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 journalArticleScientificpeer-review

30 Citations (Scopus)
491 Downloads (Pure)


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 languageEnglish
Pages (from-to)157-169
Number of pages13
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 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.


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


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