Due to the fluctuations in their production, wind farm owners are subject to financial penalties. To limit these penalties the use of a storage device is studied. We define in this paper a large class of production/storage models in continuous time which verify the physical limits of the facility. In these models, the optimal operation of the storage device becomes an optimal stochastic control problem. We prove that this problem is equivalent to solving an Hamilton-Jacobi-Bellman PDE. Further, this PDE verifies the comparison principle and has thus a unique solution. Using a Semi-Lagrangian approach, we obtain an algorithm for this PDE. As the PDE verify the maximum principle, by using classical tools, we prove that this algorithm is convergent. Finally we present some numerical results.
