Call for Paper - November 2022 Edition
IJCA solicits original research papers for the November 2022 Edition. Last date of manuscript submission is October 20, 2022. Read More

An Efficient and More Reliable Second Order Power Flow Solution Method with Interpolation Technique

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Hassan A. Kubba

Hassan A Kubba. An Efficient and More Reliable Second Order Power Flow Solution Method with Interpolation Technique. International Journal of Computer Applications 161(1):17-27, March 2017. BibTeX

	author = {Hassan A. Kubba},
	title = {An Efficient and More Reliable Second Order Power Flow Solution Method with Interpolation Technique},
	journal = {International Journal of Computer Applications},
	issue_date = {March 2017},
	volume = {161},
	number = {1},
	month = {Mar},
	year = {2017},
	issn = {0975-8887},
	pages = {17-27},
	numpages = {11},
	url = {},
	doi = {10.5120/ijca2017912940},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


This research presents a fast, reliable, and new method for solving the load (power) flow problem of electrical power systems. The proposed method is a second order load flow technique based on the "Taylor series expansion" of a multivariable function. This approach takes the first three terms of the Taylor series. The method has advantages over Newton's method in terms of computation time for solution (no. of iterations), and reliability of convergence. By inserting a minimization technique in this proposed method, the algorithm exhibits a control of the convergence. By means of this control, the method converges for cases when conventional Newton's method and some other popular methods diverge. Also this paper presents a comparison between the proposed method and Newton-Raphson method according to the major criteria, namely reliability of convergence and speed of solution. Two test systems (five busbars typical test system and forty busbars practical system based on Iraqi National Grid) are used to examine the performance of each method.


  1. Stott B, 1974. "Review of load flow calculation method", proc. IEEE, Vol. 62, July, 1974, 916-929.
  2. Sasson A. M., 1978. "An optimal ordering algorithm for sparse matrix application", IEEE Trans. power App., Vol. PAS-97, No. 6, Nov. 1978, 860-867.
  3. Kubba H.A., 1998. "A rapid and more reliable load flow solution method for ill-conditioned power system", Engineering and technology Journal, Vol. 17, No. 5, 1998, 550-568.
  4. Kubba H. A., 2001. "A improved and more reliable decoupled load flow method", Engineering, Scientific Journal of Engineering college / Baghdad University, No. 3, Vol. 7,. Sept. 2001, 35-47.
  5. Kubba H. A., 2006, "An improved Newton method for radial distribution system load flow analysis”, Engineering, Scientific Journal of Engineering College/ Baghdad University, No. 4, Vol. 12, September, 2006, 1122-1135.
  6. A. K. Laha, K. E. Bollinger, R. Billinton and S. B. Dhar, 1974. "Modified form of Newton's method for faster load flow solutions", proc. IEE, Vol. 121, Aug. 1974, 849-853.
  7. Stagg G. W., El-Abiad A. H., 1968. "Computer methods in power system analisi", Mc Graw –Hill book Company. 1968.
  8. Kubba H. A, 1991. "comparative study of different load flow solution methods", Al-Muhandis Journal, Vol. 107, 1991, 25-46.
  9. Aoki K. Nishikori A., 1984. "An algorithm for constrained load flow" IEEE transaction on pow. App. And systems. Vol. PAS-103, No. 5, May, 1984, 963-973.
  10. Kubba H. A., 2001. "An improved method of automatic adjustment of transformer and phase – shifter Taps for constrained load flow", Al-Muhandis Journal, serial-148, No. 4, December 2001, 34-50.
  11. Charles A. Gross, 1986. "power system analysis", second edition, John Wiley publ. comp.1986.


Cubic interpolation techniques, Load flow problem, Second order load flow model, Taylor series expansion, Voltage magnitude and phase angle