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This study presents an efficient control technique for computing the optimum space-vector voltage in power converters. The presented optimized direct power control (ODPC) provides a closed-form formula for the converter space-vector voltage, which, based on Lagrange operators for the optimum trajectory, provides the commanded complex apparent power. The voltage required by the ODPC is obtained with a standard modulation that synthesizes the mean value required during the control cycle. The converter's performance using the ODPC algorithm improves over existing DPC-based algorithms that use constrained optimization, such as preselected space vectors or switching tables, by providing a further harmonic in content reduction, lower computational requirements, and faster time response to changes in active and reactive power commands. The use of the ODPC results in an almost instantaneous active and reactive power reference tracking, allowing for full power inversion in less than 1.0 ms under constant switching operation. Simulation results and experimental verifications are presented to validate the advantages of the proposed control algorithm. The scope of applications of this technique is those that require low harmonic impact on the ac power supply and for power quality improvement in general.