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Virtual flux (VF)-oriented control (VFOC) and VF-based direct power control (DPC) (VF-DPC) have been developed to improve voltage-oriented control and DPC of three-phase active rectifiers. The VF space vector is utilized in transformations between stationary and rotating coordinates in VFOC and in obtaining instantaneous power in VF-DPC. The VF space vector is calculated by integrating the grid voltage space vector. This integration is usually performed using a first-order low-pass (LP) (FOLP) filter, which counteracts the saturation and dc-drift problems associated with pure integrators. However, the dynamics of FOLP filters can be enhanced to a great extent. This paper presents a new, simple, and fast integration algorithm for VF-based control methods. Simulations and experimental tests on a VF-DPC-based system showed that the proposed algorithm leads to rapid recoveries after grid voltage sags occur. Moreover, the performance of VF-DPC under nonideal grids is discussed.