Linear Approximations for the Influence of Phasor Angle Difference Errors on Line Parameter Calculation

Phase angle measurements from phasor measurement units (PMUs) may have errors that can significantly affect line parameter calculation. In this paper, approximate expressions for the influence of phase angle difference errors on line parameter calculation are derived. Specifically, first the PMU phase angle error at both ends of a line is analyzed and an equivalent synchronization error is defined; second, approximated expressions for the influence of current and voltage phase angle difference error on the line parameters are derived. The voltage amplitude ratio on the relative error of line reactance, resistance, and capacitance measurement through the π-type equivalent model are considered. The influence of voltage and current phase angle difference error on reactance and resistance is shown from the perspective of relative sensitivity. The relative sensitivity expressions in active power form are given and the identifiable conditions of line reactance parameters based on PMU data are given. In addition, this paper presents the influence mechanism of voltage magnitude and discusses the case of synchronization issue. Finally, the accuracy of the sensitivity equations is verified by simulations, and the influence of the voltage amplitude ratio and the line flow on the identification result is quantitatively analyzed.