Impedance Analysis of Grid Forming Control Based Modular Multilevel Converters

Grid-forming control(GFC)is promising for power electronics based power systems with high renewable energy penetration.Naturally,the impedance modeling for GFC is necessary and has gained significant attention recently.However,most of the impedance analyses for GFC are based on a twolevel converter(TLC)rather than a modular multilevel converter(MMC).MMC differs from TLC with respect to its dominant multi-frequency response.It is necessary to analyze the impedance of GFC-based MMC owing to its superiority in highvoltage direct current(HVDC)transmission to interlink two weak AC systems with high renewable energy penetration.As the main contribution,this paper presents the AC-and DC-side impedance analyses for the GFC-based MMC with both power and DC voltage control using the harmonic transfer function(HTF),and compares the impedances of GFC-based MMC and TLC.It is inferred that although the impedance is mainly influenced within 200 Hz,the instability still could occur owing to negative resistance triggered by relatively larger parameters.The difference in AC-side impedance with power and DC voltage control is not apparent with proper parameters,while the DC-side impedance differs significantly.The generalized Nyquist criterion is necessary for AC-side stability owing to the relatively large coupling terms under GFC.Moreover,the coupling between AC-and DC-side impedances is noneligible,especially considering the DC-side resonance around the system resonant peak.The effects of parameters,system strength,and virtual impedance on the impedance shaping are analyzed and verified through simulations.