Stability of Synchronous Machines Effect of Armature Circuit Resistance

The theory of synchronous machines as developed by Doherty and Nickle¹ has been extended to include a determination of the effect of armature circuit resistance on damping torque. Equations are developed for the damping torque of synchronous machines in general, i.e., both the salient-pole and round rotor types. These equations assume an exciting winding in the direct axis and an amortisseur winding in the quadrature axis, and further assume that all damping is due to currents induced in these two windings. The effect of an amortisseur winding in the direct axis is not considered because its damping action at the low frequency of hunting is small compared to that of the exciting winding. It is shown that the damping torque of any synchronous machine can become negative, giving instability, if the armature resistance is increased beyond a critical limiting value. This fact has been known,² but an actual determination of the value of the critical resistance in terms of constants of the machine has not, to the authors´ knowledge, been available. This value, for a salient-pole generator with normal excitation and no amortisseur winding, is r = xq tan ¿¿ where r is armature circuit resistance¿, xq is quadrature synchronous reactance, and ¿¿ is the steady-state displacement angle. If r is less than the critical limiting value, the damping torque is positive; if greater, negative. The damping of a generator increases in the positive direction with increase in load.