Research On The Electrical Low-Frequency Oscillation In The Vehicle-Grid System Of Electric Railways

Recent years, with more and more AC-DC-AC drive electric locomotives and EMUs being put into service, the low-frequency oscillation (LFO) phenomena have occurred in the traction power supply system of electric railways. The electrical low-frequency oscillation is a complicated vehicle-grid interaction problem. Therefore, a series studies toward the vehicle-grid system are implemented based on the on-site measurement data.According to the on-site measurement data of several cases, the LFOs are classified into 3 states. The unified mathematical expression of line voltage and vehicle current during the LFO can be concluded after analysing their waveforms in the LFO state. The waveform of the d-axis component of line voltage, which is obtained by the single-phase dq transformation, coincides with the envelope of its instantaneous waveform approximatively and only contains one AC component at the LFO frequency. Utilising line voltage as the detection signal, a LFO detection method based on the improved Prony method is designed with digital filtering technique involved, and verified by the measured data.The simulation model of vehicle-grid system is to designed in reference to the LFO case which is caused by multiple CRH5 EMUs in Qingdao EMU depot. The on-site measurement data testify that the traction supply network model can be simplified as Thevenin equivalent circuit when analysing LFO. According to the dynamic responses of inner electric variables of CRH5 LSC, the control parameters are reasonably tuned by the transfer-function identification. Then, the time-domain simulation model of vehicle-grid system is built by Matlab/Simulink toolbox, which can reproduce the LFO caused by CRH5 EMUs.The dynamic behaviour of one vehicle is determined by LSC when analysing LFO problem. When discussing the frequency-domain small-signal modeling methods, the feasibilities of modeling LSC as a single-phase admittance and as a dq-axis admittance matrix are both tested by time-domain simulation. After confirming dq-axis modeling method, the difficulty of modeling a single-phase AC system in the dq-axis is pointed out and solved. This is the foundation of deriving an analytical model. Based on the small-signal analysis of the synchronous system and the AC current loop and the DC voltage loop, a 2 X 2 rank dq-axis admittance matrix is established, whose frequency-domain response is verified by simulation tests.The LSC can also be modeled directly around the linear periodic trajectory as a Linear Time Periodic (LTP) system by the Harmonic Transfer Matrix (HTM) method. A 3 X 3 rank HTM model of LSC is established according to the analysis of its control equation. The HTM model is then compared to dq-axis admittance matrix model.The 2 models of LSC are obtained by the frequency-domain small-signal modeling method, so the steady-state operation point (or trajectory) should be calculated at first when analysing the vehicle-grid system. The dq-axis operation point of the vehicle-grid system in Qingdao EMU depot is calculated. And then, the vehicle-grid system is expressed as a transfer matrix, which is defined as its frequency-domain model, according to the electrical relationship. The dominant-pole concept is proposed by Multiple Input Multiple Output (MIMO) Linear Time Invariant (LTI) theory. It can be concluded by the time-domain simulation results that the damping ratio and natural oscillation frequency reflect the LFO state and frequency respectively. The under-damped mechanism of LFO is proposed through analysing the damping ratio of the dominant pole to explain the reason why line voltage can keep oscillating with large amplitude.The research works of the damping methods for LFO can be processed from the traction network side and the vehicle side. According to the under-damped mechanism, the LFO can be damped by decreasing the equivalent impedance of traction network and by adding additional damping control. Nevertheless, it is more simple and economical to damp LFO through changing LSC control, which is also very efficient. The trajectories of the dominant poles in the complex plain along with changes of the LSC control parameters can illustrate that LFO can be damped by adjusting LSC control parameters. Thus, the accommodation number of vehicles can be increased without changing the power supply. In addition, a POD control is proposed to be adding in the LSC control according to the analysis of LFO waveforms of the line voltage and vehicle current. Its damping effect is verified by the time-domain simulation and frequency-domain analysis.