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An Analysis of a Wind Turbine-Generator System in the Presence of Stochasticity and Fokker-Planck Equations
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Author(s): Ravish Himmatlal Hirpara (S.V. National Institute of Technology (SVNIT), Surat, India)and Shambhu Nath Sharma (S.V. National Institute of Technology (SVNIT), Surat, India)
Copyright: 2020
Volume: 9
Issue: 1
Pages: 26
Source title:
International Journal of System Dynamics Applications (IJSDA)
Editor(s)-in-Chief: Ahmad Taher Azar (College of Computer & Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia & Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt)
DOI: 10.4018/IJSDA.2020010102
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Abstract
In power systems dynamics and control literature, theoretical and practical aspects of the wind turbine-generator system have received considerable attentions. The evolution equation of the induction machine encompasses a system of three first-order differential equations coupled with two algebraic equations. After accounting for stochasticity in the wind speed, the wind turbine-generator system becomes a stochastic system. That is described by the standard and formal Itô stochastic differential equation. Note that the Itô process is a strong Markov process. The Itô stochasticity of the wind speed is attributed to the Markov modeling of atmospheric turbulence. The article utilizes the Fokker-Planck method, a mathematical stochastic method, to analyse the noise-influenced wind turbine-generator system by doing the following: (i) the authors develop the Fokker-Planck model for the stochastic power system problem considered here; (ii) the Fokker-Planck operator coupled with the Kolmogorov backward operator are exploited to accomplish the noise analysis from the estimation-theoretic viewpoint.
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