Power market structure and its equilibrium

This paper concentrates on building the mathematical models for a power market, and studying its basic properties. Firstly by making an assumption and defining the concept of an ideal power market, this paper proposes the mathematical models for generator, demand, and transmission. Then by defining the concept of bus market and network market, this paper proposes the mathematical model for the power market. Some basic properties, such as the existence, the sole, and the optimum of the ideal power market equilibrium are also analyzed and proved in this paper.