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1 AC Application for Single Price Auction Model (SPA) in AC Network Tsunehisa Wachi, Member, Suguru Fukutome, Member, Luonan Chen,Member, Yoshinori Makino, Member, Gentarou Koshimizu,Member This paper aims to develop a single price auction model with AC transmission network, based on the principle of maximizing social surplus of electricity market. Specifically, we first formulate the auction market as a nonlinear optimization problem, which has almost the same form as the conventional optimal power flow problem, and then propose an algorithm to derive both market clearing price and trade volume of each player even for the case of market-splitting. As indicated in the paper, the proposed approach can be used not only for the price evaluation of auction or bidding market but also for analysis of bidding strategy, congestion effect and other constraints or factors. Several numerical examples are used to demonstrate effectiveness of our method. AC Keywords: single price auction, AC network, electricity market, optimal power flow, nodal price 1. Nord Pool PJM ISO NY ISO EEX MCP Nord Pool EEX JP JP Business Service Corporation , Fukagawa, Koto-ku, Tokyo Osaka Sangyo University 3-1-1, Nakagaichi, Daito / Electric Power Development Co., Ltd , Chigasaki, Chigasaki MCP PJM ISO NY ISO LMP MCP (1) (2) (3) LMP DC AC DC AC AC DC AC DC B
2 AC AC (1) (5) (7) (11) (18) (19) (4) (8) (10) (16) (17) AC (8) (10) AC SPA Single Price Auction in AC network AC AC AC OPF OPF (6) (12) (20) (22) WEST30 (13) AC 2 3 AC 4 WEST MCP (23) (23) 1 Fig. 1. Electricity market model. 2 Fig. 2. Social surplus. 82 IEEJ Trans. PE, Vol.125, No.1, 2005
3 1 2 C (4) (6) AC 2 Karush-Kuhn-Tucker KKT KKT AC SPA AC LMP 3 1 AC SPA N d N g max F(X) = π di P di F gi (P gi ) N D P Di N G P Gi + g i (P)dP f i (P)dP P Di min P Gi min (1) s.t. G(X) = 0 H(X) 0 N G N D L(X) = P Gi P Di (1 + K) = 0 π di P di d i F gi (P gi ) g i P gi g i 3 Fig. 3. Market splitting in case of congestion. g(p Di ) D i P Di D i f (P Gi ) G i P Gi G i N d N g N D N G X = [e 1,...,e n, f 1,..., f n ] e i f i G(X) H(X) P Dimin P Gimin B
4 K AC (1) F X P gi P Gi P Di X L π di P di π di P di 4 g(p Di ) f (P Gi ) P Di P Gi F gi (P gi ) P gi i f Gi (P Gi ), P Gi f Gi (P Gi ) P Gi g Dj (P Di ), P Di g Dj (P Di ) P Di 3 3 (1) (9) (17) PJM LMP k µ p,k = F + λ G + ρ H + η L (2) P dk P dk P dk P dk µ q,k = F + λ G + ρ H + η L (3) Q dk Q dk Q dk Q dk λ ρ η G H L Lagrangian Multipliers µ p,k µ q,k k 3 4 (1) OPF (12) (20) (22) OPF X P Gi (X) P Di (X) P gi (X) π Gi = f i (P Gi ) for i = 1,...,N G, where P Gi 0 π Di = g i (P Di ) for i = 1,...,N D, where P Di 0 (4) 2 π π = π Gmax = π Dmin π Gmax π Gi = f i (P Gi ) π Dmin π Di = g i (P Di ) π Gmax = max{π Gi = f i (P Gi ): i = 1,...,N G, P Gi 0} π Dmin = min{π Di = g i (P Di ): i = 1,...,N D, P Di 0} 4 f (P G ) g(p D ) π Gmax π Dmin π π = απ Gmax + (1 α)π Dmin (5) 0 α (1) (4) AC 5 (1) (4) π G π D (5) 4 Fig. 4. Bidding curves and bidding. 5 Fig. 5. Proposed algorithm. 84 IEEJ Trans. PE, Vol.125, No.1, 2005
5 π G π D (5) 4. WEST30 WEST30 AC i 10% Spot10%Base 10% ii 10%Spot10%Cong 10% iii 90% Spot90%Base 90% iv 90%Spot90%Cong 90% 6 2 Tie Line 1 10% 90% 10% 90% Price Spot Non 7 90% AC WEST30 (13) 1 6 WEST30 A B C D E F 6 Tie Line 1500 MW Fig. 6. IEEJ WEST30-machine system. 1 Table 1. Offer volume to spot and non-spot. 2 Table 2. Data of generators. Node NameType T H P NAr Price /kwh Spot MW Non MW (1) f (P) 4 2 (7) B
6 3 Table 3. Data of demands. 4 Table 4. Result of simulation. Ref1 Ref2 Rate (%) SS pu MS Price1 /kwh Price2 /kwh Volume MW Node Ar Spot MW NonMW (1) g(p) 4 2 (7) 8 Spot10% Fig. 8. Bidding volume and trade volume of sellers (spot market 10% case). 7 Spot90% Fig. 7. Supply and demand curves (spot market 90% case). 2 x% x 3 Spot 3Non 3 G16 G30G8 G14 G24 G25 4 Spot10% G16 G30G8 G14 G24 G25 30% 2Non 70% 2 Spot 5 Spot90% G16 G30G8 G14 G24 G25 2 Spot 6 3% 7 (14) (15) Spot10% Spot90% B D MW 9 (5) α = 1 α = (pu) 1.05 (pu) 11 4 SS G2) Spot10% 9 Spot90%Cong IEEJ Trans. PE, Vol.125, No.1, 2005
7 9 Spot90% Congestion Fig. 9. Aggregated trade volume of sellers (spot market 90% congestion case). 10 Fig. 10. Nodal prices. 4 Ref.1 Ref.2 SS Spot10% Spot90% Spot10% Spot90% 8 Spot10% Spot10% Base Spot10%Cong 10 KKT Spot10%Base Ref % AC 8 Spot10%Base 8 G23 G26 Spot10%Base Ref (pu) 51.7 (pu) 3% 1% Spot10% Cong Spot90%Cong B D A B C D E F Spot 10%Cong G1 G5 G9 G13 G23 9 Spot90% Cong 2 4 Spot10% Cong Spot10%Base 1.7 (pu) 68.6 (pu) Spot90%Cong Spot90% Base 7.2 (pu) (pu) 3 Spot90%Cong Spot90%Base 129 MW MW B
8 4 4 Spot10% Cong Spot90% Cong (5) 5 (2) (3) 10 A B C D E F Spot10%Base G1 G (MW) 47.1 (MW) G1 G (pu) Spot10% Base i Spot10%Base G (pu) 1.10 (pu) G (pu) (MW) (MW) G (pu) (pu) ii Spot10%Base G (pu) (pu) G (MW) (MW) (MW) (MW) (pu) (pu) AC 5. AC SPA AC AC WEST30 AC AC , (2001) 2, (2003) 3, (2003) 4 N. Yamaguchi, H. Kita, K. Nishiya, and J. Hasegawa: Simulation of Power Price Volatility Using Power Market Model, T. IEE Japan, Vol.121-B, No.12, pp ( ) (in Japanese), B, 121, 12, pp ( ) 5 B.F. Hobbs, C.B. Metzler, and J.S. Pang: Strategic gaming analysis for electric power systems: An MPEC approach, IEEE Trans. Power Syst., Vol.15, pp (2000) 6 I. Otero-Novas, C. Meseguer, C. Batlle, and J. Alba: A simulation model for a competitive generation market, IEEE Trans. Power Syst., Vol.15, No.1, pp (2000) 7 F.C. Shweppe, M.C. Caramanis, R.D. Tabors, and R.E. Bohn: Spot Pricing of Electricity, Kluwer Academic Publishers, Boston, MA (1988) 8 P. Wei, L. Chen, and H.D. Chiang: Analysis of Bidding Price in the Payas-Bid Market, IEEE PES Summer Meeting (2003) 9 L. Chen, H. Suzuki, T. Wachi, and Y. Shimura: Components of Nodal Prices for Electric Power Systems, IEEE Trans. Power Syst., Vol.17, No.1, pp (2002) 10 K. Xie, Y. Song, J. Stonham, E. Yu, and G. Liu: Decomposition Model and Interior Point Methods for Optimal Spot Pricing of Electricity in Deregulation Environments, IEEE Trans. Power Syst., Vol.15, No.1, pp (2000) 11 D. Weber and T.J. Overbye: An Individual Welfare Maximization Algorithm for Electricity Markets, IEEE Trans. Power Syst., Vol.17, No.3, pp (2002) 12 L. Chen, S. Matoba, H. Inabe, and T. Okabe: Surrogate constraint method foroptimalpowerflow, IEEE Trans. Power Syst., Vol.13, No.3, pp (1998) 13,, No.754 ( ) meti.go.jp/faq/electric/q04.htm (1999) 88 IEEJ Trans. PE, Vol.125, No.1, 2005
9 15,, 6 partialliberali zation/pdffile/tyosa/14fyshimoki-kakaku.doc (2003) 16 H. Asano and K. Okada: Development of Computation Method for Regional Electric Transmission Capacity Pricing, T. IEE Japan, Vol.117-B, No.1, pp (1997-1) (in Japanese), B, 117, 1, pp (1997-1) 17 L. Chen, H. Suzuki, T. Wachi, and Y. Shimura: Analysis of Nodal Prices for Power Systems, T. IEE Japan, Vol.120-B, No.5, pp (2000-5) (in Japanese), B, 120, 5, pp (2000-5) 18 Geerli, L. Chen, Y. Kinoshita, and R. Yokoyama: Negotiation Models for Electric Pricing and Load Dispatch in Electricity Market, T. IEE Japan, Vol.120-B, No.2, pp (2000-2) (in Japanese), B, 120, 2, pp (2000-2) 19 Geerli, R. Yokoyama, and L. Chen: Negotiation Models for Electricity Pricing in Partially Deregulated Electricity Market, T. IEE Japan, Vol.120- B, No.11, pp ( ) (in Japanese), B, 120, 11, pp ( ) 20 L. Chen, A. Ono, Y. Tada, H. Okamoto, and R. Tanabe: Optimal Operation of Power Systems Constrained by Transient Stability, T. IEE Japan, Vol.120-B, No.12, pp ( ) (in Japanese), B, 120, 12, pp ( ) 21 L. Chen, H. Suzuki, and K. Katou: Mean field theory for optimal power flow, IEEE Trans. Power Syst., Vol.12, No.4, pp (1997) 22 L. Chen, Y. Tada, H. Okamoto, R. Tanabe, and A. Ono: Optimal Operation Solutions of Power Systems with Transient Stability Constraints, IEEE Trans. Circuits Syst. -I, Vol.48, No.3, pp (2001) 23 J. Rawls: A Theory of Justice, Revised edition, Belknap Press, Cambridge, Massachusetts (1999) IEEE Member IEEE senior Member B
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