Return Ratio Matrix Reconstruction Approach for Grid-Connected Inverters: Principle, Physical Insights, and Parameter Design

The stability of grid-connected inverter under weak grid can be analyzed with the return ratio matrix, which is the ratio of the inverter output admittance and grid admittance. Since the power control loop and phase-locked loop (PLL), which provide the grid current references, are asymmetrical, the return ratio matrix is nonsingular and has two nonzero irrational eigenvalues, posing a challenge to stability analysis and parameter design. To tackle this issue, the return ratio matrix reconstruction approach is proposed in this article to reconstruct the nonsingular return ratio matrix into the singular one, which has only one nonzero eigenvalue. On this basis, the parameter design sequence of power control loop and PLL is revealed and the step-by-step parameter design method is given. Finally, a 10-kVA three-phase LCL grid-connected inverter prototype is tested in the laboratory, and the experimental results are provided to verify the effectiveness of the stability analysis and parameter design with the reconstructed return ratio matrix.