This paper proposes new direct power control (DPC) strategies for three-phase DC/AC converters with improved dynamic response and steady-state performance. As with an electrical machine, source and converter flux which equal the integration of the respective source and converter voltage are used to define active and reactive power flow. Optimization of the look-up-table used in conventional DPC is outlined first, to improve the power control and reduce the current distortion. Then constant switching frequency DPC is developed where the required converter voltage vector within a fixed half switching period is calculated directly from the active and reactive power errors. Detailed angle compensation due to the finite sampling frequency and the use of integral controller to further improve the power control accuracy, are described. Both simulation and experimental results are used to compare conventional DPC and vector control, and to demonstrate the effectiveness and robustness of the proposed control strategies during active and reactive power steps, and line inductance variations.