This paper proposes a new control method for three-phase active power filters to reduce the dc capacitor voltage fluctuations caused by a quick load change. The new control method introduces a new k-step compensator, which maintains the mean active power at zero every 1/(k-1) ac line period. Therefore, the compensator can suppress the transient voltage fluctuations across the dc capacitor, even when a quick load change occurs. This paper theoretically reveals the relationship between the step number k and the reduction of the dc voltage fluctuations. The experimental setup introducing the proposed 7-step compensator exhibits good suppression of the dc voltage fluctuations and makes it possible to reduce the required capacitance of the dc capacitor by a factor of seven.