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

This work deals with the time-domain analysis of asymmetrical faults in three-phase systems. Conventional three-phase analysis provides steady-state solutions for asymmetrical faults. Transient analysis, however, is usually performed by resorting either to oversimplified approximate circuits, or to numerical methods. In this paper, a rigorous analytical methodology based on the time-domain Clarke transformation is presented for the most common asymmetrical faults in three-phase systems. In particular, it is shown that asymmetrical faults result in circuit coupling in the Clarke equivalent circuits. Circuit representation of coupling is also derived in the paper. Coupled equivalent circuits allow rigorous analytical solution of transients in case of asymmetrical faults. The analytical results derived in the paper are validated through proper numerical simulation of faulted radial systems.