In this work, a suitable long prediction horizon (multistep) model predictive control (MPC) formulation for cascaded H-bridge inverters is proposed. The MPC is formulated to include the full steady-state system information in terms of output current and output voltage references. Generally, basic single-step predictive controllers only track the current references. As a distinctive feature, the proposed MPC also tracks the control input references, which in this case is designed to minimize the common-mode voltage (CMV). This allows the controller to address both output current and CMV targets in a single optimization. To reduce the computational effort introduced by a long prediction horizon implementation, the proposed MPC formulation is transformed into an equivalent optimization problem that can be solved by a fast sphere decoding algorithm. Moreover, the benefits of including the control input references in the proposed formulation are analyzed based on this equivalent optimization problem. This analysis is key to understand how the proposed MPC formulation can handle both control targets. Experimental results show that the proposal provides an improved steady-state performance in terms of current distortion, inverter voltages symmetry, and CMV.

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Recently, an efficient optimization strategy based on the sphere decoding algorithm (SDA) has been proposed to solve the optimal control problem underlying direct model predictive control (MPC) formulations with long horizons. However, as will be elucidated in this work, this optimization algorithm presents some limitations during transient operation of power converters, which increase the execution time required to obtain the optimal solution. To overcome this issue, the present work presents an improved version of the SDA for direct MPC that is not affected by transient operations of the power converter. The key novelty of the proposal is to reduce the execution time of the SDA when the system is in a transient by projecting the unconstrained optimal solution onto the envelope of the original finite control set. As evidenced by the simulation results, the proposed SDA is able to quickly compute the optimal solution for the long-horizon direct MPC during both steady-state and transient operation of the power converter.