The stability of power market with cyclic load demand under the discrete bidding strategy

Abstract

The object of this work is to study the stability of electrical power market. The electrical power market is described as a nonlinear, nonautonomous, periodic difference system in this paper. In this model, several issues, such as, instantaneously clearing of power market, the cyclic pattern of load demand and discrete bidding strategy, are involved. The problem of the stability of electricity market becomes the problem of the stability of a periodic solution of the dynamic system model. To obtain the stable conditions of power market, several lemmas that a dynamic difference system has a unique bounded periodic solution are proved, and the ultimate boundary can also be estimated with one of these lemmas. Sufficient conditions for the stability of the power market are derived, and the ultimate boundary of the price is also estimated. Numerical simulation results validate the proposed models and stability conditions.