-bus, IEEE 30-bus, realistic UP75-bus Indian, and IEEE 118-bus systems for 24-h schedulingperiod. It has been demonstrated that the proposed approachleads to reduction in congestion and locational marginal pricesas compared to price responsive and price taking bids and meetsthe energy consumption targets of distribution companies/bulkconsumers.

Index Terms—Congestion management, locational marginalprice, price responsive demand shifting bidding, social welfare.

NOMENCLATURE

Abbreviations of commonly used symbols in the paper are asfollows.

, Sets of buses, GenCos and DistCos.

Sets of GenCos and DistCos located at thbus.

Set of transmission lines.

Manuscript received March 12, 2010; revised March 15, 2010, May 31, 2010,and July 13, 2010; accepted July 23, 2010. Date of publication September 20,2010; date of current version April 22, 2011. Paper no. TPWRS-00191-2010.

K. Singh is with the Department of Electrical Engineering, Guru Nanak DevEngineering College, Ludhiana, India (e-mail: [email protected]).

N. P. Padhy and J. Sharma are with the Department of Electrical Engineering,Indian Institute of Technology, Roorkee, India (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2010.2070813

Set of scheduling sub-intervals and durationof one sub-interval.

Benefit of th DistCo at th bus in thsub-interval under PRDS bidding .

Cost of real power generation of th GenCoat th bus during th sub-interval .

Cost of reactive power generation of thGenCo at th bus during th sub-interval

.

Profit term in lost opportunity cost (variesbetween 5%–10%).

Social welfare function for entire schedulingperiod .

Real and reactive power generated by thGenCo at th bus during th sub-interval.

Real and reactive price taking powerdemand of th DistCo at th bus during thsub-interval.

PRDS real and reactive power demand of thDistCo at th bus during th sub-interval.

Maximum and minimum price bids of thDistCo during th sub-interval under PRDSbidding (in ).

Slope of bidding curve of th DistCo duringth sub-interval under PRDS bidding (in

).

Coefficients of cost bid of th GenCo duringth sub-interval (in and

.

Bus voltage magnitude and angle at th busduring th sub-interval.

th element of bus admittance matrix.

Power factor angle of power demand of thDistCo during th sub-interval.

Apparent power flow over lineduring th sub-interval.

Maximum apparent power flow limit overline .

0885-8950/$26.00 © 2010 IEEE

SINGH et al.: INFLUENCE OF PRICE RESPONSIVE DEMAND SHIFTING BIDDING 887

Minimum and maximum limits on .

Maximum apparent power generationdetermined from capability curve of thgenerator.



Maximum limit on energy consumed underPRDS bid of th DistCo during entirescheduling period.

Maximum limit on .


I. INTRODUCTION

I N a pool-based competitive electricity market, the inde-pendent system operator (ISO) collects hourly/half-hourly

demand or benefit bids from distribution companies/bulk con-sumers (DistCos) and supply or cost bids from generator com-panies (GenCos) for developing day-ahead market dispatch gen-eration and demand schedule. The supply or cost bid providedby a GenCo is its minimum asking price which it would acceptfor supplying a particular amount of power. Similarly, demandor benefit bid of a DistCo is its maximum willing price, whichit would pay for consuming a particular amount of power. Thelocational marginal prices (LMPs) of real and reactive powerat any bus and at any time interval are the marginal costs ofsupplying the real and reactive powers, respectively, at that busand at that time and are the by-products of the solution of themarket dispatch problem [1]–[4]. The LMP profile varies overthe system buses and during the day due to the losses and con-gestion in the system, with congestion being the major factor forLMP variations. Hence, LMP at a particular bus and at a par-ticular time is the economic signal of delivery of power at thatbus and that time. In other words, high LMPs at demand busesand low LMPs at generator buses represent high congestion, andflat LMP profile at system buses represents no congestion in thesystem. The LMP methodology is being used by the ISOs ofNew England, New York, PJM Interconnection, Midwest, andCalifornia under the jurisdiction of Federal Energy RegulatoryCommission (FERC), as a tool for pricing and congestion man-agement in day-ahead and real-time spot power markets [5], [6].

The multi-period market clearing procedure of pool-basedday-ahead electricity markets involves determination of hourlymarket clearing prices by the ISO, based on double-sided auc-tion involving GenCos and DistCos bids. Ott [7] described theoperational and design features of LMP-based PJM market. Theauthor presented a double-sided bid based security-constrainedeconomic dispatch formulation to develop day-ahead hourlymarket clearing LMPs and real-time LMPs at 5-min intervals.In the double-sided auction models, DistCos take part in marketclearing mechanism by offering hourly price responsive demandbids, which are limited to individual periods only. Menniti et al.[8] proposed the strategic bidding by the consumer groups inday-ahead markets considering moderation of air conditioning

loads of individual consumers in response to forecasted hourlymarket clearing prices. Su and Kirschen [9] proposed the priceresponsive demand shifting bidding for market clearing mech-anism of day-ahead markets. Price responsive demand shiftingbidding quantify the demand response in day-ahead market, andsome responsive customers are able to shift the demand fromperiods of high LMP to the periods of low LMPs. However, themarket clearing mechanisms developed in [9] do not take intoaccount the operational and security constraints of transmissionnetworks. Recently, an extensive study has been performed ondemand response programs with the aims to reduce electricityprice spikes, transmission congestion management and to en-hance the market security and reliability [10]–[15]. Aalami et al.[16] presented the impact of incentive and penalty-based demandresponse programs on technical and economical performanceof power markets. Tuan et al. [17] developed an interruptibledemand auction model for congestion relief in hour-aheadbilateral contract dominating electricity markets.

A majority of the available demand response programs aremaking use of ex-post methods (i.e., after the day-ahead markethas been settled) for maintaining security and congestion man-agement of electricity markets. This may lead to loss of DistCos(in monetary terms and/or bad reputation gained by makingpower interruptions of retail consumers) due to reduction oftheir demands from scheduled values. The present paper uti-lizes the price responsive demand shifting bidding as developedin [9] for congestion management and controlling the LMPspikes in day-ahead electricity markets. The day-ahead marketdispatch problem is formulated as to maximize the socialwelfare of market participants (i.e., DistCos’ benefits minusGenCos’ costs) subject to operational and security constraints.The DistCos’ benefits are determined on the basis of their priceresponsive demand shifting bids, and GenCos’ costs includereal power generation cost and lost opportunity cost to providereactive power [18]–[20]. The cost function corresponding toreactive power procurement from GenCos is necessary to beincluded in the market dispatch formulation in order to provideincentives to the generator companies for their reactive powersupply and to determine pricing signal for delivery of reactivepower to consumers in deregulated environment. The currentpractice in deregulated power industry is to employ negativeslope bidding by DistCos, which are limited to individual pe-riods. Hence, it is very likely that DistCos have to reduce theirdemands during peak hours. In this regard, the major contri-bution of this paper is to propose a day-ahead market dispatchmethodology based on price responsive demand shifting bid-ding of DistCos under power system network constraints. Theproposed methodology has the advantages that 1) the systemcongestion and LMPs can be controlled, and 2) the consumersare able to recover their energy consumptions, which have beenlost during peak hours, in day-ahead markets.

The rest of the paper is organized as follows. Section II dis-cusses the price taking, price responsive, and price responsivedemand shifting bidding mechanisms of DistCos. Section IIIpresents the proposed formulation of day-ahead market dispatchproblem. Section IV presents results and discussions on five-bus, IEEE 30-bus, realistic UP 75-bus Indian, and IEEE 118-bussystems. Concluding remarks are presented in Section V.


Fig. 1. Price taking bid.

Fig. 2. Price responsive bid.

II. PRICE TAKING, PRICE RESPONSIVE, AND PRICE

RESPONSIVE DEMAND SHIFTING BIDS

This section discusses the price taking, price responsive,and price responsive demand shifting bidding mechanisms ofDistCos for ready reference of the readers.

A. Price Taking Bids

In price taking bids, the bidder is ready to accept a specifiedamount of power at the prevailing market price, and its powerconsumption remains constant irrespective of the variations inmarket price as shown in Fig. 1. The major part of the DistCo’sdemand bid is price taking, which is required to meet its essen-tial daily services to residential, domestic, and industrial loads.

B. Price Responsive Bids

In price responsive bids, the price to be paid by a bidder de-creases monotonically with increase in power consumption, asshown in Fig. 2. Using Fig. 2, the price responsive bidding price,

, of a DistCo corresponding to power demand of , duringany th period, can be represented as

(1)

where is the maximum bidding price and is theslope of price responsive bidding curve during the th sub-in-terval. The power demand of DistCo under price responsive bid-ding is flexible, as it is able to decrease its demand if marketprice is high and vice-versa. Large consumers would partici-pate in day-ahead markets by direct generation of price respon-

Fig. 3. Price responsive demand shifting bid.

sive offers and bids, whereas small consumers could participatethrough aggregators or load serving entities [21]. The price re-sponsive bids can be modeled in market dispatch problem interms of benefit function of DistCos, and is able to control themarket price. However, the price responsive bids are limited toindividual periods and are unable to recover the loss of load oc-curred during periods of high market price. For example, if asugar industry reduces processing of sugar canes or a paper in-dustry stockpiles paper pulp during high price hours, then thisbidding mechanism does not match to catch up with the re-duced demand in day-ahead market. Also, there are certain in-dustrial processes which involve some kind of storage (such asbatteries, air compressors, heated bricks, etc.), and are success-fully enrolled in demand response programs [8], [21]. However,the price responsive characteristics of these demand response re-sources do not match with this bidding mechanism in day-aheadmarkets.

C. Price Responsive Demand Shifting Bids

Price responsive demand shifting (PRDS) bidding mech-anism has been introduced in [9]. Under PRDS bids, anaggregator on behalf of DistCos is able to increase or decreaseits demand in response to market price as well as shift itsdemand from periods of high market price to periods in whichmarket price is comparatively low. For example, space heatingand cooling loads involving HVAC system can shift a part ofits demand from periods of high price to some consecutiveperiods of lean price. Hence, aggregators involved with suchDistCos can present demand offers and bids, which can beextended to multiple periods to maximize benefit over thecomplete scheduling period in day-ahead market [8], [21]. Alsothe technology advancement has made possible installation ofsmart meters at the customer premises for actual time-of-usemeasuring and automatic switching on/off of appliances as perthe day-ahead schedule [22].

However, the scope of the present paper is not aggregationof demand response resources, but rather to study the influenceof PRDS bidding on LMPs and congestion in day-ahead mar-kets. A typical PRDS bid is shown in Fig. 3. Under PRDS bid-ding, a DistCo (or an aggregator) specifies its maximum pricebid , minimum price bid , and corresponding


maximum power demand , during a particular th pe-riod. It is clear from negative slope bidding curves of Figs. 2and 3 that DistCo would accept that amount of demand (or ) for which its willing price ( or ) is less thanor equal to market price (i.e., LMP at its premises). Hence, itis very likely that demand of responsive DistCo is less than itsmaximum value under peak periods. In this regard, the maindifference between PRDS bidding mechanism and price respon-sive mechanism (given in Section III-B) is that during a partic-ular period, maximum demand limit under PRDS bidding canbe extended to include the loss of load occurred during otherperiods, which is not applicable under price responsive biddingmechanism. Considering the simplest form of PRDS bidding,it has been assumed that is decided on the fact that allthe energy consumed by the bidding DistCo during com-plete scheduling interval (say, 24 h) can be consumed in a singleperiod (say, 1 h) at the maximum [9]. Mathematically, it can berepresented as

(2)

(3)

III. DAY-AHEAD MARKET DISPATCH PROBLEM

FORMULATION UNDER PRDS BIDS

In this paper, following assumptions (which are close to prac-tical situations) have been made regarding DistCos taking partin day-ahead market.

• DistCos know the near history of LMPs and system con-gestion. Hence, some strategically located DistCos offertheir demands in the form of PRDS bids.

• PRDS Distcos offer major portion of their demand as pricetaking and a small portion as PRDS demandduring any th period.

• The PRDS bids submitted by the DistCos are in the formas discussed in Section III-C.

The benefit function of DistCos due to their consumptioncan be determined from the shaded area of Fig. 3 [23]

(4)

The cost function of real power generation of GenCos can bedetermined from their cost bids as follows:

(5)

The reactive power procurement cost to be paid to the GenCoscan be obtained from their lost opportunity to trade , bymaking use of an approximate capability curve of the generators[18]–[20]

(6)

The day-ahead market dispatch problem is formulated as tomaximize social welfare (DistCos’ benefits due to minus

GenCos’ real and reactive power generation costs) for the entirescheduling period subject to power balance equality constraints,line flow inequality constraints (for congestion management),and bounds on variables, in each scheduling sub-interval.

Mathematically, the problem can be formulated as

(7)

subject to the following constraints.

A. Power Flow Constraints

The power flow equations as governed by Kirchhoff’s voltageand current laws are given by (8) and (9) for all buses during allscheduling sub-intervals

(8)

(9)

B. Constraint on Constant Power Factor of Consumers

The real and reactive power consumptions of any th DistCoat th bus during th sub-interval are tied together by constantpower factor, i.e.,

(10)

C. Constraint on Energy Consumed During Entire SchedulingPeriod Under PRDS Bids

Energy consumed by PRDS demand at any th DistCo duringentire scheduling period should be less than the maximum spec-ified value. This assures that DistCos are required to shed min-imum possible (particularly nil) amount of energy for control-ling congestion and LMP spikes in day-ahead market:

(11)

D. Transmission Line Loading Limits

Transmission line flows are bounded by thermal limits forshort lines and stability limits for long lines

(12)


Fig. 4. Five-bus system.

E. Bounds on Variables

Real and reactive power generated by GenCos, price takingand PRDS demand consumed by DistCos, and bus voltages arebounded by minimum and maximum limits:

(13)

where the maximum value of PRDS demand is given by

(14)

F. Additional Constraints Due to Capability Curve

The real, reactive, and apparent power generated by the gener-ators should lie within the boundaries of capability curve. This isachieved by bounds on and as given by (13) along with(15), considering an approximate capability curve [18], [24]

(15)The proposed market dispatch problem with the objective

function of social welfare maximization (7) and subject to con-straints (8)–(15) is a nonlinear programming problem and issolved with Interior Point Direct/CG approach in AMPL [25].

IV. RESULTS AND DISCUSSION

A. Five-Bus System

The methodology described above has been applied ona five-bus system (as shown in Fig. 4) taken from [18], fordeveloping day-ahead generation and demand schedule of 24h considering scheduling sub-interval of 1 h. There are twoGenCos at buses 1 and 2, each having lower and upper powergeneration limits of 20 MW and 250 MW, respectively. Thereal power generation cost function of each GenCo duringentire scheduling period is

(16)

The maximum apparent power output of each of the twogenerators is taken to be 250 MVA, considering that armatureheating limit of each generator is represented by a circular arc

[19], [24]. The reactive power generation costs of GenCos aremodeled using (6) taking . For the sake of simplicityand better understanding of the numerical results, both genera-tors are considered to be under on-state for the entire schedulingperiod. A capacitor bank installed on bus 4 with total capacityof 50 MVAR can inject capacitive power between 0 to 50MVAR. Lower and upper bus voltage limits are considered tobe 0.95 p.u. and 1.05 p.u., respectively. Apparent power flowlimit of line 1-2 is considered to be 80 MVA and that of allother lines is taken to be 180 MVA.

In order to simulate practical conditions, the maximum de-mand of DistCos at buses 2, 3, 4, and 5 is varied over the entirescheduling period of 24 h. Power factor of each DistCo is con-sidered to be maintained at 0.9 lagging in each hour. For thesake of comparison, day-ahead power generation and demandschedule is developed under the following three cases.

• Case I: The DistCos at all buses are offering price takingbids in each hour.

• Case II: The DistCos at all buses except at bus 5 are of-fering price taking bids in each hour. The DistCo at bus 5is bidding 95% of the demand with price taking bids andremaining 5% demand with price responsive bids in eachhour. For price responsive bid of DistCo at bus 5,

, .• Case III: This case is same as Case II except the fact that

DistCo at bus 5 is bidding 95% of the demand with pricetaking bids and remaining 5% demand with PRDS bids ineach hour. For PRDS bid of DistCo at bus 5,

,. The values of and are taken to be

equal, which implies .The and values represent slope of bidding curve

under Cases II and III, respectively. The zero slope of bid-ding curve specifies that marginal benefit of DistCo re-mains constant irrespective of its power consumption. With

, the fix marginal benefit of DistCoat bus 5 is 25.0 $/MWh, under Cases II and III. The benefitbid of a DistCo is the maximum price, which that DistCo iswilling to pay for its consumption of price responsive or PRDSdemand. For this system, it has been considered that DistCo atbus 5 is willing to pay 25 $/MWh (at maximum) for its priceresponsive or PRDS demand consumption, whereas LMP atbus 5 can go up to 28.0 $/MWh under price taking bid, whichcan be forecasted from near history of day-ahead schedule[26]–[28]. The variation of scheduled real power delivered atbus 5 in three cases is given in Fig. 5. In Case I, all the demandat bus 5 is price taking; hence, scheduled power delivered atbus 5 under Case I is set to the maximum values in each hourirrespective of its LMP. In Case II, during hours 1, 2, 4, 16–24,when LMP at bus 5 is low , the scheduledpower delivered is the same as that in Case I. During remaininghours, due to high LMPs, the scheduled power delivered atbus 5 is reduced from the corresponding values under CaseI. In Case III, the PRDS demand at bus 5 is scheduled to beconsumed in off-peak hours (1, 2, 19–24). During remaininghours, only price taking demand is consumed.

Fig. 6 shows the price responsive demand scheduled to be de-livered in Case II and PRDS demand scheduled to be delivered


Fig. 5. Power consumption schedule at bus 5 under three cases.

Fig. 6. Price responsive/PRDS demand scheduled to be delivered at bus 5.

Fig. 7. Up/down variation of price responsive/PRDS demand consumptionschedule at bus 5.

in Case III in each hour. As said earlier, the maximum price re-sponsive power consumption in any hour under Case II cannotbe greater than 5% of the maximum demand during that hour.Hence, price responsive demand is delivered (as large as pos-sible) in all those hours during which LMP at bus 5 is less than25 $/MWh. On the other hand, in Case III, the PRDS demandcan be shifted from one hour to another subject to the maximumenergy consumption in the entire day. Hence, all the PRDS de-mand of the entire day has been delivered in off-peak hours asdepicted in Fig. 6.

Fig. 7 shows the up/down variation of price responsive de-mand of Case II and PRDS demand of Case III from the setlevel (5% of maximum demand) in each hour. It is clear fromFig. 7 that during hours of high LMP, price responsive demanddelivery is reduced. On the other hand, PRDS demand deliveryis reduced during hours of high LMP and increased during hoursof low LMP. With this, DistCo at bus 5 is able to consume allthe energy of 99.3 MWh set under PRDS bidding. On the other

Fig. 8. Day-ahead LMP of real power at bus 5 under three cases.

Fig. 9. Day-ahead LMP of reactive power at bus 5 under three cases.

Fig. 10. Shadow price on congested line flow.

hand, it is able to consume only 49.49 MWh of energy underprice responsive bidding of Case II. Figs. 8 and 9 show the vari-ations of day-ahead LMPs of real and reactive power, respec-tively, at bus 5 during 24 h. Due to price taking bid, real andreactive power LMP variations are highest under Case I out ofthe three Cases. Price responsive bidding under Case II reducesthese variations by reducing the LMP peaks. The PRDS biddingunder Case III, on the other hand, normalizes LMPs by reducingpeak values and increasing off-peak values.

Fig. 10 shows the variation of shadow price on power flowof congested line (1–2) during 24 h under three cases. Fig. 10depicts that shadow price on congested line flow variations arehighest under Case I. These variations are reduced under Case IIby reducing the peaks. Case III further reduces these variationsby reducing peaks and increasing off-peaks.

B. IEEE 30-Bus System

The proposed methodology has also been applied on IEEE30-bus system for developing day-ahead generation and demandschedule of 24 h considering scheduling sub-interval of 1 h. Thereal power cost functions of system GenCos located at buses 1,2, 5, 8, 11, and 13 are considered to be the same throughoutthe scheduling period as given in [29]. For the sake of sim-plicity and better understanding of results, start up and shutdown costs of generators have been neglected. Lower and upper


TABLE IPOWER FLOW LIMITS OF CONGESTED LINE AND TRANSFORMERS

bus voltage limits are considered to be 0.94 p.u. and 1.06 p.u.,respectively. The maximum and minimum reactive power gen-eration points are taken from [29] and reactive power generationcosts of GenCos are modeled using (6) taking . Line1-3 and transformers (TFs) 4–12 and 28–27 are considered to becongested with apparent power flow limits as given in Table I.

Maximum hourly real and reactive power demand of bulkpower consuming DistCos at buses 2, 5, 7, 8, 12, 21, and 30is varied over the scheduling period of 24 h. Power factor ofDistCos during any period is determined from the maximumreal and reactive power demands during that period. For thesake of comparison, day-ahead power generation and demandschedule is developed under the following three cases.

• Case A: The DistCos at all buses are offering price takingbids in each hour.

• Case B: The DistCos at all buses except at bus 30 are of-fering price taking bids in each hour. The DistCo at bus30 is bidding 95% of the demand with price taking bidsand remaining 5% demand with price responsive bids ineach hour. For price responsive bid of DistCo at bus 30,

,.

• Case C: This case is the same as Case B except the factthat DistCo at bus 30 is bidding 95% of the demand withprice taking bids and remaining 5% demand with PRDSbids in each hour. For PRDS bid of DistCo at bus 30,

, ,.

The variation of real power consumption scheduled at bus 30shows a similar behavior as that of bus 5 in Section V-A. InCase A, all the demand at bus 30 is price taking, and hencepower consumption scheduled in any hour of Case A is sameas its maximum power demand during that hour. In Case B,power delivered during hours of high price is reduced from therespective maximum values. In Case C, all the PRDS demandis to be delivered in off-peak hours (1–3 and 22–24). Duringremaining hours, only price taking demand is scheduled to bedelivered. Variations of day-ahead LMPs of real and reactivepower at bus 30 show a similar behavior as obtained earlier infive-bus system. Maximum variation in LMPs occurs in CaseA, when all the demand is price taking. The peak LMPs arereduced in Cases B and C. The off-peak LMPs in Case C area little increased, due to the fact that all the energy shaved offduring high price hours is scheduled to be consumed in off-peakhours in this case. The voltage at bus 30 is improved in Cases Band C from that of Case A, as shown in Fig. 11. However, thedip in voltage during off-peak hours 1, 2, 23, and 24 in Case Cis due to shifting of majority of price responsive demand duringthese hours.

The maximum peak in LMPs of real and reactive power andmaximum deterioration in voltage profile at the system buses

Fig. 11. Variation of voltage at bus 30 under three cases.

Fig. 12. Variation of LMP of real powers at system buses under three cases for� � ��.

Fig. 13. Variation of LMP of reactive powers at system buses under three casesfor � � ��.

Fig. 14. Bus voltages profile under three cases for � � ��.

occurs during . Hence, variations of LMPs of real and re-active power and bus voltage profile during under threeCases are plotted in Figs. 12–14, respectively. It is clear fromthese figures that LMPs of real and reactive power get reducedand voltage profile at system buses gets improved during ,


Fig. 15. Variation of shadow price on power flow in TF 28-27 under three cases.

Fig. 16. Single-line diagram of UP 75-bus Indian system [30].

in Cases B and C as compared to that of Case A. This demon-strates that price responsive and PRDS bidding of DistCo lo-cated at one bus has positive impact on DistCos located at otherbuses and on the entire system.

The shadow price on power flow in TF 28–27 (shown inFig. 15) reduces in Cases B and C during hours 9–13, 15–17from the corresponding values in Case A. During the remaininghours, the shadow price on power flow in TF 28–27 in all Casesis zero. During a few hours, shadow prices on power flow inline 1–3 and TF 4–12 in Case C are slightly more than that ofCases A and B, which tend to normalize congestion in wholeparts of the system (some figures are not presented due to lackof space). The overall system congestion reduces during the en-tire scheduling period in Cases B and C from that of Case A.A comparison between Cases B and C demonstrates that LMPstend to normalize and overall system congestion reduces underCase C as that of Case B by making use of energy consumptionshifting from peak hours to off-peak hours under Case C.

C. UP 75-Bus Indian System

The realistic network data of the UP 75-bus Indian system[30], [31] (as shown in Fig. 16) have also been used to seek theinfluence of PRDS bids on LMPs and congestion. The demandsat various buses during 24 h are obtained by varying base case

Fig. 17. Variation of LMP of real power at bus 27 during 24 h under three cases.

Fig. 18. Variation of LMP of real power at bus 60 during 24 h under three cases.

Fig. 19. Variation of shadow price on power flow of congested line 19–26during 24 h under three cases.

values over the range 50%–150%. Again for the sake of com-parison, Cases A, B, and C have been simulated. In Case A,demand of all DistCos is considered to be price taking. In CaseB, DistCos at buses 27 and 60 are considered to offer 90% pricetaking and 10% price responsive bids. In Case C, DistCos atbuses 27 and 60 are considered to offer 90% price taking and10% PRDS bids.

For the price responsive and PRDS bids, parameters of bid-ding curves are taken to be ,

, with the addi-tional assumption under PRDS bid as stated in (2) and (3). Lines19–26 and 29-22 are considered to be congested with rating of350 MVA and 80 MVA, respectively. The peak LMPs at priceresponsive buses 27 and 60 in Cases B and C have been largelyreduced as compared to Case A as shown in Figs. 17 and 18.A comparison between Cases B and C from Figs. 17 and 18shows that LMPs tend to flatten over entire scheduling periodunder Case C. The congestion in lines 19–26 and 29-22 havealso been largely reduced under Case C as compared to CasesA and B. The variation of shadow price on power flow of con-gested line 19–26 under Cases A, B, and C during 24 h is shownin Fig. 19.


Fig. 20. Variation of LMPs of real power at system buses under three casesduring � � ��.

Fig. 21. Variation of LMPs of reactive power at system buses under three casesduring � � ��.

The lines 19–26 and 29-22 are highly congested during(having shadow prices on line flows as 13.64 Rs/MVAh and

71.55 Rs/MVAh) under Case A. Hence, variation of LMPs ofreal and reactive power at all system buses during areplotted in Figs. 20 and 21, which show significant reduction insystem LMPs due to price responsiveness of selected DistCos.In Case B, price responsive DistCos at buses 27 and 60 shedenergy of 76.99 MWh and 36.31 MWh, respectively, during pe-riods 13–16. On the other hand, in Case C, DistCo at bus 27shed 259.86 MWh of energy during periods 9–20 and recoverthe same amount of energy during periods 1–8, 21–24. Simi-larly, DistCo at bus 60 shed 118.64 MWh of energy during pe-riods 9–20, 22–24 and recover the same during periods 1–8, 21,under Case C. The computational time elapsed in determiningthe day-ahead schedule of UP 75-bus Indian system for 24 hunder PRDS bidding on Pentium IV, 3 GHz, 1 GB RAM CPUis 26.688 s.

D. IEEE 118-Bus System

The three Cases A, B, and C, as discussed abov,e have alsobeen simulated for the IEEE 118-bus system, with bus 59 of-fering price responsive and PRDS bid under Cases B and C,respectively. The DistCos’ demands during each hour of thescheduling period are obtained by multiplying loading factor(0.7–1.4) to base case loadings. The assumed congested linesand their apparent power flow ratings are given in Table II.

The results obtained show similar behavior as in previous testcases. The demand profile of DistCo at bus 59 gets flattened inCase C as shown in Fig. 22.

The LMPs of real and reactive power at bus 59 also tend tonormalize under Case C over the whole scheduling period, as

TABLE IIPOWER FLOW LIMITS OF CONGESTED LINES IN IEEE 118-BUS SYSTEM

Fig. 22. Comparison of real power demand profile under three cases.

Fig. 23. LMP of real power at bus 59 during 24 h under three cases.

Fig. 24. LMP of reactive power at bus 59 during 24 h under three cases.

shown in Figs. 23 and 24. The congestion in all the congestedlines get reduced under Cases B and C as compared to Case A.Particularly, the reduction in congestion in line 63–59 is morepronounced due to the price responsiveness of DistCo at bus59 (refer to Fig. 25). During certain off-peak hours, the shadowprice on power flow over line 63–59 increases under Case Cas compared to Cases A and B, which again shows that PRDSbids tend to normalize congestion over the scheduling period.The system is highly congested in Case A during . Hence,LMPs at system buses are plotted in Figs. 26 and 27 and underthree Cases during , which show significant reduction insystem LMPs (particularly in the vicinity of bus 59) under priceresponsive and PRDS bidding. It takes 61.94 s of computational


Fig. 25. Shadow price of congested line 63-59 during 24 h under three cases.

Fig. 26. LMPs of real power at system buses under three cases during � � �.

Fig. 27. LMPs of reactive power at system buses under three cases during� � �.

time for determining day-ahead schedule of IEEE 118-bus for24 h under PRDS bidding on Pentium IV, 3 GHz, 1 GB RAMCPU.

V. CONCLUSION

In this paper, PRDS bidding mechanism of DistCos have beenutilized for congestion management and controlling the LMPspikes in pool-based day-ahead electricity markets. The conven-tional price taking demand pampers GenCos to exercise marketpower and may lead to uncontrolled LMPs and system conges-tion. The present day demand bidding of DistCos is limited toindividual periods, which is able to control the market price withcorresponding loss of load. The main thrust of this paper is to de-velop a day-ahead market dispatch methodology by employingPRDS bidding of DistCos under power system network con-straints. The studies on five-bus, IEEE 30-bus, UP 75-bus In-dian, and IEEE 118-bus systems are performed by alternativelyconsidering hourly price taking, price taking plus price respon-sive, and price taking plus PRDS bids of DistCos for scheduling

period of 24 h. The conclusions drawn from the obtained resultsare listed below.

1) The consideration of even a small portion of DistCos de-mand to be offered in terms of price responsive or PRDSbids leads to reduction in peak LMPs and shadow prices ofcongested lines in day-ahead markets as compared to pureprice taking bids.

2) PRDS bidding, being a multi-period bidding mechanism, isable to flatten the LMPs at system buses and shadow pricesof congested lines in day-ahead markets (i.e., reduction inpeak values and increase in off-peak values).

3) Under PRDS bidding, the energy lost during peak hourshas been recovered during off-peak hours of day-aheadmarket.

4) In this paper, the use of PRDS bidding mechanism has beenemployed on network model and constraints. This wouldprovide a platform to incorporate demand response pro-cesses which involve storage capabilities (storage of rawmaterial or energy) in day-ahead markets for further inves-tigations.

5) PRDS bidding proves to be a promising demand side man-agement tool for congestion management.

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Kanwardeep Singh received the M.Tech. degreein power systems from the National Institute ofTechnology, Kurukshetra, India, and is pursuing thePh.D. degree from the Indian Institute of Technology,Roorkee, India, under QIP scheme of AICTE, NewDelhi, India

He is with Department of Electrical Engineering,Guru Nanak Dev Engineering College, Ludhiana,India. His research areas include power systemoperation, congestion management, and pricingunder deregulated environment.

Narayana Prasad Padhy (SM’09) was born in India.He received the Ph.D. degree in power systems en-gineering from Anna University, Chennai, India, in1997.

He is working as a Professor in the Departmentof Electrical Engineering, Indian Institute of Tech-nology, Roorkee, India. He has worked as a ResearchFellow in the Department of Electronics and Elec-trical Engineering, University of Bath, Bath, U.K.,under a BOYSCAST Fellowship from the Govern-ment of India during 2005–2006. He has also worked

as a Research Fellow in the Department of Electrical and Computer Engineering,Ryerson University, Toronto, ON, Canada, during June 2009–May 2010. His re-search interests are in power systems analysis, pricing, economics, optimization,and AI.

Dr. Padhy has been awarded a Humboldt Research Fellowship for Experi-enced Researchers in 2009 to carry out research at the University Duisburg-Essen, Germany.

Jaydev Sharma received the B.E. degree in electricalengineering from Jiwaji University, Gwalior, India,in 1968 and the M.E. and Ph.D. degrees in electricalengineering from University of Roorkee (presentlythe Indian Institute of Technology), Roorkee, India,in 1971 and 1974, respectively.

His research interests include power system plan-ning, power system operation and control, securityanalysis and optimization of power systems, artifi-cial neural networks, and fuzzy- neural applicationsto power system and distributed generation.

congestion management

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social welfare

market clearing

locational

market dispatch

articial neural

constant power

narayana prasad

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