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

• Main Authors: Muftahov, Ildar, Sidorov, Denis, Zhukov, Aleksei, Panasetsky, Daniil, Foley, Aoife, Li, Yong, Tynda, Aleksandr
• Format: Report
• Language: unknown
• Published: arXiv 2016
• Subjects: Systems and Control eess.SY; Functional Analysis math.FA; Numerical Analysis math.NA; FOS Electrical engineering, electronic engineering, information engineering; FOS Mathematics; 65R32, 45D05, 65R20; Moder; Sakhalin
• Online Access: https://dx.doi.org/10.48550/arxiv.1608.05221; https://arxiv.org/abs/1608.05221

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. : arXiv admin note: text overlap with arXiv:1507.06484