Saturated Synchronous Machines Under Transient Conditions in the Pole Axis

Abstract

By reducing to the same parameter with saturation the voltage-current equations for stator, rotor, and magnetic circuits of synchronous machines, a differential equation in time for the main-pole flux and the induced electromotive force is derived, a relation easy to evaluate graphically. The difference of current between the magnetic characteristic of the machine and the electric characteristic of the stator circuit determines the rate of change of the electromotive force from which all the other slow-transient magnitudes can be derived. For constant excitation voltage, a closed solution for the variation of flux and electromotive force is given, valid for any sudden change of load, including short-circuit current formation or capacitive superexcitation. The combined effect of damper circuits and rotor leakage causes a superposed rapid-transient variation manifested by an additional current peak at sudden short circuits and by a rapid initial voltage rise at sudden interruptions of the circuit. The method of solution is in principle independent of the distribution of the saturation on rotor and stator, as well as of the character of loading of the machine, be it by constant or variable impedance, by symmetrical or unbalanced currents, by active or reactive power. The common subdivision into transient and sub-transient phenomena is not identical with the separation into slowand rapid-transient effects, the physical significance of which is derived in this paper.