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In this study, the equation for the reactive and harmonic power compensation of a shunt active power filter (APF) system has been derived by studying the power exchange mechanism and power tetrahedron phasor diagram. The switching dynamics of a voltage source inverter (VSI)-based three-phase, three-wire (three-leg /half-bridge) shunt APF system with hysteresis band current control has been studied and verified by simulation. The relation between the design parameters and their effects on the active losses has also been identified. Detailed calculation and extensive simulation have been performed for a three-phase, three-wire shunt APF implemented in a 400VL-L distribution system, as an example, to study the effects of design parameter selection and their role in active power loss calculation. Simulated and calculated results are presented for the important design parameters for different switching frequencies together with their associated losses and kVA ratings. The procedure can be followed to design the parameters for other topologies, such as three-phase, four-wire or single-phase systems.