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In this paper, the imbricated cells multilevel converters are studied and modeled from a control viewpoint. These converters make use of several switches connected in a series, which allows using switches with reduced voltage ratings; these low voltage switches have lower conduction losses and can switch at higher frequency. In addition to this feature common to all converters using series connected switches, the control signals of multilevel converters can be phase shifted to increase the apparent switching frequency and improve the dynamic performances of the whole converter. It is shown that a multilevel inverter leg, composed of p pairs of switches and p-1 capacitors, forms a multivariable nonlinear system that cannot be properly modeled by standard methods such as state-space averaging. The transient behavior of this system depends on the current harmonics and their phase shift with the different control signals. A specific model is detailed, studied, and used to illustrate the properties of these converters. In particular, the natural balancing of the voltage across the switches is demonstrated and the time constants involved in this process are determined.
Meynard et al. (1997) studied this question.