Establish of Electricity Market Model with Variable Coefficient and Analysis of Its Practical Stability

Abstract-The paper analyzes the dynamic equilibrium of the electricity market by using the principle of economics and establishes the non-autonomous linear discrete periodic mathematic models, the models describe the actions of the electricity market under the assumption that market demand is the linear function with variable coefficient of forecast price and that the market supply is the linear equation with varied coefficient of spot price. The practical stability of the electric market is discussed by using Lyapunov function and the calculus inequality. A number of critical conditions to judge the practical stability of electric market and the existing of practically asymptotically stable periodic solution of electricity market are obtained and these conclusions are explained by example. Keywords-Electric market; model of deference equation; practical stability; periodic solution; practically quasi-stable