The Saturated Synchronous Machine

Abstract

W t wHILE the unsaturated synchronous machine is several reactances, and linear relations existing throughin general well understood, the effects of saturaout the machine. Assuming no saturation in the armation upon its performance are still subject to ture or cross-field paths, figure 27 of the paper by Doherty discussion. Knowledge on the influence of saturation is and Nickle shows an additional field excitation along the important because of power-angle relations, steady-state pole axis to take into account -saturation in the pole body. stability limits, and excitation requirements. The prob-Under these assumptions, the torque-angle is not affected lem of saturation may be approached in several ways. by saturation. Under conditions of saturation, and One method' is to determine empirical factors which certainly for high saturation, all of the machine reactances modify characteristics of the unsaturated machine, the are decreased in magnitude. The cross-field path, by way saturation factors being single average values for a group of the pole tips, and the armature teeth, will saturate as of machines. A second way2 leads to the introduction of well as the pole body. Torque-angle therefore is apequivalent reactances which allow calculation of the ef-preciably affected as well as is the excitation requirement.fects of saturation on small load changes about an initial operating point. Third, there is the derivation3 of satu-Machine Constants rated synchronous reactances to be used in the investigation of power-angle curves and maximum power.The machine constants which must be considered in any It is the purpose of this paper to present the physical steady-state analysis of the synchronous machine are concepts underlying the highly saturated synchronous armature resistance, armature leakage reactance, and the machine operating under steady load, and to show how direct and quadrature synchronous reactances. The efthe theory developed for such a machine is in agreement fective armature resistance may be determined by methods with test results. With terminal voltage, current, and previously described.6 Tests on armature leakage re-actance7 have shown that it varies somewhat with saturation, being a function of the density in the armature teeth Figure 1. General vector A which in turn depends upon the air-gap flux. The variadiagram of an alternator Lxd tion, however, is relatively small, and without introducing appreciable error this quantity may be taken as a function of terminal voltage..dxd The synchronous reactances are a measure of the flux /X/ q \ which the armature magnetomotive force produces in its \6 ea / ) magnetic circuit. In the case of the direct synchronous, d d reactance the magnetic circuit consists of the armature t e+ ra iron, the air-gaps, and the rotor poles and spider. For the quadrature synchronous reactance the magnetic circuit consists of the armature iron, the air-gaps, the pole tips, and the interpolar region. With increasing flux tq through these circuits, the synchronous reactances decrease....