Title :
Fokker-Planck equation application to analysis of a simplified wind turbine model
Author :
Wang, Keyou ; Crow, Mariesa L.
Author_Institution :
Electr. & Comput. Eng. Dept., Missouri Univ. of Sci. & Technol., Rolla, MO, USA
Abstract :
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.
Keywords :
Fokker-Planck equation; differential equations; squirrel cage motors; stochastic processes; wind turbines; FPE; Fokker-Planck equation application; Rayleigh distribution; constant-speed wind turbine model; multidimensional stochastic differential equations; one-dimensional nonlinear SDE; probability density function; simplified wind turbine model; squirrel cage induction generator; stochastic dynamic model; wind speed SDE; Differential equations; Equations; Mathematical model; Power system dynamics; Stochastic processes; Wind speed; Wind turbines; Finite difference methods; Fokker-Planck equation; Probability density function; Stationary stochastic processes; Stochastic differential equations; Wind turbine generator;
Conference_Titel :
North American Power Symposium (NAPS), 2012
Conference_Location :
Champaign, IL
Print_ISBN :
978-1-4673-2306-2
Electronic_ISBN :
978-1-4673-2307-9
DOI :
10.1109/NAPS.2012.6336340
