# Unbalanced Power Flow Analysis in Distribution Systems Using TRX Matrix: Implementation Using DIgSILENT Programming Language

Chapter

First Online:

## Abstract

In this chapter, a generalized model to solve multigrounded distribution networks under DIgSILENT platform taking into account current flows and voltages across neutral and ground paths is presented. The fundamental idea developed in this work is solving the 5-wire power flow problem using a unique matrix called TRX that includes all feeder characteristics related to phase, neutral, and equivalent ground paths. Proposed power flow routines are run from MATLAB engine using DIgSILENT databases. The method is suitable to be applied on unbalanced aerial and underground distribution systems with distributed generation. Proposed methodology has been successfully applied in an illustrative test system.

## Keywords

Backward/forward sweep Load flow Power flow Distribution system analysis DIgSILENT Programming Language MATLAB## Supplementary material

321979_1_En_4_MOESM1_ESM.zip (537 kb)

## References

- 1.DIgSILENT (2012) PowerFactory users manual 14.1—power system analysis functions, vol II. DIgSILENT GmbH, Technical ReportGoogle Scholar
- 2.Kersting WH (2002) Distribution system modeling and analysis. CRC Press, Boca RatonGoogle Scholar
- 3.Carson JR (1926) Wave propagation in overhead wires with ground return. Bell Syst Tech J 5:539–554Google Scholar
- 4.Monfared M, Daryani AM, Abedi M (2006) Three phase asymmetrical load flow for four-wire distribution networks. In: Power systems conference and exposition, pp 1899–1903Google Scholar
- 5.Penido DRR, Araujo LR, Pereira JLR, Garcia PAN, Carneiro J (2004) Four wire Newton-Raphson power flow based on the current injection method. In: Proceedings of 2004 IEEE power engineering society power systems conference and exposition, vol 1. pp 239–242Google Scholar
- 6.Penido DRR, Araujo LR, Carneiro S (2008) Three-phase power flow based on four-conductor current injection method for unbalanced distribution networks. IEEE Trans Power Syst 23(2):494–503CrossRefGoogle Scholar
- 7.Penido DRR, de Araujo LR, Junior SC, Rezende Pereira JL (2013) A new tool for multiphase electrical systems analysis based on current injection method. Electr Power Energy Syst 44:410–420Google Scholar
- 8.Ciric RM, Padilha-Feltrin A, Ochoa LF (2003) Power flow in four-wire distribution networks. IEEE Trans Power Syst 18(4):1283–1290CrossRefGoogle Scholar
- 9.Ciric RM, Ochoa LF, Padilha-Feltrin A (2004) Power plow in distribution networks with earth return. Electr Power Energy Syst 26:373–380CrossRefGoogle Scholar
- 10.De Oliveira-De Jesus PM, Alvarez MA, Yusta JM (2013) Distribution power flow method based on a real quasi-symmetric matrix. Electr Power Syst Res 95:148–159CrossRefGoogle Scholar
- 11.IEC 61968-1 (2003) Application integration at electric utilities—system interfaces for distribution management, part 1: interface architecture and general requirements. International Electrotechnical Commission, pp 1–7Google Scholar
- 12.Shirmohammadi D, Hong HW, Semlyen A, Luo GX (1988) A compensation-based power flow method for weakly meshed distribution and transmission networks. IEEE Trans Power Deliv 3(2):753–762CrossRefGoogle Scholar
- 13.MATLAB/Simulink, The language of technical computing. Available at http://www.mathworks.com. Accessed on Feb 2013
- 14.Sunderman WG, Dugan RC, Dorr DS (2008) The neutral-to-earth voltage (NEV) test case and distribution system analysis. In: Power and energy society general meeting—conversion and delivery of electrical energy in the 21st Century, 20–24 July 2008Google Scholar
- 15.Kersting WH (2008) A three-phase unbalanced line model with grounded neutrals through a resistance. In: Power and energy society general meeting—conversion and delivery of electrical energy in the 21st Century, 20–24 July 2008Google Scholar
- 16.Blackburn JL (1993) Symmetrical components for power systems engineering. In: Series on electrical engineering and electronics. Marcel Decker, New York, pp 296–297Google Scholar
- 17.Beaty HW (2001) Handbook of electric power calculations. In: Series on electrical engineering and electronics. McGraw-Hill, New York, pp 9.13–9.14 (Chapter 9: Overhead transmission lines and underground cables)Google Scholar
- 18.Anderson PM (1995) Analysis of faulted power systems, power systems engineering series. IEEE Press, Piscataway, pp 71–83Google Scholar
- 19.IEEE recommended practice for grounding of industrial and commercial power systems. IEEE Std. 142-1991, June 1992Google Scholar

## Copyright information

© Springer International Publishing Switzerland 2014