Solvability and Numerical Solutions of Systems of Nonlinear Volterra Integral Equations of the First Kind with Piecewise Continuous Kernels

Muftahov, Ildar; Sidorov, Denis

doi:10.14529/mmp160111

Cited by 9 publications

(6 citation statements)

References 4 publications

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“…С. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Since the data on the load and its forecasts are given in tabular form, we used the approximations of load and its forecasts by a 4th degree polynomials by 10 points for solving Volterra integral equation by Taylor collocations. The result of the work on accurate and forecast data is shown in the figure (2).…”

Section: Results Of Numerical Experiments On Real Datamentioning

confidence: 99%

Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem

Noeiaghdam¹,

Sidorov²,

Muftahov³

et al. 2019

Bull.ISU.Ser.Math.

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High penetration of renewable energy sources coupled with decentralization of transport and heating loads in future power systems will result even more complex unit commitment problem solution using energy storage system scheduling for efficient load leveling. This paper employees an adaptive approach to load leveling problem using the Volterra integral dynamical models. The problem is formulated as solution of the Volterra integral equation of the first kind which is attacked using Taylor-collocation numerical method which has the second-order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. Also the CESTAC method is applied to find the optimal approximation, optimal error and optimal step of collocation method. 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.

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Section: Results Of Numerical Experiments On Real Datamentioning

confidence: 99%

Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem

Noeiaghdam¹,

Sidorov²,

Muftahov³

et al. 2019

Bull.ISU.Ser.Math.

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“…Such models can be employed to simulate the degradation processes in storage systems of MGs using retrospective time series of generation and load for specific location. Numerical results of proposed integral model were derived using the collocation numerical method proposed in [36,37] for determination APF and SoC will be shown on real datasets below.…”

Section: The Relationship Between Local and Centralized Levelsmentioning

confidence: 99%

Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region

et al. 2020

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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.

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“…For the statements concerning the existence and uniqueness of solutions of systems of VIEs with discontinuous kernels readers may refer to [22].…”

Section: Problem Statementmentioning

confidence: 99%

Numeric solution of systems of nonlinear Volterra integral equations of the first kind with discontinuous kernels

Tynda,

Sidorov,

Sidorov

2019

Preprint

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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 Newton-Kantorovich iterative process for the integral operators linearization. On each step of the iterative process the linear system of integral equations is obtained and resolved using the discontinuity driven piecewise constant approximation of the exact solution. The convergence theorem is proved. The polynomial collocation technique is also applied to solve such systems as the alternative method. The accuracy of proposed numerical methods is discussed. The model examples are examined in order to demonstrate the efficiency of proposed numerical methods and illustrate the constructed theory.

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Solvability and Numerical Solutions of Systems of Nonlinear Volterra Integral Equations of the First Kind with Piecewise Continuous Kernels

Cited by 9 publications

References 4 publications

Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem

Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem

Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region

Numeric solution of systems of nonlinear Volterra integral equations of the first kind with discontinuous kernels

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