There has been a growing demand of using multi-function inverters for grid-connected systems applied to nonconventional energy sources, such as solar, wind and so on. In addition to power quality conditioning, the inverter can also be used for bidirectional active power exchange with a three-phase four-wire grid. Therefore, the inverter acts as a multi-function compensator. The functions of the proposed inverter system include active power injection, rectification and active power filtering (APF) (including phase power balancing). This paper presents design and implementation of a three-leg split-capacitor shunt multi-function inverter with division-summation (D-Sigma) digital control. The adopted D-Sigma digital control can accommodate filter inductance variation, reducing core size significantly, and its control laws can be derived directly to cancel the variation effects of dc-bus voltage, switching period and filter inductance. An average power method is adopted in this paper for determining fundamental currents at the source side. 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 insure system stability. Measured results from a three-phase four-wire inverter have confirmed the analysis and discussion.