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

## TL;DR

This paper introduces a dynamic Volterra integral equation model for optimizing energy storage in renewable and diesel power systems, demonstrating improved dispatch strategies considering health and availability factors.

## Contribution

It presents a novel adaptive Volterra integral equation approach for real-time energy storage optimization in renewable energy systems.

## Key findings

- The Volterra model effectively generalizes traditional discrete models.
- Validation on real data confirms improved dispatch efficiency.
- The method accounts for state of health and generation/storage availability.

## Abstract

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