Calculation of machine end-winding inductances with special reference to turbogenerators

A simple numerical procedure for the determination of the self and mutual inductances of coils of arbitrary shape is presented. The basic method involves the use of a digital computer and is capable of yielding results of very high accuracy. For application to machine end windings, the influences of the various permeable and/or eddy-current-carrying boundaries near the end coils (i.e. core end, coil-retaining ring, casing) are treated approximately (although it is believed entirely adequately) by employing the method of images. For the particular example of turbogenerator involute coils, the numerical procedure for the determination of self inductance is used to establish a simple equation which reduces routine design calculations to trivial manual ones. The equation allows for the true shape and the cross-section of the coils. The evaluation of mutual inductance between stator coils is reduced to the use of a single curve. The mutual inductance with the rotor is estimated. The numerical results presented permit good estimates, for general use, of the magnitudes of the various boundary influences on the inductances and of the variation in inductance between steady-state and transient conditions. Large differences between inductances under steady-state and transient conditions are found to occur, and the small value of the latter is emphasised.