Multivariable High-Frequency Input-Admittance of Grid-Connected Converters: Modeling, Validation, and Implications on Stability

Modern grids are facing a massive integration of power electronics devices, usually associated to instability issues. In order to assess the likelihood and severity of harmonic instability in the high-frequency region, this paper develops a multivariable input-admittance model that accurately reflects the following aspects: 1) the discrete controller frequencies are defined inside a spectrum region limited by the Nyquist frequency and 2) the physical system aliases are transformed into lower frequency component inside the discrete controller. The proposed model shows that dynamic interactions are not theoretically band-limited; however, the control action tends to be strongly limited in a low-frequency range, due to the natural low-pass filter behavior of acquisition and modulation blocks. This is reflected in a reduced resistive part (either positive or negative) of the input-admittance in the high-frequency range. More specifically, considering the input-admittance passivity criterion, the excursions into the nonpassive area are very smooth at high frequencies, where the input-admittance is well-described by simply its inductive filter. Comprehensive experiments are conducted on a lab scale prototype, which includes measurements beyond the Nyquist frequency and alias identification. The experimental results well-match the theoretical model.