Synchronous Machines?IV

Abstract
The special case of cylindrical rotor machines has been treated previously by Boucherot and others. The present paper solves the general case, including salient pole machines. The cylindrical rotor type thus becomes merely a limiting case. The principal assumption which distinguishes the present theory from the extensively studied cylindrical rotor theory is that the total armature self-inductance is here taken as variable with respect to rotor position, whereas the previous theory of short circuits, as represented by Boucherot, for instance, assumes this inductance to be constantߞin other words, that the air-gap is uniform. The four basic concepts underlying the improvement in theory, both as applied here and in the authors' previous work on Synchronous Machines, are: 1. Characterization of the machine by four reactance coefficients, two corresponding to the main pole axis, i. e., direct axis, and two to the interpolar axis, i. e., quadrature axis. These are: xD, xD', xQ, xQ'. (See notation.) Thus the theory has been referred to, more or less aptly, as the "Four-Constant Theory." 2. Resolution of flux and m. m. f. waves traveling with respect to the rotor into stationary, pulsating components in line with the direct and quadrature axes. The theory involves also, of course, the usual Blondel resolution of the stationary fundamental waves. 3. That the variable component of armature inductance varies between the direct axis value and the quadrature axis value as a second harmonic function of the electrical space angle.

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