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This paper introduces and develops i) a novel unified dynamic model, and ii) new control schemes for a grid-connected static energy conversion system that is based on the voltage-sourced converter (VSC) configuration. The model and the controls are applicable to both the conventional two-level and the three-level neutral point diode clamped (NPC) VSCs. The model is unified since it represents the dynamic behavior of the VSC with respect to both positiveand negative-sequence components, due to unbalanced grid conditions and disturbances. To develop the unified model, the concepts of "generalized sinusoidal pulse-width modulation (SPWM)" and "VSC sequence subsystems" are presented. Based on the negative-sequence subsystem control, a new control strategy, to either balance the ac line currents or to mitigate dc-bus voltage ripples, is introduced. Application of the developed model and the controls to a variable-speed wind-power unit is presented in the paper.