A comparison of the optimal multiplier in polar and rectangular coordinates

• Published in: IEEE transactions on power systems Vol. 20; no. 4; pp. 1667 - 1674
• Main Authors: Tate, J.E., Overbye, T.J.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Electric potential; Equations; Load flow; Load flow analysis; load flow convergence; Multipliers; Newton Raphson methods; optimal multipliers; Optimization; Performance analysis; Phasors; polar and rectangular coordinates; Power grids; Power system reliability; Robustness; step-size optimization; Testing; Voltage
• ISSN: 0885-8950; 1558-0679
• DOI: 10.1109/TPWRS.2005.857388

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.