This paper presents a shunt active power filter (APF) with division-summation (D-Sigma) digital control and based on a three-phase three-wire inverter configuration. The APF shapes source current by introducing one degree of freedom to compensate load harmonic currents. The adopted D-Sigma digital control approach can accommodate filter-inductance variation, reducing core size significantly, and it can derive control laws directly. An average power method is adopted in this paper for determining the fundamental current at the source side, which can readily be implemented without complex calculation, frame transformation, and extra filter. In the design and implementation, the inductances corresponding to various inductor currents were estimated at the startup and stored in the microcontroller for scheduling loop gain cycle by cycle, which can ensure the system stability. Measured results from a 5-kVA three-phase APF have confirmed the analysis and discussion of the APF.