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A new theory and a conceptual design for the three-phase shunt active power filter (APF) control strategy under imbalanced and distorted supply voltages are presented. Conventionally, the compensation currents injected by the APF are determined according to reference frame transformation-based approaches, where the load instantaneous real and reactive powers are calculated in the new reference frame. The APF injection currents are then computed to maintain the balanced and sinusoidal source currents, as well as the least active power consumption by the APF. However, if current harmonics set by harmonic standards or other constraints are considered, the load harmonic currents after APF compensation can be controlled to meet the requirements. Therefore, the APF may have an adjustable performance. An optimal algorithm for the APF control in steady state is proposed, in which the individual and total harmonic current distortion limits, the minimum load power factor, levels of current imbalance and the size of the APF can be taken into account. The planned APF does not consume or produce active power and only the passive energy-storage elements are required in the new APF design. Results obtained by simulations with Matlab and Simulink show that the proposed approach is more flexible than conventional approaches for compensating reactive power and harmonic/neutral currents of the load, even if the source voltages are severely distorted and imbalanced. The new control strategy is very suitable for planning the APF when several alternative objective functions and constraints are under considerations.