Energy Conversion by Nonlinear Slip-Ring Electric Machines

The matrix theory of electric machines is based on the assumption of magnetically linear iron. This paper removes the linearity assumption at the start, while permitting its reintroduction at a later stage as a computational simplification. A definition is given for inductance in the nonlinear case that leads to single-valued continuous inductances, with reciprocal mutual inductances. The resulting differential equations are solved to give a method for determining the inductances associated with any machine. The torque of a slip-ring machine is then expressed in terms of its inductance matrix. The expression is shown to reduce to the usual result in the special case of a linear machine, and to predict, with a high degree of accuracy, the torque of a small heavily saturated experimental machine.