Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network

Operations Research

Volumn 56, Issue 1, 2008, Pages 34-47

  Yao, Jian ^a   Adler, Ilan ^a   Oren, Shmuel S ^a  

^a DEPARTMENT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH   (United States)

Author keywords

Electricity market; Equilibrium problem with equilibrium constraints; Linear complementarity problem; Noncooperative games: cournot equilibrium; Programming: mathematical program with equilibrium constraints; Two settlements

Indexed keywords

ELECTRICITY MARKET; EQUILIBRIUM CONSTRAINTS; LINEAR COMPLEMENTARITY PROBLEM;

ALGORITHMS; COMPUTER SIMULATION; COST FUNCTIONS; MARKETING;

ELECTRIC NETWORK ANALYSIS;

EID: 41549090830     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1070.0416     Document Type: Article

References (38)

1. Allaz, B. 1992. Oligopoly, uncertainty and strategic forward transactions. Internal J. Indust. Organ. 10 297-308.
2. Allaz, B., J.-L. Vila. 1993. Cournot competition, forward markets and efficiency. J. Econom. Theory 59 1-16.
3. Borenstein, S., J. Bushnell, S. Stoft. 2000. The competitive effects of transmission capacity in a deregulated electricity industry. RAND J. Econom. 31(2) 294-325.
4. Chao, H.-P., S. C. Peck. 1996. A market mechanism for electric power transmission. J. Regulatory Econom. 10(1) 25-60.
5. Chen, X., M. Fukushima. 2004. A smoothing method for a mathematical program, with P-matrix linear complementarity constraints. Computational Optim. Appl. 27 223-246.
6. Cottle, R. W., J. S. Pang, R. E. Stone. 1992. The Linear Complementarity Problem. Academic Press, Boston, MA.
7. Facchinei, F., H. Jiang, L. Qi. 1999. A smoothing method for mathematical programs with equilibrium constraints. Math. Programming 85 107-134.
8. Fletcher, R., S. Leyffer. 2004. Solving mathematical programs with complementarity constraints as nonlinear programs. Optim. Methods Software 19 15-40.
9. Fudenberg, D., J. Tirole. 1991. Game Theory. MIT Press, Cambridge, MA.
10. Fukushima, M., G.-H. Lin. 2004. Smoothing methods for mathematical programs with equilibrium, constraints. Internat. Conf. Informatics Res. for Development Knowledge Soc. Infrastructure (ICKS'04), Kyoto, Japan, 206-213.
11. Fukushima, M., P. Tseng. 2002. An implementable active-set algorithm for computing a B-stationary point of a mathematical problem with linear complementarity constraints. SIAM J. Optim. 12(3) 724-739.
12. Fukushima, M., Z.-Q. Luo, J.-S. Pang. 1998. A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints. Computational Optim. Appl. 10(1) 5-34.
13. Green, R. J. 1999. The electricity contract market in England and Wales. J. Indust. Econom. 47(1) 107-124.
14. Hambley, A. R. 2004. Electrical Engineering: Principles and Applications, 3rd ed. Prentice Hall, Upper Saddle River, NJ.
15. Harker, P. T. 1991. Generalized Nash games and quasivariational inequalities. Eur. J. Oper. Res. 54 81-94.
16. Hobbs, B. F. 2001. Linear complementarity models of Nash-Cournot competition, in bilateral and POOLCO power markets. IEEE Trans. Power-Systems 16(2) 194-202.
17. 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(2) 638-645.
18. Hu, X. 2002. Mathematical programs with complementarity constraints and game theory models in electricity markets. Ph.D. thesis, Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia.
19. Hu, X. M., D. Ralph. 2004. Convergence of a penalty method for mathematical programming with complementarity constraints. J. Optim. Theory Appl. 123(2) 365-390.
20. Jiang, H., D. Ralph. 1999. QPECgen: A MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints. Computational Optim. Appl. 13 25-49.
21. Kamat, R., S. S. Oren. 2004. Multi-settlement systems for electricity markets: Zonal aggregation under network uncertainty and market power. J. Regulatory Econom. 25(1) 5-37.
22. Luo, Z. Q., J. S. Pang, D. Ralph. 1996. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK.
23. Metzler, C., B. F. Hobbs, J. S. Pang. 2003. Nash-Cournot equilibria in power markets on a linearized DC network with arbitrage: Formulations and properties. Networks Spatial Theory 3(2) 123-150.
24. Neuhoff, K., J. Barquin, M. G. Boots, A. Ehrenmann, B. F. Hobbs, F. A. M. Rijkers, M. Vázquez. 2005. Network-constrained models of liberalized electricity markets: The devil is in the details. Energy Econom. 27(3) 495-525.
25. Newbery, D. M. 1998. Competition, contracts, and entry in the electricity spot market. Rand J. Econom. 29(4) 726-749.
26. Oren, S. S. 1997. Economic inefficiency of passive transmission rights in congested electricity systems with competitive generation. Energy J. 18 63-83.
27. Pang, J.-S., M. Fukushima. 2005. Quasi-variational inequalities, generalized Nash equilibria and multi-leader-follower games. Computational Management Sci. 2 21-56.
28. Powell, A. 1993. Trading forward in an imperfect market: The case of electricity in Britain. Econom. J. 103 444-453.
29. Ralph, D., S. J. Wright. 2004. Some properties of regularization and penalization schemes for MPECs. Optim. Methods Software 19(5) 527-556.
30. Scheel, H., S. Scholtes. 2000. Mathematical programs with equilibrium constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 1-22.
31. Scholtes, S. 2001. Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11 918-936.
32. Smeers, Y., J.-Y. Wei. 1997. Spatial oligopolistic electricity models with Cournot firms and opportunity cost transmission prices. Working paper, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
33. Su, C.-L. 2005. Equilibrium problem with equilibrium constraints: Stationarities, algorithms and applications. Ph.D. thesis, Department of Management Science and Engineering, Stanford University, Stanford, CA.
34. von der Fehr, N.-H. M., D. Harbord. 1992. Long-term contracts and imperfectly competitive spot markets: A study of UK electricity industry. Memorandum 14, Department of Economics, University of Oslo, Oslo, Norway.
35. Wei, J.-Y., Y. Smeers. 1999. Spatial oligopolistic electricity models with Cournot firms and regulated transmission prices. Oper. Res. 47(1) 102-112.
36. Yao, J., S. S. Oren, I. Adler. 2004. Computing Cournot equlibria in two-settlement electricity markets with transmission constraints. Proc. 37th Hawaii Internat. Conf. Systems Sci., Big Island, HI.
37. Yao, J., S. S. Oren, B. F. Hobbs. 2006. A hybrid Bertrand-Cournot model of electricity markets with multiple subnetworks. Working paper, Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA.
38. Yao, J., B. Willems, S. S. Oren, I. Adler. 2005. Cournot equilibrium in price-capped two-settlement electricity markets. Proc. 38th Hawaii Internat. Conf. Systems Sci., Big Island, HI.