Characterization of Voltage Sags Due to Faults in Radial Systems Using Three-Phase Voltage Ellipse Parameters

A characterization and classification of voltage sags due to faults in radial systems considering the grounding method of the source using parametric equations and voltage ellipse parameters is presented in this paper. The Clarke's transformation is used to compute parametric equations in the αβ framework based on the expressions of three-phase voltages in the time domain. The parametric equations deduced allow us to calculate, point-bypoint, the values of the ellipses of each type of fault in each time. The deduced parametric equations and voltage ellipse parameters are tested in a simulated distribution system and with real data provided by IEEE 1159.2 Working Group and the Department of Energy. Also, the relation with the well-known ABC classification was established. The deduced parametric equations is a useful tool for the people that need to make decisions with limited time in order to reduce the time to obtain results and the uncertainty in the decision-making process. The value of the present work is that it is an extension of previous works which goes beyond the simple description of the ellipses and add the relation between the ellipses and the parameters of the system.