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This paper presents a comparative analysis between results from applications of the p-q and the p-q-r theories in shunt active power filters for three-phase four-wire systems, discussing aspects related to the influence of the system voltage in the control methods that calculate the compensating currents. It is shown that in some cases, a preprocessing of the system voltage is required if the goal is to achieve sinusoidal compensated currents. On the other hand, when the goal is to compensate zero-sequence current, the need of energy storage elements in the active filter is discussed. In this case, if zero-sequence components are present simultaneously in the system voltage and load current, they produce zero-sequence power flow, and the control methods based on both theories must contain additional calculations to allow the elimination of energy storage elements in the active filter. A control strategy based on the p-q theory is proposed to eliminate the neutral current without the need of energy storage elements, with the advantage of avoiding the extra transformation from [alpha][beta]0 to pqr coordinates that is needed in the p-q-r theory. Simulation results are presented for the purpose of comparing the performance of both control methods. Index Terms--Active filters, p-q theory, p-q-r theory.