Volterra Models in Load Leveling Problem

¹ Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
² Institute of Solar-Terrestrial Physics, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
³ School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Belfast, UK
⁴ Department of Computer Engineering, Penza State University, Penza, Russia
⁵ Irkutsk Division of Main Computer Centre, JSC Russian Railways, Irkutsk, Russia
⁶ College of Electrical and Information Engineering, Hunan University, Changsha, China

^* Corresponding author: zhukovalex13@gmail.com

Abstract

Further growth in renewable energy and planned electrification and decentralization of transport and heating loads in future power systems will result in a more complex unit commitment problem (UCP). This paper proposes 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. This approach employs a direct numerical method. The considered collocation-type numerical method has the 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 optimization in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of the Island of Ireland.