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 and Fang Liu
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Denis Sidorov: Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Aleksandr Tynda: Faculty of Computer Engineering, Penza State University, 440026 Penza, Russia
Ildar Muftahov: Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Aliona Dreglea: Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Fang Liu: School of Automation, Central South University, Changsha 410083, China

Mathematics, 2020, vol. 8, issue 8, 1-19

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: inverse problem; Newton–Kantorovich method; nonlinear Volterra equations; discontinuous kernels; energy storage; direct discretization; load leveling; polynomial-collocation scheme; midpoint rectangles (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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