On a comparison of Newton–Raphson solvers for power flow problems

Baljinnyam Sereeter; Cornelis Vuik; Cees Witteveen

doi:10.1016/j.cam.2019.04.007

On a comparison of Newton–Raphson solvers for power flow problems

Baljinnyam Sereeter^*, Cornelis Vuik, Cees Witteveen

^*Corresponding author for this work

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

36 Citations (Scopus)

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Abstract

A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.

Original language	English
Pages (from-to)	157-169
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	360
DOIs	https://doi.org/10.1016/j.cam.2019.04.007
Publication status	Published - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Cartesian
Current mismatch
Newton–Raphson method
Polar
Power flow analysis
Power mismatch

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10.1016/j.cam.2019.04.007

1-s2.0-S0377042719301876-mainFinal published version, 414 KB

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title = "On a comparison of Newton–Raphson solvers for power flow problems",

abstract = "A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.",

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AU - Sereeter, Baljinnyam

AU - Vuik, Cornelis

AU - Witteveen, Cees

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2019

Y1 - 2019

N2 - A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.

AB - A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.

KW - Cartesian

KW - Current mismatch

KW - Newton–Raphson method

KW - Polar

KW - Power flow analysis

KW - Power mismatch

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DO - 10.1016/j.cam.2019.04.007

M3 - Article

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SN - 0377-0427

VL - 360

SP - 157

EP - 169

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

On a comparison of Newton–Raphson solvers for power flow problems

Abstract

Bibliographical note

Keywords

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On a comparison of Newton-Raphson solvers for power flow problems

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