ANALYSIS OF TRIPARTITE GAME IN POWER SYSTEMS BASED ON UNCERTAIN NASH EQUILIBRIUM THEORY

Power systems serve as the fundamental infrastructure for the socioeconomic development of modern societies. Researching power systems can stimulate the growth of the power industry and contribute to the sustainable development of society. This paper aims to address uncertainties prevalent in power systems, including extreme weather events, disruptions in renewable energy supply, and adjustments in economic policies. To achieve this objective, an uncertain Nash equilibrium model is established. Subsequently, a game theoretic analysis is conducted to maximize the interests of users, grid companies, and proxy purchasers. Under the condition of not necessarily continuous differentiability, the Riemann-Stieltjes discrete approximation method has been proposed. The difficulty of calculating the expectation of the optimal revenue function has been resolved. Weak first-order equilibrium condition based on Clarke's generalized gradient, the convergence and convergence rate of uncertain Nash equilibrium solutions are proved.