The paper discusses the process whereby some of the kinetic energy stored in a generator rotor is converted to magnetic energy when a generator is short circuited. This gives rise to oscillatory electrical torques at fundamental frequency which, hitherto, have not been recognised as an important factor in the initial angular movement of a generator rotor and have usually been ignored; this is shown to be a serious omission which, when corrected, will influence future studies of generator stability. The effect of these oscillatory torques is to cause a back swing of the rotor when a generator is faulted. This phenomenon has been noticed during several system tests, and the results of such tests are used in the paper to support the theory which is presented. The practical system conditions necessary for the existence of these torques is discussed. Since these torques are of fundamental frequency, the exact calculation of them in digitalcomputer programs is time consuming, and thus a simple approximate method for simulating their effect on rotor movement is presented. 1 List of symbols x d = direct-axis synchronous reactance, p.u. x' d = direct-axis transient reactance, p.u. x'y -subtransient reactances in direct and quadrature axes, respectively, p.u. H = inertia constant, kWs/kVA V = terminal voltage, p.u. T e = electrical torque, p.u. T m = prime-mover torque, p.u. T s = magnitude of oscillatory torque, p.u. r a = armature time constant, s r' d = transient time constant, s T'J = subtransient time constant, s OJQ = rated speed, rad/s /o = rated frequency, Hz 6 = change of rotor angle, deg
IntroductionThat generator rotors, when subjected to close-up 3-phase faults, tend to pause or even swing backwards* prior to accelerating under prime-mover action, is now a recognised and accepted phenomenon. It was first noticed in the results of field tests which were held at Cliff Quay 1 in 1956, and Powell 2 made the first attempt to quantify the observed back swing. Based on experience, he chose to delay the forward movement of the rotor by 0 06 s in his calculation, and was then able to obtain satisfactory agreement with the test result. Since that time, a pause or back swing of generator rotors has been seen in other system test results 3 -4 and also in micromachine studies. 5 Fig. 1 demonstrates typical variations of the total electrical torque on the rotor when a generator is subjected to a 3-phase fault, which is applied simultaneously to all three phases. The prefault torque (curve a) represents the generator with full load and the postfault torque (curve b) has two components; one is a unidirectional torque (curve c) which is due to resistive losses in the set, and the other is an oscillatory torque which is almost entirely of fundamental frequency and which is much larger than the prefault torque. 6 The resistive losses during the initial period of a fault (say, the first 50ms) can be quite high, and there is no doubt that these do influence the movement of the rotor. The resulting
