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This paper presents a division-summation (D- Σ) digital control for a three-phase inverter to achieve active and reactive power injection to the ac grid. The proposed D- Σ approach summarizes the inductor-current variations over one switching cycle to derive control laws directly, which can overcome the limitation of d- q transformation. The inverter with this control can achieve various power factors (PFs) leading or lagging, by taking into account wide filter-inductance variation and grid-voltage distortion, reducing core size significantly. The control laws for achieving the desired features are derived in detail, and they are expressed in general forms for readily software programming. With the enhancement work of previous research, active and reactive power injection with PF from 0 to 1 can be controlled effectively, so that these control laws can be extended to wide current-tracking applications, such as static synchronous compensator and active power filter. In the design and implementation, the inductance values corresponding to various inductor currents were measured at the startup and stored in the controller for scheduling loop gain cycle by cycle. Measured results from a 10-kVA 3 φ inverter have confirmed the analysis and discussion of the proposed control approaches.