Abstract :
Part I treats of the calculation and application of the armature self-inductive reactance of synchronous machines. A short, reliable method is given in the form of curves, Figs. 20a, b, c, making the calculation from design sheet data a matter of a few minutes. Table I shows a comparison of calculated and test values (obtained from saturation and synchronous impedance curves) for 138 machines, ranging from high-speed turbine generators to the low-speed engine type. Three points were brought out during the investigation: (1) That in polyphase machines, the armature self-inductive reactance, just as the armature reaction, is a polyphase, not a single-phase, phenomenon, and therefore the mutual induction of phases in a three-phase machine increases the effective self-induction of each phase by approximately 50 per cent over the single-phase value, while in two-phase machines, in which the mutual induction of phases is zero, the effective self-induction of the phase is the same for two-phase or single-phase operation. (2) That the variation of armature reactance during the cycle, due to salient-pole construction, is practically eliminated in Y-connected, three-phase machines for the reason that the variation, consisting almost entirely of a third harmonic, is cancelled in such machines. This leaves, in effect, a uniform reluctance for the leakage flux emanating from the tooth tips. (3) That in the familiar method of obtaining the armature self-induction from the saturation and synchronous impedance curves (i.e., by subtracting the armature reaction, that is, the demagnetizing ampere turns of normal current under sustained short circuit, from the corresponding field ampere turns), a very large error in this test value of self-induction may occur, if, as is usually done, the armature reaction is calculated on sine wave assumptions. A set of curves shown in Fig. 20, which are plotted from results derived in Appendices A and B, give values of the correction factor which ap- lies to calculations based on sine wave. An approximate, but convenient, method of applying the armature reactance in the calculation of field excitation under load is given in Appendix C. In Part II it is shown that the initial short-circuit current of synchronous machines is determined not only by the armature self-inductive reactance, as is often assumed, but also by the field self-inductive reactance. Neglecting the field reactance in calculation may give a calculated short-circuit current 50 per cent or more, too high. A formula is derived for calculating the field reactance which, added to the armature reactance, gives the total which determines the initial short-circuit current and which it is proposed should be called, as previously recommended by other authors, transient reactance. Table IV shows a comparison on eleven machines of the actual short-circuit currents as determined by oscillograph, and as calculated by methods proposed in the paper. The calculations of transient reactance apply strictly to salient laminated pole alternators without amortisseur winding. However, such experience as is recorded in Table IV, if analyzed in connection with theoretical considerations, affords a basis for estimating the transient reactance of turbine generators with massive steel rotors and of salient-pole machines with amortisseur windings. These points are summed up in “Summary and Conclusions”. An attempt is made to describe the apparently complicated physical phenomena of sudden short circuits in terms as free as possible from mathematics. One interesting and important point which the authors establish from the physical interpretation of the problem is that there is a very significant rise in flux at the bottom of the pole at short circuit. This may be (if the rotor is entirely laminated) 30 or 40 per cent of normal flux, and apparently explains why, in machines with solid steel rotor rims, the field attenuation factor, αf, chan
