Dynamic modeling of the power market and analysis of its complex behavior based on a nonlinear complementarity function

In order to accurately simulate the dynamic decision-making behaviors of market participants, a new dynamic model of power markets that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of market clearing. Compared with existing dynamic models, the remarkable characteristic of the proposed model is twofold: it accurately reflects the process of market clearing by the Independent System Operator (ISO) while considering the inherent physical characteristics of power networks, i.e., the complex network constraints; and it describes the market condition that the generation and demand sides bid simultaneously. Using a nonlinear complementary function, the complex discrete difference dynamic model is transformed into a set of familiar discrete difference algebraic equations. Then, the complex dynamic behaviors of power markets are quantitatively analyzed. Corresponding to different operating conditions of power network, such as congestion or non-congestion, the Nash equilibrium of power markets and its stability are calculated, and the periodic and even chaotic dynamic behaviors are exhibited when the market parameters are beyond the stability region of the Nash equilibrium.