Vector Form Implementation in Three-Phase Power Flow Analysis Based on Power Injection Rectangular Coordinate

Main Article Content

Lukmanul Hakim
Fandi Prayoga
Khairudin Khairudin
Herri Gusmedi

Keywords

Abstract

This paper aims to propose the vector form implementation into three-phase power flow analysis. The developed algorithm is based on Newton-Raphson method with voltage is represented in rectangular coordinate. The Python programming language and its mathematical libraries are used in this works. Three-phase power flow analysis in vector form utilizes sparse matrix ordering algorithm, so the elements of the coefficient correction matrix can be rearranged easily. This method was used to solve three-phase power flow for balance or unbalance network in two actual distribution system feeders in Lampung, i.e. 119 nodes and 191 nodes. Comparison with traditional Newton-Raphson method (non-vector) shows the vector form is able to solve computation up to eight times faster than non-vector.

 

Keywords: Three-phase power flow, Vector form, Newton-Raphson, Rectangular, Python

References

Demirok, E; Kjær, S. B.; Dezso, S.; and Teodorescu, R.,“Three-Phase Unbalanced Load Flow Tool for Distribution Networks,” Proc. of 2nd Int'l. Workshop on Integration of Solar Power System, p. 9, 2012.

[2] Sereeter, B.; Vuik, K.; and Witteveen, C.; “Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks,” Energies, vol. 10, no. 10, p. 1658, 2017.

[3] Milano, F., “Continuous Newton ’ s Method for Power Flow Analysis,” IEEE. Trans. on Power Systems, vol. 24, no. 1, pp. 50–57, Feb. 2009.

[4] Hakim, L.; Wahidi, M.; Murdika, U.; Milano, F.; Kubokawa, J.; Yorino, N.,“A Three-phase Power Flow Analysis for Electrical Power Distribution System with Low Voltage Profile,” Proc. 2015 2nd Int. Conf. Inf. Technol. Comput. Electr. Eng. (ICITACEE), Semarang, 16-18 Oct. 2015.

[5] Alvarado, F. L.,“Solving Power Flow Problems with a Matlab Implementation of the Power System Applications Data Dictionary,” Proc. of the 32nd Annual Hawaii Int'l Conf. on Systems Sciences, Maui, 5-8 Jan 1999.

[6] Yude, Y.; Zhijun, Q.; and Wei, H., “Power Flow Calculation Based on Non-linear Programming Model and Vectorization Mode,” Proc. of 2007 Int'l Conf. on Mechatronics and Automation, Harbin, 5-8 Aug. 2007.

[7] P. R. Amestoy, I. Enseeiht, T. A. Davis, and I. S. Duff, “Algorithm 837: AMD, an Approximate Minimum Degree Ordering Algorithm,” ACM Trans. on Mathematical Software (TOMS), vol. 30, no. 3, pp. 381–388, Sep. 2004.

[8] Gaviano, M.; Kvasov, D. E.; Lera, D.; and Sergeyev, Y.D.; “Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization,” ACM Trans. on Mathematical Software (TOMS), vol. 29, no. 4, pp. 469–480, Dec. 2003.

[9] Qin, Z.; and Yang, Y.; “Vectorization implementation of optimal power flow in rectangular form based on interior point method,” Proc. of 2008 IEEE PES GM - Convers. Deliv. Electr. Energy in the 21st Century, Pittsburgh, 20-24 Jul. 2008.

[10] Milano, F.,“A python-based software tool for power system analysis,” Proc. of 2013 IEEE PES Gen. Meet., Vancouver, 21-25 Jul. 2013

[11] Birt, K. A.; Graffy, J. J.; Mcdonald, J. D.; El-Abiad, A. H.,“Three Phase Load Flow Program,” IEEE Trans. on Power App. and Systs., vol. 95, no. 1, pp. 59–65, Jan. 1976.

[12] Xi-Fan Wang, Y. Song, and M. Irving, Modern Power Systems Analysis. , Springer, India, 2013.