Research On The Small-Signal Stability Of A Modular Multilevel Converter Based HVDC Grid System

Modular multilevel converter(MMC)based high-voltage direct-current(HVDC)grid is an effective means to support bulk proliferation of renewable energy and realize long distance transmission of large-scale power,which provides a practical solution to solve the problem of reverse distribution of energy resources and load centers in China,so it will become an important part of the future "Energy Internet".Compared with the HVAC grid,the MMC-based HVDC grid,due to operating with a large amount of power electronic equipment,improves the power control ability and concurrently introduces the influence of complex control-loops to the system power-transfer-limit.Therefore,it is of great theoretical and engineering significance to explore the coupling mechanism of electrical links and control-loops ?)between the AC-and DC-sides,?)among multiple terminals to help figure out the stability of power transmission,guide the parameter optimization/design and propose strategies to improve stability margin.Zhangbei HVDC grid is the world's first 4-terminal,MMC-based(±500kV)HVDC grid demonstration project.Based on the actual parameters of Zhangbei project,firstly,this paper establishes a mathematical model of 4-terminal HVDC grid which can reflect the internal harmonic dynamics of MMC;then,focusing on stability issues of the MMC-based HVDC grid,modal structures and the effects of AC-system impedance characteristics are investigated thoroughly to reveal the oscillation mechanism and improve the stability margin of HVDC grid;furthermore,a supplementary frequency-deviation-based damping control(SFDC)is proposed to enhance the stability of HVDC grid in weak AC-system scenarios.(1)Establishment of the small-signal model for HVDC gridAs the model basis of small-signal stability analysis of HVDC grid,a linearized small-signal model of the 4-terminal MMC-based HVDC grid is developed through dynamic phasor method,which can accurately describe the internal harmonic dynamics of MMC,the electrical coupling of AC-and DC-sides,and the synergy of control-systems.In order to improve the flexibility and versatility of the model,this paper adopts the modular modeling method;divides the HVDC grid into four sub-systems,i.e.,converter,AC-system,control-system and DC network;and constructs the mathematical model of the 4-terminal HVDC grid through establishing the interface model among those sub-systems.The converter model can reflect fluctuation processes of the capacitor voltage(including DC,fundamental,2nd-and 3rd-order components)and the arm current(including DC,fundamental and 2nd-order components)in detail.The circulating current suppression control(CCSC)is considered in the control-system model,and the DC current limiter is considered in the DC network(overhead-lines)model.The deduced small-signal model of HVDC grid is validated based on the time-domain simulation of the system,including switched-model of the MMC stations,in the PSCAD/EMTDC platform.(2)Modal identification and analysis of the HVDC gridBased on the established small-signal model of the 4-terminal MMC-based HVDC grid,all modes(featured by eigenvalue,oscillation-frequency and damping-ratio)are identified firstly.Participation factor analysis is applied to characterize modal classification,and the modal structure of HVDC grid can be divided into four categories,i.e.,mode of ?)DC transmission-line,?)MMC internal harmonics,?)station control-system,?)multi-terminal interactions.Comparative study on modal structures of the HVDC grid and single-terminal MMC system is conducted to reveal the influence of"grid-forming" on modal classification(including characteristics of the new modes and differences of the reserved modes).From the time-domain simulations in PSCAD/EMTDC platform,damping oscillations of the poorly-damped modes can be captured,which not only verifies the correctness of theoretical analysis,but also indicates the necessity of tracking poorly-damped modes(that is,this kind of mode is likely to appear in the dynamic responses when the system is subjected to a variety of disturbances,or even cause oscillation/instability).(3)Small-signal stability of the HVDC grid under weak AC-sy stemsBased on the established small-signal model of the 4-terminal MMC-based HVDC grid,the dynamic interactions between the HVDC grid and its host AC-system(s)are investigated.Eigen-analysis is applied to identify the oscillation modes with damping-ratio rapidly decaying as the AC-system strength of each station gradually weakens.The critical value(lower limit)of AC-system strength which satisfies the small-signal stability constraint is obtained,and the dominant modes inducing system instability under weak AC-system conditions are accordingly distinguished.The results show that the weakening of AC-system strength will urge the damping-ratios of some MMC internal harmonic modes to decay rapidly,which seriously threatens the stability of HVDC grid.Therefore,in order to obtain more accurate and reliable stability-analysis results,it is necessary to describe the internal harmonic dynamics of MMC during modeling process.Besides,the oscillation characteristics and manifestation of HVDC grid under weak AC-system conditions show diversity according to the control strategy of MMC-station and the power level of HVDC grid,which makes the countermeasures to suppress oscillation/enhance system stability of more targeted.Furthermore,the dimension of "impedance-angle variation" is added to explore the influence of impedance-angle on the critical value of AC-system strength and the dominant modes.For MMC in reactive-power control mode,a new index to evaluate stability margin,i.e.,the critical operating short circuit ratio(COSCR)is proposed,with both the small-signal stability constraint and the AC-bus voltage constraint(the allowable fluctuation range of voltage amplitude is ±5%around its rated value)integrated.In order to reduce the critical value of AC-system strength in each MMC-station and improve the stability margin of HVDC grid under weak AC-system conditions,sensitivity analysis is applied to obtain the control-parameters(called "sensitive parameters")which can effectively restrain the damping-ratio attenuation of dominant modes.The PSCAD/EMTDC simulation responses show that those identified sensitive parameters(with reasonable adjustment)can quickly suppress the oscillations induced by weak AC-system strength.Meanwhile,the coupling relationship between sensitive parameters and AC-system strength on small-signal stability is investigated.The results show that the demand from HVDC grid stability for AC-system strength could be reduced,to a certain extent,if the sensitive parameters are set properly;conversely,that would be significantly increased if the sensitive parameters of improper setting.(4)Supplementary controller design for improving the stability margin of HVDC grid under weak AC-systemsConsidering some special scenarios in which the parameters of original control-system cannot be adjusted or initial value(s)is(are)not set properly,a simple but effective supplementary control,i.e.,supplementary frequency-deviation-based damping control(SFDC),is proposed to enhance the stability of HVDC grid under weak AC-system conditions.The proposed SFDC utilizes the frequency deviation between the tracked frequency from PLL and the system nominal frequency as the input signal,introduces a damping component(i.e.,active-power damping component PDK or DC-voltage damping component UDC_Dk)into the outer-loop of vector current controller.Theoretical analysis and PSCAD/EMTDC simulation results show that the proposed SFDC method can effectively mitigate the instability issues induced by lower AC-system strength,and improve the maximum power transfer capability of converter station under extremely weak AC-system conditions.Besides,the proposed SFDC can help the HVDC grid maintain stable operation even if the parameters of original control-system are not conducive to weak AC-system conditions;that is to say,the feasible region of the original control-parameters can be significantly widened by proper selection of the damping coefficient Dk within its recommended range.Furthermore,the proposed SFDC does not affect the dynamic performance of the HVDC grid to disturbances,and the new control-system still has the fault-current-limiting capability.