| With the development of high-speed and heavy-load electrical railways,a large number of ac-dc-ac electric multiple units(EMUS)and large power electric vehicles(hereinafter referred to as vehicles)have been put into operation.Some issues between the traction power supply system and vehicles(vehicle-network system)have occurred,which are high-order harmonic resonance,high and low frequency oscillations(the latter two are also named resonance instability and low-frequency oscillation).These issues are in the form of voltage and current harmonic amplification,harmonic continuous amplifying,and amplitude lowfrequency oscillating,respectively,which can cause damage to the traction substation and vehicle equipment due to the voltage increased effective value.The accuracy and effective of analyzing these different electrical characteristics of the vehicle-network system depend on the accuracy and applicability of the system model.However,the vehicle-network has its complexity and particularity:(a)Autotransformer(AT)traction power supply system has a complex structure with multiple conductors and asymmetric nature.(b)There are many types of ac-dc-ac vehicles,and the grid-connected converter generates rich high-order harmonics due to the PWM modulation.(c)When the vehicle is running,its position connected to the network is dynamically changing.Therefore,the research on mathematical modelling and oscillation mechanism of the vehicle-network system,and on suppression method is important to improve safe and stable running of high-speed and heavy-load electrical railways.For the high-speed and heavy-load electrical railways,this paper carries out the research works on the transient modelling of AT traction power supply system,the transient modelling of the vehicle-network system,the oscillation characteristics and the suppression method.Some innovative results in terms of models,mechanisms analysis and the suppression method have been achieved and some important conclusions have been reached.(1)Based on the real structure and multiple conductor nature of electrical railway allparallel AT traction power supply system,a modular equivalent circuit is built,including traction substation,and AT traction network.The differential equations of sub-modules are derived using the node voltages of traction network,the currents of conductors and ATs as state variables.According to the structure and operation conditions from the traction substation to the sectioning post,the state-space model of all-parallel AT traction power supply system is established by combining these sub-modules in order.The steady-state voltage distributions of the network,electromagnetic transients during short circuit and disconnection faults are then analyzed,and finally verify the correctness of the model.This proposed modular modelling method for all-parallel AT traction power supply system simplifies the model establishment when the topology of the network changes due to the load movements or changes of the fault location.(2)The improved dynamic phasor modelling method is proposed.This method firstly carries out the coordinate transformation of single-phase circuit,and then uses the phasor amplitude and phase as variables to derive the differential equations for the system dynamic elements,so that the model time-invariance is achieved.In addition,based on the phasedomain control of the vehicle grid-connected converters,the accuracy modelling of the voltage controller and current controller is realized.Then the small-signal models of traction power supply system including traction substation and AT traction network,and the single-phase grid-connected converter of the vehicles are established.(3)Based on the state-space model of all-parallel AT traction power supply system and Norton harmonic equivalent model of the vehicle,the state-space model of the vehiclenetwork passive system is established.Then the eigenvalue analysis for harmonic resonance of high-speed electrical railway is proposed.By calculating the eigenvalues of the system state matrix and judging the dominant modes,the natural resonance frequencies of this passive system are accurately identified.By mode shape,the harmonic resonance observabilities of node voltages of network are analyzed.Furthermore,the influence of the system different transformer parameters and catenary length on harmonic resonance frequency,and the influence of the vehicle running positions on the mode shape are analyzed.(4)Based on the small-signal model of traction power supply system including traction substation and AT traction network,and the small-signal model of the single-phase gridconnected converter of the vehicle,the small-signal model of the vehicle-network system taking into account the vehicle moving is established.The modular modelling method is also adopted,which combines the sub-modules of AT traction power supply system and the vehicle converters according to the running position of the vehicle.This system small-signal model is easy to update even if the network topology changes with the vehicle moving,and can accurately describe the inherent impedance characteristics of the network.The mechanism of high-frequency oscillation due to the interaction between the vehicle grid-connected converters and the traction power supply system,and the state variables which have great contributions to the oscillation are revealed.The influence of the controller parameters,sampling frequency,vehicle locations on the high-frequency oscillation are analyzed.Mode shape gives the observabilites of network nodes under high-frequency oscillation modes.Then a comprehensive control strategy based on resonance damping and negative sequence,harmonic and reactive current compensation for railway power conditioner(RPC)with energy storage device is proposed,which can effectively suppress the system high-frequency oscillation and balance the three phase currents on the grid side.Finally,the nonlinear timedomain simulations and actual test results verify the correctness of the theoretical analysis.(5)Based on the Thevenin equivalent circuit of the traction power supply system and the small-signal model of the vehicle single-phase grid-connected converter,the small-signal model of vehicle-network system taking into account multiple vehicles raising pantographs for preparation is established.With this model,the eigenvalue-based method is applied to analyze the system low-frequency stability.Mode shape reveals two types of low-frequency oscillations,one is due to the interaction between the vehicle grid-connected converters and the traction power supply system,and the other one is due to the interaction among the different grid-connected converters.Theoretical analysis shows that both modes may lead to system low-frequency instability.It also reveals that the occurance of the low-frequency oscillation caused by the increase number of the connected vehicles is equivalent to the unstable nature of the system that a single grid-connected converter connected to the grid and the grid is becoming weak.The state variables that contribute significantly to the lowfrequency oscillation are obtained by participation factors.The influence of the controller parameters,sampling frequency,the dc-side capacitance and the grid-side impedance on these two low-frequency modes are analyzed.Finally,the theoretical analysis are verified by the nonlinear time-domain simulations and the modal analysis based on estimation of signal parameters via rotational invariance techniques(ESPRIT)method. |
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