Using EPECs to model bilevel games in restructured electricity markets with locational prices

Operations Research

Volumn 55, Issue 5, 2007, Pages 809-827

  Hu, Xinmin ^a   Ralph, Daniel ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Bidding auctions; Economic dispatch; Electricity market; Game group decisions: noncooperative; Government: energy policies; Industries: electric

Indexed keywords

CONSTRAINT THEORY; DECISION SUPPORT SYSTEMS; GAME THEORY; MATHEMATICAL PROGRAMMING; PROBLEM SOLVING;

ELECTRICITY MARKETS; MATHEMATICAL PROGRAM WITH EQUILIBRIUM CONSTRAINTS (MPEC); NASH EQUILIBRIA;

ELECTRICITY;

EID: 38549176844     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1070.0431     Document Type: Article

References (56)

1. Ahn, B. H., W. W. Hogan. 1982. On convergence of the PIES algorithm for computing equilibria. Oper. Res. 30 281-300.
2. Alvarado, F., J. Meng, C. L. DeMarco, W. S. Mota. 2001. Stability analysis of interconnected power systems coupled with market dynamics. IEEE Trans. Power Systems 16(4) 696-701.
3. Anitescu, M. 2005. On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints. SIAM J. Optim. 15(4) 1203-1236.
4. Backerman, S. R., S. J. Rassenti, V. L. Smith. 2000. Efficiency and income shares in high demand energy networks: Who receives the congestion rents when a line is constrained? Pacific Econom. Rev. 5 331-347.
5. Balder, E. J. 1995. A unifying approach to existence of Nash equilibria. Internat. J. Game Theory 24 79-94.
6. Ben-Tal, A., J. Zowe. 1982. A simplified theory of first and second order conditions for extreme problems in topological vector spaces. Math. Programming Stud. 19 39-76.
7. Berry, C. A., B. F. Hobbs, W. A. Meroney, R. P. O'Neill, W. R. Stewart Jr. 1999. Understanding how market power can arise in network competition: A game theoretic approach. Utilities Policy 8 139-158.
8. Bonnans, J. F., A. Shapiro. 1998. Optimization problems with perturbations: A guided tour. SIAM Rev. 40 202-227.
9. Brooke, A., D. Kendrick, A. Meeraus. 1992. GAMS - A User's Guide, Release 2.25. The Scientific Press, South San Francisco, CA.
10. Cardell, J. B., C. C. Hitt, W. W. Hogan. 1997. Market power and strategic interaction in electricity networks. Resource Energy Econom. 19 109-137.
11. Chao, H.-R, S. Peck. 1997. An institutional design for an electricity contract market with central dispatch. Energy J. 18 85-110.
12. Clarke, F. 1993. Nonsmooth Analysis. Wiley-Interscience, New York.
13. David Butchers & Associates. 2001. The New Zealand electricity market (NZEM). http://www.dba.org.nz/PDFs/Electricity%20Market.pdf.
14. Dirkse, S., M. C. Ferris. 1995. The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optim. Methods Software 5 123-156.
15. Drud, A. S. 1994. CONOPT - A large-scale GRG code. ORSA J. Comput. 6 207-216.
16. Ehrenmann, A. 2004a. Equilibrium problems with equilibrium constraints and their application to electricity markets. Ph.D. dissertation, Judge Institute of Management, University of Cambridge, Cambridge, UK.
17. Ehrenmann, A. 2004b. Manifolds of multi-leader Cournot equilibria. Oper. Res. Lett. 32 121-125.
18. Ehrenmann, A., K. Neuhoff. 2003. A comparison of electricity market designs in networks. Working paper CMIEP 31, The CMI Electricity Project, Department of Applied Economics, University of Cambridge, Cambridge, UK.
19. Facchinei, F., J. S. Pang. 2003. Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol. I. Springer Series in Operations Research, Springer, New York.
20. Ferris, M. C., T. S. Munson. 1999. Interfaces to PATH 3.0: Design, implementation and usage. Comput. Optim. Appl. 12 207-227.
21. Fletcher, R., S. Leyffer. 2004. Solving mathematical program with complementarity constraints as nonlinear programs. Optim. Methods Software 19 15-40.
22. Fletcher, R., S. Leyffer, D. Ralph, S. Scholtes. 2006. Local convergence of SQP methods for mathematical programs with equilibrium constraints. SIAM J. Optim. 17(1) 259-286.
23. Fukushima, M., J.-S. Pang. 2000. Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. M. Théra, R. Tichatschke, eds. Ill-Posed Variational Problems and Regularization Techniques. Springer, Berlin, Heidelberg, Germany, 99-110.
24. Green, R. J., D. M. Newbery. 1992. Competition in the British electricity spot market. J. Political Econom. 100 929-953.
25. Hobbs, B. F., C. B. Metzler, J.-S. Pang. 2000. Strategic gaming analysis for electric power systems: An MPEC approach. IEEE Trans. Power Systems 15 637-645.
26. Hogan, W. 1992. Contract networks for electric power transmission. J. Regulatory Econom. 4 211-242.
27. Hu, X. 2003. Mathematical programs with complementarity constraints and game theory models in electricity markets. Ph.D. thesis, Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia.
28. Hu, X., D. Ralph. 2001. Nash equilibria for games in competitive electricity markets under network constraints. D. Li, ed. Proc. ICOTA 2001, 5th Internat. Conf Optim.: Techniques and Appl, University of Hong Kong, Hong Kong, China.
29. Hu, X., D. Ralph. 2004. Convergence of a penalty method for mathematical programming with complementarity constraints. J. Optim. Theory Appl. 123 365-390.
30. Hu, X., D. Ralph, E. Ralph, P. Bardsley, M. Ferris. Revised 2004. Electricity generation with looped transmission networks: Bidding to an ISO. Working paper CMI EP 65, The CMI Electricity Project, Department of Applied Economics, University of Cambridge, Cambridge, UK.
31. Klemperer, P. D., M. A. Meyer. 1989. Supply function equilibria in oligopoly under uncertainty. Econometrica 57 1243-1277.
32. Leyffer, S., T. Munson. 2005. Solving multi-leader-follower games. Preprint, ANL/MCS-P1243-0405, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL.
33. Liu, M., G. Gross. 2004. Role of distribution factors in congestion revenue rights applications. IEEE Trans. Power Systems 19 802-810.
34. Luo, Z. Q., J.-S. Pang, D. Ralph. 1996. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK.
35. Murphy, F., Y. Smeers. 2002. Generation capacity expansion in imperfect competitive restructured electricity markets. Discussion paper 2002/69, CORE, Université Catholique de Louvain, Louvain-laNeuve, Belgium.
36. Myerson, R. B. 1991. Game Theory: Analysis of Conflict. Harvard University Press, Cambridge, MA.
37. Nasser, T-O. 1998. Transmission congestion contracts and strategic behavior in generation. Electricity J. 11 32-39.
38. Oren, S. S. 1997. Economic inefficiency of passive transmission rights in congested electricity systems with competitive generation. Energy J. 18 63-83.
39. Outrata, J. V 2003. A note on a class of equilibrium problems with equilibrium constraints. Kybernetika 40 585-594.
40. Ralph, D. 1994. Global convergence of Newton's method for nonsmooth equations, via the path search. Math. Oper. Res. 19 352-389.
41. Robinson, S. M. 1994. Newton's method for a class of nonsmooth functions. Set-Valued Anal. 2 291-305.
42. Saadat, H. 1999. Power Systems. McGraw-Hill, Boston, MA.
43. Scheel, M., S. Scholtes. 2000. Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 1-22.
44. Scholtes, S. 2001. Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11 918-936.
45. Scholtes, S., M. Stöhr. 2001. How stringent is the linear independence assumption for mathematical programs with stationarity constraints? Math. Oper. Res. 21 851-863.
46. Seeley, K., J. Lawarrée, C. C. Liu. 2000. Analysis of electricity market rules and their effects on strategic behaviour in a noncongestive grid. IEEE Trans. Power Systems 15 157-162.
47. Shapiro, A. 1990. On concepts of directional differentiability. J. Optim. Theory Appl. 66 477-487.
48. Stoft, S. 1999. Financial transmission rights meet Cournot: How TCCs curb market power. Energy J. 20 1-23.
49. Su, C.-L. 2004a. Analysis on forward market equilibrium model. Manuscript, Department of Management Science and Engineering, Stanford University, Stanford, CA.
50. Su, C-L. 2004b. A sequential NCP algorithm for solving equilibrium problems with equilibrium constraints. Manuscript, Department of Management Science and Engineering, Stanford University, Stanford, CA.
51. Wang, X., Y. Li, S. Zhang. 2004. Oligopolistic equilibrium analysis for electricity markets: A nonlinear complementarity approach. IEEE Trans. Power Systems 19 1348-1355.
52. Weber, J. D., T. J. Overbye. 1999. A two-level optimization problem for analysis of market bidding strategies. IEEE PES Summer Meeting, Edmonton, Alberta, Canada.
53. Wood, A. J., B. F. Wollenberg. 1996. Power Generation, Operation, and Control. John Wiley & Sons, New York.
54. Wu, F., P. Varaiya. 1999. Coordinated multilateral trades for electric power networks: Theory and implementation. Internat. J. Electrical Power Energy Systems 21(2) 75-102.
55. Yao, J., I. Adler, S. S. Oren. 2007. Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. Oper. Res. Forthcoming.
56. Younes, Z., M. Ilic. 1999. Generation strategies for gaming transmission constraints: Will the deregulated electric power market be an oligopoly? Decision Support Systems 24 207-222.