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Mathematical Problems in Engineering
Volume 2014, Article ID 547485, 8 pages
http://dx.doi.org/10.1155/2014/547485
Research Article

The Interval Stability of an Electricity Market Model

1School of Mathematics and Physical Science, North China Electric Power University, Beijing 102206, China
2School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, China

Received 29 October 2014; Accepted 12 December 2014; Published 30 December 2014

Academic Editor: Xinkai Chen

Copyright © 2014 Weijuan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Combined with the electric power market dynamic model put forward by Alvarado, an interval model of electricity markets is established and investigated in this paper pertaining to the range of demand elasticity with suppliers and consumers. The stability of an electricity market framework with demand elasticity interval is analyzed. The conclusions characterizing the interval model provided are derived by constructing a suitable Lyapunov function and using the theory of interval dynamical system in differential equations and matrix inequality theory and so forth. Applying the corollary obtained can judge the system stability by available data about demand elasticity. The obtained results are validated and illustrated by a case example.