Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

TL;DR

This paper introduces a novel adaptive method using Volterra integral equations for optimizing energy storage and generation, enabling real-time, cost-effective dispatch in power systems with variable efficiencies and storage availabilities.

Contribution

It presents a new dynamic modeling approach based on Volterra equations for energy storage optimization, with a second-order accurate numerical method suitable for real-time applications.

Findings

Demonstrated on Irish and Sakhalin power markets.

Achieved efficient, reliable energy dispatch solutions.

Validated the method's accuracy and adaptability.

Abstract

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in moder power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Sakhalin island in the Russian Far East.