Abstract
This paper develops a frequency-dependent analytical representation for a multilevel cascaded converter, with fundamental frequency switching. The gain and phase angle are studied with the firing angle as a parameter, where the converter is subjected to oscillatory excitation at a range of frequencies. This paper presents analytical formulae for a single cell and for a generic cascade multilevel converter where the number of cells is a parameter. Also, the formula for fundamental frequency studies is separately developed. The equivalent capacitance concept is introduced and its convergence to a constant value for high frequencies is demonstrated. The analytical formulae are tested against detailed digital simulation and good matching is reported. The formulae developed in this study will be of particular importance in studying interactions between a multilevel STATCOM and the host ac grid (similar to harmonic resonance) and in studying converter transient responses.
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