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Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation

Author

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  • Denis Sidorov

    (Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
    Baikal School of BRICS, Irkutsk National Research Technical University, 664074 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
    Main Computing Center, Joint Stock Company “Russian Railways”, 664005 Irkutsk, Russia)

  • Aliona Dreglea

    (Applied Mathematics Department, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
    Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia)

  • Fang Liu

    (School of Automation, Central South University, Changsha 410083, China)

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.

Suggested Citation

  • Denis Sidorov & Aleksandr Tynda & Ildar Muftahov & Aliona Dreglea & Fang Liu, 2020. "Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation," Mathematics, MDPI, vol. 8(8), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1257-:d:393090
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    References listed on IDEAS

    as
    1. Natali Hritonenko & Yuri Yatsenko, 2013. "Mathematical Modeling in Economics, Ecology and the Environment," Springer Optimization and Its Applications, Springer, edition 2, number 978-1-4614-9311-2, December.
    2. Denis Sidorov & Daniil Panasetsky & Nikita Tomin & Dmitriy Karamov & Aleksei Zhukov & Ildar Muftahov & Aliona Dreglea & Fang Liu & Yong Li, 2020. "Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region," Energies, MDPI, vol. 13(5), pages 1-18, March.
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    Cited by:

    1. Aleksandr N. Tynda & Denis N. Sidorov, 2022. "Inverse Problem for the Integral Dynamic Models with Discontinuous Kernels," Mathematics, MDPI, vol. 10(21), pages 1-9, October.

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