On the Fokker-Planck equation for stochastic hybrid systems: application to a wind turbine model

Julien Bect (1) , Yannick Phulpin (1) , Hana Baili (1) , Gilles Fleury (1)

1 E3S - Supélec Sciences des Systèmes

This paper presents some recent results concerning a class of continuous-time Markov processes called ``stochastic hybrid systems''. These processes describe the evolution of a multidimensional hybrid-state dynamical system subject to Gaussian white noise inputs. After a brief recall of the formalism, we state the generalized Fokker-Planck equation, which is a partial differential equation satisfied by the probability density function of the system. As an illustration, we consider a variable-speed wind turbine, with a switching controller that combines stall regulation and pitch control. For a given value of the mean wind speed, the stationary distribution of the state variables is computed numerically. This truly dynamical analysis of the system yields a complete probabilistic characterization of the uncertain power output, which is much more accurate than the usual static analysis.

Mots clés: Probabilistic Uncertainty Analysis; Wind Turbines; Piecewise-continuous Markov Processes; Fokker-Planck; Stochastic Hybrid Systems

Domaines: Energie électrique

Julien Bect, Yannick Phulpin, Hana Baili, Gilles Fleury. On the Fokker-Planck equation for stochastic hybrid systems: application to a wind turbine model. PMAPS 2006, Jun 2006, Stockholm, Sweden. pp.N.A., ⟨10.1109/PMAPS.2006.360298⟩. ⟨hal-00016375⟩