Ildar Muftahov

Ildar Muftahov, Denis Sidorov, Aleksei Zhukov et al.

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.

Denis Sidorov, Ildar Muftahov, Nikita Tomin et al.

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.

Ildar Muftahov, Aleksandr Tynda, Denis Sidorov

We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves (endogenous delays) which starts at the origin. In order to linearize these equations we use the modified Newton-Kantorovich iterative process. Then for linear equations we propose two direct quadrature methods based on the piecewise constant and piecewise linear approximation of the exact solution. The accuracy of proposed numerical methods is $\mathcal{O}(1/N)$ and $\mathcal{O}(1/N^2)$ respectively. We also suggest a certain iterative numerical scheme enjoying the regularization properties. Furthermore, we adduce generalized numerical method for nonlinear equations. We employ the midpoint quadrature rule in all the cases. In conclusion we include several numerical examples in order to demonstrate the efficiency of proposed numerical methods