Impacts of Dynamic Frequency Feedback Loop in SOGI-PLL 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 second-order generalized integrator (SOGI)-based phase-locked loops (PLLs) have been widely used and also have significant impacts on the LFO. In the SOGI-PLL, the frequency signal is dynamically feedback from PLL to SOGI for adapting frequency variety, which causes complex nonlinearity and may deteriorate the small-signal stability of train-network systems. In previous works, the small-signal impedance model of train supposes that the feedback frequency is quasi-steady-state, which ignores impacts of dynamic frequency feedback loop (DFFL) on system-level stability and causes inaccurate analysis results. Therefore, this article builds an improved impedance model of train in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> frame with considering the DFFL. Compared with fixed frequency feedback loop (FFFL) based SOGI-PLL, the DFFL-based SOGI-PLL results in an additional negative resistance behavior, which is more likely to induce the LFO. Moreover, based on proposed impedance model of train, three FFFL-based SOGI-PLLs are compared among the filtering capability, phase-locked error and negative resistance range. Finally, experiment results by hardware in the loop (HIL) platform and real low-power experimental platform are employed to verity the correctness of theoretical analysis results.