Low-Frequency Stability Analysis of Single-Phase System With dq-Frame Impedance Approach—Part I: Impedance Modeling and Verification

The utilization of a large number of power electronic converters in the high-speed railway system results in the low-frequency instability for the single-phase vehicle-grid system. In order to probe into the problem, the impedance-based approach is adopted. This paper focuses on the dq-frame impedance modeling and verification of the single-phase converters in the electric multiple units. The closed-loop input impedance modeling methods for both single converter and interleaved converters considering the second-order generalized integrator-based phase-locked loop (PLL) are put forward. Then, the dq-frame impedance measurement method for single-phase systems based on the Hilbert transform is proposed, and the modeling approach is verified by the frequency-domain simulations on the switching models. The good agreement of the model and simulation illustrates that the modeling method is suitable and accurate enough until half of the switching frequency. It is elucidated that the single-phase rectifier's impedance has the off-diagonal characteristic and the negative-impedance characteristic on the dd channel at low frequencies. Moreover, both the current and voltage controls have influences on the negative impedance shaping, while PLL does not.