Multi-Functional Impedance Measurement by Means of Fractional-Order Harmonic Injection

As power electronic converters increase in scale, impedance measurement has become critical for assessing system stability, detecting islanding, and performing other critical analyses. This paper derives the impedance from the voltage and current responses measured after controlled perturbations, employing d-q frame impedance matrices. A static var generator (SVG) with redundant capacity is employed as the perturbation source, and a fractional-order repetitive control (FORC) strategy is introduced to inject the multi-frequency signal efficiently, eliminating the need for additional hardware. By optimizing the perturbation design and suppressing the dynamic error of the phase-locked loop, the method achieves both convergence and accuracy. Comprehensive simulations and experiments validate the approach.