# American Institute of Mathematical Sciences

July  2008, 4(3): 617-630. doi: 10.3934/jimo.2008.4.617

## Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function

 1 College of Electrical and Information Engineering, Changsha University of Science and Technology, China 2 Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong, China 3 Mathematics and Computing Science, Changsha University of Science and Technology 4 College of Mathematics, Changsha University of Science and Technology, China

Received  October 2006 Revised  February 2008 Published  July 2008

In order to accurately simulate the game behaviors of market participants, a new dynamic Cournot game model of power market considering the constraints of power network is proposed in this paper. The model is represented by a discrete difference equations embedded with the maximization problem of the social benefit of power market. Compared with those existing dynamic models, the proposed one has the following remarkable characteristics: it adopts a dynamic adjustment where the limit point is the Nash equilibrium of power market, and the system of discrete difference equations embedded with the maximization problem considers the inherent physical characteristics of power network, i.e., the complex network constraints. Both of the properties show that the proposed model is much closer to the practical market. By using the nonlinear complementarity function to reformulate the Karush-Kuhn-Tucker (KKT) system of maximization problem, the Nash equilibrium of power market and its stability are quantitatively analyzed. Numerical simulations are carried out to evaluate the dynamic behaviors of market participants with different market parameters, especially the periodic and chaotic dynamic behaviors when the market parameters are beyond the stability region of Nash equilibrium.
Citation: Hongming Yang, C. Y. Chung, Xiaojiao Tong, Pingping Bing. Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function. Journal of Industrial & Management Optimization, 2008, 4 (3) : 617-630. doi: 10.3934/jimo.2008.4.617
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