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Ramp-rate limitation is a strategy to reduce wind power variability and to permit the integration of wind power into the grid. However, penalties occur whenever the ramp-rate limitations are not respected. The purpose of this paper is to compute the penalties to which a wind farm may undergo when a battery storage system is put alongside the wind farm. This is achieved by advancing a semi-Markov model which mimes the operations on the battery and considers a new reward structure which is dependent on the time length of the battery operations. Two Monte Carlo algorithms are proposed for simulating the penalty process. The paper shows the validity of the methodology by verifying the model assumptions directly on real data and through a comparison of the real and the simulated results. This paper contributes to the literature by extending previous stochastic models and providing a general methodology for the economical characterization of ramp-rate limitation policies.

Modelling and simulation of a storage system connected to a wind farm under ramp-rate limitation