Characterizing Synchronized Lissajous Curves to Scrutinize Power Distribution Synchro-Waveform Measurements

A new concept, called synchronized Lissajous curve, is proposed to study synchro-waveform measurements that are obtained from waveform measurement units (WMUs) in power distribution systems. Two types of synchronized Lissajous curves are discussed. The first one is created by plotting the difference of two synchronized voltage waveforms versus the difference of two synchronized current waveforms. The second one is created by plotting the difference of two synchronized voltage waveforms versus the difference of the derivatives of two synchronized current waveforms. These two curves carry valuable and complementary information about the state of the power system and the root cause of events and disturbances. We characterize the area, rotational angle, and shape of the introduced synchronized Lissajous curves to study events and disturbances in power distribution feeders.