Analytical Investigation of the Properties of Transients in Unbalanced Three-Phase Four-Wire Networks

In this paper, the theoretical properties of transients in three-phase networks, including fourth wire and unbalanced source, are systematically investigated by resorting to several analytical tools. First, a Cartesian space vector is introduced provide geometrical three-dimensional representation voltage/current transient. It shown that transient can be always represented as trajectory leaving one plane (corresponding previous steady state) towards another new state at end transient). The quantity driving from Park/Clarke zero component. Second, Clarke transformation used study original circuit superposition two independent transients: vectors components. Third, Park evaluate dq0 components voltages/currents. Since related through simple frequency shift, effects on content steady-state waveforms put into evidence. Three case studies presented solved prove results.