Nonlinear systems of Volterra equations with piecewise smooth kernels: Numerical solution and application for power systems operation

Denis Sidorov; Aleksandr Tynda; Ildar Muftahov; Aliona Dreglea; Fang Liu

doi:10.3390/MATH8081257

Nonlinear systems of Volterra equations with piecewise smooth kernels: Numerical solution and application for power systems operation

Denis Sidorov^*
, Aleksandr Tynda
, Ildar Muftahov
, Aliona Dreglea
, Fang Liu^*

^*Corresponding author for this work

Siberian Branch of Russian Academy of Sciences
Irkutsk National Research Technical University
Penza State University
Open Joint Stock Company Russian Railways
Central South University

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton-Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

Original language	English
Article number	1257
Journal	Mathematics
Volume	8
Issue number	8
DOIs	https://doi.org/10.3390/MATH8081257
State	Published - Aug 2020
Externally published	Yes

Keywords

Direct discretization
Discontinuous kernels
Energy storage
Inverse problem
Load leveling
Midpoint rectangles
Newton-Kantorovich method
Nonlinear Volterra equations
Polynomial-collocation scheme

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title = "Nonlinear systems of Volterra equations with piecewise smooth kernels: Numerical solution and application for power systems operation",

abstract = "The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton-Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.",

keywords = "Direct discretization, Discontinuous kernels, Energy storage, Inverse problem, Load leveling, Midpoint rectangles, Newton-Kantorovich method, Nonlinear Volterra equations, Polynomial-collocation scheme",

author = "Denis Sidorov and Aleksandr Tynda and Ildar Muftahov and Aliona Dreglea and Fang Liu",

note = "Publisher Copyright: {\textcopyright} 2020 by the authors.",

year = "2020",

month = aug,

doi = "10.3390/MATH8081257",

language = "英语",

volume = "8",

journal = "Mathematics",

issn = "2227-7390",

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T1 - Nonlinear systems of Volterra equations with piecewise smooth kernels

T2 - Numerical solution and application for power systems operation

AU - Sidorov, Denis

AU - Tynda, Aleksandr

AU - Muftahov, Ildar

AU - Dreglea, Aliona

AU - Liu, Fang

PY - 2020/8

Y1 - 2020/8

N2 - The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton-Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

AB - The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton-Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

KW - Direct discretization

KW - Discontinuous kernels

KW - Energy storage

KW - Inverse problem

KW - Load leveling

KW - Midpoint rectangles

KW - Newton-Kantorovich method

KW - Nonlinear Volterra equations

KW - Polynomial-collocation scheme

UR - https://www.scopus.com/pages/publications/85090086543

U2 - 10.3390/MATH8081257

DO - 10.3390/MATH8081257

M3 - 文章

AN - SCOPUS:85090086543

SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 1257

ER -

Nonlinear systems of Volterra equations with piecewise smooth kernels: Numerical solution and application for power systems operation

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Keywords

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