CHAPTER XVII. ALTERNATING-CURRENT GENERATOR. 182. In the alternating-current generator, E.M.F. is induced in the armature conductors by their relative motion through a constant or approximately constant magnetic field. When yielding current, two distinctly different M.M.Fs. are acting upon the alternator armature — the M.M.F. of the field due to the field-exciting 'spools, and the M.M.F. of the armature current. The former is constant, or approx- imately so, while the latter is alternating, and in synchro- nous motion relatively to the former ; hence, fixed in space relative to the field M.M.F., or uni-directional, but pulsating in a single-phase alternator. In the polyphase alternator, when evenly loaded or balanced, the resultant M.M.F. of the armature current is more or less constant. The E.M.F. induced in the armature is due to the mag- netic flux passing through and interlinked with the arma- ture conductors. This flux is produced by the resultant of both M.M.Fs., that of the field, and that of the armature. On open circuit, the M.M.F. of the armature is zero, and the E.M.F. of the armature is due to the M.M.F. of the field coils only. In this case the E.M.F. is, in general, a maximum at the moment when the armature coil faces the position midway between adjacent field coils, as shown in Fig. 126, and thus incloses no magnetism. The E.M.F. wave in this case is, in general, symmetrical. An exception from this statement may take place only in those types of alternators where the magnetic reluctance of the armature is different in different directions ; thereby, 298 AL TERNA TING-CURRENT PHENOMENA. during the synchronous rotation of the armature, a pulsa- tion of the magnetic flux passing through it is produced. This pulsation of the magnetic flux induces E.M.F. in the field spools, and thereby makes the field current pulsating also. Thus, we havet in this case, even on open circuit, no Fig. 126. rotation through a constant magnetic field, but rotation through a pulsating field, which makes the E.M.F. wave unsymmetrical, and shifts the maximum point from its the- oretical position midway between the field poles. In gen- eral this secondary reaction can be neglected, and the field M.M.F. be assumed as constant. The relative position of the armature M.M.F. with re- spect to the field M.M.F. depends upon the phase rela- tion existing in the electric circuit. Thus, if there is no displacement of phase between current and E.M.F., the current reaches its maximum at the same moment as the E.M.F. ; or, in the position of the armature shown in Fig. 126, midway between the field poles. In this case the arma- ture current tends neither to magnetize nor demagnetize the field, but merely distorts it ; that is, demagnetizes the trail- ing-pole corner, a, and magnetizes the leading-pole corner, b. A change of the total flux, and thereby of the resultant E.M.F., will take place in this case only when the magnetic densities are so near to saturation that the rise of density at the leading-pole corner will be less than the decrease of AL TERN A TING-CURRENT GENERA TOR. 299 density at the trailing-pole corner. Since the internal self- inductance of the alternator itself causes a certain lag of the current behind the induced E.M.F., this condition of no displacement can exist only in a circuit with external nega- tive reactance, as capacity, etc. If the armature current lags, it reaches the maximum later than the E.M.F. ; that is, in a position where the armature coil partly faces the following-field pole, as shown in diagram in Fig. 127. Since the armature current flows Fig. 127. in opposite direction to the current in the following-field pole (in a generator), the armature in this case will tend to demagnetize the field. If, however, the armature current leads, — that is, reaches its maximum while the armature coil still partly faces the Fig. 128. preceding-field pole, as shown in diagram Fig. 128, — it tends to magnetize this field coil, since the armature current flows in the same direction with the exciting current of the pre- ceding-field spools. 300 ALTERNA TING-CURRENT PHENOMENA. Thus, with a leading current, the armature reaction of the alternator strengthens the field, and thereby, at con- stant-field excitation, increases the voltage ; with lagging current it weakens the field, and thereby decreases the vol- tage in a generator. Obviously, the opposite holds for a synchronous motor, in which the armature current flows in the opposite direction ; and thus a lagging current tends to magnetize, a leading current to demagnetize, the field. 183. The E.M.F. induced in the armature by the re- sultant magnetic flux, produced by the resultant M.M.F. of the field and of the armature, is not the terminal voltage of the machine ; the terminal voltage is the resultant of this induced E.M.F. and the E.M.F. of self-inductance and the E.M.F. representing the energy loss by resistance in the alternator armature. That is, in other words, the armature current not only opposes or assists the field M.M.F. in cre- ating the resultant magnetic flux, but sends a second mag- netic flux in a local circuit through the armature, which flux does not pass through the field spools, and is called the magnetic flux of armature self-inductance. Thus we have to distinguish in an alternator between armature reaction, or the magnetizing action of the arma- ture upon the field, and armature self-inductance, or the E.M.F. induced in the armature conductors by the current flowing therein. This E.M.F. of self-inductance is (if the magnetic reluctance, and consequently the reactance, of the armature circuit is assumed as constant) in quadrature behind the armature current, and will thus combine with the induced E.M.F. in the proper phase relation. Obvi- ously the E.M.F. of self-inductance and the induced E.M.F. do not in reality combine, but their respective magnetic fluxes combine in the armature core, where they pass through the same structure. These component E.M.Fs. are there- fore mathematical fictions, but their resultant is real. This means that, if the armature current lags, the E.M.F. of self- ALTERNATING-CURRENT GENERATOR. 301 inductance will be more than 90° behind the induced E.M.F., and therefore in partial opposition, and will tend to reduce the terminal voltage. On the other hand, if the armature current leads, the E.M.F. of self-inductance will be less than 90° behind the induced E.M.F., or in partial conjunc- tion therewith, and increase the terminal voltage. This means that the E.M.F. of self -inductance increases the ter- minal voltage with a leading, and decreases it with a lagging current, or, in other words, acts in the same manner as the armature reaction. For this reason both actions can be combined in one, and represented by what is called the syn- cJironous reactance of the alternator. In the following, we shall represent the total reaction of the armature of the alternator by the one term, synchronous reactance. While this is not exact, as stated above, since the reactance should be resolved into the magnetic reaction due to the magnet- izing action of the armature current, and the electric reac- tion due to the self-induction of the armature current, it is in general sufficiently near for practical purposes, and well suited to explain the phenomena taking place under the various conditions of load. This synchronous reactance, x, Is frequently not constant, but is pulsating, owing to the synchronously varying reluctance of the armature magnetic circuit, and the field magnetic circuit ; it may, however, be considered in what follows as constant ; that is, the E.M.Fs. induced thereby may be represented by their equivalent sine waves. A specific discussion of the distortions of the wave shape due to the pulsation of the synchronous reactance is found in Chapter XX. The synchronous reactance, x, is not a true reactance in the ordinary sense of the word, but an equivalent or effective reactance. Sometimes the total effects taking place in the alternator armature, are repre- sented by a magnetic reaction, neglecting the self -inductance.' altogether, or rather replacing it by an increase of the arma- ture reaction or armature M.M.F. to such a value as to in- clude the self-inductance. This assumption is mostly made in the preliminary designs of alternators. "302 ALTERNATING-CURRENT PHENOMENA. 184. Let E0 = induced E.M.F. of the alternator, or the E.M.F. induced in the armature coils by their rotation through the constant magnetic field produced by the cur- rent in the field spools, or the open circuit voltage, more properly called the "nominal induced E.M.F.," since in reality it does not exist, as before stated. Then E0 where n = total number of turns in series on the armature, JV = frequency, M = total magnetic flux per field pole. Let x0 = synchronous reactance, r0 = internal resistance of alternator ; then Z0 — r0 — j x0 = internal impedance. If the circuit of the alternator is closed by the external impedance, Z = r-jx, the current is E0 E0 or, /= and, terminal voltage, or, +x- ALTERNA TING-CURRENT GENERA TOR. 303 or, expanded in a series, As shown, the terminal voltage varies with the condi- tions of the external circuit. 185. As an instance, in Figs. 129-134, at constant induced E.M.F., Eo = 2500 ; . ^ / ' x\ \ *- — / / \ \ \ \ \ / \ i / \ ***>. 1 / / ^ X^o I 1 i ^J \ 4S . ( .1 '/ \ \ \ Si &' > \ \ n 2°' ^ f \ I \ 1 / F ELD CHA MCI ERIS TIC \ 1 1 1 E0= 1 250( R = >, Zo-MOj, E, xko \ I , 1 1 1 1 \ 1 ± 20 10 60 80 100 180 140 160 18P 2 X) 2 0 210 2 0 Fig. 129. Field Characteristic of Alternator on Non-inductive Load. ' + and the values of the internal impedance, z0 = r0 -jXo = i - ioy. With the current / as abscissae, the terminal voltages E as ordinates in drawn line, and the kilowatts output, = /2 r, in dotted lines, the kilovolt-amperes output, = / £, in dash- 304 AL TEKNA TING-CURRENT PHENOMENA. dotted lines, we have, for the following conditions of external circuit : In Fig. 129, non-inductive external circuit, x = 0. In Fig. 130, inductive external circuit, of the condition, r / x = -f .75, with a power factor, .6. In Fig. 131, inductive external circuit, of the condition, r= <>, with a power factor, 0. In Fig. 132, external circuit with leading current, of the condi- tion, r/x = — .75, with a power factor, .6. In Fig. 133, external circuit with leading current, of the condi- tion, r = 0, with a power factor, 0. In Fig. 134, all the volt-ampere curves are shown together as complete ellipses, giving also the negative or synchronous motor part of the curves. \ E72 FIE 500, .D CHARA Zf MOj. i CTERIST(C -.75jop60^P.F "\ \ S \ \ \ -^ ^X \ *\ I* / S fe \ II* So >/ X \ ^ "i x'' \ \ / J ^ \ \ / X^N \ / ^ \\ \v (/_ \ ^ 20 40 60 80 1 K» 120 140 1 H) 180 200 220 glQ 20 0 Amp Fig. 130. Field Characteristic of Alternator, at 60% Power-factor on Inductive Load. Such a curve is called a field characteristic. As shown, the E.M.F. curve at non-inductive load is nearly horizontal at open circuit, nearly vertical at short circuit, and is similar to an arc of an ellipse. ALTERNATING-CURRENT GENERATOR. 305 \ s, FIELD CHARACTt :0=25OO, Z?1-10j, r = RISTIC o, 90° Lag \ \ 1 R = 0. \ \ \ \ \ \ k o » >C" -X A / S \%< \ o 2" X X t s % \ / / \ \ \ / \ \ > / \ \ \ / \ 0 / s, \ Fig. 131. Field Characteristic of Alternator, on Wattless Inductive Load. 5 I li'.'U 1000 HM ^ ^ Ns V x^ \ .'.X'OU ^ X" \ X ? X F EU Ch AR ACT ER ST c E f 2 50C ), Z 1-1 3j. : = -.75 c r 6 3^F .F. iloo / «••"" fc y ^ KM £ / / / f ItilK < / / j / ,-* '"' / j ^ 400 " lain.. ^ s v£ -- 1 > > , ,.»*' / / j 800 f* . X / / / , 7 ,,*" / / / m /- -*''" A -n pe •M /y /x. **' ;-r *•"' 1 B , £ I | 2 0^ **•!•• 0 • 0 m Fig. 732. Field Characteristic of Alternator, at 60% Power-factor on Condenser Load. 306 AL TERNA TING-CURRENT PHENOMENA. 1 I 1 1 '/ FIE LD CHARACTERISTIC / / i / f E0-2500, Zo-1-IOj, = o. 90°Leading Current / / I'R = O L / / / / / 7 / / r tu / / 2 / 1 / ? / / / s / ?/ r / J / ^ *X / / 7 I* 11 ^ / / ^x / // / // / / // ! / / / I/ / / // / / / / / / g / ^-x ^ x'' xlO 3- A, nps. fig. 133. Field Characteristic of Alternator, on Wattless Condenser Load. With reactive load the curves are more nearly straight lines. The voltage drops on inductive, rises on capacity load. The output increases from zero at open circuit to a maxi- mum, and then decreases again to zero at short circuit. AL TERN A TING-CURRENT GENERA TOR. 307 M VK 4^z W Fig. 134. Field Characteristic of Alternator. 186. The dependence of the terminal voltage, E, upon the phase relation of the external circuit is shown in Fig. 135, which gives, at impressed E.M.F., E0 = 2,500 volts, for the currents, 1= 50, 100, 150, 200, 250 amperes, the terminal voltages, E, as ordinates, with the inductance factor of the external circuit, as abscissas. 187. If the internal impedance is negligible compared with the external impedance, then, approximately, w 308 AL TERNA TING-CURRENT PHENOMENA, ' .C .5 .4 .3 .2 .1 0 -.1 -.2 -.3 -.1 -.5 -.0 -.7 -.8 Fig. 135. Regulation of Alternator on Various Loads. that is, an alternator with small internal resistance and syn- chronous reactance tends to regulate for constant terminal voltage. Every alternator does this near open circuit, especially on non-inductive load. Even if the synchronous reactance, x0 , is not quite neg- ligible, this regulation takes place, to a certain extent, on non-inductive circuit, since for * = 0, E and thus the expression of the terminal voltage, E, contains the synchronous reactance, x0, only as a term of second order in the denominator. On inductive circuit, however, x0 appears in the denom- inator as a term of first order, and therefore constant poten- tial regulation does not take place as well. ALTERNATING-CURRENT GENERATOR. 309 With a non-inductive external circuit, if the synchronous reactance, XQ, of the alternator is very large compared with the external resistance, r, current /= — x -g. 1 _E, approximately, or constant ; or, if the external circuit con- tains the reactance, x, T=-** 1 - * approximately, or constant. The terminal voltage of a non-inductive circuit is approximately, or proportional to the external resistance. In an inductive circuit, £° x approximately, or proportional to the external impedance. 188. That is, on a non-inductive external circuit, an alternator with very low synchronous reactance regulates for constant terminal voltage, as a constant-potential ma- chine ; an alternator with a very high synchronous reac- tance regulates for a terminal voltage proportional to the external resistance, as a constant-current machine. Thus, every alternator acts as a constant-potential ma- chine near open circuit, and as a constant-current machine near short circuit. Between these conditions, there is a range where the alternator regulates approximately as a constant power machine, that is current and E.M.F. vary in inverse proportion, as between 130 and 200 amperes in Fig. 129. The modern alternators are generally more or less ma- 310 ALTERNATING-CURRENT PHENOMENA. chines of the first class ; the old alternators, as built by Jablockkoff, Gramme, etc., were machines of the second class, used for arc lighting, where constant-current regula- tion is an advantage. Obviously, large external reactances cause the same reg- ulation for constant current independently of the resistance, r, as a large internal reactance, .r0. On non-inductive circuit, if theoutputis hence, if or then dr That is, the power is a maximum, and £ and 7 = V2 So {so + r0) Therefore, with an external resistance equal to the inter- nal impedance, or, r — ^0 = VV02 + x^ , the output of an alternator is a maximum, and near this point it regulates for constant output ; that is, an mcrease of current causes a proportional decrease of terminal voltage, and inversely. The field characteristic of the alternator shows this effect plainly. SYNCHRONIZING ALTERNATORS. 311