To derive the machine model of a six-phase induction machine (6φIM ), the following assumptions have been made:space harmonics, magnetic saturation, and core losses are neglected. In the same way as for three-phase systems, the use of a(6 × 6) transformation matrix [2], [6] allows the stator variablesto be expressed in an orthogonal base. The transformation usedhere was proposed in [7] and [10]. Using this transformation,the original six-dimensional (6-D) stator system can be decomposed into three two-dimensional (2-D) uncoupled subsystems.These are the usual (d−q) one, a zero-sequence (o 1−o 2) one,and another nonelectromechanical energy conversion relatedone named (x−y). The transformation has the property toseparate harmonics into different groups and to project theminto each subsystem. The (x−y) components are responsiblefor the large circulating harmonic currents. So, the impedancerelated to these components should be as high as possible,and/or the applied voltages should contain minimum amplitude (x−y) components. The final model expressed in the stationaryreference frame is given by [10], [11]where Ls = Llsdq + 3Lms, M = 3Msr/√2, and Lr = Llr +(3/2)Lmr. Llsdq is the stator leakage inductance of the (d−q)equivalent circuit, and Llsxy for the (x−y) equivalent circuit[10], [11].
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