Direct power control of shunt active filter using high selectivity filter (HSF) under distorted or unbalanced conditions

•Extraction of power references components of shunt active power filter.•New formulation of direct power control DPC based on high selectivity filter HSF are proposed and detailed.•Comparison between conventional DPC and proposed DPC with IEEE-519 power definitions.•Performances are evaluated under distorted or unbalanced conditions.•Proposed DPC with HSF has a good performance in the harmonic compensation under non-ideal conditions.