  The output impedance matrix of a grid-connected converter plays an important
role in analyzing system stability. Due to the dynamics of the DC-link control
and the phase locked loop (PLL), the output impedance matrices of the converter
and grid are difficult to be diagonally decoupled simultaneously, neither in
the dq domain nor in the phase domain. It weakens the effectiveness of
impedance-based stability criterion (ISC) in system oscillation analysis. To
this end, this paper innovatively proposes the generalized-impedance based
stability criterion (GISC) to reduce the dimension of the transfer function
matrix and simplify system small-signal stability analysis. Firstly, the
impedances of the converter and the grid in polar coordinates are formulated,
and the concept of generalized-impedance of the converter and the grid is put
forward. Secondly, through strict mathematical derivation, the equation that
implies the dynamic interaction between the converter and the grid is then
extracted from the characteristic equation of the grid-connected converter
system. Using the proposed method, the small-signal instability of system can
be interpreted as the resonance of the generalized-impedances of the converter
and the grid. Besides, the GISC is equivalent to ISC when the dynamics of the
outer-loop control and PLL are not considered. Finally, the effectiveness of
the proposed method is further verified using the MATLAB based digital
simulation and RT-LAB based hardware-in-the-loop (HIL) simulation.
