A Synchronized Lissajous D-Axis Based on Detecting and Classifying Events in Synchro-Waveform Measurements in Unbalanced Systems

This paper presents a novel method for detecting and classifying power events in unbalanced Power Distribution Networks (PDNs) using Synchro-Waveform Measurement Units (SWMUs). The proposed approach utilizes a self-synchronized (SS) transformation to convert three-phase voltage and current into d-axis components, forming a synchronized Lissajous d-axis curve. This curve effectively captures both the occurrence of power events and the system's balance condition within a single, compact plot. A dynamic event detection mechanism is introduced, combining a sigmoid-based adaptive threshold with an Euclidean speed-based similarity score to identify disturbances. Case studies explore the effects of system unbalance, event type, location, parameters, and firing angle. Results show that the curve shape reflects event characteristics while remaining unaffected by firing angle variations. The method accurately detects both sustained and transient events using only two SWMUs, without requiring knowledge of PDN parameters, making it highly practical for modern smart grid applications.