Modeling And Stability Analysis Of Modular Multilevel Converter Connected System In AC Current Control Timescale Based On Linear Time Periodic Theory

High voltage direct current(HVDC)technology based on Modular Multilevel Converter(MMC)plays an important role in modern power systems due to its advantages.However,the oscillation problem in a wide frequency range of the MMC grid-connected system poses a potential threat to the safe operation of the power system.According to the theory of multitimescale of power electronics in power systems,the oscillation problem in a wide frequency range of MMC grid-connected systems can be divided into different timescales,and this paper focuses on the AC current control timescale,which has a wider frequency range and is more serious stability problem.The nonlinear time-varying relationships of the MMC in AC current control timescale mainly include the product operation of the time-varying capacitance and the voltage and current in the internal dynamic process and the trigonometric function operation in the rotating reference frame of the control system.The existing modeling methods that transform the original nonlinear time-varying relationship into non-linear time-invariant relationships all have the disadvantages of relying on the subjective experience of researchers to model and unable to deal with the time-varying characteristics of phase lock control system.Therefore,this paper directly performs linearization on the periodic trajectory of the original nonlinear time-varying equation,and establish a linear time-periodic(LTP)model in AC current control timescale of the MMC grid-connected system under different grid conditions.This modeling method needs fewer assume and can be extended to various complex grid conditions.Due to the incompleteness of the LTP theory,it is impossible to determine all the characteristics of system stability with a single model,that is,the system stability,the oscillation frequency of the system instability,and the factors leading to the system instability.Therefore,this paper proposes to establish a connection between the LTP state-space model analysis and Harmonic State Space(HSS)model analysis,and their results support and complete each other,which perfect the LTP theory of system motion stability analysis.Finally,the theory is extended to the unbalanced grid conditions and the problem of the high-frequency oscillation(HFO)of the MMC grid-connected system.The details are as follows:1.Under a balanced grid condition,this paper performs the linearization directly on the time-varying periodic trajectory of the nonlinear equation of the MMC grid-connected system.Thus,the LTP state-space model of MMC in AC current control timescale is built.Because the established LTP model is extremely complex,it is impossible to give the analytical expression of the P(t)transformation matrix of the LTP system.Therefore,the relationship between the LTP system and the LTI system in the Floquet-Lyapunov theory is used to transfer the state transition matrix of the LTP system to a time-invariant Q matrix of LTI system,where the eigenvalues of the Q matrix is also called the Floquet characteristic exponents.The real part of the characteristic exponents determines the system stability,and the imaginary part of the characteristic exponents is related to the system oscillation frequency.Therefore,the analysis results are more informative,and this analysis method is called the LTP system characteristic exponents analysis method in this paper.Then the influence of MMC AC current control timescale controller parameters and operating point on the stability of the MMC grid-connected system is explored by this analysis method under weak AC grid condition.2.For the deficiency of the analysis of characteristic exponents of the LTP system to determine the oscillation frequency and the participation of each state variable,the HSS theory is introduced into MMC modeling.Besides,for the problem of the infinite-order truncation of the HSS model,the characteristic exponents are set as the theoretical basis for this truncation.The HSS model and the LTP state-space model support and complement each other,and they perfect the LTP theory of system motion stability analysis.For the HSS modeling of complex MMC systems,the method of modular HSS modeling is proposed,which is conducive to the model expansion and simplified processing.Furthermore,the simplification of the complex modular HSS model is realized according to the operating characteristics of the system.Finally,depending on modal participation factor analysis,on the one hand,the internal mechanism of the oscillation problem caused by the parameters of the AC current control timescale controller is explored.On the other hand,a simplified model adapted to the stability problem caused by the parameters of the AC current control timescale controller is proposed.3.The MMC system under unbalanced AC grid voltage conditions exhibits nonlinear periodic time-varying characteristics and more complex coupling characteristics of multiple frequency components,but the existing literature does not accurately describe those characteristics.Therefore,the LTP theory is introduced into the small-signal modeling and stability analysis of this grid condition.Since the control protection will cut off the fault line at the first time for a single-phase ground fault,when ignoring the transient process,two LTP state-space models in AC current control timescales are built under unbalanced AC grid voltage conditions during the duration of single-phase grounding and single-phase disconnection faults,respectively.Furthermore,the influence of AC current control timescale controller parameters on the system stability is analyzed comparatively under two unbalanced grid conditions.The analysis results can be used as the theoretical basis for the optimization of MMC controller parameters after the control and protection action,thereby avoiding the problem of system instability caused by the action of the control and protection system within some parameters ranges.4.For the problem of HFO of the MMC grid-connected system,the LTP system motion stability analysis theoretical system improved by the LTP state-space model and the HSS model is used to establish an MMC small-signal model suitable for HFO analysis.Furthermore,due to the mechanism analysis of HFO by the terminal voltage perspective cannot describe clearly,the perspective of internal potential that can reflect the essence of the dynamic characteristics of power electronic equipment is introduced into mechanism analysis of HFO,which clarify the leading role of the long delay link in HFO.For the fact that the existing HFO suppression scheme of adding a first-order low-pass filter to the terminal voltage feedforward branch cannot eliminate HFO completely,an improved suppressing scheme of adding a high-order low-pass filter to the terminal voltage feedforward branch and the current PI controller proportional branch at the same time is proposed by Nyquist curve analysis method,and the design method of related parameters is given.Finally,the experiment platform is used to verify the correctness of the mechanism analysis and the rationality of the proposed suppression scheme.