Modular multilevel converters, based on cascading of halfbridge converter cells, can combine low switching frequency with low harmonic interference. They can be designed for high operating voltages without direct series connection of semiconductor elements. This has led to a rapid adoption within high-power applications such as HVDC, STATCOM and railway interties. Analysing the operation of these converters in the frequency domain poses a few challenges due to the presence of significant low-order harmonic voltages in the cell capacitors. This paper presents a frequency-domain model of the MMC converter with halfbridge cells, based on a two-stage approach. First, the circuit equations are decoupled by a simple linear transformation, whereby the circuit schematic can be separated into a dc-side and an ac-side part. Second, the switching operation within the phase arms is modelled in the frequency domain by iterated convolution. The model is verified against a timedomain simulation of a converter with ratings valid for HVDC applications. It is shown that the proposed methodology, where all calculations are made in the frequency domain, can accurately reproduce the results from the simulation.
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