On the Use of Clarke Transformation for the Transient Analysis of Asymmetrical Faults in Three-Phase Power Systems

This work provides a theoretical/methodological contribution to the transient analysis of asymmetrical faults in three-phase systems. Transient analysis of three-phase systems is usually performed by resorting either to the instantaneous Symmetrical Component Transformation (SCT) or to numerical methods. In this paper, an analytical methodology based on the time-domain Clarke transformation is presented for the transient analysis of the most common asymmetrical faults. For each kind of asymmetrical fault, a specific circuit coupling between the Clarke αβ0 circuits is derived. Two main advantages are obtained over the SCT approach. First, the Clarke circuits involve real-valued voltages/currents, instead of complex variables as with the SCT. Second, the Clarke circuits αβ0 are not all coupled to each other. Therefore, the dynamic order of the Clarke equivalent circuits is lower than that of the SCT circuits. This property can be of interest in both the derivation of analytical and numerical solutions. A simple radial system is used to exemplify the proposed methodology.