Traditional linear time-invariant theory fails to effectively analyze the small-signal instability of grid-connected DFIG systems during low-voltage ride-through due to its neglect of periodic time-varying components. To address this issue

this paper presents a linear time-periodic (LTP) small-signal model for a single DFIG grid-connected system

and derives the system's eigenvalue indices using the state transition matrix for the first time. Based on the analysis of these eigenvalue indices

the impact of phase-locked loop (PLL) bandwidth and short-circuit ratio (SCR) of the weak grid on system stability is investigated

and thus an improved PLL control strategy is put forward. Finally

simulations and experiments verify the correctness of the theoretical analysis and the effectiveness of the proposed control strategy. The research results indicate that the established model can accurately reflect the periodic time-varying characteristics of the system

and the proposed control strategy can effectively improve system stability.