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This paper presents an optimal predictive controller for a multilevel converter-based dynamic voltage restorer (DVR), which is able to improve the voltage quality of sensitive loads connected to the electrical power network. The optimal predictive controlled multilevel DVR can restore sags and short interruptions while reducing the total harmonic distortion (THD) of the ac line voltages to values lower than 1%. The DVR is based on a three-phase neutral point clamped converter to dynamically inject a compensation voltage vector in series with the line voltage, through series-connected transformer secondary windings. To assure high-quality voltages for sensitive loads, we devise optimal predictive control laws for the injected compensation ac voltages. A suitable quadratic weighed cost functional is used to choose the voltage vector, minimizing both the ac voltage errors through current injection and the dc side capacitor voltage unbalancing. The performance of the proposed predictive controller is compared to classical proportional integral (PI): synchronous frame and stationary frame (P+resonant) controllers. The line-side filter capacitor topology is compared to the regular converter-side filter capacitor. Obtained experimental results show that the ac voltages are almost sinusoidal in steady-state operation when facing balanced and unbalanced sags and short interruptions with unbalanced loads. Voltage THD is reduced to values lower than 1%; the DVR is behaving also as a series active power filter for the ac voltages.