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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 the uncertainty. Power system operators have always 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 to reliability control is a reformulation as stochastic optimal control for hybrid stochastic differential system, namely, by means of modeling 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. In most cases, indeed, Bellman's equation cannot be solved analytically. 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). On the one hand, these successive approximations stipulate by construction a stochastic optimal control of the feedback type, and on the other hand, they enjoy the convenience of a cost that is pathwise decreasing sufficiently fast until reaching a terminal value. Optimizing over feedback controls conforms with common practice according to experts and makes the Markov property hold true for the controlled process. 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. Effectiveness of the SLDP approach has been demonstrated by simulation experiments.
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Submitted on : Tuesday, September 6, 2022 - 9:18:09 AM
Last modification on : Monday, September 12, 2022 - 8:17:48 AM

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Hana Baili. Wind Markov Models and Reliability Control in Wind Energy Conversion Systems. International Journal of Ambient Energy, 2022, ⟨10.1080/01430750.2022.2120911⟩. ⟨hal-03769992⟩

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