Fokker-Planck equation application to analysis of a simplified wind turbine model

This paper presents a new method to evaluate the stochastic dynamic model of the wind turbine system using stochastic differential equations (SDE). The wind speed is described by the Rayleigh distribution which is constructed as the stationary solution of a one-dimensional nonlinear SDE. The dynamic model of the wind turbine system can be combined with this SDE of wind speed to expand to multi-dimensional stochastic differential equations. The time evolution of the probability density function of the system is described by the Fokker-Planck equation (FPE) which can be derived from the corresponding stochastic differential equations. The procedure is illustrated using a constant-speed wind turbine model with squirrel cage induction generator.