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.