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Integral Models Based on Volterra Equations with Prehistory and Their Applications in Energy

Author

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  • Evgeniia Markova

    (Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

  • Inna Sidler

    (Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

  • Svetlana Solodusha

    (Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

Abstract

The paper addresses the application of Volterra integral equations of the first kind for modeling dynamic power systems. We study the problem of forecasting the commissioning of capacities of the electric power system, taking into account various hypotheses about the dynamics of equipment aging, and the known prehistory. The numerical results of the application of two models to the problem of the development of a large electric power system using the example of the Unified Energy System of Russia are presented. Theoretical results were formulated for a two-dimensional Volterra integral equation of the first kind with variable limits of integration. This class of equations arises when solving the actual problem of identifying variable characteristics of a nonlinear dynamic system of the “input-output” type.

Suggested Citation

  • Evgeniia Markova & Inna Sidler & Svetlana Solodusha, 2021. "Integral Models Based on Volterra Equations with Prehistory and Their Applications in Energy," Mathematics, MDPI, vol. 9(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1127-:d:555619
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    References listed on IDEAS

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    1. E. V. Markova & I. V. Sidler & V. V. Trufanov, 2013. "Integral Models of Developing Electric Power Systems," International Journal of Energy Optimization and Engineering (IJEOE), IGI Global, vol. 2(4), pages 44-58, October.
    2. Kler, Aleksandr M. & Zharkov, Pavel V. & Epishkin, Nikolai O., 2019. "Parametric optimization of supercritical power plants using gradient methods," Energy, Elsevier, vol. 189(C).
    3. Anatoly S. Apartsyn, 2014. "On Some Classes of Linear Volterra Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, July.
    4. Schwarz, Hans-Gunter, 2005. "Modernisation of existing and new construction of power plants in Germany: results of an optimisation model," Energy Economics, Elsevier, vol. 27(1), pages 113-137, January.
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