Small Signal Model Of Series Compensated Transmission Line Based On Vector Of Time-varying Amplitude And Time-varying Frequency For SSR Analysis

With the rapid development of new energy generation,especially the wind power generation,the problem of subsynchronous oscillation(SSO)caused by power system with new energy units has become more and more prominent.Studies have shown that one of the important characteristics of SSO caused by power system with wind power grid generation is that the frequency of electrical quantity is time-varying;and the subsynchronous resonance(SSR)of power system with wind units is different from the SSR of traditional power system with thermal power generation,it has nothing to do with the torsional vibration of the shafting,but is related to the series-compensated transmission line,which indicates the importance of the series-compensated transmission line in this problem.The current research is mainly based on SSO at one frequency point or SSO at multiple harmonic frequencies,failing to explain the phenomenon of time-varying frequency,and the existing research on SSO is mainly aimed at analyzing the dynamics and characteristics of equipment,but the modeling of the network is the state equation of LC transmission line,and haven't systematically studied the modeling and dynamic characteristics of the network.Therefore,this paper first explains the nature of the amplitude and frequency modulation of the internal potential,which can explain the frequency variation of the electrical quantity of SSR.Then,based on the timevarying amplitude and time-varying frequency vector,establishes the small perturbation model of the series-compensated transmission line,and studies the dynamics of supplementary transmission lines and the application of different small disturbance models.This new method provides a new idea for network modeling and characterization.The specific research content are as follows:(1)Reveals the nature of the amplitude and frequency modulation of the internal potential of the device.Taking the synchronous machine as an example,a small-signal model of synchronous machine used for SSO analysis is established.And analyzed the essence of amplitude and frequency modulation of the synchronous machine,which is verified by timedomain simulation.The amplitude and frequency modulation of the internal potential of the wind turbine during the SSO is verified by the actual data of a wind farm in China;and finally,the characteristics of the amplitude and frequency modulation signal are analyzed by contrasting with harmonic signal.(2)Based on the essence of amplitude and frequency modulation of internal potential,a small disturbance model of series-compensated transmission line based on time-varying amplitude-frequency vector is established,and analyzes the applicability of the dynamic and small-perturbation model of the line.According to the original mathematical relationship of the series-compensated transmission line of time-varying amplitude and time-varying frequency vector,a small perturbation model of series-compensated transmission line based on linearization of voltage and current relationship and a small perturbation model based on linearization of amplitude and frequency modulation signal are established from different linearization methods.Taking the single-machine infinity system as an example,the dynamics of the series-compensated transmission line and the applicability of the two small perturbation models are analyzed.It is found that at the resonance frequency point,the two small perturbation model are not suitable,which indicates that the model of seriescompensated transmission line are highly nonlinear.And finally take a of amplitude and frequency modulation internal potential with multiple modes as the excitation,which illustrates the limitation of the small perturbation model,and illustrates the cumbersomeness of the small perturbation model based on the linearization of the amplitude and frequency modulation signal.