Game Theory Project

GAME THEORY Project Phase I

1. Introduction

Decision concerning electrical transmission network expansion has become harder in the last two decades. As a matter of fact, the power sector has been decentralized and the electricity market is now a competitive market. Thus a transmission expansion plan cannot follow the traditional planning criteria anymore. As a result, new techniques are developed in order to solve the transmission expansion problem TEP.

Usually different optimization methods are used to solve the TEP: genetic algorithm (GA), Tabu search (TS) and several heuristic and metaheuristic techniques. Those are called static scenarios. Dynamic scenarios are the one based on game theory which represents the behavior of different participants in the electricity market. Different games and models like cournot, Stackelberg, bargaining etc.. are recently used to obtain an optimal decision concerning TEP.

This paper presents a non-cooperative game theory approach in order to solve the TEP. First the transmission expansion problem is formulated in Section II in a manner to minimize the cost of the expansion subject to voltage, power flow and other constraints. In Section III, the proposed expansion plans given by the investors are subject to the following steps: valuation of the expansion plan, determining the optimal effort using a principle-agent model and the bidding competition in order to get the efficient bid. Section IV presents a numerical application using the classical Garver six-bus system. Finally conclusions are drawn in Section V.

2. Survey of previous work

In the literature, there are examples of transmission expansion problems solved by cooperative and non-cooperative games.

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...7] J. D. Molina, J. Contreras, H. Rudnick, “A Principal-Agent Approach to Transmission Expansion—Part I: Regulatory Framework,” Power Systems, IEEE Transactions Vol. 28, pp 256- 263, 2013.

[8] M. Jenabi, S. Mohammad, T. F. Ghomi, and Y.Smeers

“Bi-Level Game Approaches for Coordination of Generation and Transmission Expansion Planning Within a Market Environment,” Power Systems, IEEE Transactions Vol. 28, pp. 2639 – 2650, 2013

[9] M. R. Hesamzadeh, D.R. Biggar, N.Hosseinzadeh, and P. J. Wolfs, “Transmission Augmentation With Mathematical Modeling of Market Power and Strategic Generation Expansion—Part I” Power Systems, IEEE Transactions Vol. 26, pp 2040-2048, 2011

[10] L.Xiaotong, L.Yimei, Z. Xiaoli, and Z.Ming “Generation and Transmission Expansion Planning Based on Game Theory in Power Engineering” Systems Engineering Procedia 4 (2012) 79 – 86.