This article presents a new approach for classification and localization of voltage sags triggered by symmetrical and unsymmetrical faults in electricity networks. The proposed method utilizes five unique parameters of three-dimensional (3-D) polarization ellipse (PE) obtained from the mapping of three-phase voltage signals in 3-D coordinates. The decision boundaries, which are set by the parametric equations exploiting the five ellipse parameters, namely, elevation, azimuth, tilt angles, semi-major axis, and semi-minor axis, are used to classify the fault-initiated sags. The localization of faults is conducted from the parametric equations demonstrating the variation of ellipse parameters with respect to distance from the fault-location. These parametric equations would be helpful to make decision faster and thereby, eliminate the uncertainty in decision-making process. The applicability of the proposed method is tested and validated using real data measured by DOE/EPRI, the recorded waveforms of IEEE 1159.2 Working Group, and the data extracted from the simulation of faults at several feeders of IEEE 14-bus test system using RSCAD and Real Time Digital Simulator (RTDS) platform.