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.

Tourism development in ecologically vulnerable areas like the lake Baikal region in Eastern Siberia is a challenging problem. To this end, the dynamical models of AC/DC hybrid isolated power system consisting of four power grids with renewable generation units and energy storage systems are proposed using the advanced methods based on deep reinforcement learning and integral equations. First, the wind and solar irradiance potential of several sites on the lake Baikal’s banks is analyzed as well as the electric load as a function of the climatic conditions. The optimal selection of the energy storage system components is supported in online mode. The approach is justified using the retrospective meteorological datasets. Such a formulation will allow us to develop a number of valuable recommendations related to the optimal control of several autonomous AC/DC hybrid power systems with different structures, equipment composition and kind of AC or DC current. Developed approach provides the valuable information at different stages of AC/DC hybrid power systems projects development with stand-alone hybrid solar-wind power generation systems.

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.