Mathematical model of grid-connected inverter system in weak grid

Impedance-based analysis is widely used to study the grid-connected inverter system in a weak grid. The advantage of the analysis is that without knowing the accurate parameters of an inverter, its equivalent output impedance can be obtained by specific methods (e.g. the specific harmonic injection method) to investigate the system´s stability. However, using Z_grid/Z_inv to represent the phase margin (Pm) of the system is inaccurate. A more complete mathematical model of the grid-connected inverter system in a weak grid is proposed, which contains the grid impedance and the load at the point of common coupling being neglected in the traditional model. Then, the error of the Pm from the impedance-based analysis is proved in detail in theory which indicates that the Pm of the analysis can hardly reflect the real state of the grid-connected system. Simulations validate the theoretical analysis.