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Conference Papers Year : 2006

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

Julien Bect
Yannick Phulpin
• Function : Author
• PersonId : 831678
Hana Baili
Gilles Fleury
• Function : Author
• PersonId : 831677

#### Abstract

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.

#### Domains

Engineering Sciences [physics] Electric power

### Dates and versions

hal-00016375 , version 1 (02-01-2006)

### Identifiers

• HAL Id : hal-00016375 , version 1
• DOI :

### Cite

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⟩

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