Probabilistic game approaches for network cost allocation

bhakar, Rohit and sriram, V.s. and padhy, Narayana prasad and gupta, Hari om (2010): Probabilistic game approaches for network cost allocation. Published in: IEEE Transactions on Power Systems , Vol. 25, No. 1 (20 January 2010): pp. 51-58.

Abstract

In a restructured power market, the network cost is to be allocated between multiple players utilizing the system in varying capacities. Cooperative game approaches based on Shapley value and Nucleolus provide stable models for embedded cost allocation of power networks. Varying network usage necessitates the introduction of probabilistic approaches to cooperative games. This paper proposes a variety of probabilistic cooperative game approaches. These have variably been modeled based upon the probability of existence of players, the probability of existence of coalitions, and the probability of players joining a particular coalition along with their joining in a particular sequence. Application of these approaches to power networks reflects the system usage in a more justified way. Consistent and stable results qualify the application of probabilistic cooperative game approaches for cost allocation of power networks.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative games, embedded cost allocation, probabilistic games, transmission pricing
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

[1] J. W. M. Lima, “Allocation of transmission fixed charges: An overview,” IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1409–1418, Aug. 1996.

[2] Y. R. Sood, N. P. Padhy, and H. O. Gupta, “Wheeling of power under deregulated environment of power system—A bibliographical survey,” IEEE Trans. Power Syst., vol. 17, no. 3, pp. 870–878, Aug. 2002.

[3] H. P.Young, “Cost allocation,” in Handbook of Game Theory, R. J. Aumann and S. Hart, Eds. Amsterdam, The Netherlands: Elsevier Science,1994, vol. 2, pp. 1193–1235.

[4] Y. Tsukamoto and I. Iyoda, “Allocation of fixed transmission cost to wheeling transactions by cooperative game theory,” IEEE Trans. Power Syst., vol. 11, no. 2, pp. 620–629, May 1996.

[5] C. W. Yu, A. K. David, and Y. K. Wong, “The use of game theory in transmission embedded cost allocation,” in Proc. 5th Int. Conf. Advances in Power Systems Control, Operation and Management, Hong Kong, 2000, pp. 139–143.

[6] X. Tan and T. T. Lie, “Application of the Shapley value on transmission cost allocation in the competitive power market environment,” Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 149, no. 1, pp. 15–20, Jan. 2002.

[7] J. M. Zolezzi and H. Rudnick, “Transmission cost allocation by cooperative games and coalition formation,” IEEE Trans. Power Syst., vol. 17, no. 4, pp. 1008–1015, Nov. 2002.

[8] C. W. Yu, A. K. David, C. T. Tse, and C. Y. Chung, “Capacity-use andreliability based transmission embedded cost allocation with temporal considerations,” Int. J. Elect. Power Energy Syst., vol. 25, pp. 201–208, 2003.

[9] G. C. Stamtsis and I. Erlich, “Use of cooperative game theory in power system fixed-cost allocation,” Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 151, no. 3, pp. 401–406, May 2004.

[10] E. Bjorndal, G. C. Stamtsis, and I. Erlich, “Finding core solutions for power system fixed cost allocation,” Proc. Inst. Elect. Eng., Gen., Transm., Distrib., vol. 152, no. 2, pp. 173–179, Mar. 2005.

[11] R. J. Weber, “Probabilistic values for games,” in The Shapley Value:Essays in Honor of Lloyd S. Shapley, L. S. Shapley and A. E. Roth, Eds. Cambridge, U.K.: Cambridge Univ. Press, 1988, pp. 101–120.

[12] P. Dubey and R. J. Weber, Probabilistic Values for Games, Cowles Foundation Disc. Papers 471, Cowles Foundation, Yale Univ., 1977. [Online]. Available: http://cowles.econ.yale.edu/P/cd/d04b/d0471.pdf.

[13] D. Schmeidler, “The nucleolus of a characteristic function game,” SIAM J. Appl. Math., vol. 17, no. 6, pp. 1163–1170, Nov. 1969.

[14] L. Krus and P. Bronisz, “Cooperative game solution concepts to a cost allocation problem,” Eur. J. Oper. Res., vol. 122, pp. 258–271, 2000.

[15] I. Parrachino, A. Dinar, and F. Patrone, Cooperative Game Theory and Its Application to Natural, Environmental, andWater Resource Issues: Application to Water Resources, World Bank Policy Research, Working Paper no. 4074 Nov. 2006. [Online]. Available: http://ssrn.com/abstract=946833.

[16] A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control. Singapore: Wiley, 2003, p. 112.

[17] R. F. Ghajar and R. Billinton, “Economic costs of power interruptions: A consistent model and methodology,” Int. J. Elect. Power Energy Syst., vol. 28, no. 1, pp. 29–35, Jan. 2006.

[18] The Statement of the Use of System Charging Methodology, Issue 3,Revision 1, U.K., National Grid plc, 2007.

[19] MATPOWER Version 3.0b4. (2005, Jan.). A MATLAB Power System Simulation Package by PSERC. Ithaca, NY, Cornell Univ. [Online]. Available: http://www.pserc.cornell.edu/matpower/matpower.html.

[20] H. I. Meinhardt, TuGames v1.1 beta,MATHEMATICA Package, 2004. [Online]. Available: http://library.wolfram.com/infocenter/Math-Source/5709/.