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For direct model predictive control with reference tracking of the converter current, we derive an efficient optimization algorithm that allows us to solve the control problem for very long prediction horizons. This is achieved by adapting sphere decoding principles to the underlying optimization problem. The proposed algorithm requires only few computations and directly provides the optimal switch positions. Since the computational burden of our algorithm is effectively independent of the number of converter output levels, the concept is particularly suitable for multilevel topologies with a large number of voltage levels. Our method is illustrated for the case of a variable speed drive system with a three-level voltage source converter.Index Terms-Branch and bound, drive systems, finite control set, model predictive control (MPC), power electronics, quantization, sphere decoding.

Model predictive control (MPC) has established itself as a promising control methodology in power electronics. This survey paper highlights the most relevant MPC techniques for power electronic systems. These can be classified into two major groups, namely, MPC without modulator, referred to as direct MPC, and MPC with a subsequent modulation stage, known as indirect MPC. Design choices and parameters that affect the system performance, closed-loop stability and controller robustness are discussed. Moreover, solvers and control platforms that can be employed for the real-time implementation of MPC algorithms are presented. Finally, the MPC schemes in question are assessed, among others, in terms of design and computational complexity, along with their performance and applicability depending on the power electronic system at hand.

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