The wide adoption of a new type of electric trains results in multiple frequency-scale instability problems, such as low-frequency oscillation (LFO), harmonic resonance and harmonic instability. Among them, LFO has been commonly reported at electric railway depots with multiple energized electric trains. This phenomenon occurs at rail depots around the whole world, thus attracting widespread research attention. LFOs cause adverse ef-fects on the system stability and protection infrastructure of both the traction network and electric trains. This paper presents a comprehensive review of LFOs that consider both academic theoretical analysis and industrial engineering requirements. A unified mathematical model of the traction network and electric train is derived with a view to revealing the mechanism and factors that induce LFOs when these two systems interact. The study also draws deep insights from results of experimental measurements and industrial mitigation schemes already implemented in Chinese railway systems. A variety of mitigation techniques and recommendations based on theoretical principles and practical constraints are presented.

The low-frequency oscillation (LFO) phenomenon has frequently occurred in the railway electrification systems (RESs) and deteriorates the safety and reliability of the RESs. This paper proposes a simplified and analytical impedance model of the electric train and traction network interaction system (hereinafter train-network system) in the synchronous frame (-dq), which reveals that the DC-link voltage proportional-integral (PI) controller mainly brings the negative resistor to the d-d channel impedance of the train in the low-frequency range. The in-depth stability analysis elaborates that the introduced negative resistor will cause the phase margin (PM) of the eigenvalues of the impedance ratio matrix become negative under some conditions and lead to the LFO issue. Moreover, case studies also illustrate that the narrower negative real-part area (NRA) caused by negative resistor and the higher magnitude of the train-impedance in the low frequency range can enhance the stability of the train-network system. Therefore, for suppressing the LFO, a proportion-derivation (P-D) feedback of the current based on the analytical impedance model is then proposed to decrease the NRA and increase the magnitude of the train-impedance in the low frequency range. Both simulation and experimental results validate the effectiveness and correctness of the theoretical analysis.

The high-frequency negative damping characteristics of the electric train and the traction network interaction system may excite harmonic instability issues. This paper proposes a detailed impedance model and a simplified method in the αβ-frame for investigating the high-frequency impedance characteristic of the electric train. Meanwhile, the impedance model is validated by means of the frequency sweeping method. Based on the αβ-frame impedance model of the train, the negative damping range is mathematically expressed. It is helpful for analyzing the impacts of controller bandwidths and network impedances on the harmonic instability. In addition, a voltage feedforward filter combining its transfer function is proposed to enhance the system stability. Taking advantages of the proposed voltage feedforward filter, the output impedance of the train can maintain passive characteristics well in a specific high-frequency range, effectively avoiding harmonic instability issues. Simulation and experimental results validate the effectiveness of the proposed harmonic instability analysis and suppression methods.

The low-frequency oscillation (LFO) issue has occurred frequently in single-phase electric train and traction network interactive systems (hereinafter train-network systems). On a single-phase electric train, the quadrature signal generation-based phase-locked loop (QSG-PLL) has been widely used to achieve unit power factor operation. The bandwidth of the single-phase PLL is close to the frequency of the LFO, but its impacts on the LFO are not considered fully in previous works. In this article, three typical QSG-PLLs are studied in depth, and their unified model is derived in the dq frame. Furthermore, the impacts of the QSG-PLL structure and parameters on the LFO are revealed. The analysis results indicate that the QSG part plays an important role in the LFO analysis, but the parameters of the PLL part have slight impacts on the train’s impedance under the low-power operation mode. Three different QSGs can all be regarded as providing a second-order low-pass filter (LPF) to generate the virtual $\beta $ component in the single-phase system. The higher damping ratio of the second-order LPF can increase the magnitude of the train’s impedance, which is beneficial to enhance the stability of the train-network system. Finally, experimental results via hardware in loop (HIL) are employed to verify the correctness of the theoretical analysis results.

A novel forbidden-region-based criterion (N-FRBC) is proposed in modified sequence-domain for an ac grid-converter system. Compared with the forbidden-region-based criterion (FRBC) in dq-domain, the number of constraint conditions is reduced due to the mirror frequency symmetry of the impedance ratio matrix in modified sequence-domain. In addition, the improved forbidden region decreases the conservatism of the FRBC. Simulation and experimental results verify the effectiveness and correctness of the proposed N-FRBC in studying the stability issues of the ac grid-converter system.

The low-frequency oscillation (LFO) phenomenon has been frequently happened in railway electrification systems (RESs) and often caused the traction atresia of electric trains and the protection malfunction of traction system. In this letter, a mitigation approach is presented based on impedance analysis and it is found that changing the operation mode of the rectifier to diode-bridge rectification (DBR) circuit can mitigate the LFO due to increase the impedance of the rectifier. Then, combining the Prony technology, a real-time identification and mitigation approach is proposed for mitigating the LFO phenomenon. Experimental results verify that the effectiveness of the proposed method in stabilizing voltage fluctuation of traction system and identifying oscillatory frequency and corresponding attenuation factor.