The Research On Electricity Markets Stability

The worldwide reform of power industry market-oriented makes the birth of a large number of new issues in various fields, such as the power system planning, operation, dispatching, management, security stability analysis and control. So electri- city market needs new theories and methods to guide it. The stability of electricity market does not only embody physical stability such as the power angle stability, voltage stability and frequency stability of the system, but it also needs to consider the stability of economic system related with the electricity market. Because the economic stability of electricity market and the physical stability of the power system are lined and affect each other, the study on the stability of electricity market has become a very challenging task.Combining the characteristics of the electricity market, this paper deeply studies some issues related to electricity market stability by the stability theory, control theory and economics research ideas and methods.This paper includes the following content.The electricity market is the process that the seller and the buyer affect each other to determine power prices and demand. This paper studies time series, including the power prices and the power demand and so on. Based on this, the separated modeling method of Gompertz model is put forward, and Lyapunov index forecasting method is improved. The reasonableness of separation of mergence for the time series is proved and the forecast accuracy is improved. Paper also gives examples to verify the validity of these in theory.The paper uses the principle of economic to analysis the dynamic balance of the electricity, establishes a number of actions described and differential-difference model in electricity market. In the assumption that market demand is the linear equation (or non-linear equation) with variable coefficient of forecast price and market supply is the linear equation (or non-linear equation) with varied coefficient of spot price, paper analysis time series of the power price and the power demand. And paper establishes autonomous and non-autonomous continuous or discrete linear periodic mathematic models to describe actions of electricity market.Combining models have been established to describe the behavior of the electri- city market; the paper studies the Lyapunov stability and practical stability of the autonomous and non-autonomous continuous or discrete linear periodic system by tools, for example, the appropriate structure Lyapunov functions, comparison, the calculus inequality, the matrix measures. The paper obtains series of stable critical conditions and estimated formula of ultimate convergence boundary .At last it gives continuation of discrete system conditions and the relations between coefficients of continuous and discrete systems.Theories and methods of the practical stability are first time used for the studying of the electricity market stability. Paper studies the practical stability of electricity market models by tools, for example, the appropriate structure Lyapunov functions, Cauchy matrix, the matrix measure, constant variation. Judging practical stability sufficient conditions and estimating formula of ultimate convergence boundary are provided. Conditions are descriptive by coefficients of models. At the same time, paper studies the Lyapunov stability of the electricity market. As well as the sufficient conditions of judging electricity market Lyapunov stability are provided. Some of conclusions improved the results of Alvarado and others. The conclusion of Lyapunov stability has made a comparative with practical results. Finally, in order to prove the effectiveness of conditions of the models stability, paper uses Matlab and Maple mathematical softwares to analysis the date of California power market. And paper analysis the affection of power supply, supply prices, user demand and demand price make stability and reasonable electricity market economy mechanism.