D-Q Impedance Modeling and Stability Analysis of a Three-Phase Four-Wire System With Single-Phase Loads

The impedance-based method has been widely adopted for the stability analysis of ac systems. The
d-q
frame impedance modeling method is commonly used for balanced three-phase three-wire system analysis because it transforms the system into a time-invariant one and makes linearization achievable. However, for three-phase four-wire systems with considerable neutral line impedance, it is not feasible to directly apply the conventional
d-q
frame impedance modeling method. This article exploits the virtual frame concept to model and analyze the stability of a three-phase four-wire system with single-phase loads in a time-invariant framework. The upstream and downstream impedance models are proposed, which can accurately predict system stability conditions. The proposed models can be used for impedance specifications and assist system-level design from the stability perspective. Both simulation and experimental results validate the model and demonstrate its effectiveness in analyzing the stability of a three-phase four-wire system.