A Floquet theory of the general linear rotating machine

As is well-known, the fundamental assumption underlying Park's decisive analysis of the ideal linear three-phase rotating machine is that all windings on the (nonsalient) stator are in effect sinnsoidally spacially distributed as far as concerns the calculation of any self or mutual magnetic flux linkage. As Park has shown, there exists a suitable reference frame in which such an "ideal" machine admits an internal constant-coefficient differential equation description under the condition of constant rotor angular velocity. On the other hand, if the machine is not Ideal, the various mmf's are no longer sinusoldally distributed and it is not at all obvious that stationarity can be achieved by any choice of frame. Nevertheless, it is shown in this paper that such a "Floquet" frame does Indeed exist and that it may be possible to devise experimental procedures for its determination. This new Park-like theory of the general linear rotating machine subsumes the Ideal case and is based squarely on the obvious geometric periodicity of the machine structure.