Harmonic Instability and Amplification for Grid-Connected Inverter With Voltage Harmonics Compensation Considering Phase-Locked Loop

Grid-connected inverters (GCIs) with a voltage harmonics compensation function (VHCF) have been widely applied to ensure the quality of bus voltages in weak grids, while in the analysis and design process of VHCF-GCIs, the influence of the phase-locked loop (PLL) is usually ignored. To cover this gap, the harmonic instability and the harmonic amplification of the VHCF-GCI considering the influence of the PLL are explored. With the small-signal model of the PLL, the mathematical descriptions of the influence of PLL dynamics on the harmonic impedance control loop and the current control loop are derived, and the small-signal output impedance of the VHCF-GCI including the PLL dynamics is presented. Based on the impedance-based analysis, the stability and the harmonic suppression performance of the VHCF-GCI with different parameters of stability margin and the bandwidth for the PLL are studied. The study results reveal that differing from the conventional conclusion that the PLL with a high bandwidth and a high stability margin ensures stability for the GCI in a low-frequency domain, the PLL with a high bandwidth and a high stability margin brings about the instability and the harmonic amplification for the VHCF-GCI in the harmonic-frequency domain. Thus, to attain stability and harmonic suppression performance of the VHCF-GCI, the design approach for PLL parameters in a full-frequency range is presented. Lastly, the theoretical analysis is verified by simulation and experimental results.