This paper presents an impedance-based model to systematically investigate the interaction performance of multiple trains and traction network interaction system, aiming to evaluate the serious phenomena, including low-frequency oscillation (LFO), harmonic resonance and resonance instability. The train-network interaction mechanism is therefore studied and one presents a detailed coupling model for investigating the three interactive phenomena and their characteristics, influential factors, analysis methods and possible mitigation schemes. In the Part I of the two-part paper, the measured waveforms of such three phenomena are firstly characterized to indicate their features and principles. An interactive model of the train-traction network system for investigating the three problems is then presented. In order to reveal the interaction mechanism, the all-frequency impedance behaviors of the electric trains and traction network are equally modeled. In which, an impedance-based input behavior of the train is fully investigated with considering available controllers and their parameters in DQ-domain. While, the entire traction network, including traction transformer, catenary, supply lines, is represented in a frequency-domain nodal matrix. Furthermore, the impedance-frequency responses of both electric train and traction network are measured and validated through frequency scan method. Finally, a generalized train-network simulation and experimental systems are proposed for verifying the theoretical results of the two-part paper.

Low-frequency oscillation (LFO), harmonic resonance, and harmonic instability phenomena in high-speed railways (HSRs) result from the interactions between multiple electric trains and the traction network. A train-network interaction system and a unified impedance-based model are therefore presented to reveal the mechanism of these three phenomena in Part I of the two-part paper. Part II of the paper presents and compares the detailed simulation and experiment results to investigate the available possible influential factors, verifications, and discussions of the three phenomena. The influential factors include the following: 1) four-quadrant converter (4QC) parameters involving the control parameters of the current controller (CC), the voltage controller (VC), and the phase-locked loop (PLL); 2) network parameters involving the utility power system, traction transformer, primary/secondary supply lines, catenary lines, and autotransformers (ATs); and 3) different numbers and positions of trains and railway lines will also be considered and discussed. In order to validate the theoretical results, the time-domain simulation and experiment system have been conducted. Finally, the differences and the relations among the three phenomena are discussed.

This paper presents an impedance-based method to systematically investigate the interaction between multiple trains and a traction network, focusing on evaluating the harmonic instability problem. First, the interaction mechanism of the multitrain and the traction network is represented as a feedback interconnection of the two subsystems, i.e., an equivalent output impedance of the traction network and an equivalent input admittance of the multitrain. Then, the harmonic instability is evaluated through a series of pole-zero diagrams drawn from the closed-loop transfer matrix of the multitrain and network system. The interaction system is unstable, and the harmonic instability will happen if there are some high-frequency poles of the closed-loop system locating in the right-half plane. This method is used for analyzing the harmonic instability phenomena, the characteristics, influential factors, and potential mitigation schemes. The theoretical results are further validated by the simulations and experiments.

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 integration of photovoltaic (PV) system into electrified railways holds promising prospects. However, with the integration of PVs, traction power supply system (TPSS) has transformed into complex hybrid system with multiple sources and loads, including both AC and DC converters. Traditional small-signal stability enhancement methods designed for vehicle-network system are challenging to apply in multiple converter configurations. To address this challenge, virtual impedance control with adaptive damping gain is proposed. The damping gain adaptively adjusts with the fluctuation of the vehicle DC voltage. The damping gain decreases as the fluctuation decreases, which reduces the impact on the dynamic characteristics of the control system. This adaptive control approach extends the applicability of virtual impedance control. In addition, a comprehensive modeling method for the hybrid system is provided, including components such as the DC impedance of the PV, the AC and DC impedances of the railway power conditioner (RPC), and the AC impedance of the vehicle. AC–DC impedance coupling is considered in the modeling process. This approach solves the difficulties in analyzing the coupling between the DC impedances of the PV and RPC, as well as the AC impedances of the vehicle and RPC. On this basis, the impacts of the circuit and control parameters on system stability, as well as the effectiveness of the proposed control strategy, are quantitatively analyzed. The proposed modeling and control methods are validated through the construction of a hardware-in-the-loop test platform.