Analytical analysis and performance characterization of brushless doubly fed induction machines based on general air-gap field modulation theory

Air-gap magnetic field modulation has been widely observed in electric machines. In this study, we present an analytical analysis and performance characterization of brushless doubly fed induction machines (BDFIMs) fed by two independent converters from the perspective of air-gap field modulation. The spiral-loop winding is studied in detail as an example to show the generalized workflow that can also be used to analyze other short-circuited rotor winding types, such as nested-loop and multiphase double-layer windings. Magnetic field conversion factors are introduced to characterize the modulation behavior of special rotor windings and facilitate their comparison in terms of cross-coupling capability, average torque, and harmonic content of the air-gap flux density waveforms. The stator magnetomotive force (MMF), rotor MMF, and resultant air-gap MMF are considered, based on which the closed-form inductance formulas are derived, and the torque equation is obtained along with the optimal current angle for maximum torque operation by using the virtual work principle. The design equations are then developed for the initial sizing and geometry scaling of the BDFIMs. Transient finite element analysis and experimental measurements are performed to validate the analysis.