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

This paper 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 frequency-adaptive 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 from degrading 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 (MAF) 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.