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Three-phase voltage source pulsewidth modulation (PWM) rectifiers can achieve constant dc voltage and sinusoidal grid currents under ideal grid voltages. However, under unbalanced grid voltage conditions, there are ripples at twice the grid frequency in the dc voltage, and the grid currents become highly distorted. To address the aforementioned problems, control methods developed under ideal grid voltage conditions should be modified. Various techniques have been proposed in the literature to calculate the new current reference or power reference. However, most methods use conventional pq theory and only consider the grid-side power control. Hence, the dc voltage ripples are not completely eliminated. Furthermore, the derived mathematical expressions for reference calculations are usually very complicated. In contrast to current methods, this paper proposes a very simple yet effective direct power control (DPC) method based on extended pq theory. By analyzing the instantaneous extended power of the line inductance, a simple and concise power compensation is analytically derived and added to the original power references. As a result, the dc voltage ripples are significantly reduced, and the grid currents remain sinusoidal even under unbalanced grid voltage conditions. The proposed method is compared to conventional DPC methods, and its effectiveness is confirmed by the presented experimental results. [ABSTRACT FROM AUTHOR]