Modeling and Harmonic Stability of MMC-HVDC with Passive Circulating Current Filters

A modular multilevel converter (MMC) is an emerging converter technology widely used in wind power applications using high-voltage direct current (HVDC) transmission, and it has been largely investigated in medium-voltage solar harvesting as well as electric motor drives. Different from studies dealing with active circulating current control loops, this paper focuses on impedance modeling and harmonic stability studies for MMCs with passive circulating current filters (PCCFs). A power stage circuit including a PCCF is transformed and remodeled to obtain small-signal formulations. This transformation leads to additional high-order matrix computing complexity due to the added impedance subnetwork matrix from the PCCF as well as relevant crossed-frequency impacts. To simplify the computational burden, the proposed model aims to solve one arm equation instead of all six MMC arm equations. To achieve this result, additional challenges occur when the MMC is connected to a renewable energy source instead of the grid voltage, where low-level zero-sequence components might exist in the neutral point of three phases, especially in the case of no integrated advanced modular voltage balancing control, which prevents computational simplification. To overcome this challenge, further impedance matrix adjustments are conducted in this paper to theoretically suppress the impact of zero-sequence harmonics when obtaining small-signal impedance, taking into account the frequency coupling effect. Finally, simulations are carried out to validate the developed impedance model under different operating scenarios. Harmonic stability case studies of MMCs with PCCFs connected to renewable energy current sources are also presented, where frequency-domain stability analyses based on Bode diagrams are compared to time-domain simulation waveforms and FFTs, which validate the effectiveness of the proposed impedance model.