Frequency-Adaptive Energy Control for Grid-Forming MMCs Under Unbalanced Conditions

Thisarticle presents a frequency-adaptive energy control strategy for a modular multilevel converter (MMC), which is suitable for grid-forming operation under unbalanced conditions. The average components of the energy sum and energy difference feedback signals for each phase are extracted by frequencyadaptive notch filters based on second order generalized integrators (SOGIs). Frequency-adaptivity is provided by utilizing the internal frequency defined by the power-balance-based synchronization mechanism of the grid-forming control. This approach prevents the filtering performance fromdegrading under islanded operation and other weak grid conditions where large frequency variations can occur. A comparative analysis between the frequency-adaptive notch filtering (FA-NF) and an implementation based on conventional fixed-width moving average filters (MAFs) is presented. In addition to the improved performance at off-nominal frequency, the SOGI-based FA-NF implementation reduces the delay in the energy feedback signals compared to the MAF-based reference case, resulting in improved stability margins and a more damped response. The performance of the proposed energy control strategy is comprehensively demonstrated by time-domain simulations of an HVdc terminal and by experimental testing on a 50 kVA MMC prototype. Both grid connected and islanded conditions are evaluated while considering 5 different strategies for controlling the negative sequence currents during unbalanced conditions.