arXiv subjects

Julien Bect

Publications and source records attributed to Julien Bect.

39 records · Page 3Linked to original sources

arXiv2008

Probabilistic computation of wind farm power generation based on wind turbine dynamic modeling

This paper addresses the problem of predicting a wind farm's power generation when no or few statistical data is available. The study is based on a time-series wind speed model and on a simple dynamic model of a DFIG wind turbine including cut-off and cut-in behaviours. The wind turbine is modeled as a stochastic hybrid system with three operation modes. Numerical results, obtained using Monte-Carlo simulations, provide the annual distribution of a wind farm's active power generation. For different numbers of wind turbines, we compare the numerical results obtained using the dynamic model with those obtained considering the wind turbine's steady-state power curve. Simulations show that the wind turbine's dynamics do not need to be considered for analyzing the annual distribution of a wind farm generation.

stat.AP↗

arXiv2008

A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems

A general formulation of the Fokker-Planck-Kolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHS). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based on the concept of mean jump intensity, which is related to both the usual stochastic intensity (in the case of spontaneous jumps) and the notion of probability current (in the case of forced jumps). This work unifies all previously known instances of the FPK equation for stochastic hybrid systems, and provides GSHS practitioners with a tool to derive the correct evolution equation for the probability law of the state in any given example.

math.PR↗

arXiv2005

Fokker-Planck-Kolmogorov equation for stochastic differential equations with boundary hitting resets

We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial differential equation for the probability density function, involving a non-local boundary condition which accounts for the jumping behaviour of the process. This is a generalisation of the usual Fokker-Planck-Kolmogorov equation for diffusion processes. The result is illustrated with an example in the field of stochastic hybrid systems.

math.PR↗