Flying-capacitor stacked multicell multilevel voltage source inverters: analysis and modelling

The aim of this study is to investigate the natural voltage balancing dynamics of the single/three-phase stacked multicell converters (SMCs). First, explicit analytic solutions for switching functions' implicit equations, which are, utilised in modulating of the SMCs operated under phase disposition phase shifted carrier pulse width modulation (PD-PSC-PWM) technique whereas being initiated from the Kepler's transcendental equation, are derived. Next, utilising above-mentioned calculated Kapteyn (Fourier-Bessel)-based infinite series, a time-variant differential equation-based analytical model for single/three-phase SMCs is suggested. This strategy reduces to a model that can facilitate the analytic investigation of the start-up behaviour, dynamic response and natural voltage balancing phenomenon for SMCs owning any number of voltage-levels and phase numbers. Furthermore, it is also inferred that under the PD-PSC-PWM modulation technique, the flying-capacitor (FC) voltages balance naturally for higher number of stacks and cells, hence substantiating that the natural balancing exists for high-level SMCs. Moreover, precise analysis of the experimental observations reveals that settling time of the FC voltages in the positive and negative stacks positioned in the immediate vicinity of the SMC's midpoint is higher than the settling time of the FC voltages in the correspondent positive and negative stacks outlying the SMC's midpoint.