Abstract
Electrical Machines with accelerated fields are studied. These machines carry an excitation such that the magnetic field in its airgap is accelerated. As a consequence of pos- sessing peculiar winding distributions, in order to obtain accelerated fields, the airgap fields are rich in space harmonics.
The equations of motion, derived from the Lagrangian formulation, constitute a set of simultaneous nonlinear differ- ential equations with time-varying coefficients. Formulas are derived to determine the (inductance-) coefficients, involved in the equations, by solving the field equations. To predict the behavior of the machine and to solve the equations of mo- tion, a change of variables is introduced. A logical approach to such a transformation is by using the concepts of linear algebra and the symmetry properties of the inductance sub- matrices to determine the eigenvalues and eigenvectors of these submatrices. The transformation thus introduced is an extension of the generalized symmetrical-component transfpr- mation in the sense that the effects of space harmonics can be included. The transformations are power-invariant and decouple all but two of the simultaneous equations from each other for each harmonic present. The sets of two decoupled equations involve the torque-producing terms. The time-depen- dence of the coefficients is eliminated by using an appropri- ate complex-type rotating transformation. The machine perfor- mance is calculated from these equations and equivalent cir- cuits are derived.
A new real transformation is given which can be used for quasi-cyclic symmetric windings and a modified complex transformation is obtained for almost-balanced windings.
An example is considered. Results are calculated from the theory developed, and are compared with those obtained experimentally.