Frequency scanning of weakly damped single-phase VSCs with chirp error control

The chirp sweep is a go-to wide-band impedance measurement technique when speed and simplicity are of main concern. Additionally, the time-frequency trait of chirp scans provide unique benefits for systems exhibiting frequency couplings - a phenomenon often encountered in single-phase VSCs. Unfortunately, time domain interpretation of chirp responses are inaccurate if the VSC-based system exhibits weak damping, as the free response induced by the chirp cannot be safely neglected. We quantify this error for linear(ised) time-invariant and time-periodic systems, with impedance representations of scalar transfer functions and harmonic transfer functions, respectively. An observer termed the Multiple Chirp Reference Frame Filter is proposed which enables real-time estimation of the harmonic transfer functions and their corresponding chirp errors. By controlling the relative errors to negligible values, the chirp exhibits low rate around resonances and high rate elsewhere. An experimental admittance sweep of a single-phase STATCOM operated by dispatchable Virtual Oscillator Control, consolidates the proposed approach as a simple frequency scan technique for weakly damped and frequency coupled systems.