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The modular multilevel converter (MMC) has become one of the most promising candidates for medium-/high-power applications, specifically for high-voltage direct current transmission systems. This paper proposes a control strategy for the MMC based on the sum-of-squares decomposition method. A bilinear mathematical discrete model of the MMC is derived in the rotating reference frame by including the dynamics of ac-side currents, circulating currents, dc-side current, and stored energy of the converter. The coordinates of the developed model are transformed to the origin, and the steady-state operating point of the MMC is calculated based on the desired reference values of the states. A quadratic Lyapunov function is defined and by converting the Lyapunov difference inequality to an SOS problem, a stabilizing controller is designed. The designed controller not only guarantees the Lyapunov stability of the states, but also controls the external and internal dynamics of the MMC with only one controller, instead of using several proportional-integral controllers. To improve the region of stability of the MMC, an optimization problem is formulated and solved, so the controller can stabilize the MMC from an initial operating point far from the steady-state operating point. The performance of the proposed strategy for a 20-level MMC is evaluated based on the time-domain simulation studies and is compared with the existing control methods. [ABSTRACT FROM PUBLISHER]

The modular multilevel converter (MMC) is a potential candidate for medium/high-power applications, specifically for high-voltage direct current transmission systems. One of the main challenges in the control of an MMC is to eliminate/minimize the circulating currents while the capacitor voltages are maintained balanced. This paper proposes a control strategy for the MMC using finite control set model predictive control (FCS-MPC). A bilinear mathematical model of the MMC is derived and discretized to predict the states of the MMC one step ahead. Within each switching cycle, the best switching state of the MMC is selected based on evaluation and minimization of a defined cost function. The defined cost function is aimed at the elimination of the MMC circulating currents, regulating the arm voltages, and controlling the ac-side currents. To reduce the calculation burden of the MPC, the submodule (SM) capacitor voltage balancing controller based on the conventional sorting method is combined with the proposed FCS-MPC strategy. The proposed FCS-MPC strategy determines the number of inserted/bypassed SMs within each arm of the MMC while the sorting algorithm is used to keep the SM capacitor voltages balanced. Using this strategy, only the summation of SM capacitor voltages of each arm is required for control purposes, which simplifies the communication among the SMs and the central controller. This paper also introduces a modified switching strategy, which not only reduces the calculation burden of the FCS-MPC strategy even more, but also simplifies the SM capacitor voltage balancing algorithm. In addition, this strategy reduces the SM switching frequency and power losses by avoiding the unnecessary switching transitions. The performance of the proposed strategies for a 20-level MMC is evaluated based on the time-domain simulation studies. [ABSTRACT FROM PUBLISHER]