Modeling And Stability Analysis Of CRH3 Emus Based On Harmonic Linerization

When the traction electrical vehicles that adopt the single-phase pulse width modulation(PWM)rectifier are connected into the traction grid,phenomena of low-frequency oscilation(LFO),harmonic instability and harmonic resonance perhaps happen.These will lead to traction blockade and jeopardize the railway operation safety.In general,the impedance model is considered as an effective way to analyze system stability.However,the existed state-space averaged model utilized by China Railway High-speed 3(CRH3)is unable to find a stable operating point;Moreover,dynamics of phase locked loop(PLL)and voltage outer-loop control is neglected during modeling.Therefore,this method will cause inaccurate modeling and stability analysis.Based on harmonic linearization,this paper takes the single-phase PWM rectifier of CRH3 electrical multiple units(EMUs)as the research object and estabilishes its open-loop and closed-loop input impedance with considering voltage outer-loop control and dyamics of PLL.In addition,this paper,which uses the impedance-based criterion,analyzes the impact of grid inductance,current control parameter and voltage control parameters on vehicle-grid system stability by Bode diagrams.First,this paper estabilishes the impedance model of CRH3 EMUs single-phase PWM rectifiers by traditional state-space averaged method.Then,based on harmonic linearization,the positive and negative mirror-frequency open-loop impedance is proposed and another positive and negative mirror-frequency impedance measurement and calculation method is put forward.In the end,frequency sweeping method is used to verify the impedance model,which accounts for the drawback of traditional state-space averaged method and proves the accuracy of positive and negative mirror-frequency impedance model.Second,second order generailized integrator-phase locked loop(SOGI-PLL)is well modeled and verified.Next,considering the outer voltage control loop,this paper estabilishes the positive and negative mirror-frequency closed-loop impedance model of CRH3 single-phase PWM rectifier,which is demonstrated on a hardware in the loop platform by frequency scanning.At last,taking high-order harmonic coupling effects into account,this paper adopts multiple harmonic linearization to obtain high-order small-signal impedance model,accuracy of which is proved by measureming its SISO impedance.Last but not least,on the basis of the estabilished high-order small-signal impedance model,not only the impedance-based criterion but also Bode diagrams are utilized to analyze the impact of the grid inductance,current controller proporational gain,voltage controller proporational gain and integral gain on the vehicle-grid system stability.It is found that the grid inductance is larger,the current controller proporational gain is smaller,the voltage controller proporational gain is samller and the voltage controller integral gain is larger,the system turns into instability more easily.At last,the conclusion is verified by Simulink simulations.The results can be applied to design CRH3 EMUs system parameters.In order to improve the stability,in the aspect of the grid,the inductance can be properly decreased;in the aspect of CRH3 EMUs,proportional gain of current and voltage controller can be properly increased and integral gain of voltage controller can be properly decreased.