Detailed and comprehensive mathematical modeling of flying-capacitor stacked multicell multilevel converters

Abstract

Purpose – This study aims to propose a mathematical model for stacked multicell converters (SMCs), to be exploited in the analytic determination of natural voltage balancing dynamics of the flying-capacitor (FC) stacked multicell multilevel converters, i.e. investigations of the start-up behavior, dynamic response, and natural voltage balancing phenomenon. Design/methodology/approach – The crux of the proposed strategy is based on the closed-form analytic solution derivation for the switching functions used in the switching of the SMCs operated under phase disposition (PD) and phase shifted carrier (PSC) pulse width modulation (PD-PSC-PWM) technique. Hence, the suggested approach develops an analytic solution for the Fourier series and associated Fourier coefficients pertinent to the switching functions of the SMCs by obtaining the switching instants of the PD-PSC-PWM modulator in terms of Kapteyn series when the frequency of the triangular carrier waveform (fc) and that of the sinusoidal reference waveform (fr) have an integer ratio, i.e. f c · f r −1=k, k∈N. Findings – This approach results into a model, first order differential equation based model, which can be readily developed for the SMCs with any number of levels expediting the investigation of their performance. Furthermore, by an experimental scrutiny conducted on a 4×2-cell-nine-level topology of an SMC, it is inferred that under PD-PSC-PWM modulation technique, FC voltages balance naturally for higher number of stacks and cells, therefore the natural balancing exist for high-level SMCs. Research limitations/implications – Despite the sophistication of the proposed methodology and mathematical model, this study presents an alternative approach with high potential of applicability for derivation of the multilevel converter mathematical model exploiting the Kapteyn (Bessel-Fourier) series. Practical implications – Numeric computation results of the proposed analytic model for the SMCs and the simulation results as well as investigational measurements taken from 2×2-cell-five-level and 4×2-cell-nine-level experimental set-ups are presented in order to substantiate the suggested approach, derived model, and verification of natural balancing. Originality/value – This article and its innovations are original.