Asymmetric operation of the power grid will seriously deteriorate the control performance of grid-forming converters and induce instability risks. Traditional linear time-invariant modeling is difficult to accurately characterize the periodic time-varying characteristics of the system under asymmetric conditions

resulting in theoretical limitations in stability assessment. To this end

this paper innovatively introduces the linear time-periodic (LTP) theory

establishes a periodic time-varying state space model of the grid-forming converter under an asymmetric power grid

and accurately characterizes the periodic time-varying dynamic behavior of the grid-forming converter under an asymmetric power grid. Based on the Floquet eigenvalue analysis method

the evolution law of the system characteristic index with the variation of the bandwidth/damping of the positive and negative sequence current loops under different control methods is described

and the influence of the positive and negative sequence current loops of the grid-forming converter on the stability of the periodic time-varying system under the asymmetric power grid is systematically revealed. Theoretical analysis shows that

under a three-phase asymmetric power grid

the negative sequence current loop of the grid-forming converter is sensitive to parameter changes. Low damping or high bandwidth is prone to cause instability

while the positive sequence current loop has better robustness. Time-domain simulation and hardware-in-the-loop experiments verified the accuracy of the model and the universality of the conclusion

providing an important theoretical support for the optimization of control strategies and parameter tuning of grid-forming converters in non-ideal power grids.