Three-Phase Impedance Measurement for System Stability Analysis

The purpose of this work is to review three-phase impedance measurement methods, with an emphasis on practical issues such as instruments required, form and level of injection, background harmonics, and measurement noise. In general, measuring three-phase impedance requires special frequency response analyzers that are capable of injecting two independent voltage or current signals at a sufficiently high level compared to the operational voltage and current of the system, and measuring three-phase voltages and currents simultaneously. Since such instruments are not commercially available and are difficult to construct in general, this paper discusses measurement techniques using existing commercial frequency response analyzers, power amplifiers and injection transformers. Different methods to inject a voltage perturbation into three-phase circuits are reviewed and applied to determine the small-signal impedance in both positive and negative sequences, with or without coupling. The proposed methods allow to measure sequence impedances over a wide frequency range for stability analysis and control design of three-phase power electronic systems.