Modeling And Stablility Analysis Of Modular Multilevel Converter In DC Voltage Control Timescale

Compared to traditional AC transmission technology,flexible DC transmission systems have some incomparable advantages on long-distance power transmission,isolated island power supply and non-synchronous AC system interconnection.Modular multilevel converter(MMC)has become a preferred topology for high-voltage direct-current(HVDC)transmission system because of its significant advantages,such as,its modular design,high quality of output waveform and low loss.However,the discrete submodule(SM)structure makes it with more complex internal dynamics,which brings challenges to understanding the dynamics of the system.It is of great theoretical and practical significance to research the stability of MMC-HVDC system.How to abstract a physical model based on the existing mathematical models of MMC is the key to analyze the stability of the system.The concept of timescale and motion equation is introduced in this paper,then a small signal model of MMC based on the motion equation concept in DC voltage control(DVC)timescale is presented.The relations between the active/reactive powers and the phase/magnitude dynamics of the internal voltage vector are developed with considering the SMs capacitor voltage ripple.It is found that the fundamental frequency ripple in the capacitor voltage of SMs will result in new oscillation modes in DVC timescale when compared with the conventional two-level voltage source converter(VSC).While,the oscillation modes dominated by the double frequency ripple are faster,which is in the timescale of AC current.Therefore,the fundamental ripple should be considered in DVC timescale,while the double and higher frequency ripples can be ignored for modeling and analysis in DVC timescale.Furthermore,the coupled relationship between the reactive power and phase dynamics of internal voltage is revealed,which has great effect on the system stability property.It is difficult to extract the equivalent inertia and damping coefficients of MMC due to the complexity of MMC model.In this paper,a generalized calculation method of the equivalent inertia and damping coefficients for arbitrarily system is proposed for the first time,based on the extracted equivalent inertia and damping coefficient,the physical meaning of the model and the amplitude/phase motion mechanism of internal voltage are explained.In addition,the accuracy and validity of the proposed MMC model based onmotion equation model is verified by comparing the time domain simulation results with the detailed model,and the eigenvalues analysis show the proposed model can hold the main behaviours of concern.Furthermore,the influence factors of equivalent inertia and damping and their relationship with the stability of the system are emphatically studied.It is found that the greater the equivalent inertia and damping of MMC are,the system is more stable.The equivalent coefficients are dominantly influenced by the controller parameters,which indicates that the stability performance of the system can be improved by optimizing the controller parameters.Finally,the idea of system stability analysis under the condition of multiple computers is introduced briefly,and the general methods and steps for power equipment modeling based on motion equation are summarized.