SOCIAL WELFARE MAXIMIZATION IN DEREGULATED POWER SYSTEM

Transcription

1 SOCIAL WELFARE MAXIMIZATION IN DEREGULATED OWER SYSTEM REKHA SWAMI Department of Electrcal Enneerng, Inan Insttute of Technology, Roorkee, Ina E-mal: Abstract - In power systems, transmsson network provdes the nfrastructure to support a compettve electrcty market, but congeston occurs frequently n the weakly connected networks. Transmsson congeston can enhance the locatonal market power n the congested area and weaken the effcency of electrcty market. In ths paper market spatch problem n the pool-based electrcty market s formulated so as to mze the socal welfare of market partcpants subect to operatonal constrants ven by real and reactve power balance equatons, and securty constrants n the form of apparent power flow lmts over the congested transmsson lnes. The comparsons of the real and reactve power costs of generators, beneft value of consumers, producers surplus, locatonal marnal prces (LMs) under uncongested or congested contons are evaluated by usng a fve-bus system. Keywords - Transmsson Congeston, market power, locatonal marnal prces, socal welfare. I. INTRODUCTION Wth the ntroducton of deregulaton n the power ndustry open access s provded to the transmsson system. Due to transmsson open access (TOA) the flow n the lnes reach the power transfer lmt and thereby creatng a conton known as congeston [1-3]. The congeston may be caused due to varous reasons, such as transmsson lne outages, generator outages and change n energy demand. Transmsson congeston has mpact on the entre system as well as on the nvdual market partcpants.e. sellers and buyers. Wthout congeston lowest-prced resources are used to meet the demand but f congeston s present n the transmsson network then t prevents the demand to be met by the lowest-prced resources due to transmsson constrants and some energy s purchased from alternatve sources at hgher prces. The supplers at the mport sde may rase ther prces as hgh as they want and thus creates market power, (the contons where a market partcpant can proftably mantan prces above a compettve level for a sgnfcant perod of tme) [4-5]. Congeston results an ncrease n locatonal marnal prces (LM), defned as the marnal cost of supplyng the next MW of load to the locaton usng the lowest producton cost of all avalable generaton wthout volatng any system securty lmt. If the lowest prced electrcty can reach all locatons, prces are the same across the entre grd. When there s transmsson congeston, energy cannot freely flow to certan locatons. In such cases, more expensve electrcty s needed to meet that demand and so the locatonal marnal prce s hgher n those locatons. So ts management becomes necessary and ths task s performed by Independent System Operator (ISO) [7]. In pool-based electrcty market ISO collects hourly/half-hourly supply and demand bds from generator servng traders (GSTs) on behalf of GenCos and load servng traders (LSTs) on behalf of pool consumers. ISO determnes the generaton and demand schedule as well as LMs based on mzaton of socal welfare, subect to system operatonal and securty constrants [8-10]. The supply bds collected by ISO from GenCos are generally for real power generaton and reactve power generaton s assumed to be produced at neglble cost. In recent developments, the use of reactve power prcng s emphaszed n parallel to actve power prcng. Many authors have explored the opportunty cost of generators based on - capablty curve to develop reactve power generaton cost functon. Bhattacharya and Bollen et. Al. [1] explaned the emergence of deregulaton from the tratonal power ndustry. Authors of References [-3] explaned the transmsson open access n deregulated structure. L and Bo [6] explaned how LMs are calculated wth DC optmal power flow and then comparson s made wth AC optmal power flow. Caramans et al. [8] developed the theory of optmal spot prcng, accorng to whch supplers should be pad real-tme prce more than or equal to ther cost ncurred, and consumers should be charged real-tme prce less than or equal to ther beneft, such that overall welfare s obtaned. Authors n Ref. [11] scussed techncal and economc ssues for determnng the reactve power prcng structure under an open-access envronment. Da et al. [1] modeled the lost spnnng reserve of synchronous generators and deprecaton charges on captal nvestment of capactor banks to develop a reactve Internatonal Journal of ower System Operaton and Energy Management ISSN (RINT): , Volume-1, Issue-4, 01 4

2 Socal Welfare Maxmzaton n Deregulated ower System power producton cost functon. It ncludes ths functon nto the OF problem to determne LMs of real and reactve power. Cho et al. [13] performed the mzaton of socal beneft, representng response (or marnal beneft) of consumers as the nverse of demand functon. Sngh et al. [14] mofes the reactve power generaton cost functon, as ven n [1], by makng use of an approxmate - capablty curve of synchronous generators. The reactve power generaton cost functon obtaned from the - capablty curve s added to the real power generaton cost functon to get total generaton cost. II. ROBLEM FORMULATION In pool-based electrcty market ISO collects hourly/half-hourly supply and demand bds from generator servng traders (GSTs) on behalf of GenCos and load servng traders (LSTs) on behalf of pool consumers. The supply bds provded by a GenCo (or related GST) s ts mnmum askng prce whch t would accept for supplyng a partcular amount of power. Smlarly, demand bd of a consumer s ts mum wllng prce, whch t would pay for consumng a partcular amount of power. ISO determnes the generaton and demand schedule as well as locatonal marnal prces (LMs) based on mzaton of socal welfare, subect to system operatonal and securty constrants The obectve functon for the optmzaton problem s to mze the socal welfare, whch s the fference of beneft of consumers and the overall cost of actve and reactve power producton of supplers. The obectve functon can be expressed as: Max. Socal Welfare = B ) C ( ) C ( ) (1) D ( p q G G where {G} s the generator set, {D} s the consumer set, C ) s the actve power producton cost of p ( generator, C ) s the reactve power q ( producton cost of generator ; B ) s the beneft of the consumer, and ( are the actve and reactve power output of the generator on bus, s the actve power demand on bus. The real power generaton cost functon of each generator s modeled by a quadratc functon where a, b and c are predetermned coeffcents: C ( ) a b c () The reactve power cost of generator s also called as opportunty cost. The reactve power output of a generator wll reduce ts actve power generaton capablty whch can serve at least as spnnng reserve, and the corresponng mplct fnancal loss to generator s modeled as an opportunty cost. For smplcty, the reactve power cost of generator from the approxmated capablty curve can be modeled as: Cq ( ) [ C ( ) Cq ( )] k (3) Where k s the proft rate of actve power generaton, usually les between 5 to 10%. Consumers beneft as a functon of real power demand s consdered to follow a straght lne passng through orn between and whch mn specfes a fxed marnal beneft equal to the slope of lne. Usng Fg. 1., the beneft of consumer can be wrtten as B ( ) b * (4) where b s the slope of beneft curve of consumer at th bus. CONSTRAINTS Fg. 1 : Beneft curve of a consumer 1) ower Flow Equatons (Equalty Constrants): A set of equatons that characterzes the flow of real and reactve powers through a system are ven by (5) (6) N 1 N 1 V V Y V V Y cos( sn( ) 0 ) 0 where N s total number of buses n the system, and V are the magntudes of the voltages of bus and, and are the voltage angles of bus and, V. Internatonal Journal of ower System Operaton and Energy Management ISSN (RINT): , Volume-1, Issue-4, 01 5

3 Socal Welfare Maxmzaton n Deregulated ower System and Y and, are the magntude and angle of th element of the bus admttance matrx. ) Generaton Lmt: The generators have a mum generatng capacty, above whch s not feasble to generate due to techncal or economc reasons. Generatng lmts are usually expressed as mum or mnmum real and reactve power outputs, mn (7) mn (8) 3) Load Lmt: Consumers also have ther capacty lmts of consumpton. Load lmts are expressed as follows n the formulaton, mn mn (9) (10) respectvely. The real power generaton cost of each Genco s C( )= The nomnal apparent power output of each generator s 15 MVA. The reactve power generaton costs of Gencos are modelled usng eq. b (3), takng k = 5%. In base case, values of for all the consumers are set to be farly hgh (50 $/MWh), such that these do not affect generaton and demand schedules produced by OF. A capactor bank s nstalled on bus 4 wth total capacty of 50 MVAR can nect capactve power between 0 to 50 MVAR. The systems loads on buses 1-5 are lsted n Table A1 of the Appenx A wth a common power factor of 0.9. The transmsson lne mpedance and charng admttance are ven n Table A of the Appenx A. Lower and upper bus voltage lmts are consdered to be 0.95 p.u. and 1.05 p.u. Apparent power flow lmt of lnes s taken to be 180 MVA. 4) Constrant on constant power factor of loads: The real and reactve power consumpton at any bus are ted together by constant power factor. =tanα (11) 5) Transmsson lne lmts: Transmsson lmts refer to the mum power that ven transmsson lne s capable of transmttng under ven contons. S S, (1) 6) Voltage lmts: The voltage at each bus should be wthn the specfed range. V V V (13), mn, 7) Adtonal constrant due to capablty curve: The apparent power generated by the generator should le wthn the boundares of capablty curve. + (14) The proposed market spatch problem s a nonlnear programmng problem and s solved wth Sequental quadratc programmng method n AML. III. RESULTS Fve-Bus System: The methodology descrbed above has been appled on a fve-bus system. There are two Gencos at buses 1 and, each havng lower and upper power generaton lmts of 10 MW and 00 MW, Fg. : Fve-bus system Under heavy loang conton loads on buses 1-5 ncrease to [0, 0.6, 0.9, 0.8, 1.0] per unt wth same power factor of 0.9 and the power generaton lmts of two Gencos are set to 50 MVA. The system s qute stressed. Now congeston can be created by reducng the flow over lne 1- by 60 MVA. Socal Welfare Maxmzaton Consderng Reactve ower rocurement: In Table total generaton cost, real and reactve power generaton costs, power generated values, producers surplus, LM of real and reactve power at system buses under congested and un-congested contons are obtaned by the proposed methodology. As depcted n Table I the beneft values of LSTs become twce wth a two fold ncrease n demand under heavy loang from that of normal loang, because of assumed lnear beneft characterstc. But, the socal welfare value becomes less than double Internatonal Journal of ower System Operaton and Energy Management ISSN (RINT): , Volume-1, Issue-4, 01 6

4 Socal Welfare Maxmzaton n Deregulated ower System under heavy loang due to the nonlnear cost characterstcs of generators. Although, the reactve power generaton cost s small under normal loang, but t ncreases sgnfcantly wth ncrease n loang. Ths llustrates that there s an utmost need of ncluson of reactve power cost n socal welfare mzaton. Table I Comparson of Results Uncongested Congested Socal Welfare Total Generaton Cost Real ower Generaton Cost Reactve ower Generaton Cost Beneft Value of Consumer ower Generaton (MW+ MVAR) roducers Surplus Fg. 4 : LMs of Real ower for Uncongested and Congested System From Fg. 4. It can be seen that for uncongested system LMs for real power and reactve power are low, but when congeston occurs then generators have ablty to create market power thereby there wll be so LMs become hgher n congested system. The system bus voltage profles under normal and congested contons corresponng to proposed results of Table I are shown n Fgure 3. Fg. 5 : LMs of Reactve ower for Uncongested and Congested System Fg. 3: System Bus Voltage rofle for Uncongested and Congested System IV. CONCLUSION In ths paper, market spatch problem wth the obectve of mzaton of socal welfare s solved n the pool-based electrcty market. From the optmzaton results ven of fve-bus system t can be concluded that although the presence of congeston results n an ncrease n market power along wth producer surplus but wth the ven methodology there s also ncrease n consumers beneft value. So wth the proposed method each market partcpant.e. sellers or buyers are gettng beneft n the case of congeston n the electrcty market. Internatonal Journal of ower System Operaton and Energy Management ISSN (RINT): , Volume-1, Issue-4, 01 7

5 Socal Welfare Maxmzaton n Deregulated ower System Appenx A Table A1 Test system loads Bus Actve ower Reactve ower Bus node Table A Test system lne data Lne mpedance z Lne charng y [10] Gedra, T. W., On transmsson congeston and prcng, IEEE Trans. ower Syst., Vol. 14, pp , February [11] Hao, S., and apalexopoulos, A., Reactve power prcng and management, IEEE Trans. ower Syst., Vol. 1, pp , February [1] Da, Y., N, Y. X., Shen, C. M., Wen, F. S., Han, Z. X., and Wu, F. F., A study of reactve power marnal prce n electrcty market, Elect. ower Syst. Res., Vol. 57, pp , 001. [13] J.Y. Cho, S. Rm, J. ark, Optmal real tme prcng of real and reactve powers, IEEE Trans. ower Syst., Vol. 13, No. 4, pp , [14] Kanwardeep Sngh, N.. adhy, J. D. Sharma, Socal Welfare Maxmzaton Consderng Reactve ower and Congeston Management n the Deregulated Envronment, Electrc ower Components and Systems, pp , Dec REFERENCES [1] Kakar Bhattacharya, Math H.J. Bollen and Jaap E. Daalder, Operaton of Restructured ower Systems, Chalmers Unversty of Technology, Kluwer Academc publshers, 001. [] Mohammad Shahdehpour, Hatm Yamn and Zuy L, Market Operatons n Electrc ower Systems, ublshed by John Wley & Sons Ltd, 00. [3] Loa Le La, ower System Restructurng and Deregulaton, ublshed by John Wley & Sons Ltd, 00. [4] A. Kumar Davd and Fushuan Wen, Market ower n Electrcty Supply, IEEE Transactons on energy converson, Vol. 16, No. 4, pp , December 001. [5] R. Morera e Slva and L.D.B. Terra, Market power under transmsson congeston constrants, n roc Internatonal Conference on Electrcal ower Enneerng, pp. 8. [6] Fangxng L, Ru Bo, DCOF-Based LM Smulaton: Algorthm, Comparson Wth ACOF, and Senstvty, IEEE Trans. ower Syst., Vol., No. 4, pp , November 007. [7] S. Charles Raa,. Venkatesh, B.V. Mankandan, Transmsson Congeston Management n Restructured ower Systems, roc. of ICETECT 011. [8] Caramans, M. C., Bohn, R. E., and Schweppe, F. C., Optmal spot prcng: ractce and theory, IEEE Trans. ower Apparatus Syst., Vol. AS-101, pp , September 198. [9] Baughman, M. L., and Sdq, S. N., Real-tme prcng of reactve power: Theory and case study results, IEEE Trans. ower Syst., Vol. 6, pp. 3 9, February Internatonal Journal of ower System Operaton and Energy Management ISSN (RINT): , Volume-1, Issue-4, 01 8