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A multilevel H-bridge StatCom inherently contains redundancy in the available switching states. This paper develops a variation on the typical model predictive control scheme which is able to exploit this redundancy to simultaneously balance the H-bridge capacitor voltages, provide excellent current reference tracking, and minimize converter switching losses. The scheme consists of a dead-beat current controller that has been integrated with heuristic models of the voltage balancing and switching loss characteristics. The integration of a pulsewidth modulation scheme is also described. Simulation and experimental results are presented that confirm the correct operation of the control and modulation strategies. Comparison with traditional control and modulation schemes is provided in terms of the key performance indicators associated with multilevel H-bridge StatComs.