A Dynamic Analysis of Energy Storage with Renewable and Diesel Generation Using Volterra Equations

Energy storage systems will play a key role in the power system of the 21st century considering the large penetrations of variable renewable energy, growth in transport electrification, and decentralization of heating loads. Therefore, reliable real-time methods to optimize energy storage, demand response, and generation are vital for power system operations. This article presents a concise review of battery energy storage and an example of battery modeling for renewable energy applications and details an adaptive approach to solve this load leveling problem with storage. A dynamic evolutionary model based on the first-kind Volterra integral equation is used in both cases. A direct regularized numerical method is employed to find the least-cost dispatch of the battery in terms of the integral equation solution. Validation on real data shows that the proposed evolutionary Volterra model effectively generalizes a conventional discrete integral model taking into account both the state of health and the availability of generation/storage.