Positive sequence, negative sequence, and coupling impedance model of a grid-connected inverter with LCL filters under unbalanced grid and stability analysis considering frequency coupling

An impedance model is the mathematical basis of stability analysis for a grid-connected inverter (GCI) system by an impedance analysis method. However, the equivalent output impedance model of GCI with an inductance-capacitance-inductance (LCL) filter under unbalanced grid voltage is missing in the existing studies, and the influence mechanism of the change of filter and other main parameters on the output impedance is still unclear. To solve the above problems, first, considering multiple links such as a phase-locked loop (PLL), a current regulator, and sampling delay, the positive sequence, negative sequence, and coupling impedance model of GCI with LCL filters under unbalanced grid voltage is built by the harmonic linearization method, and the accuracy of the impedance model is verified by the frequency scanning method. Second, the effects of PLL, bandwidth of the current regulator, and parameters of the LCL filter on the positive sequence, negative sequence, and coupling impedance are analyzed. At the same time, a comparative analysis of the differences in output impedance characteristics between the L filter GCI and LCL filter GCI is conducted. Finally, according to the Nyquist criterion of the determinant of the return difference matrix, the system interaction stability under different grid impedance conditions when the grid voltage is unbalanced is analyzed, and the correctness of the theoretical analysis is verified by time domain simulation.