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This paper proposes a unified mathematical model of a voltage-sourced converter (VSC) based on positive and negative synchronously rotating frames under both unbalanced grid supply and imbalanced input impedances. Based on the developed model, a new definition of instantaneous reactive power is introduced, and an accurate mathematical model of the instantaneous active and reactive powers at different locations of the VSC is derived. To avoid the use of band-trap filter for decomposing the positive- and negative-sequence dq components of current and voltage, a new control scheme with multifrequency proportional-resonant controller in the stationary alphabeta frame is employed to improve the steady state and dynamic response under generalized unbalanced operation conditions. Simulation and experimental studies with various factors were conducted and compared under different types of unbalanced conditions. The simulated and experimental results demonstrate that the proposed control scheme in the stationary alphabeta frame provides sufficiently steady-state tracking capability for ac input current, and a better transient response in compensation for wide-range generalized unbalanced operation conditions.