Dynamic Model And Small-signal Stability Analysis Of MMC-HVDC Under Unbalanced Grid Conditions

Modular multilevel converter based high voltage direct current(MMC-HVDC)system has been the preferred topology of flexible HVDC projects,owing to its advantages such as the low harmonics,low switching frequency and loss and so on.The unbalanced grid conditions occur constantly,AC grid voltage and load imbalance,parameters asymmetry for example,which result in negative sequence components in AC syetem.The complex internal dynamic characteristics of MMC and the coupling between internal and external dynamic characteristics lead to distinct differences of dynamic model and the small-signal stability under balanced and unbalanced grid conditions.Therefore,the dynamic model and the small-signal stability analysis results under unbalanced grid conditions will have significant meaning and engineering value.Firstly,the mathematical model and control strategy of MMC-HVDC under unbalanced grid conditions are investigated.To mitigate the negative current,the extraction of positive and negative sequence components and negative-current suppressing controller are considered.The switching function adds the modified component due to negative-current suppressing control.Many non-ignorable positive-,negative-and zero-sequence harmonics appear in MMC by switching function.Secondly,a dynamic model of MMC-HVDC system under unbalanced gird conditions in d-q reference frame is presented,which integrates the dynamics of MMC station,control system,AC and DC system.The MMC dynamics include the emergence of the asymmetric-,negative-and zero-sequence components of first order and the positive-,zero-sequence components of second-order sub-module capacitor voltage and the asymmetric-,negative-sequence components of first order,the positive-,zero-sequence components of second-order arm current.The control system includes the dynamic process of the extraction of positive and negative sequence components,the vector current controller and the negative-current suppressing controller.A 201-level MMC-HVDC system is developed in PSCAD/EMTDC.By comparing the detailed electromagnetic transient simulation with the dynamic model under the step changes of dc voltage and reactive power with or without the negative-current suppressing controller,the proposed dynamic model is well verified.Finally,the small-signal model of the MMC system under unbalanced grid conditions is developed.Based on the eigen-analysis,the feasible region and damping of the vector current controller and circulating current suppressing controller,under both balanced and unbalanced conditions,are studied.And the dominant electric and control variables are revealed by participation factor analysis.The impact of negative-current suppressing controller on system stability is investigated.