The mean square stability analysis of a stochastic dynamic model for electricity market
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ORIGINAL ARTICLE
The mean square stability analysis of a stochastic dynamic model for electricity market Zhanhui Lu1 • Weijuan Wang1 • Quanxin Zhu2 • Gengyin Li3
Received: 21 January 2015 / Accepted: 6 December 2015 Ó Springer-Verlag Berlin Heidelberg 2015
Abstract The mean square stability pertaining to a stochastic electricity market model is analyzed in this paper. Considering the random nature of demand elasticity, the stochastic electricity market model under small Gauss type random excitation has already been presented. Using the theory of stochastic differential equations, matrix theory and eigenvalue techniques, the sufficient conditions of the mean square stability for this electricity market model are provided and testified theoretically. The conclusions can judge the stability of the system by available data on demand elasticity. The obtained results are validated and illustrated by numerical examples. Keywords Power system Electricity market Stochastic differential equation Stochastic stability Euler– Maruyama numerical methods
1 Introduction As is well known, stochastic differential equation has been booming as a cross-discipline of probability theory and differential equation. Whether the system is large or small, ranging from a specific control system to a social system, a
& Quanxin Zhu [email protected] 1
School of Mathematics and Physical Science, North China Electric Power University, Beijing 102206, China
2
School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, China
3
School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China
financial system or an ecosystem, it always runs in random or persistent disturbance. With the random disturbance, it is essential that the system can maintain a predetermined running or operating state, instead of wavering or being out of control. The so-called stability of stochastic system movement is to study the stability in equilibrium state. That is to say, the disturbed movement, deviating from the equilibrium state, can return to the equilibrium state or restrict to its finite neighborhood when it only relies on factors of the system internal structure. Electricity market is based on power system and it is the operating mode of power system meanwhile. The economic stability of electricity market and the physical stability of power system are linked and affected by each other. In 1990, Beavis and Dobbs began to study economic system stability [1]. While the research of electricity market stability begins to perk up in recent years [2–10], the research on the dynamic evolution and stable behavior of economy and management system has been arousing wide attention in the field of mathematical economics, system science and so on for the past two decades. In particular, the stability analysis of economic systems branch is the emphasis and difficulty. Market mechanism is employed to reasonably allocate power resources in electricity market. The res
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