A fault classification and voltage sag parameters computation using voltage ellipses in Clarke's domain is presented in this paper. The voltage sag parameters computed are the point-on-wave of initiation and recovery, residual voltage, and phase-angle jump. A change in the phase reference in Clarke's transformation is proposed to simplify the fault classification procedure. The point-on-wave of initiation and recovery are defined based on the reference circle in Clarke's domain described by the system during normal operation. The residual voltage and phase-angle jump are computed using the expressions of alpha and beta components in Clarke's domain and using some trigonometric theorems. The proposed fault classification and voltage sag characteristics computation are applied to real data provided by IEEE 1159.2 WG. The proposed fault classification algorithm is capable of classifying events and computing the residual voltage and phase-angle jump. Also, the voltage sag duration of short events and multistage events is successfully computed. This work is an incremental contribution in the field of voltage sag analysis in the time domain using Clarke's transformation.