Convergence of volatile power markets with price-based demand response

Price-based demand response (DR) program is a mechanism for encouraging electricity consumers to dynamically manage their energy consumptions in response to time-varying electricity prices, and thereby reduce peak electricity demands and alleviate the pressure to power systems. However, it brings additional dynamics and new challenges to the real-time supply and demand balance. Specifically, if real-time price based DR programs are widely deployed in the future, price-sensitive DR load levels would constantly change in response to dynamic real-time prices, which will impact the economic dispatch (ED) schedule and in turn affect electricity market clearing prices. This paper adopts two methods for examining the impacts of different DR price elasticity characteristics and DR participation levels on the convergence of volatile power market: a closed-loop iterative simulation method and a non-iterative method based on the contraction mapping theorem. In this paper, convergence refers to the fact that load and/or price values will finally converge to a fixed point after a finite number of iterations between the ED problem and the price-sensitive DR load adjustment. Five price-sensitive DR performance function categories are used to simulate different nonlinear price elasticity characteristics of DR loads. Numerical studies illustrate how the convergence status of power markets will be affected by the nonlinear price elasticity DR curves, the DR penetration levels, and the capacity limits of generating units.