Research On Mechanism And Suppression Of The Low Frequency Oscillation In Train-network System Of Electric Railways

With the fast development of Chinese electric railways,more and more AC-DC-AC electric trains are put into operation,which enhances the transport efficiency and speed of the electric railway.However,complex electrical interactions between control loops of electric trains and the traction network may also cause the low frequency oscillation(LFO)phenomenon in the traction network and electric train cascade system(hereinafter train-network system)if their parameters are mismatching,which causes the malfunction of the protection system and delay the normal transportation organization.Therefore,this thesis focuses on the LFO issue of the train-network system in electric railways and systematically develops the theoretical researches including impedance modeling,stability criteria,mechanism and suppression in the train-network system.The main works of the thesis can be summarized as follows.(1)The quadrature signal generator(QSG)is widely implemented in single-phase converter of electric trains to create the virtual β component for achieving the Park transformation and synchronous phase locked.A mapping approach is proposed based on the harmonic balance principle,which can map the transfer function of QSG from αβ frame to dq frame for any QGG whose transfer functions are known.Furthermore,a detailed impedance model of the four-quadrant converter(4QC)in the electric train is built with considering the phase-locked loop(PLL),dc-link voltage controller,current controller and modulation modular,which provides a way to get the impedance model of single-phase converter in dq frame.(2)In dq frame,the thesis proposes a novel forbidden-region-based stability criterion based on the second-order impedance ratio matrix and estimation principles of its eigenvalues.Compared with existing forbidden-region-based criteria,the proposed criterion has less conservatism.As a result,it can predict the stability of multiple input and multiple output(MIMO)systems more accurately and simply.Additionally,based on the forbidden-region-based criterion and passive theory,two impedance matching specifications that decouple parameters of electric trains and parameters of the traction network are derived.When parameters of either side of traction network subsystem or electric train subsystem are known,individual impedance specifications for another subsystem can be provided,such as magnitude,real-part and so on.It avoids the parameters’ coupling between subsystems when judging the stability of MIMO cascade system.(3)Since every element in the dq impedance matrix of the electric train is a high-order multinomial,it is difficult to directly reveal the impacts of control loops on the train’s impedance and stability of the train-network system.Therefore,considering the actual occurrence condition of the LFO,a simplified and analytical impedance model of the electric train is derived,which reveals reasons why dd channel impedance and qq channel impedance of the electric train have negative resistance behavior.Moreover,based on equivalent single input and single output(SISO)model of the train-network system,the in-depth stability analysis results elaborate how the introduced negative resistor causes the LFO and clarify key influence factors of the LFO.(4)The small-signal stability theory cannot explain the mechanism of sustained LFO and is failed to calculate its oscillatory magnitude.Therefore,considering the impact of saturation limiter in the 4QC on the LFO,a closed-loop transfer function of the train-network system with separating the linear part and the nonlinear part is established.Analysis results indicates the sustained LFO is a kind of self-excited oscillation caused by the saturation limiter.Based on the describing function,calculating the oscillatory frequency and oscillatory magnitude approximately,which provide a reference to design the threshold of protection device.(5)In order to reduce the frequency range of negative resistance and increase the impedance magnitude of the 4QC.This thesis proposes virtual impedance control strategy based on proportional differential(PD)feedback of the input current.Additionally,in order to enhance the adaptability of proposed method when parameters of the train-network system are dynamically changing,an adaptive dynamic gain control strategy is proposed.According to the oscillatory amplitude of the measured dc-link voltage,the adaptive strategy can provide appropriate dynamic PD gain to guarantee that the oscillatory amplitude of voltage is within the acceptable range.In summary,this thesis establishes the frequency-domain impedance model and impedance matching specifications of the train-network system in dq frame.Analysis results reveal the mechanism of the LFO and approximately calculate the oscillatory frequency and oscillatory magnitude of the sustained LFO.Lastly,a simple virtual impedance control strategy is proposed to suppress the LFO.The field measurement results and time domain simulation results verify the validity and correctness of theoretical analysis results.This thesis provides a theoretical reference for solving the LFO issue in the train-network system of electric railway.