A characterization and classification of 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 to calculate, point by point, 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. Also, the relation with the well-known ABC classification was established. The deduced parametric equations are 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.