Stochastic modeling of rechargeable battery life in a photovoltaic power system

The authors have developed a stochastic model for the power generated by a photovoltaic (PV) power supply system that includes a rechargeable energy storage device. The ultimate objective of this work is to integrate this photovoltaic generator along with other generation sources to perform power flow calculations to estimate the reliability of different electricity grid configurations. For this reason, the photovoltaic power supply model must provide robust, efficient realizations of the photovoltaic electricity output under a variety of conditions and at different geographical locations. This has been achieved by use of a Karhunen-Loeve framework to model the solar insolation data. The capacity of the energy storage device, in this case a lead-acid battery, is represented by a deterministic model that uses an artificial neural network to estimate the reduction in capacity that occurs over time. When combined with an appropriate stochastic load model, all three elements yield a stochastic model for the photovoltaic power system. This model has been operated on the Monte Carlo principle in stand-alone mode to infer the probabilistic behavior of the system. In particular, numerical examples are shown to illustrate the use of the model to estimate battery life. By the end of one year of operation, there is a 50% probability for the test case shown that the battery will be at or below 95% of initial capacity.