The reference current generation (RCG) is a crucial part in the control of a shunt active power filter (APF). A variety of RCG techniques have been proposed in literature. Among these, the instantaneous reactive power theory, called pq theory, is probably the most widely used technique. The pq theory offers advantages such as satisfactory steady-state and dynamic performance, and at the same time simple digital implementation, however its application was limited to three-phase systems. To exploit the advantages of pq theory in single-phase systems, the single-phase pq theory has been proposed recently. In this paper, a simple and effective implementation of the single phase pq theory for single-phase shunt APFs is proposed. The suggested approach is based on employing second order generalized integrators (SOGI), and a phase locked loop (PLL). To fine tune the control parameters, a systematic design procedure based on the pole-zero cancellation, and the extended symmetrical optimum theory is proposed. During the design procedure, the effects of grid frequency variations and the presence of distortion in the grid voltage are taken into account. Finally, to confirm the effectiveness of the suggested approach, simulation results are presented.

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