Power electronic traction transformers (PETTs) will be increasingly applied to locomotives in the future for their small volume and light weight. However, similar to conventional trains, PETTs behave as constant power loads and may cause low-frequency oscillation (LFO) to the train-network system. To solve this issue, a mathematical model of the PETT is firstly proposed and verified based on the extended describing function (EDF) method in this paper. In the proposed model, the LLC converter is simplified to an equivalent circuit consisting of a capacitor and a resistor in parallel. It is further demonstrated that the model can apply to various LLC converters with different topologies and controls. Particularly, when the parameter differences between cells are not obvious, the PETT can be simplified to a single-phase rectifier (i.e., conventional train) by equivalent transformation. Based on the model of PETT, the system low-frequency stability and influential factors are analyzed by using the generalized Nyquist criterion. Lastly, the correctness and accuracy of theoretical analyses are validated by off-line and hardware-in-the-loop simulation results.

In DC distributed power systems (DPSs), the complex impedance interactions possibly lead to DC bus voltage oscillation or collapse. In previous research, the stability analysis of DPSs is implemented based on mathematical analysis in control theory. The specific mechanisms of the instability of the cascade system have not been intuitively clarified. In this paper, the stability analysis of DPSs based on the traditional Nyquist criterion is simplified to the resonance analysis of the series-connected port impedance (Z = R + jX) of source and load converters. It reveals that the essential reason for impedance instability of a DC cascade system is that the negative damping characteristic (R < 0) of the port the overall impedance amplifies the internal resonance source at reactance zero-crossing frequency. The simplified stability criterion for DC cascade systems can be concluded as: in the negative damping frequency ranges (R < 0), there exists no zero-crossing point of the reactance component (i.e., X = 0). According to the proposed stability criterion, the oscillation modes of cascade systems are classified. A typical one is the internal impedance instability excited by the negative damping, and the other one is that the external disturbance amplified by negativity in a low stability margin. Thus, the impedance reshaping method for stability improvement of the system can be further specified. The validity of the simplified criterion is verified theoretically and experimentally by a positive damping reshaping method.