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This paper proposes a new definition of instantaneous reactive power in the complex synchronous rotating frame and control scheme under unbalanced networks. The mathematical model of instantaneous active and reactive power has been derived for a pulsewidth-modulated (pwm) ac/dc converter under generalized unbalanced operating conditions. Based on this model, an unbalanced compensating control algorithm is proposed. Simulation and experimental results confirm the mathematical model as well as the control performance. The ripple component of instantaneous reactive power is found to be exactly the same as that of active power. The proposed definition of instantaneous reactive power in the synchronous rotating frame is shown to be consistent with the classical definition in both time and phasor domain. The proposed definition makes it possible to effectively design the controller for pwm converters under unbalance conditions.