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In this paper, a generalized multiband hysteresis modulation and its characterization have been proposed for the sliding-mode control of cascaded H-bridge multilevel-inverter (CHBMLI)-controlled systems. A frequency-domain method is proposed for the determination of net hysteresis bandwidth for a given desired maximum switching frequency of the inverter. The switching transition concept of Tsypkin's method and the describing function of nonlinear relay have been used for the derivation of results. A hierarchical switching algorithm has been suggested for the modular cells of the cascaded multilevel inverter. The hierarchy of each cell is swapped sequentially to provide the self-balancing capability in case the dc-link voltage is supported by the capacitors. The simulation and experimental verification of the derived results are provided through a single-phase distribution static compensator (DSTATCOM) model. The application in the three-phase system has been shown through simulation studies on a 3.3-kV distribution-system compensation using DSTATCOM. Verification on both single- and three-phase systems is obtained using a five-level cascaded-multilevel-inverter topology.
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Gupta et al. (2009) studied this question.
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