Wind Markov Models and Reliability Control in Wind Energy Conversion Systems
Abstract
The integration of renewable energy systems affects the entire power system by increasing uncertainty. Power system operators always have to manage uncertainty in one way or another; the fundamental principle in this regard is to guarantee reliability, i.e. balancing load variations with generation resources. This paper addresses the problem of uncertainty management or equivalently reliability control in power systems with wind generation. Our main approach is a reformulation as stochastic optimal control for a hybrid stochastic differential system, namely, by means of modelling the wind speed as a diffusion process in steady state. Accordingly, in theory, the dynamic programming principle provides the only closed-form exact solution to the problem of reliability control. But in practice, its complexity resides in the resolution of the Hamilton–Jacobi–Bellman equation. This paper explores a systematic and feasible alternative: successive approximations of the exact solution that could be referred to as sequential linear-dynamic programming (SLDP in abridged notation). The convergence result of the approximating solution brings together two key points: first, the convergence in the sense of the L2-norm; second, the decay rate of the cost over the course of the iterations until convergence. The effectiveness of the SLDP approach has been demonstrated by simulation experiments.