Staircase output voltage waveform for a 5-level converter 

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... control has gained much attention recently due to its property of being easily implemented, especially in the field of power converters. Power converters play an important role in the field of renewable energy: they are used to connect renewable sources to powergrids, optimize the efficiency of solar panels and wind generators (see, e.g., [1]). In some topologies, there is however a dramatic increase of the number of switches, which entails an increasing number of degrees of freedom, and complicates the controller design . There is therefore a niche of application for formal methods in order to produce correct-by-design control methods. The general function of a multilevel power converter is to synthesize a desired voltage from several levels of DC voltage. For this reason, multilevel power converters can easily provide the high power required by large electric drive systems. A multilevel converter is a power converter made of capacitors and switching cells (as well as opposite switching cells which are in complementary positions); In this paper, we consider the design of control policies for power converters with a number of levels = 5 and = 7. A multilevel converter for = 5 is schematized on Figure 1. According to the positions of the cells, one is able to fraction the load voltage. By controlling the global position of the switches during a simple fixed time-stepping procedure, it is then possible to generate a staircase voltage with levels that approximates a triangular or a sinusoidal waveform (see Figure 2, for 5 levels). The problem which arises is to select the appropriate switching control strategy among a number of combinations of switch positions which increases exponentially with the number of levels (and pairs of switches). A crucial difficulty comes from the fact that, in order to be admissible, the control of the switching cells must guarantee that the voltages across the cell-capacitors are constrained within a ...