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This paper presents a generic vector model for the brushless doubly-fed machine (BDFM) with a nested-loop rotor. The vector model is presented for a generic p1/p2 pole-pair BDFM which may have any number of loops per nest. The vector transformations utilized in the derivation of the vector model are provided in general form such that the model can be represented in any appropriate reference frames according to the specific application of the model, such as BDFM analysis, simulations, or control system synthesis. The derived vector model benefits from the feature of reduced order in comparison with the coupled-circuit model, which is the most detailed model for the BDFM, while maintaining the accuracy by including the effects of all loops in each nest. The vector model is developed in MATLAB/Simulink based on the rotor reference frames for a 180-frame-size prototype BDFM, and its predictions for the machine performance have been compared with those of the coupled-circuit model as well as verified experimentally.