Modular multilevel converters (MMC), based on cascading of half-bridge 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 high voltage direct current transmission, railway interties and medium voltage industrial motor drives. Analyzing 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 treats a frequency-domain methodology for computing inner variables of the MMC with half-bridge 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 variables of the cell strings are computed in the frequency domain by iterated convolution. It is shown that the proposed methodology, where all calculations are made in the frequency domain, can accurately reproduce the results from a PSCAD simulation. Furthermore, the model is successfully employed as part of an optimization algorithm for maximizing the power handling capability of the converter by appropriately controlling the circulating current and zero-sequence ac-side voltage. Results from this work point to significant possibilities for improvement.