Impacts of Dynamic Frequency Feedback Loop in SOGI-PLL on Low-Frequency Oscillation in an Electric Railway System

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 dq 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.