A comparison of the optimal multiplier in polar and rectangular coordinates

Joseph Euzebe Tate, Thomas J. Overbye

Research output: Contribution to journalArticlepeer-review


Studies of the optimal multiplier (or optimal step size) modification to the standard Newton-Raphson (NR) load flow have mainly focused on highly stressed and unsolvable systems. This paper extends these previous studies by comparing performance of the NR load flow with and without optimal multipliers for a variety of unstressed, stressed, and unsolvable systems. Also, the impact of coordinate system choice in representing the voltage phasor at each bus is considered. In total, four solution methods are compared: the NR algorithm with and without optimal multipliers using polar and rectangular coordinates. This comparison is carried out by combining analysis of the optimal multiplier technique with empirical results for two-bus, 118-bus, and 10 274-bus test cases. These results indicate that the polar NR load flow with optimal multipliers is the best method of solution for both solvable and unsolvable cases.

Original languageEnglish (US)
Pages (from-to)1667-1674
Number of pages8
JournalIEEE Transactions on Power Systems
Issue number4
StatePublished - Nov 2005
Externally publishedYes


  • Load flow analysis
  • Load flow convergence
  • Optimal multipliers
  • Polar and rectangular coordinates
  • Step-size optimization

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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