A Model for the State of Charge of a Battery Connected to a Wind Power Plant Under a Ramp Rate Limitation Regime

In this paper, the expected value of the first hitting time of a threshold of the state of charge of a battery is investigated. The model considers a battery storage system connected to a wind power plant under a ramp rate limitation scheme. The level of charge in the battery is the result of operations that are modelled by a Markov chain model with random rewards. The Markov chain and reward characteristics do depend on the considered ramp rate limitation scheme that the wind power producer has to respect in order to guarantee a quasi-stable output power to the grid. In this paper, we derive a system of integral equations for the hitting time of the state of charge of the battery and the application to real data validates the analytical results.