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A new current control strategy is proposed for the control of three-phase three-wire shunt active power filters. In this strategy it is sufficient to measure the source voltage and the load currents. Analyses of the balanced nonlinear and unbalanced linear load cases are performed. Simulations are performed for these cases as well as for a nonlinear load drawing quasi-square-wave currents from the mains. Stability analysis is also performed to determine the stability region of the proportional-integral controller gains used in the voltage control loop. Simulation studies show that the proposed strategy is quite effective in eliminating harmonics, compensating for reactive power and also balancing unbalanced loads. It is simpler than most strategies proposed in the literature.