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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…
Finding the optimal parameters and functions of iterative methods is among the main problems of the Numerical Analysis. For this aim, a technique of the stochastic arithmetic (SA) is used to control of accuracy on Taylor-collocation method…
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.…
Renewable-energy-based grids development needs new methods to maintain the balance between the load and generation using the efficient energy storages models. Most of the available energy storages models do not take into account such…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gauss-type quadrature formula is used to approximate integrals during the…
Photovoltaic (PV) smart inverters can improve the voltage profile of distribution networks. A multi-objective optimization framework for coordination of reactive power injection of smart inverters and tap operations of on-load tap changers…
Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral…
Cell inconsistency within a lithium-ion battery system poses a significant challenge in maximizing the system operational time. This study presents an optimization-driven active balancing method to minimize the effects of cell inconsistency…
This paper presents a method to determine the optimal location, energy capacity, and power rating of distributed battery energy storage systems at multiple voltage levels to accomplish grid control and reserve provision. We model…
This paper focuses on multi-stage coordination for a population of thermostatically controlled loads (TCL). Each load maximizes the individual utility in response to an energy price, while the coordinator determines the price to maximize…
This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete…
Current-day data centers and high-volume cloud services employ a broad set of heterogeneous servers. In such settings, client requests typically arrive at multiple entry points, and dispatching them to servers is an urgent distributed…
A M\"untz spectral collocation method is implemented for solving weakly singular Volterra integro-differential equations (VDIEs) with proportional delays. After constructing the numerical scheme to seek an approximate solution, we derive…
The rapid expansion of wind and solar energy leads to an increasing volatility in the electricity generation. Previous studies have shown that storage devices provide an opportunity to balance fluctuations in the power grid. An economical…
A general and new stochastic linear quadratic optimal control problem is studied, where the coefficients are allowed to be time-varying, and both state delay and control delay can appear simultaneously in the state equation and the cost…
Unit commitment and load dispatch problems are important and complex problems in power system operations that have being traditionally solved separately. In this paper, both problems are solved together without approximations or…