基于光滑非线性互补函数的电力市场动态研究

为了模拟电力市场中发电商的有限理性博弈行为,提出了考虑输电网约束的有限理性古诺博弈动态模型,即内嵌社会效益最大化问题的差分动态模型。借助数学理论中的非线性互补方法,利用光滑的非线性互补函数将这一数学结构复杂的模型转换为常见的差分?代数方程,从而为进一步开展有限理性古诺博弈动态演化的定量分析奠定了基础。最后针对3寡头古诺博弈进行数值仿真,计算得出不同市场参数下的市场动态行为,并着重探讨了当市场参数超出均衡点稳定域时出现了周期甚至混沌的动态行为。

Research on Dynamic Status of Electricity Market Based on Smooth Nonlinear Complementary Function

To accurately simulate the game behaviors of generation companies with bounded rationality in electricity market, the authors propose a dynamic Cournot game model with bounded rationality considering power network constraints,i.e., a discrete differential equations embedded with the maximization problem of the social benefit of market. By means of nonlinear complementary method and by use of smooth nonlinear complementary function, this complex discrete differential dynamic system is transformed into a set of familiar discrete differential algebraic equations, so a foundation is laid for further quantitative analysis of dynamic evolution of Cournot game with bounded rationality. The numerical simulation for Cournot game, in which three oligarchs participate, is performed and the dynamic behaviors of the market under different market parameters are obtained, in which the periodic or chaotic dynamic behaviors are focused while market parameters are out of the stability region of the equilibrium.