Impacts of Quadrature Signal Generation-Based PLLs on Low-Frequency Oscillation in an Electric Railway System

Abstract

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> 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.