XVII. Short-circuit Currents of Alternators 31. The short-circuit current of an alternator at full-load excitation usually is from two to five times full-load current, and even less in very large high-speed steam turbine alternators. It is where EQ = nominal generated e.m.f., ZQ = synchronous impe- dance of alternator, representing the combined effect of arma- ture reaction and armature self-inductance. In the first moment after short circuiting, however, the current frequently is many times larger than the permanent short- circuit current, that is, where z = self-inductive impedance of the alternator. That is, in the first moment after short circuiting the poly- phase alternator the armature current is limited only by the arma- ture self-inductance, and not by the armature reaction, and some appreciable time — occasionally several seconds — elapses before the armature reaction becomes effective. At short circuit, the magnetic field flux is greatly reduced by the demagnetizing action of the armature current, and the gen- SYNCHRONOUS MACHINES 161 erated e.m.f. thereby reduced from the nominal value EQ to the virtual value Ez; the latter is consumed by the armature self- inductive impedance z, or self-inductive reactance, which is practically the same in most cases. The armature self-inductance is instantaneous, since the magnetic field rises simultaneously with the armature current which produces it; armature reaction, however, requires an appre- ciable time to reduce the magnetic flux from the open-circuit value to the much lower short-circuit value, since the magnetic field flux is surrounded by the field exciting coils, which act as a short-circuited secondary opposing a rapid change of field flux; that is, in the moment when the short-circuit current starts it begins to demagnetize the field, and the magnetic field flux there- fore begins to decrease; in decreasing, however, it generates an e.m.f. in the field coils, which opposes the change of field flux, that is, increases the field current so as momentarily to main- tain the full field flux against the demagnetizing action of the armature reaction. In the first moment the armature current thus rises to the value given by the e.m.f. generated by the full field flux, while the field current rises, frequently to many times its normal value (hence, if circuit breakers are in the field circuit, they may open the circuit). Gradually the field flux decreases, and with it decrease the field current and the armature current to their normal values, at a rate depending on the resistance and the inductance of the field-exciting circuit. The decrease in value of the field flux will be the more rapid the higher the re- sistance of the field circuit, the slower the higher the inductance, that is, the greater the magnetic flux of the machine. Thus, the momentary short-circuit current of the machine can be made to decrease somewhat more rapidly by increasing the resistance of the field circuit, that is, wasting exciting power in the field rheostat. In the very first moment the short-circuit current waves are unsymmetrical, as they must simultaneously start from zero in all phases and gradually approach their symmetrical appear- ance, i.e., in a three-phase machine three currents displaced by 120 degrees. Hereby the field current is made pulsating, with nor- mal or synchronous frequency, that is, with the same frequency as the armature current. This full frequency pulsation gradually dies out and the field current becomes constant with a polyphase short circuit, while with a single-phase short circuit it remains 162 ELEMENTS OF ELECTRICAL ENGINEERING pulsating with double frequency, due to the pulsating armature reaction. In a polyphase short circuit this full frequency pul- sation due to the unsymmetrical starting of the currents is inde- pendent of the point of the wave at which the short circuit starts, since the resultant asymmetry of all the polyphase cur- rents is the same regardless of the point of the wave at which the circuit is closed. In a single-phase short circuit, however, the full frequency pulsation depends on the point of the wave at which the circuit is closed, and is absent if the circuit is closed at that moment at which the short-circuit current would pass through zero. The momentary short-circuit current of an alternator thus represents one of the few cases in which armature self-induc- tance and armature reaction do not act in the same manner, and the synchronous reactance can be split into two components, thus, XQ = x -\- x', where x = self-inductive reactance, which is due to a true self-inductance, and x' = effective reactance of armature reaction, which is not instantaneous. 32. In machines of high self-inductance and low armature re- action, as high frequency alternators, this momentary increase of short-circuit current over its normal value is negligible, and moderate in machines in which armature reaction and self-in- ductance are of the same magnitude, as large modern multi- polar low-speed alternators. In large high-speed alternators of high armature reaction and low self -inductance, as steam turbine alternators, the momentary short-circuit current may exceed the permanent value ten or more times. With such large currents magnetic saturation of the self-inductive armature circuit still further reduces the reactance x, that is, increases the current, and in such cases the mechanical shock on the generator becomes so enormous that it is necessary to reduce the momentary short-cir- cuit current by inserting self-inductance, that is, reactance coils into the generator leads, or by specifically designing the alterna- tor for high armature reactance, or by both. In view of the excessive momentary short-circuit current, it may be*desirable that automatic circuit breakers on such systems have a time limit, so as to keep the circuit closed until the short- circuit current has somewhat decreased. 33. In single-phase machines, and in polyphase machines in case of a short circuit on one phase only, the armature reaction is pulsating, and the field current in the first moment after the SYNCHRONOUS MACHINES 163 short circuit therefore pulsates, with double frequency, and remains pulsating even after the permanent condition has been reached. The double frequency pulsation of the field current in case of a single-phase short circuit generates in the armature a third harmonic of e.m.f. The short-circuit current wave be- comes greatly distorted thereby, showing the saw-tooth shape characteristics of the third harmonic, and in a polyphase machine on single-phase short circuit, in the phase in quadrature with the short-circuited phase, a very high voltage appears, which is greatly Field Current Armature Current FIG. 74. — Three-phase short-circuit current in a turbo-alternator. distorted by the third harmonic and may reach several times the value of the open-circuit voltage. Thus, with a single- phase short circuit on a polyphase system, destructive voltages may appear in the open-circuited phase, of saw-tooth wave shape. Upon- this double frequency pulsation of the field current during a single-phase short circuit the transient full frequency pulsation resulting from the unsymmetrical start of the armature current is superimposed and thus causes a difference in the in- tensity of successive waves of the double frequency pulsation, 164 ELEMENTS OF ELECTRICAL ENGINEERING which gradually disappears with the dying out of the transient full frequency pulsation, and depends upon the point of the wave at which the short circuit is closed, and thus is absent, and the Armature current. Field Current FIG. 75. — Single-phase short-circuit current in a three-phase turbo- alternator. .Armature current Field current 52.5 amp. EJ amp. FIG. 76. — Single-phase short-circuit current in a three-phase turbo- alternator. double frequency pulsation symmetrical, if the circuit is closed at the moment when the short-circuit current should be zero. 34. As illustration is shown, in Fig. 74, the oscillogram of SYNCHRONOUS MACHINES 165 one phase of the three-phase short circuit of a three-phase turbo- alternator, giving the unsymmetrical start of the armature currents and the full frequency pulsation of the field current. In Fig. 75 is shown a single-phase short circuit of the same machine, in which the circuit is closed at the zero value of the current; the current wave therefore is symmetrical, and the field current shows only the double frequency pulsation due to the single-phase armature reaction. In Fig. 76 is shown another single-phase short circuit, in which the armature current wave starts unsymmetrical, thus giving a transient full frequency term in the field current. Thus in the double frequency pulsation of the field current at first large and small waves alternate, but the successive waves gradually be- come equal with the dying out of the full frequency term. In Figs. 75 and 76 the oscillogram is cut off by the open- ing of the circuit breaker. For further discussion, and the theoretical investigation of momentary short-circuit currents, see "Theory and Calculation of Transient Electric Phenomena and Oscillations," Part I, Chapters XI and XII. For further discussion of the terms reactance, armature re- action and field excitation and their relation, see "Theory and Calculation of Electric Circuits. " 11 B. DIRECT-CURRENT COMMUTATING MACHINES