Measurement-based Analysis of the Harmonic Couplings Below the Switching Frequency of Single-Phase Inverter-Based Resources

The impedance model of inverter-based resources can be obtained with a white-box approach if all system information is readily available, or by a black-box approach via experimental or simulation measurements. The later becomes very attractive when studying the relevance of complex characteristics such as frequency couplings, i.e., when the inverter observes a voltage harmonic distortion at its terminals and reacts to it by injecting a current distortion in another harmonic. This paper presents a mathematical development for a measurement-based approach with the linear minimum mean squared errors formulation to obtain a frequency coupled Norton equivalent of inverter-based resources (admittance matrix and current spectrum). The method is tested with a detailed model of a small-scale single-phase inverter for photovoltaic generation and the results are presented as 3D bar plots which show that harmonic couplings for such device below the switching frequency should not be a concern and can be safely neglected for system scale studies.