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On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Author

Listed:
  • Talal Alharbi

    (Department of Electrical Engineering, College of Engineering, Qassim University, Buraydah 52571, Saudi Arabia)

  • Marcos Tostado-Véliz

    (Department of Electrical Engineering, University of Jaén, 23700 Linares, Spain)

  • Omar Alrumayh

    (Department of Electrical Engineering, College of Engineering, Qassim University, Unaizah 56452, Saudi Arabia)

  • Francisco Jurado

    (Department of Electrical Engineering, University of Jaén, 23700 Linares, Spain)

Abstract

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising.

Suggested Citation

  • Talal Alharbi & Marcos Tostado-Véliz & Omar Alrumayh & Francisco Jurado, 2021. "On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases," Mathematics, MDPI, vol. 9(17), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2019-:d:620384
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    References listed on IDEAS

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    1. Fabio V. Difonzo & Costantino Masciopinto & Michele Vurro & Marco Berardi, 2021. "Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models: A Python Tool," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(8), pages 2553-2567, June.
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    Cited by:

    1. Marcos Tostado-Véliz & Talal Alharbi & Hisham Alharbi & Salah Kamel & Francisco Jurado, 2022. "On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases," Mathematics, MDPI, vol. 10(8), pages 1-19, April.

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