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This study presents a minimum inverter capacity design for three-phase four-wire centre-split inductor-capacitor (LC) coupling hybrid active power filters (LC-HAPFs). Based on its equivalent circuit models in d-q-0 coordinate, the coupling part filtering characteristics of the LC-HAPF without or with neutral inductor can be more clearly illustrated and easily understood, compared with the past analysis based on the generic filter structure. According to the current quality data, the minimum dc-link voltage expressions for the LC-HAPF without and with neutral inductor are deduced and compared. Conventionally, the coupling LC is usually tuned at a higher fifth- or seventh-order harmonic frequency to reduce its cost and size compared with third-order case. When triplen harmonic currents exist significantly, the LC-HAPF with a small tuned neutral inductor can further reduce its minimum dc-link voltage requirement. Thus, the initial cost, switching loss and switching noise of the LC-HAPF can be lowered. Representative simulation and experimental results of the three-phase four-wire LC-HAPF with neutral inductor are presented to verify the filtering characteristics analysis and minimum dc-link voltage expressions, to show the effectiveness of reducing its inverter capacity, switching loss and switching noise in current quality compensation compared with the conventional LC-HAPF.