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The brushless doubly fed induction generator (DFIG) (BDFIG) shows commercial promise for wind power generation because of its lower maintenance needs compared to the widely used DFIG. From power grid codes, installed wind turbines are sometimes required to be capable of operating under unbalanced grid conditions. This paper presents a novel controller for BDFIG-based wind generators operated with asymmetrical voltage supplies. Two synchronous reference frames, the positive and the negative, are introduced for applying a vector control scheme to separately control two sequences arising from the unbalanced voltage. Different control strategies are discussed for reducing the consequent oscillations. It is demonstrated that the proposed controller shows a significant performance improvement over the conventional controller and is effective to cope with potentially unbalanced conditions.