Dynamic Phasor of Radial Distribution Systems

This paper develops an analytical model of an unbalanced radial distribution system consisting of a single-phase photovoltaic (PV), a three-phase induction machine load, a three-phase power factor correction capacitor (PFC), and a load. The analytical model is based on dynamic phasors (DP) for $abc$ phases. The single-phase PV model includes inverter current control [proportional resonance (PR) controller], an L, or an LCL filter. The induction machine model is based on positive-, negative-, and zero-sequence components’ dynamic phasors. The sequence-based induction machine model was converted to the DP-$abc$ reference frame and interconnected with other grid components.

The developed analytical model is capable of small-signal analysis and can be used to identify variety of stability and/or harmonic issues in distribution networks, e.g., instability due to weak grid. Impact of unbalance on system dynamic performance can also be investigated using this model. The analytical model is benchmarked with a high-fidelity model built in Matlab/SimPowerSystems where power electronicswitching details are included. The small-signal analysis results are validated via Matlab/SimPowerSystems time-domain simulations.