An Upper Bound on Magnitude Error of Voltage Drop Phasors in Distribution Lines Due to Phase Transposition Assumption

Abstract

A renewed interest in comprehensive modeling of distribution system components arose in recent literature. This trend can be attributed to, aside from the inherent imbalance of such systems, the rapid and system-wide integration of technologies, e.g. non-linear loads and distributed generators, which further increase grid imbalance effects. Such phenomena, in turn, demand sufficiently detailed models for their proper assessment. Despite the described scenario, it remains reasonable to inquire whether approximate component models can still be used for simplifying computations without causing exceedingly high modeling error. In this context, an approximation of particular interest is assuming phase transposition for distribution lines, due to its property of impedance matrix decoupling on the symmetric component frame. In this paper, the derivation of a closed-form upper bound for voltage drop magnitude error, due to assuming transposition in a general M-phase line, is carried out. The bound is validated by means of a case study based on the IEEE 4-bus feeder considering generalized feeder geometries. Obtained results suggest that the upper bound is tight with respect to actual error and thus provides a practical means of estimating voltage drop error yielded by the assumption of distribution line transposition.

Keywords:

• power system
• distribution line
• transposition
• approximation
• error upper bound

Additional information

Notes on contributors

Henrique Pires Corrêa

Henrique Pires Corrêa received the bachelor’s degree in Electrical Engineering from the Federal University of Goiás (UFG), Brazil, in 2017, the master’s degree in Electrical and Computer Engineering from UFG, in 2019, and is currently pursuing the Ph.D. degree in Electrical and Computer Engineering at the same institution. His main topics of interest are: power distribution networks, photovoltaic systems and power system optimization.

Flávio Henrique Teles Vieira

Flávio Henrique Teles Vieira received the bachelor’s degree in Electrical Engineering from the Federal University of Goiás (UFG), Brazil, in 2000, the master’s degree in Electrical and Computer Engineering from UFG, in 2002, and the Ph.D. degree in Electrical Engineering from the State University of Campinas (UNICAMP), in 2006. He is an associate professor at the School of Electrical, Mechanical and Computer Engineering (EMC) of UFG. His main topics of interest are: modeling and control of network traffic, communication networks, computational intelligence and optimization applied to communication and power systems.

Maria Leonor Silva de Almeida

Maria Leonor Silva de Almeida received the bachelor’s degree in Electrical Engineering from the Federal University of Uberlândia (UFU), Brazil, in 2010, the master’s degree in Electrical Engineering from University of Brasília (UNB), in 2013, and the Ph.D. degree in Electrical Engineering from UNB, in 2016. She is an adjunct professor at the School of Electrical, Mechanical and Computer Engineering (EMC) of the Federal University of Goiás (UFG). Her main topic of interest is power system protection, including the protection of power systems equipped with distributed generation.