Average modeling and control for three-phase three-level non-regenerate rectifier with unbalanced DC loads

Averaged modeling and analysis of multilevel converters

“…Using these duty cycles the average converter voltage from (2) is given by (5) where and . The midpoint potential is found from (1) assuming the current summation is zero for three wire systems, yielding (6) Equations (5) and (6) together represent the average of the converter ac terminal voltages that can be used in place of the instantaneous converter voltages in (1). Note that no assumptions have been made so far about the operation condition of the converter.…”

“…Defining , one can find that the dynamics of the voltage imbalance are governed by . (16) The typical approach to controlling Δv dc consists of adding a common component v 0 to the modulating functions v am , b bm , and v cm [5][6][7][8]. To design a controller that injects such common-mode component, the nonlinear and time-varying model (16) has to be linearized to develop a small-signal linear model.…”

“…Previous work on modeling of multilevel converters can be found in [4][5][6][7][8]. In [4] two separate models were obtained for positive and negative cycles of the ac inductor current, resulting in a discontinuous converter model.…”

“…A more recent work [5] used line-cycle averaging to remove such discontinuity However, line-cycle averaging also limits the validity of the model to half the fundamental frequency. It is also a common practice to assume balanced line conditions and develop converter models in the dqcoordinate frame [6], which limits the application of the method to balanced three-phase systems [7][8].…”