Locational Marginal Pricing (LMP) in Deregulated Electricity Market

Transcription

1 Locatal Marginal Pricing () in Deregulated Electricity Market ABSTRACT The deregulat of electricity market ha a very large impact on almot all the power ytem around the world. Competitive market are complex ytem with many participant who buy and ell electricity. Much of the complexity arie from the limitat of the underlying tranmi ytem and the fact that upply and demand mut be in balance at all time. Generally the Locatal marginal pricing () i obtained by olving a linear programming formulat. Network loe are conidered through the preet lo factor baed on hitorical operatal informat. Thi uually bring error in the calculated lo under different new cenario. In thi paper a new iterative calculat method i propoed to overcome the aforemented drawback aociated with the tradital calculat. At each iterat, a linear programming problem for market clearing i olved firt.e on branche are conidered a fictitiou nodal demand at their terminal bue.secondly the AC power flow calculated according to the dipatch reult. factor and fictitiou nodal demand are then updated according to the AC power flow olut. The effectivene of the propoed method i illutrated on PJM 5 bu Keyword-AC power flow,active power lo,conget,locatal marginal pricing,power market,reference bu NOMENCLATURE Baanta Kumar Panigrahi Department Of Electrical Engineering. IIT, Roorkee, Roorkee, INDIA baanta1983@gmail.com -Suceptance between bu i and j. -Generat bid price vector. -Voltage phae angle between bu i and j. ditribut factor. Vector whoe element are 1., -Conductance and reitance between bu i and j. Tap ratio of the branch between bu i and j. LF- factor - number of branche -Sytem lo linearizat offet., - upply vector and demand vector, -Lower and upper limit of generator output -Branch active power flow from bu i to j. II. LITERATURE REVIEW -Sytem loe variable G. Hamoud [1] tate that in a deregulated environment,, -Fictitiou nodal demand at bu i. the number of bilateral tranact will grow rapidly and Q-Reactive power inject vector there-fore, new method and tool will be required to help ytem operator evaluate their impact on the operat of 101 S- Senitivity matrix of nodal voltage to nodal power inject. T- Senitivity matrix of line flow to nodal power inject. -Maximum allowable line flow. λ, µ - Shadow price for the energy balance and branch flow contraint equat I. INTRODUCTION Electricity Supply Indutry throughout the world, i retructuring for better utilizat of reource and providing quality ervice and choice to the conumer at competitive price. Retructuring of the power indutry abolihing the monopoly in the generat and trading ector, thereby, introducing competit at variou level wherever it i poible. Electricity ector retructuring, alo popularly known a deregulat, i expected to draw private invetment, increae efficiency, promote technical growth and improve cutomer atifact a different partie compete with each other to win their market hare and remain in buine. Competitive electricity market are complex ytem with many participant who buy and ell electricity. Much of the complexity arie from the limitat of the underlying tranmi ytem and the fact that upply and demand mut be in balance at all time. When the producer and conumer of electrical energy deire to produce and conume in amount that would caue the tranmi ytem to operate at or beyond one or more tranfer limit, the ytem i aid to be congeted. The (Locatal Marginal Pricing)at a locat i defined a the marginal cot to upply an addital increment of power to the locat without violating any ytem ecurity limit. Thi price reflect not only the marginal cot of energy product, but alo it delivery. Becaue of the effect of both tranmi loe and tranmi ytem conget, can vary ignificantly from one locat to another. The ret of thi paper i organized a follow. Sect II dicu about the literature review. In Sect III, the propoed calculat model and the detail calculat procedure are decribed. An example preented in Sect IV. Finally, concluding remark are given in Sect V.

2 Locatal Marginal pricing () in Deregulated Electricity Market the ytem. It tate that a tranact i divided into two type feaible and unfeaible. It tate that bilateral tranact i deemed to be unfeaible if it violate any of ytem operating contraint. In order to accommodate an unfeaible tranact, the ytem economic dipatch may be altered and, in thi cae, there will be a penalty (addital fuel cot) aociated with the tranact. A methodology baed on non linear optimal power flow (OPF) model propoed in [2] to break down into a variety of part correponding to different factor, uch a generat, tranmi conget, voltage limitat and other contraint. Neverthele, calculat are uually baed on a linear programming model and DC power flow[3] for computatal efficiency and tability.reearch in [4] how that the reult of the DC approximat are cloe to the full AC olut. A uch, i uually decompoed into three component: marginal energy price (MEP), marginal lo price (MLP), and marginal conget price (MCP), which i carefully analyzed in [5]. However, it i proved in [6] that uch decompoit i not unique and there i a rather large level of arbitrarine in any decompoit. Becaue of the inherent nonlinearity of tranmi loe, there i a great deire to improve the accuracy in lo calculat and pricing [7].Baed on the ditributed-lack power flow formulat, the calculat formulat. and the three component decompoit are propoed in [8]. The idea i widely accepted and employed in American power market [9], although the difference of the lo component between any node pair depend explicitly on the elected reference bue and participat factor. In order to conider network loe in the DC power flow model, [10] propoed a fictitiou nodal demand(fnd)model to offet the effect of active power loe.however the major drawback with the approach i that the reult are dependent on the choice of reference bu.[11] preented a new model to balance the conumed loe in the DC model by introducing lo ditribut factor.however,the lo factor and lo ditribut factor in[11] mut be preet and the reult of and it component are heavily dependent on thee preet value. II. PROBLEM FORMULATION A. Propoed Model In real power market ecurity check are performed after the market clearing and calculat. In the ecurity check Step, reactive power may alo be conidered.the influence of reactive power can be taking into account if the full AC intead of DC power flow contraint i conidered in the procedure of calculat. Non linear programming model i not employed becaue of the problem in olut robutne algorithm and the difficultie in the oftware development for practical implementat. The following model i propoed for the iterative calculat Min 102 St. ( - ) = (1) = ( - )+ (2) T (( - -. ) (3) (4) Where,,and are not preet before olving thi model. Intead they are obtained from the olut of the full AC power flow. B. and Senitivity Vector At firt, and all element of, can be et equal to 0.Solving the propoed model give a generator dipatch.then the full AC power flow can be olved. Chooing power inject into the ytem a the poitive direct of power, the active power flow of a branch can be calculated by = - ( o + in ) (5) The total ytem lo i an accumulat of the loe of all branche = + ) (6) = ( + -2 o ) Where node i and j are the end of branch l. Now, it i not difficult to build the following equat, repreenting the enitivity of the ytem total lo to the nodal power inject: = = SΔ Δ (7) Senitivity matrix S i the invere of the jacobian matrix of the AC power flow equat. For the propoed model, the enitivitie of active power inject to the ytem lo are deired, which i given by the following equat: = + (8) Then the lo offet can be eaily obtained by = - - ) (9) C.Nodal Fictitiou Demand and Ditribut By analogy with the approximat idea of the DC power flow model, the following approximate formula can be derived: -( o + in ) = (1- o ) - in ) (10) For DC power flow, equal -.So 0.5 can be conidered a the approximate active power lo at one

3 Locatal Marginal pricing () in Deregulated Electricity Market terminal of a branch. The approximate lo at the other terminal alo equal 0.5.The total lo of a branch equal. If the lo 0.5 i repreented a a fictitiou nodal demand at each end of a branch, branch loe can be approximately conidered For the propoed method, the full AC power flow i olved. Accurate branch flow and branch loe can be obtained. According to the above dicu, the lo of each branch can be divided into two equal halve and attached to the two node of the branch. The fictitiou nodal demand i then defined a follow:, =0.5 ) (11) Where J mean node i and j are the two end of a branch. Now, each element of can be determined a the ratio of the correponding fictitiou nodal demand to and calculated a =, / (12) D. Calculat Procedure and Convergence The baic procedure of the propoed calculat method i hown in the Fig. 2.The criter for checking convergence i given a follow. Compare the clearing reult for each generator with the reult of the previou iterat. If the difference in the output of each generator i maller than a predefined tolerance, then top the iterat. Otherwie, continue the iterat. If converge after the (i+1)th iterat, the olut of AC power flow obtained at the ith and the (i+1)th iterat are almot the ame. Thu, and all converge. Although,,and are not preet in the propoed model, it can be proved that the primary olut and the reult of each and it conget component are independent of the elect of reference bu Initialize (Including,, ) Solve the model, Obtain market clearing reult IV.AN EXAMPLE It ha been applied to everal tet ytem. If not particularly pointed out, the initial value of, and are all zero. A. PJM Five- Sytem The diagram of the lightly modified PJM five-bu ytem i hown in Fig.3.Table I lit the line impedance and power flow limit. Generator bid and upper power limit are given in Table II. The voltage magnitude of reference bu and PV bue are all et equal to 1.0.p.u.Reactive power demand at bue B,C and D are all 100MVar.The convergence criter i the maximum power output error of all unit between two ucceive iterat i lower than 0.01 MW. 1) Reult of the Propoed Method: The reult obtained by the propoed method with reference at bu A, C, D and E are lited in Table III-repectively. Taking the convergence criter into account, one can ee that (a)the generat dipatch reult are the ame in all four table(the tiny difference i relate to the convergence critert) (b)for different reference bue fictitiou nodal demand are the ame in pite of different lo factor. (c) + and, at each bu are the ame for all four cae. The initial output for all generator ) are et to 0.The propoed method converge after three iterat. B.Dicu on Convergence of the Propoed Method For the zero initial value of,,and the generator dipatch reult are the ame at the firt iterat for any choice of lack bu. At the econd iterat, the clearing reult for ) are lightly different for different lack bu. At convergence, the clearing reult for )are almot the ame becaue i almot equal to the power lo obtained by the AC power flow. Node E Node D 300MW. Calculate AC power flow.update,, No Converge? YES Calculate Component? Node A Node B Node C 103

4 Locatal Marginal pricing () in Deregulated Electricity Market 300MW 300MW PJM five-bu diagram E Table I Line Impedance and Power Flow Limit Per A-B A-D A-E B-C C-D D-E Unit R X Limit Table-IV (Clearing reult of the propoed method with reference at C): Conget A Table II Bid Price and Economic Maximum of Generator Unit Alta Park Solitude Sundance Brighton City A A C D E Bid Price($/MW) B C D E It i poible that the AC power flow fail to converge with a dipatch reult obtained from the propoed linear programming model. t thi i not a problem that bring only with the propoed method. All DC power flow baed olver have the ame problem becaue AC power flow hould be run in order to check the feaibility and network ecurity of the dipatch reult. The following meaure can improve the convergence and tability of the propoed method. Table-V (Clearing reult of the propoed method with reference at D): Conget A B C Table-III (Clearing reult of the propoed method with reference at A): D Conget A E B C D Table-VI(Clearing reult of the propoed method with reference at E): Congetio n 104

5 Locatal Marginal pricing () in Deregulated Electricity Market A B C D REFERENCES E (1)Set good initial value of, and from hitoric data and offline analyi (2)Set good initial value of from hitoric data and offline analyi. (3)Ue ditributed reference bue. During the iterative proce, there i ome mimatch between the um of dipatched generat power and the um of power demand and loe. Comparing to ingle lack bu, the amount of power that each ditributed reference bu i reponible for balance i maller. Thi will generally reduce the poibility of AC power flow divergence if the participat factor of reference bue are choen according to the ytem operat condit (not choen randomly). V.CONCLUSION In thi paper, a new method to calculate iteratively i preented to tackle the main drawback with the DC power flow baed calculat that would lead to inaccuracie in lo calculat and dependency on the choice of reference bu. For eay implementat and conitency with the widely ued model, a linear programming problem i formulated and olved at each iterat. It i proved that the market clearing reult are independent of the elect of reference bu, more importantly, the conget component of i alo reference bu independent.thi i a deirable property for providing conitent and accuracy conget informat for market participant, which i crucial for effective conget management. Tet on a PJM five bu ytem how that the propoed method can obtain reference bu independent conget component of without preetting the lo factor, lo offet, and lo ditribut factor. The improvement and contribut of the propoed method are demontrated through comparing the reulting and their component. The calculat of the propoed method converge after 3 4 iterat. Tet reult alo indicate that appropriate initial value for lo factor, lo offet, and nodal lo ditribut factor would further improve the convergent peed. 1) G.Hamoud Feaibility Aement of Simultaneou Bilateral Tranact in a Deregulated Environment, IEEE Tranact on Power ytem, Vo15.No.1, pp.22-26, February ) L. Chen, H. Suzuki, T.Wachi, and Y. Shimura, Component of nodal price for electric power ytem, IEEE Tran. Power Syt., vol. 17, no. 1, pp , Feb ) B. Stott, J. Jardim, and O. Alaç, DC power flow reviited, IEEE Tran. Power Syt., vol. 24, no. 3, pp , Aug ) T. J. Overbye, X. Cheng, and Y. Sun, A compar of the AC and DC power plow model for calculat, in Proc. 37th Annu. Hawaii Int. Conf. Sytem Science, Jan. 5 8, 2004, 9 pp. 5) M. Rivier and J. I. Perez-Arriaga, Computat and decompoit of pot price for tranmi pricing, in Proc. 11th PSC Conf., ) T. Orfanogianni and G. Gro, A general formulat for evaluat, IEEE Tran. Power Syt., vol. 22, no. 3, pp , Aug ) J. B. Cardell, Marginal lo pricing for hour with tranmi conget, IEEE Tran. Power Syt., vol. 22, no. 4, pp , Nov ) T. Wu, Z. Alaywan, and A. D. Papalexopoulo, Locatal marginal price calculat uing the ditributed-lack power-flow formulat, IEEE Tran. Power Syt., vol. 20, no. 2, pp , May ) J. E. Price, Market-baed price differential in zonal and market deign, IEEE Tran. Power Syt., vol. 22, no. 4, pp , Nov ) F. Li and R. Bo, DCOPF-baed imulat: Algorithm, compar with ACOPF, and enitivity, IEEE Tran. Power Syt., vol. 22,no. 4, pp , Nov ) E. Litvinov, T. Zheng, G. Roenwald, and P. Shamollahi, Marginal lo modeling in calculat, IEEE Tran. Power Syt., vol. 19,no. 2, pp , May