When multiple EMUs are simultaneously in a light-load starting condition within the traction network, it can lead to low-frequency oscillations in the traction network voltage. In severe cases, this may trigger traction locking, which poses a risk to the operational safety of high-speed trains. To address the issue of low-frequency oscillation, this study proposes a method based on virtual impedance for its suppression.

First, the impedance model of the EMUs-traction network coupling system is derived, and its stability is analyzed using the impedance ratio stability criterion and the Bode diagram. Second, based on the stability criterion, virtual impedance is incorporated into the EMU control strategy to correct the impedance characteristics of the load subsystem, thereby proposing a low-frequency oscillation suppression method. Third, an adaptive control method for virtual impedance is designed to handle the complex and dynamic working conditions, enabling the system to adjust the virtual impedance parameters and enhance the effectiveness of the suppression method. Finally, the proposed control strategy is compared with the traditional approach through a low-power experimental platform, validating the effectiveness of the suppression method.

The results of the system stability analysis indicate that the logarithmic amplitude-frequency characteristic curve of the system impedance ratio is significantly lower than 0 dB when only one unit (m=1) is connected to the traction network, and the absolute value of the system impedance ratio |T_sn(s)| is much less than 1, suggesting system stability. As the value of m increases, the amplitude-frequency characteristic curve approaches 0 dB, resulting in a decline in system stability. When m=6, the amplitude-frequency characteristic curve crosses 0 dB at 7.032 Hz, and the phase angle at the crossover frequency (f_c) is 182°. The absolute value of the phase angle exceeds 180°, and the system impedance ratio |T_sn(s)| does not meet the condition of being significantly less than 1, indicating an unstable state. Simulation results with the virtual impedance control strategy indicate that when six EMUs are connected to the traction network at the same time, when the virtual impedance R_p values are 10 Ω, 5 Ω, 2 Ω and 1 Ω respectively, the system voltage and current reach a steady state at 1.6 s, 1 s, 0.3 s, and 0.2 s, respectively. The suppression effect improves as the virtual impedance decreases. The simulation results with the adaptive virtual impedance control strategy show that when six EMUs are connected to the traction network, the system reaches a steady state in approximately 0.5 s. The voltage regulation time for the DC side of the EMUs is 0.46 s, with an overshoot of 37.71% and a post-stabilization voltage fluctuation of 58 V. Subsequently, one EMU with adaptive virtual impedance control is added every 2 seconds, resulting in a total of 11 EMUs. The system remains stable, and the virtual impedance value is reduced to 4.61. The comparative experimental results indicate that, after transitioning from the traditional control strategy to the adaptive virtual impedance control strategy, the system can rapidly recover from a low-frequency oscillation at approximately 7 Hz. Furthermore, the AC-side voltage stabilizes at 20 V, while the DC-side voltage remains stable at 40 V.

Based on the analysis, the following conclusions can be drawn: (1) A higher impedance ratio between the two sides of the EMUs-traction network coupling system results in decreased system stability. When the impedance ratio does not meet the stability criterion, system instability is induced, leading to low-frequency oscillations. (2) The incorporation of parallel virtual impedance in the control strategy for the EMU's four-quadrant converter can correct the impedance characteristics of the load subsystem, enhance system stability, and suppress low-frequency oscillation. (3) The adaptive virtual impedance control method can autonomously adjust the virtual impedance value based on the intensity of voltage oscillations on the network side of the EMU, thereby suppressing low-frequency oscillations under varying load conditions, improving the adaptability of the control strategy, and ensuring the stable operation of the EMUs-traction network coupling system across different operating conditions.