Impact of the Grid Impedance on the Single-Phase Grid-Tied Inverter Output Impedance Concerning the Frequency-Coupling Effect of the PLL

In the inverter-grid interconnected system, the impedance model which breaks the entire system into two independent subsystems is widely adopted to facilitate the stability analysis. This paper shows that the inverter output impedance Z(o) may be erroneously estimated if the frequency coupling effect of the phase-locked loop (PLL) is overlooked. To fully capture the dynamic interactions between the single-phase inverter and the grid, a multifrequency admittance matrix is proposed based on the linearized small-signal PLL model. Further on, a developed single-frequency output impedance model characterized by clear physical meaning is derived to facilitate the resonance identification and the stability assessment. It is found that Z(o) also depends on the grid impedance, which significantly influences the interconnected system stability under the weak grid. Using the impedance-based stability criterion, the stability of the single- phase grid-tied inverter system can be clearly identified. The close match between the theoretical output impedance curve and the measurement result validates the correctness of the proposed impedance model. The experimental waveforms also verify that the dynamic interactions contributed by the frequency-coupling effect of the PLL and the grid impedance.