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'd _ """W’HC ' ‘ 'l. . 4 y’ _ .I ‘ . ‘1 "'l". ‘- I "- it: ‘ ‘ ~ ~‘A. ‘_‘ . ' . . .II ‘ ‘ . ‘q’ C . _ L ‘2 . ‘ ‘ , ‘ ' " .l . ~ ~ -- ,"r If“ _ 'M '1‘ h . ‘m : u‘ . -' ' I ' . ' ‘ t~ ’l " I r’ ‘9; 1' .~ I“? "\ “3’- " _.‘ in '1': ["374 " m “m '4‘ I' I g I I L a . ‘ . L ‘4 , 'fl' ' . 4n- «J , I ‘ .‘ .' . _.-.. 1 u‘ - . n . . Y . .t ‘1 . r + P . s .1 9 ' l I J . . \I ~ \ ‘ or a l J ‘ .. I’ ‘ ‘ ‘ r ': ‘ 5 uh" - . . ‘ V, , ‘ «' a . . ’ - _" .9. ‘V t- ?' ." r , , . ‘J‘JJ'U' ( A i‘ }5-‘~-\ - --1 § i ‘ V l" ‘ 0 1 - '4'... b."'l 4 ,- ‘- ‘ » “~r ( ‘ "l.-s~~’|‘:l . ' | - ‘ " '.l ‘ ’ {v *1“ I, u ‘. ‘1'“ ‘ d If ..' ~32 ‘ . , .1 " H. n‘ z" .‘ :3 .L‘ '1‘“; .1 ' I a . . ‘ . . ._. ‘ ' ~- " ‘- " ' '. .r ‘1. .z’ ‘_ ...~.'. 9 .1". 1' -* ‘ ‘u’ TA. .411“ t , Ll I 4 > “ .,l . Q: ' ' ' ‘» I“ I '1‘ .. L ’J' "‘ - l ‘. ’ V: L -“ tr ‘- . ,. I . ‘e. I '5‘! v ‘ 'l I :3 1 ‘ ; I 'l ' ' " I ‘ - | . h . ~’. ‘ I ‘u' I. K . I I ‘ g’. . .\ ~ -, _ . r ‘ ' ‘ 3 ”fl-K, _‘ |'.‘ "‘n' ”.5 E: .“1" I I‘ {5 _ ,. '1'.‘J\v. ’p -|"‘ I. I k 9. ‘\ . 3. ". \. w ' ( " .{~. A. '0: I t I“(\ k “ k | y 1“ ‘(' f . \ .w'l‘ ‘J :‘f’:}vt. . l' ‘ ',“", ’9 ‘Q " - '7’. '.:J: r...- ' ’l. ." "ft‘ "1 . “a": r ‘3' .-‘"V‘3‘_ 19".} if "(3..” {I ._ ..\".-‘ l- ~. .‘-‘:'.'.f, ".‘ . n'W: \. y I“ - ~..' .,“J ~tf v ‘ Q I". .9, t“ »~)-‘ '4- . - ‘- m ._- ‘4‘.¢ 1“" ‘g' N". 3'lf.‘"‘$f.‘.. {a ‘I‘brg "rm, 1% M . .‘t‘t‘l " A TEST MED Ammls ALTMNHHG mum LABORATORY OF IICHIGAI STATE COLLME A. m 5mm TO “ME FACULTY . or RICHIE“ STATE COLLEE B! I A4. m xii. m t—. CANDIDATE FOR 13mm 0? momma 0? SCIENCE JUNE. 1950 TH E515 1312:: we": r1 the parallel Operation of alternators has been of great practical and theoretical interest for about forty ye rs. Tb enable the elect- rical engineering students at lichigan State College to more therely study this subject. a special motor~generator set w s lately purchased from the Burke Electric Company of Erie; Pa. While this set zas been tzscd in various ways no complete test has been.made of it. The authors of this thesis have undertaken to make such a test and some of the fruits of thtlr labors are prevented in the followirg pages. Preliminary to the laboratory work a survey’was wade of the theory and :rrctice of the operation of altornators in parallel. All data was then secured with gre-t care, and it is believed that the results are reliable. we extend our thanks to the Staff of the Electricvl Engineering Department and to others who helped us in our undertaking. 1039 3’ a cum-.1. Pegel. beer: of elternating current machinery. men. Pege 9. heretical neon-elm er synchronous machines. 6301.111. P080 20. Description and pictures of file m 14 let. 61102.11. Pege 26. lethods e! W. 63013. Pege 80. ’rerfomnee of the hub Set. ”.71. M “In Perellel exam-“lea."l MENU. Page 71. Regulatin. cans-mu. Pae- 00. We fem. m It“. Pig. .8. m1- ALMA“: Ingenerel itwbe eeidthatenelteneter is ueleetri. generate:- i’er producing elterneting current or urn-onto w a rel- ative notion of 00th ad e hepatic field. Here mum. e synchronous alternator ie one in which he metie field is ex- cited ‘0‘ aireot correct. his is the next general type e! amm- inue et themeent tine enlthe «mm ports of note. We neckine ere indicated in Diego: no.1. .rms ture ”fore Armature Voile .- A ' ' (Laminated) ~1- . .044”, I... “1910:0118 ,,/4-’/¢.i.. .5 7’5“” "Slip Ring-1's i. f} u I". v gk‘fgg‘fifji e!" I Q In! Field Leads ".TM“ tune 1 leads ' Diem le.1.- heentiel Ports e: We Altos-um. he stationery emu-e one consists of soft steel leninetiue held together in e out iron from. bole leninations ere elettea. and the entire cello placed it the" not! are held there w nubile vets-e. In luepeelneehinee. therenlvingepiur ienleofoeet in. on! in high speed whim. er steel e! greater tceile eta-out. 8. loch polo piece is fastened to this spider. and in turn is provided with . £1.14 cell. on. field.e§ited sith direct current. is so sound and connected. that tho- oppesite mastic polarity is produced in adJaeont pole pieces. the direct current is conducted to fire field coils by too slip rings as indicated. no alternator sheen in diagram le.l. is u) eiat pole three phase nchino: it has four couture coils per fines. or one coil side per pole. A echo-tic shtdl of the suture vinding and field poles is ohm in diagram lo.z. partly developed for purposes of explanation. 1 l “ v .Poai "”5 8‘ In" . - "‘ ‘50 [It‘rir' , ’5 ,, 1‘ DLJIBCZZY O L‘ ”KPJ f/«I.L xPuS. l . "£91565? _ tha; 1 phase ” , ’ its m ‘ '30: ' t. “t‘pgere 1 ’ e I Q 5| O . . o ‘ 0/ el fi‘ ’ ‘ ‘ Rotation 'map- so.2.- Armature Winding and Hold Poles of Ann-am. to entire conductors shich are electrically connected in series. belong to phase one. and are under the sectors of tins poles at the instant ohm. Hence. the voltages leaned in those conductors arsenal—.becansethqareatbytlsemestd-seportiuoffie aogotic field. are respective directions of be induced voltages together sith those of the smelting current are obese conventionally with crosses indicating airs-out flowing tonrd the page. and a dot ewes-dimly designating the opposite direction. is the poles move on in the direction of rotation. the voltages induced in this moo. decrease to sore and then increase in the opposite directin. to reach an opposing marina after the poles have noved one empletflmle pitch. has a complete altemation eomrs in the interval of time which oliapses as the pole moves one pole pitch. The coils of phase two are the same as those of phase are. but are displaced from then two thirds of a pole pitch measured alug the periphery of the amature structure. in the direction of the rotation of the poles. i pole pitch equals one hundred eighty electrical degrees. therefore. the second phase is displaced one kindred twenty electrical degrees in the direction of field rotation. fr. to first. Sincephasetvo is thesamsasxhasoono. thesamovoltage is induced in it as one induced in phase use. no third of a cycle later. i'hus the save or the vector of the voltaadndnced in phase tvo lags hshind that ofphasombycnchuidredtvmtyolectrioaldsgreos. Cos-responding the coils of phase three are so arranged that the voltage induced in then leads mat of phase one by one hundred twenty electrical degrees. lhe arrsngsncxt indicated above is called a three fiase winding andthevoltago resultingfraseaeheftho throephasesaaybeusod either singly or in combination. this type of nechine with three phases is the most new in use in poser and lighting cyst-o. Lihovise IachiIss efthe typo shosn indiagranh'ed. maisonette-u. ra- reason fcr the use of this type is that the arntsro is frn a superstive standpoint. easily sound for fairly high voltsgesand the stationary structure is more easily insulated and more easily supervised in operation. An alternator is not only capdable of converting uchoniool energy into electrical energy. but it is likewise capda‘hle of converting an- eloctrical energy input into mechanical enorg at to shaft tho operating as a motor. i'hus utilised the Isohine is called a synchrmsus notor. the material to follow. concerns synchraous nachinos in general and their operation both as actors and as generators. 4. If a machine similar to the one shown in diners! no.1. is driven by a steam turbine. a water turbine. or some other suitable device. and at the cam time if the field is excited by a suitable direct current source. an alternating voltage will appear at the terminals of each phase. The frequency of this voltage is obviously a motion of the upeed of the driving machine. home it is may in order that a standard frequency of generation be maintained. that the drivers be held alnst exactly at the required speed by suitable governing devices. the relationship betseen the lumber of poles.p. of an alternator. the speed or rotatioa.a. in r.p.n. and the frequency.f. of the induced voltage in cycles per secmd. is as follows: it f cycles per «cue. the induced voltage has a mquancy of 60: of or 120 alternatine pu- nts-m. because each cycle eorreepondhs to toe sltematins. During one revolution of the whinup. poles pass under out map of We thus inducing p alternatiuo. Consequently the outer of altomtieas per ninete is p. and 120 f equals p. Likewise with a fined source frequncy. the synchrm speedofanchine operatingas anta' equals lZOpr. In order to understand clearly the mode of operation of a synohonaus machine it is essential to be failiar with the Win and properties of rotating n.n.f.s lace a discussion of the priuiples ilfll‘nd in this consideration fallen. RHOLYIHG FIELDS: A gliding mtic field produced by means of three phase en's-ants is sheen in diam-me no.3. i‘ho machine ensuered is of as type of diagram no.1. is connected to a source of three phase LC. he rotor for the purpose of explanation is supposed to be raved. but the rotor core actually serves as a path for the lines of face. the cylindrieal inner surface of the stator is shown reduced to the plane s-sxru the ask-e‘of simplicity and cloernees. only one coil per pole per phase is indicated in the sketch. m1; a. winding is distributed over a camarativsly large number of slots per pole. The flu density in. space due to current in no phase onlyslsybe seemed tobe'nearly sinusoidal at aw ad every instmt. i‘his is indicated by the m at x-x. H. and V-V. Phase 1 Phase 2 Phase 3 _____— Alternating Flux due to Phase 1. ‘ The Resulting Gliding Flux. ,~'A1ternating‘F1ux due to Phase 2. R Kr Alternating Flux due to Phase 3. Diego-an Ina-Gliding henetic field by three phase currents. it the stator currents vary fro instant to instant. the cor- responding flu: densities also charge accordingly. but each flu racial distributed simsoidally in space. Each of the thee nveo retain their positions. but dorm a cycle of .umiiflé’m. all of the ordinates decrease. pass thru sore. reach an eppesifi ‘11—. ad return to the original value. We shall suppose that the current in phase tee leads that in phase three and lags behind that of phase one; also that the current in phase two reaches its positive maxi-n when t equals sore and that the windings two and three are displaced are displaced one hundred tauty electrical degrees to the right of winding one. The expressing for the arrest are. 11 equals I (Cos It plus 211/: ) i2 equals I (Cos It plus 6) ._ i3 equals I (Cos It 4.11/3 ) Ie’here I is the amplitude ef each current save. The curves at I. R. and V are drasn for the instants ehsn the corresponding currents reach their maxim. Consider the instant when the current in phase two is a uni-n that 'is to say. the instant when t equals sore. li’he cupuont distributions of flux density at this instant are plotted on the axis '1'. The dis- tributiu due to phase two is the same as the curve at R. For phase one. 11 equals I Cos Zi'ils equals -.!5 I . Therefore the curve 1-1 is show as of amplitude .6 B and reversed with respect to the curve at I. Binilarly ia equals I Cos («til/3) equals -.51. and the corresponding 3 urve is shown accordingly. By adding these three cones point by point. the resultant flux density distribution r-r. is obtained. By asming different values of t. and entrusting the according sine eaves. of flu distribution. the resultant distributiu nay be deter-ined at any instant. It rill be found that its amplitude is equal to 1.5 B at all times. and that it glides synohonously fr. the leading to the lagging phase always having its maxim evertb phase in ehich the current at that instant is a maxi... Rollover. and a point-hybpoint addition is exceedingly tedious. md the cm result my be obtained analytically as follow: it a certain point T. along the air gap of diagram No.3. let the flux density resulting from the current in phase two be 3 Cos u‘t Ceca. no angle 2 is measured from the point I at which the flu: in phase tuo reaches its maxim in space. The mgentie field at the point T due to the other two phases is obtained by changing- the tine angle st. and the space angle 1. by the amounts plus er uinus 2111:. has the resultant emetic flux T. due to all three phases issu- htxfi.) equals(3 Cos ut Cosx)plus ( B Cos (vt plus 2!!!!) Cos (a plus 211/3) plus B Cos (wt-21113) Cos (r-Ziils).‘ In the above expression. each cosine of the sun or of the difference of two‘sngles new be replaced by its expansion according to the familiar trigonometric female: Cosh plus or mime y) equals Cos x Cos 1’ minus or pins Sin x Sin y After mltiplieaticn and reduction I. get: . B(x.t) equals 1.5 l (Cos wt Cos x plus Sin wt Sin: ) which reduces finally to B (x.t) equals 1.5 B Ces (wt 4) It may be seen. that a sinusoidal wave of amplitude B synchronously gliding fru- left to rigt satisfies the required auditions of he s quatien. This means that the instantaneous flux density will be found to be constant at am point and neving to the right at the velocity w. Since I equls 21‘! f. slush-which value is the electric‘angular velocity of the exciting currents. all points for which flux density remains constant. move along the air gap at synchronous velocity. Thus with the stator of a synchronous machine connected as indicated in the above general discussion. to a mltiphase earns. a rotating mietic field is produced traveling in a sense. about the 8 . perifisery of the inside of the stator. new the rotor is excited with direct current as already indicated. and the one is designed so that when it is rotating at the same speed as the revolving field. each pole.ef fixed polarity. will he under a stator mastic pole of exactly opposite polarity. Thus since unlike magistio pc] es attract each ether.uhder the above conditions. the stator with its rotating field tends to drag the rotor around with file?” at synchrnsns speed as determined by to rotation of the field. The naehinsl resists an effort tending to pull the rotor out 9! step with a counter torque. and than we have typical motor action. The greater the lead. the greater will be the corresponding torque. and the greater the current supplied to the stator. Fran the shore discussion it may be seen. the synchronous notor is thus a caistant speed sunshine the speed of which is fixed by to standard frequency of the source and the number of‘pcles of the nachine. his particular feature nabs such machines desinoable for constant speed service. though the lack of starting torque frequently prohibits their use for an traction service. when a synchronous naehine is being used as a meter. it is obviously necessary to bring the rotor up to the speed of to rotating field befcreany power can be developed fien the the-rotating n.n.i’. and ammo m.m.f. are locked together.'into synchronise. Several methods of aecanplishing this result are in common use. though the cmest methodIbecause if its simplicity. is to provide the rob! wifi'La squirrel cage winding so that the machine may be started as an induction motor. The nethods of bringing synchraious motors up to speed are discussed in greater detail at a l.ter point. 12m .3- rnomiw. mscossxos or stunner-toss mm: For the sake of explanation consider two identical alternate" connected to the sans bus bar as indicated in diagran le.4. From the bus betweenthenachines: with theuchinesliandcrunning insyn- chronim with equal field excitation. the voltages as. vectcrially 180 degrees apart. and there is consequently no current flowing in the series circuit. This condition is indicated vecterially in diagra- I.050 _Q(l‘) +__—__+_______+_m Diem HOe e D m N°e5e If not the poser apply of the machine K is refined. the voltage vecter R. lags behind the first position relative to the suites 1:: byensngleas shcsnindiagranlcd. ThevoltegeE .. thevectorsun of 8‘ and 3. is ten effective in prehcing a circulating arrent I. biaenthetwonschinesthratheirilpedaneee. Mopouer istrensnitted frus G tel. if the supply of external poser is completely moved frcnl. the'sa-evilleentinmeterunbeingdriunasanetor. and receiving the necessary poser fro the generater O. m in addition, the sunshine I is loaded nechsnically. nere poser will be tree-itted from G to I and more cue-rut sill fine in the series circuit betseen the machines. the application of the achanical lead results in a difference in phase position of I. in respect to 3‘ resulting in an increase of B. shich cases the increase in current already noted. Despite the change in phase angle. the .chines will continue to operate in synchronin. provided or course. the pull out terque of thruster is not M —| 10. Diagram No.6. Diagram No.7. All of the above discussion is based on identical excitation of identical machins. Hence. 3-. the induced actor voltage. and E‘ . the induced generator voltage is}? in each instance equal-in magnitude. ler. the excitation of either the motor or the generator is changed. the phase angle of the voltage for a given notor load vill also be changed. Diagram 30.7. shove a decreased excitation for the generator with the q}- encitation for the sister. he generator hue delivers a loading meat to the line. vhile fie notor takes a lagging current I. as sheen. Accordingly for changes of field excitation of the actor and for different phase positions of the nctor voltage I. in respect to the generator voltage ’8' the resultant voltage 1. changes in heth mime and in phase position. Likewise the current vhich results from 3. changes in both ugnitude and phase position under the above conditiais. svmosxzm cums: When two alternators are operating in parallel. the vecter' sun of their induced voltages results in a voltage duet prtdaces a syuhreflsingeurrent mimmmz..fieveetersun.hy an angle depending upon the total resistance and reactanee of the series circuit. therefore. including the total resistanoe and lreactance of the tve arnatnres. line no uchine supplies poser to the series circuit. shile the other receives poser fr- it. the 11. . naohino iiioh- gives off power tendsto drive the nehim receiving poser em than: they I... be both operating fran the external eta-spam” as alternators on a comm load. nits flow of synchronising current results in a tendency torretard the machine supplying the power coupled with a tendency to accelerate the one receiving the same. has the synchronising current tends to keep the two nachinec in synchronise. then there is synchronising current flowing in the series circuit between two‘nachines. the difference betwoen the power supplied by the one nachine and that received by the other. is equal to thin . power lost in the series circuit. lf several alternators. are cannectod to nio set of bus-bars the synchronising current as tit-saw W tends to imp the. in step. If the prime mover of any one mahine tends to decrease its speed. the nachine lags behind. and receives poser by the syuhreuising current which accelerates the legging alternator thus tending to keep it in Milli-If on he etherhand. the prineneveref aw one nachine tends to increase its speed. a resultant voltage is generatoieuusing a synchronising current to flow. The machine that leads. delivers porn. is thus retarded. and thereby is held in synchronism . METHODS OF SYHCKROFIZIHGS .. ‘i'wo direct currentnachines nay be connected in parallel as soon as their voltages are approximately equal provided the proper polarity is observed in connecting thus together. however. before two altos-haters can be switched in parallel. three conditiue not be fulfilled: their terminal voltages not be: (1) of the some mgiitude , \,_ 12. (z) of the same frequency] (5) in phase vith each other. Unless all of these conditions are net. there will be a circulating current between the two machines when they are mooted together. Who the terninal voltages of the two altemtcrs are equal and opposite at all instants. the above conditions sill be not. its process of adJusting a machine to be connected to a bus bar or to mother machine. eeifiiat the above conditions vill be not is m «Wmmmmm Literally the torn synchronising means "bringing into step”. - Let us candida shat veald happen if two alternators were connected to the same bus bars without having all of the above stated conditions fulfilled. (1) If the two machines are so excited as to give different voltages the other two conditions being fulfilled. a reactive current will circulate betveen the machines/ leading in fine machine excited loner. and lagging in the machine excited hifler. ihis results in a strugthening of the field at the first machine. and a weakening of that at the second. the resultant voltage at the bus will be somewhere between the voltages of the two machines. the set may still work satisfactorily providing the reactive current is not too heavy. however. such a circulatiw curl-mt does not help the operatin. and results in en mecessery 1&8 lose in the armateres of the tee mohines. Should this mt becue sufficiently large. it my sense a dangerous mature rise intheematurewindings. eropmaeircuitbreehrmm the external lead is not messive. (2)1fthetuomchinesarenot inxhaeevithoach other. eventhoud: 13. thq are of the same frequency and magnitude. an onerg current will circulate between til... this current tends to bring the two machines um step and it may be quite large if the differemo in phase is considerable. if the torque due to the synchronising current is large enough to bring the two mchines into phase promptly. the surge l current till be of short duration and will not damage fie machines. Otherwise the srnaten findings may be overheated. and the insulflon duos-d. (S) If coupling without synchronise is attempted when the two frequmcies differ from each other by a fee percent. the conditions are approximately the some as described in (2) above. If two simcvaves of nearly as a.» frequency are drawn this condition may easily be she-n. It will be found that at some instants the waves are in phase with each other. than they are in phase quadrature. in phase opposition. and after a umber of cycles in phase again. Unless the cnorg component of the circulating current is sufficient to pull the logging machine into stop pranptly. and to hold it there. we of the machines my be injured by the inrush of meat. An ordinary oil typo circuit breaker is meh too slow to protect an alternator against excessive transient currents dno to short circuit or to faculty mehroxtsing. therefore. it is necessary that great care be exercised shen synchronising a large whingfor the first the. After the correct speed of an alternator to be synchronised to the bus has boa approximately obtained thereby meeting the frequency requirements. the field currents are so adJ‘zgted as to give about the sons voltage amthat of the bus to ehichtfnaohino is to be connected. It only ruins to bring the machines into phasesith the bus. This is done with the aid, of synohonising lamps. or a mial I W’s 14. 82131135 EE'I'BODS : A motor of ehioh one member-(say the stator) is excited with alternating current and the other (the rotor) with direct current. possesses no starting torque beams the direction of attraction bet-eon the We members is reversed vith ouch alternation of the supply voltage. For the same reason. the machine has no torque ‘ for speeds other than synchruious. It is only ehen poles alternate undu- s given armature soil at the same rate at shich the current in m coil itself changes direction. that a unidirectiaiul tugaitial effort vill result. For this reason a synchronous ester bus to be brought up to speed either by Icons of snether machine or by tuporarily converting it into on induction motor. The fellcsing estheds of starting are among those nest commonly used. (1) When a synchronous sister is part of a motor generator set the other machine being a direct current or an induction generator. to generator may sometimes be converted into a motor for starting shes the proper source is available. he machine may be thus started and synchronisedbynesns ofthenotoronfie some shaft. (2) A smell induction motor or LC. cmtntornotor can be used to bringssynchronousnotunptespoehprotihdthettholuttoreeu be synchronised before the lead is applied. When directly eesneeted. the starting induetiai sister should has a smaller mbor of poles than the synchronous machine in order to be able to bring the letter up to synchronous speed. (3) the field structure of the synehrums motor is provide: with s squirrel cage winding of sufficient resistance to give the required starting torque. liiiis is at the present tine. be neat cm sothed of starting sycnhronous motors. 15. (d) i cylindrical three phase sound rotor like that of an induction noter of this We is smetimes used. This winding is closed on a resistance for starting and. is excited with direct current for ' operation. (5) A friction clutch is sometimes interposed bet-eon the synchraems meter and its lead. to reduce the required starting current and the else of the nachine. The stator itself may be used as seeh a clutch. It is thonnountcd ensuriltiarybeeringsuhidareuseddurisgtho starting period. A brake is provided of such proportius as to bring the stat» quickly.“ syndironous speed to a step. A high startinr? tuque is thus obtained by virus of the fact that no torque whatever is ones-team theleaduntil the staterhas osnenp to We speed and full excitation has boa! applied. Thus the torque which is available as the rotor speeds up and as the stator retards is fie neximnloedtorqse. orehat isknosnae ”pulleuttorqus”. mm: In a synchronous motor. torque is a function of the relative phase position ef flie rotor and the impressed stator voltageJherefere. when the load changes on a synchronous motor. the rotor is required to change its relative moo position eithout chem of speed. It is obvious that these two eonditions are not strictly eenpstable - hmce the rialt is effected in a series of oscillatory changes ehioh nay produce serious disturmes in the systole. If the load ed sush a motor is decreased. the torque is in excess of that required for the decreased load hence an acceleration of the creature follees. non due to this acceleration together vith inertia ofthe comparatively heavy armature. the speed of the same increases to some value elifitly in ensues of synchronous. Subsequently this to this new change of phase 16. peeitiui. the torque decreases and becomes less than that required by the load and this difference mat be adjusted by the subsequent deceleration of the armature. then once more the armature has reached synchronous speed. its phase position is such as to give less torque than required by the load. nie deceleration thus continues and the phase positiui is retraoed until the torque again balances as lead. However. the armature speed is by this time less than synchronous and again passes the desired position. 'nie change in kinetic energ of the rotating mass thus eases the erasure fl oscillate around the desired position which is fired by the torque Just nfficiout to equal the load. DAIPIRG: the results of this oscillatory action any is she instances be eunlative so but each successive Oscillatiu increases is use- nitude until the machine finally drops out of synchrellel. fie coo-snout mid nest effecting method of reducing this oscillatory action known as hunting. is the use of urtisssur windings. tie winding consists simply of a short oircuited grid sinilar to the squirreleagevindingofsnindnetiunstsr. placed iaslots along the periphery of the field iron core. With such vindings. the Ming oscillations of the antes-e cause a correspuding change of flux interlinhges of he windings thee cousin a M to flee in the some. the magnetic effect of ehich senate tb elnanteryluas shtedbyhons. aetsasabrateonthearuature oscillatius. the squirrel cage rinsing provided on case machines for starting as on Mien actor. effects in additin the purpose ofacmgasansnortissarvinding. max-name- isruaning in synohronisn no lines .r force out one squirrel cage strue‘hre hence under normal operating conditions the presence of this winding does not affect the Operation of the machine. The winding presides a means for gradual Moment of the motor phase positions for ‘ugee ef load. and thus tends to eliminate troublesome surging er hunting of the synchronous machine. SYNCBROE’OUS CONDEIISERS: Let a polyphase synchronous motor be brought up to speed. synchronised. and placed on the line at no load. If axing fie process of synchronization. the field current of the machine has hem se ad- J'ested that the indneed e.n.f. of the motor is approximately equal tethelineVoltege.thenachinetakesenlyassnlle1n-rsntnecenary to evereom the no load losses. If the field ens-lent then be sasshat decreased. the meta adjusts itself to the new conditius hy taking a lagging current from the line or delivering a leading component to the line which amounts to the same thing. imis reactive current cans“ an sonata-e n.n.f. Inch strengthens the field althoug: not quite to the value corresponding to the line voltage. me has voltage exceeds the notes- connter voltage by an want equal to the reactance drop in the armature. 'Ihe counter voltage nay be wt of as consisting of a voltage induced by the weakened field. and a voltage (his to amtare reaction. Of course the field n.n.f. and the mature n.n.f. seabird into one effecti. Is.n.f. . is no load. and with a machine with! salient poles. the field excitation nay be "diced almost to sero vilhoet the machine's dropping out ef step. Sons motors w cmtime to run even vithont aw excitation eporatinr'ss 'reactanse machines". 0: the other hand. if the ensitstion is increased above normal the machine will draw a leading current free the line. In this case. the resulting amatnre reaction reduces the field. The more the achine u everemcited. the Ian-su- will be the leading current which n sill 18. draw from the line. This effect is demonstrated in Enrther detail in a later discussion of current loci. The property of the synchronous motor which enables it to draw titer loading or a lowing current from the line at no load. is utilised when it is desired to dress such a current: for example. for voltage regulation. for fir factor correction! etc. to obtain this offset. a synchronous meter is cemectod across the line at his ‘ desired point and is run idle with flie proper excitatiai. file fipld current may becontrolled either by hand a- ‘by on «tactic register for a desired performance. A synchroims machine used at no load for the purpose of regulatiu is called a'qnehraicus condenser". A better nalse is "mu. adjuster" since at times the machine nay be called upon to draw a lagging instead of a leading current. AEIATURE REACT! 0R There are thrcem causes of the difference betseen no load voltage and voltage under load with the some field current and speed in an alternator. may see. armture resume. senators leakage reactance. and armature reaction. be lattter canoe is the one in which we "{ffitomatea... this poi-c or W. ‘ Whenacurrent is flowingthruthearmaturewindingitbecnes a source of nfiietonetive force shich is confined with that of the field winding. weakening (or Whaling) and disteeting the field flux. i'he flux having thus been modified . the e.n.f. induced by it in the armature windings is different fras that induced by the originl flux at no load. The achal effect of the armature reaction is quite complicated; but for practical purposes the nsgiietonctive feces of the amatare new be resolved into two compenents; 19. (a) Direct armature reaction. whose ampere turns con be directly subtracted ( or added to) those of the field wi d’ng. (b) benewrse armature reaction, whose effect ‘:n a generator is to shift the field flux against the directim: of rotrtion of the poles. and in a synchronous motor in the direction of rotation of the poles. 'me armature reaction is simpler in a polyplmse m-"chine then in a single one. because in n polyphcse machine the monetomotive forces of the individual phases are combined into one resultant neaetmotive force which glides along the air gap at the some emler velocity as the field poles. Therefore. the relative posi— tion of the field and ermture mn.f.s remains unchanged with the t ins. 20. gyzcrg 59.3. E m M fill file Burke motor-generator set new installed in the alternating current laboratory of Michigan State College w: s manufactured by the Burke Electric Company of Erie. Pennsylvania according to spprex'imte specifications furnished by the Michigan State College Electrical Department. The design of the set was supervised by Mr. Burke. of the Burke Company. has set consists of three units mounted on a sermon shaft; e 2200 volt synchronous motor together with two 220-240 volt synchronous generators. lite stator structure of one of the 220 volt mchines has been so designed that its position in respect to the rotor may be edJusted by means of 9. hand Operated, worm gear drive. Since all of the machines are on the some shaft. it has merely been necessary to srrenge the 220 volt srnstures in identical positions relative to their respective stators in order that the two machines may at all times satisfy the phase and frequency requirements for parallel opers— tion with the movable stator set. of course, at e fixed sero position. i3113.5 by shifting the edJustabls stetor‘s position numerous parallel operation conditions my be obtained for study using the 2200 volt mehine as e prime mover and testing the two 220 volt machines in parallel. l‘he effect of an effort to her use the speed of the prime mover of the one machine may also be effected by merely shifting the phase adjusting device in the proper mamer. QL. Photographic disgren no.8. indicetes the general leyout of the set shoeing also its relative loostia in the laboratory. he switch beer! sheen in the foreground ef Diegran He... is provided with circuit terminals of the ensures of be”: small machines so that meters m be emollient]: inserted in these circuits for test purposes. Also en opening in the field circuit of out: of the moraines is provided for the insertion of field clusters or additional field resistance units when desired. There are also mounted on the board. field rheostats and switches for the cull nechines . I P 0‘ s11w' I 4 if” 1‘ a [i ‘i 5;. _. Li 171m _' Ema- Burfi 2W ‘ M 7 *eai-“ser* he connections of the 2200 volt ma chine are permanently installed though there is a fuse box on the opposite side of the set from he one show in diagn- lo.8. in midi connections me; be made for my: voltage tests of the lye-533%. Disgra- le.9. indicates the General Electric Starting mm which is permanently eennected to the 2300 volt machine. he field switch my be seen in the upper right corner with the field rheoetet i-sedietely beloe it. Resistance units are provided thru finish the field sindings are shorted during the process of starting until the creature has reached synchronous speed. in creature cluster and line vol‘hetor ere also installed on the nain board though they are out of the fonge of vision included in diagram lo... Diagram 30.10. she's the cosmectien details of the hand starting cupexletor. 'i'he armature emotions of both smll nechines together with their field terminals load to the min board shore they new be ca:- veniently comected for various experiments. Diagrams lo. 11 end 12 indicate other vices of the set. l'hs hand phase rotation adJuster may be seen on the left hand machine in each instance. Disgrus 30.11. Diagram ”.13. Diagram ”.13. is a close-up of the machine eith the noeoeble tau. stator. no scale indicating olectriosl degrees phase rotation my be seen in the foreground of the view. the salient pole structure nsy also be seen. f a ~Q " ‘ ' . .A‘D e f ;a ,1, _ Z r ‘f. [I z ' y ‘ . ~ e fifngE- Over-e1” if isfioT’su-b“ a. _ inch machine is provided with a squirrel cage winding shich serves to provet hinting and also m be used for starting as on induction motor. - no nae plete specifications so furnished by the nonficturer are given on to following page. for each machine. Dim-n In -9- 24, 9.“! lent-stared by: Barb meetrio Comp-1w. Eries Pa. Bari-.1 lo. 138264 mo 1.0. 85~ Alternating current Generator IJJ. - 33.1. 4- vat- up. Cy n 7.5 1800 240-220 10-19.? 60 ' 3 3-1. Serial lo. 1258686 Type LC. 85 KJJ. 3.2.x. Volts up. Cy P11 7.5 1300 240—220 18-19.? so 5 15-7 “" Masha-ed in Barb Electric Comm. Erie Pa. sum so. 138609 Type 153309 Rating Continua 'r emp 0’40 WM 1.1.1. 3.2. B‘.‘ 12.x. Volts up. Cy Ph 21.0 25.0 moo 2300 5.5 so 3 PJ. 100 field amps 3.8 Exciter Volts 220. lotor '1" V V C entrel Circuit Trans. m / OH 0 fl“ i‘rip Under Voltage fine 31s: L m __, ,_. W . w { J»— (W: Auto frusteraer mmgmmwmmm Diagram No.10. 26, WM- 5.- IO LOAD LOSSES: The first test conducted in the laboratory was that of det- ermining all no load losses. For this purpose. a direct current motor w. arranged to drive the set as indicated in diagram No.14. Since no accurately calibrated d.e. machine was available. it was first necessary to calibrate this machine by determining its no load losses together with the corresponding field and armature current at the speed of 1800 r.p.a.. the synchronous speed of the set. A Imp bank was provided in series with the d.e. armature to conveniently vary the terminal voltage. In the following tetts. the armature re- action of the d.e. machine is inored and iron loss is regarded as substantially constant for a constant field excitation. After determining the no load losses of the direct current machine. belt friction in the drive was estimated at 1800 r.p.a. The direct current machine was then started/driving all three alternatcrs. Keeping the field curl-em constant atthe no load value already determined. the speed was adJusted to 1800 r.p.n. with no excitation on the alternators. The power input of the due. naohino was then noted and recorded together with the amatare surrent value. . hen the field of ll—‘I was excited from the d... souree . me direct current machine's power input and annature current values were then noted for each of a series of field excitations of [-7. thereby obtaining data for iron loss at various excitations of 11-7. ‘ ..‘ ‘ . . _ .'. 'I." .‘ ’ :fi',~({ ~ 7 ‘ 27. 0 Direct Current Rotor .; . .15 ~ ’ (v1 ‘ ‘t '1 .:3" ' V t '1 fOItS' do 0. .13.... ‘ . ,9: L;'- ~ - " . - .'_. o ‘J ' l we." ." - Field Rhee f."- 2' w ,. ' ’ C 1 Hold hheo r1814 moo J “#7 'I 28.’ ihis same procedure was repeated for 6-7 and 6-8. the coupling between 6-7 and n—1 was next removed and power with direct sun-ant input noted for the driving machine without ox- oitation of [-7 and (3-8. The 6-8- li-‘I coupling was then removed noting again the input to the direct current whine without excitation of 6-8. Thus data was obtained for computing all losses. oils CIRCUIT TESTS: 0-7 and 0-8 were connected for open circuit test as shown schematically in diagran ls.15. The driving notor E4 was started and connected to the line source. Then beginning with very snail field current values for 6-7 and 0-8. their respective excitations were increased in wall steps noting for each step the corroepading field currents and terminal voltages. SHORT CIRCUIT TESTS): 'ihe armature ternimls of 6-7 md 6-8 were connected in a shorted I with on motor in each bromh as show in ding-an lo.ld. as driving notcr 3-7 was started and connected to the line. 'iho field currents of 6-7 and 6-8 were til. increased, starting with very snll values. in convenient steps noting in each instance the current value in the field and in the armature. '1' Curves for [-71 For this test 0-? and C—8 were provided with a variable resistance load as shown in diagram 10.17. 'V" curve data was obtained for each of a series of loads of ma indirectly provided by 0-7 and 6-8. Full lead was regarded as such load as required rated current at unity poser factor. lith this in view 6-? and (1—8 were uncoupled for no load data. Then startding with a all value Field Rhee Field 110 Volts d.c. {a 220 volts d.c. Field ' 3 6 2200 volt! Source ofA.C. Field Rhee ‘.,‘..-IJO . All Field Rhee Field 110 volts d.c. Field Rhee Field 2 20 Volts d.c. I'ield Rhee 110 volts d.c.!ield \ MW” c a 2200 volts !_. A .C . Source ‘V'TT 7" " '* 'uv n ‘ 77 ‘ \ ." ,_ p I. ‘ . . o ‘ o ‘. ~ ._.ue1‘ &. . "h’ %. A‘. &.a .r‘. \W a. &.1 a .Q\ ._ r. r- . .1. .. it ..... . .. . v w: .. d . n).. ‘,.. .7 e ed . ‘~ 1.. o. . ,.,., In. . a: x... ....v.un. w. 5| 1 I‘D ‘ a a. “D's’ . p y? . .. .. . I. o . .‘l . ...o . new _ e . 5‘ . m g .N 1 r’ l. _ as . . ~ 1 I .5 ’ _ -. u a s .e ... . _ n‘.‘ .W .e. . o. ... | a .C . 1. OK 7 t . u .e . 4 U I .l ..§ I . N .. —— 110 V. 13.0. ‘10 Yo p.05 Balanced Resistance 110 v. Doe. H wmmmnmnn sag. D 131,5:er If" .18e 33. of field current for 1-7. the excitation was increased in steps noting in each instance corresponding values of field current. armature, powerg-curront, and voltage. 'l'hc point at which the two watheters recorded indentical values was particularly noted as that of unity power factor. i'hus values were likewise obtained for a series of leads by rccoupling 6-7 and 6-8 and loading then as already in— dioated. For determining the ”Y” curve data for Go? and 6-8 the alternate machine was respectively loaded. Diagren lc.18 indicates the set up for 0—7 '7' curves. The one gueral procedure as noted for 33-73: was followed. This procedure was again repeated for M with 6-7 loaded. manor 3 to percent regulation of (3-7 and G—B was detemined in tin laboratory for unity power factor. .'I log and .7 load. no connection diogrns for this determination is Emit. To provide a means of varying the power factor 0-? was loaded with a synchronous motor which in turn was arranged to drive a d.c. machine. This d.c. as hino was used for starting and synohronbising with 0-1. and was later used as a generator to lead the synchrcnsos notor. no load was first adjusted for unity power factor and the sanitation of G0? was so adjusted that rated current at rated voltage was obtained. This rated voltage value was noted. and the load switch was subsequently opened. as aw no load voltage value of 607 was then again noted and recorded. low power input to the load (or synchronous noter) remins substantially constant (but for copper loss ) regardless of the excitation of the machine. Hence the required wattaoter readings 4114.. “Ii-4]“ . ...... . “Qty... ..i . eqwnr \. m. .11.. u.L.~....r...w...:.. do?“ haw-.44. «:43 14.1.1.1“... 3.4... ..... .9 ha“ o . . kivav V.. ”.2.. Wu... ..4 .4‘3 ue. . .11.: .. .hvsflw. . 3.9.4.de “fiszfid; . _ - .. .. . . . . is 4 “'G\ ‘a JIe 41". ‘N.’ o . . . . . . 4 . . . . 4' _. _ 1.. .jl. 4.. j,“ 3‘... m. x .1. ‘5 o... .. . . . . Suez. .53.... ... 4J3“! . . 1...... .2... . .\ L. . .. . w 4 . d“... e svxvr. 4 . . . a . . .... .U: ~ -. e_. .4? ... . . e ’4 s D . . >r’ {b 4 I .r. ‘ -0. 61‘s.. 4 ‘ . .'e -. e9. . ..‘s L. a 4 . . . . .. c . . 4 . s . . ... w 6.. o. . .s'. u . .. _ .. . .2.... .. . .. . . .. .... t . . .eu. .‘- . W 3. . .4 . . s a t n . .h 1— 4 r . 4 e‘ C . q. . ~ . s . 4 x r . . s . e a 0| .4. . . V. . O _ o o . . . . . O ‘ . . A ‘ ‘ . - . . 4 ' . . ‘ ‘ O C 4.1!. f s 1. . .x... . . a.. o \ . . .a V . I O '1. .4. 0. e .a s. . e e ... .4 t S u r... . e r _ w . . . ‘. ‘ I . w . . a A.‘ V f I O f D . ‘ em a n a .Cd. 1 n to . . ... . . .. - .. .. . u C c . . .... e. “m1. 6 e‘... J5:- i a»)... ...... 3.9.. 4...... .r.... .._.._ b.“ .. 55. fer rated current and .7 (1m) power factor were Immted. The load and the Inf-Mn. o-v were then so adjusted that rated current was attained at rated voltage with a power factor of .7 leading. be lead was then again thrown off noting the new voltage a, the teminals. his preeeinre was then repeated for a power factor of .70” ). he one schem was utilised in this test of 6-0. PARALLEL OPERATIOIH me two machine were connected for parallel operation on a common load is indicated in diagram 10.20. The voltage of each machine was adjusted to rated value and the switch between then was closed letting the load switch (open. no phase angle of 6-7 was then shifted in incrmts of five electrical degrees noting fer each setting ef the 0-7 stator. all mtg-voltages and power values. A lead was then applied by closing the lead switch and adJusting the lap bent resistance. i'hen starting again with the sere pesitien of 0-7. the phase was again shifted in the salsa increments noting the sane meter readings hoping the to: voltage constant as rated. the phase shifter of (1-7 was then again returned to the ear. position. he excitation of 0—7 was increased and that of we decreased simltentoush' in convenient steps maintaining rated hes voltage and consequently constant retistence load. All meter readings were noted for each setting of the field rheostats. OSC ILLOGBAHS: Oscillegrems were obtained of the voltage waves of 6-7 and H equal and in phase. and equal but 180 degrees out of phase. 2300 V. Balanced Resistance “0‘ cg?“ : A mm - 0‘ , ~ _ x4 . « _ v 5 ‘v e ‘ - 37 1b revell harmonicsescillograms of the current for each machine under a heavy condensive load were also obtained. A three phase voltage wrve was photographcd’with a resistance load an each phase so balanced as to give equal voltage values. Starting armature current. field current. and armature voltage sane forms were also studied and a photograph was obtained of each of these during the process of starting'flh7. BESISTAECES: Cold resistance values were measured for each phase by the drop-ef-potential method using direct dnrrent. These values were checked by means of a portable wheatstone bridge. GENERAL PROCEDURE: the general characteristics of the set were observed during all tests. Ehe effectiveness of the damper windings on each.machins was noted. as a prevention of hunting’action. All of the individual peculiarities of the set which were noted during the procedure were recorded. PERFOMCE CURVES: In.nbtaining'the data for performance curves, the same connec- tions'sere'used.as for "1” curves as indicated in diagrams no. 17 and 18‘ lbr various field excitations of each machine respectively; the ‘load was varricd in convenient steps noting for each step. the cor- responding’current and power input to the machine under test keeping' the voltage of that machine constant as rated. 38. PERFOE‘MCE CURVES: It is probable that the performance curves included in this chapter are good indices of the actual performance of the machines under test. Inch time has been devoted to their completion to as great a degree of accuracy as has been possible. 'me first dingrmns shown. 30's. 21 and 22 respectively. indicate the iron loss rt no load for the machine 0-7: 0-8 and 3-7. In obtaining performance curve drta in the laboratory. current and power inmt rerdings to each machine. together with terminal voltages. were obtained in respective order for different loads. From the input values for each load 123 losses. together with friction, Iindage and iron losses were subtrected to secure corresponding output values. ‘Bien efficiency was calculated as equal to input/output. All performance curves are plotted again-2t K. W. output of the particular machine under consideration. Current values are plotted directly as obtained in the above mentioned procedure while power factor values [In calculated in each instance. as equal to Power/f3 El. Losses 'vere also plotted as computed for various loads. A set of curves are included for various excitation of each machine.- 59. the shape of the efficiency and power footer curves ie typical. In general. atoning true eere they reach e maxi-n te- rme’}: alight]: beyond rated lead. Fer e given power output it is evident it ie evil-t that for an: excitation other than that for unity pour factor; sore current met flow, hence there ie here 128 ion end'leeer efficiency. Liberia the poeer factor decreeeeo. Hence this genera shape g! per- fme enrree fer «111’er excitations is explained a a Mind b“:. e The obvieue new in the determination of hose perfomnee curves is that the curvee of diagram lee. 21 and 22 are not mete indications e! iron ioee under load becenee they do not one! fer nature reection. However. eince it is very difficult to m the npitndo of enetnre reaction. the method here need ie Jutifiebie. no reunite here indieeted ere in all probability very oieee to theee ofeotnel leading. in input-output tutnialt haxebeenneeihede whine been eveilebie ehioh ha! been eeenretely calibre“; toting eeoount of its amt-re reaction. A mideretiom of the ehapee of the enreee of diagra- lee. 21 end 22 leads te the oonelneion thet vifinin the nun! operetieg coalitine ef the machines their fields are not counted. If fie: were then came would elent shun-ply upward t“ te the right. lent modern neehinee ere deeigned to operate under nor-e1 eonditieu eifi e eetureted fieli heme thie reunite in greater etebility. In spite of this obeervetial the machines of the Burke Set ere emperetirely' stable in operetion. Another interesting thing to be observed in emetic: with general performance is that the trictien leee ef 0-7 is eoeeehet ierger theathetofa-Ladeepitethefeettheteacheftheporteereef 4o. ; iMieal 41.5mm. cm: is due to the fact that the noveeble stator W of 6—7 is suspended directly from the shaft. mic is further W i by the fact M the bearings of machine No.7. tend to run hettl' the then of 6-8 and 1-7. It is to be noted that frictionIvvindage and iron losses ere r practically constant as shown on the performance curves. for a given excitatim. Here again erasure reaction rould tend to alter it. E lees W friction and windage ere actually constent since u are functions of speed and the structure of file rotating parts only. *v'cmmas: 1 curves are a plot of field current against armature current fer ‘ Kim M on a synchronpus‘motor. A complete set of these curves differing by steps of 20% of rated load are included up to 10“ load . i'hese curves are shown in diagram hos. 23-24-25. For " a fixed load on a synchronous motor it is evident that for any excitation otter than that for unity power factor a greater current not flow than at unity. i'hus at unity power factor. the current is a nit:- for a synchronous motor with a fixed lead. The smaller the field Wbelevthat faulty poser fetter . the greetu'v‘illbe the arlatu'e mt. Likewise for excitations above that of unity pwer factor. the arrest inemsee with an increase of mitotic. Mitotion’as alresxbv explained‘eesults in a.leading current. while under excitation results in a lagging current. Kernel excitation of 1005 is regarded as that excitation which vill give unity pol. factor at rated load. mm LOCI: tt mmmmbemfitérzmyundersteodifthem loci for me machine (soy 6-8) be considered. Diagra- lo.26 is a plot of seeh loei for actual value obtained from M . the loci of Voltages and Marcus-mt for different £1.14 emitatims are indicated. Diagrams lo. 27 to 59 are the performnee curves already d. 1m‘.de Itsusnotedthatthedmpervindings efeaehnachineeere effective in presenting "hunting aetin” vith the nechinee operating as actors. Of PARTMENT OF MATHFflAVICI e-e tee a 90-h. let's-0.." 9.. .4 Y . 'Oosv ‘v P‘. ’0 JhYTO . o e MICHIGAN stave COLLEGE e.‘ 4. o .1. .. O» Q” 1 o e . e-b oeoeoveue | P ’v-é-ve .16! 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'0‘. -A ~ ¢ .49.- ...V. « .'Q-... . . ..... . . -v .. ,,4-....‘.--_ ---... .. .0 . ... l ". - . . - - o . . ..... . .. .. . . ., ..--W . ' . . ......- . . . ‘. . .. - ” Q-O‘ -—.-‘v—. V moo-”m .. ‘.... . .a. u .) ‘.... . - -o . . ..«Q' ~. 0 . V .n . . . . .. ;.,.. ... . ~-o ..4- . t ‘V . . ), _ 4. f —... u—-.-~.- -- O . . -.t... .... ... H b .. ‘ ....Y ‘ .7 . . ..v‘l ." -O- <. I ' - - -.. p --- loo‘ -6—> ‘.. ' .IX'. . -> . ..- .. . . " ‘ .‘ ... .1... . . g .L¢O' I -. “~ .oAH-V t O ‘1. ' ‘r4 . . ... . , _,,. . _ . ..‘.;1Aa ..o- n . ' -Ov- n c I 1 '; II I. . 0 O . ~~ .- . .4"... ..-_. . .-.. .- . . ‘- .9. I-v .‘ .... . . '. - . . . . 1 . ... ooy .— }H- o . .» ! . ov- «'. ..‘ ‘, -q.‘l§ no. .. ..- _... - o - ¢k . ' ‘ r‘ '. o .. . J -3'yq~x . '. .1 & .'noo—‘.»_. . A‘—~“-~-—~ .4 o: - -, I.f,_,..¢. YI"’ . . ,, . W,,.... 4 .. .... . ., . ., .- $H . .. . 0. 0 <90 ., . .9t~00 4‘ ‘0. . , ,, ..i ....-- o. -.v.-T ‘ . . . .m“ D . ‘.. .‘3 . .1. ., .ov<>oo-O-‘ .zo"< .0 . -... ‘ . 4— o... 10"- V-‘" .W ,. .‘v 49""- ‘ .< .... ‘t o0 9"“; . 'o-- Ov#0V~’ o f . ?"‘ .Aoo‘o‘i O 'O 00—- 0 < .- -’yo.“‘ DEPARYH (NY OF HATHEMATIC. 61. W 12-9.- REULTS OP TESTS: When two alternators have been adjusted to series opposition U fleece as described in an earlier chapter. their voltages are in the proper relation to canoe tha to operate in parallel,- delivering current to an external circuit attached between the. to the bus fire. In the initial consideration. 0-? and 6-8 were placed in parallel without lead but with equal terminal voltage. The phase of (3-7 was shifted which effects the same result as a tendency to change the speed of the prime mover. .dll values of current and pewer were noted for various phase shifted under these conditions. Diagram He. 45 is a plot of power and current values for each machine against phase shift in electrical degrees for 0-7. Since the same went flowed thru each machim the current curves are identical. Also the pew. supplied by we machine is practically equal to that supplied by the other ( with exceptien ed’ 123 less in bus bars beteeen tel). he. current and power increase and at an increasing rate with increase in phase angle. A given cmditien new be better understoed free a rector diagram. Diagrm He.“ shows all currents and voltages at no load with a phase shift of 60’. It can be seen hat a phase shift of 60.resIJts practically in . shift ef the ya... of induced voltages ef 50'. As already suggested. the logging mm. 0-7 supplies power which the other machine receives. Diagrams He.” is a plet d‘ power factor for each machine at no lead against phase shift. It can be seen that the rover factor of each machine remains about unity.- this (allows fran the fact that the in.“ voltages are ...!+‘ I. .1" ll ‘1' It}! . 62. equal and the eurrut less about OO’behind 3. thus bringing it in phase with the bus voltage. a resistance load of constant magnitude was then applied to the bus and the phase angle was again shifted. Diagram lo. 48 shows meat and power values for each machine against phase shift under these conditions. It can be seen that as the phase angle is shifted he currents frua each machine increase though in an oppgite directional ease. lhe lagging machine 0-? supplies more power with each shift of fines until, in addition to supplying the lead power. it is driving 6-8 as a sister. Diagram to. ‘7 also indicates power factor plotted against phase shift for these eonditiaxs. do fiase shift increases the power factor of each machine decreases though only as small amount as chem. The vector dings-an for a phase shift of 80' is ten in diagram lo.49. At this point 0-? is supplying all of the power to the load and 0-8 is merely floating on the line wit inheed voltage therefore, equal to its terminal voltage. In the last part of the parallel operation consideration. has voltage was maintained constant but excitation of c-Vtwlo imed while that of H was decreased. This eased an increooe of induced voltage 7 and a decrease of induced voltage 8. line 6-7 supplied a logging current and G-B a leading currmt. no vecter diagram is lo. 50 for a ourr-t value of 11.15 amped-es for the surrent of 6-7. Diagra- Io. Bl is a plot of power factor of each machine against its respective field mitotic. Since the machines are salt idntieal unity power factor for each oecurs head at W excitations. As already elpuined. above this value P.F. decreases and beinw it PJ'ylikowise/decreasos theual not by be some mount da- te a difference in armature reaction. 63. It is of interest to note that in each instance with a. synohrusoas generators operating in parallel on a eomnn lead. the roster on of the currents oupplied by toss Mince is eqnl to fie loed current while the vector differeme equals the circulating current. mmmorvnmmonrmsormnon : the able desiper,c.3.h. BremIeerly operated his one alternate", with moth iron erasure cores/in parallel with Gene alter-ems whid have highly reactive’pele type enemas. the former gas a voltage curve which approximated a simseid while the new: arse was quite irregular an peaked. Dr. Stein-eta also early operated machineswith smooth irn enters sores in parallel with Whaling toothed cores. these experiments flowed that machines wit different volfige curves only be run together satisfactorily. as is now very thy done. but toy require considerably increased change of mt as cupared with flu synchronising current of machines with voltage curves which are exactly alike. ror. since the uflihe oerves cannot eoincidecveniienthenachinesereoreotlyin step.aoerrentef a more erless irregularweve fernwill be enchangedbeteeenthe the machines and this is oeperinpeud upon the tree syndroeising current. i'his Wechrrent-yhave everydifferent frequency frat M of the machines. Wit is not noses-arily withont a power amt. because I23 losses always result from the flow of this current. MICHIGAN STATE COLLEGE o“. :19.’ 090 .- ...:iu OWOOo. Ib-fOOefle 0605 e e O O l‘ee O'°-' 009 0 be e A ' ofiQOOO eh ..-. floooeeohfo-v- 9 e e . . C 9-. o '00...‘ o -f. ~eeeee Covereeoe ‘. ¢D.eo4e. O. Q 5..- ooantu‘nfc’l" or summaries MICHIGAN STATE COLLEGE .....o“ e a‘. t v 6 o . ’4‘. .t e .L . v. I .|1\s e to arse . .OeQ .vv .‘5 -— wot-e -..-.-.. --—... I OOOr?‘w' eeteeoee o Q to Aoott.ee ole...e 9 ‘56 to s O . 1H4 .tt es. 0". 0. ... . DEPARTHFNT or MATHEMATICS \ \ MICHIGAN our: course: . . o ‘— W>‘ ‘e-...- a ‘ ‘v‘t . ."" ~ . ..- . . ‘ . . . "' e- I ‘ s I I u ‘n-o~ -. ' ‘.‘ .. e ‘ee. -e ‘ I .F..- ‘7 7 mO-u ‘- e s’l. o ‘-\ .-'oo‘ . ‘ O< -. 'sba... . e~ ....-- , o. . .4 . 5 ww—‘ pn-oO-o-uo-nrq .‘.. '.. ... . ... I -. I z ‘ .. 7' . _¢- ‘. ‘ . . v7 -VTW. , ._'. y . -- ‘ fl ‘ r ‘ L "'i ..- I. .. , - *' .J' v-.-4—<. e~ e“ oaeaLo ‘ . . «ed+-'_0. ~9>e~do .- e‘ . in! e - o ..+ o -‘ *ft+r‘erqs - ”+40an - va eeOQe;Q fO-v-t ""4fr o—‘O- 'Y7.-MQ.,. . r “1“"“‘r o ...eGrJ- v-- e 90“. o ,.,.. .. .'.. 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' ' o . .- - - .. . ,. ~e.... ’ - ' "‘ oe- ‘ ' I I. . l ' to , _ - ' _ e l. . z . .I - -> -- L . ._ " - "~4‘_ ‘ e l l . 1‘. ._ —-'—o«- MICHIGAN STATE COLLEGE e .\ e 9 w’. .0 we as. .e0.'e... a o... seeder-us '0 O .noooO ...o-soooe .——H t. -' 9‘ 0 9., O. :‘ne so..e. -fi‘oyb-‘o b .0. .. I >1 '- 90 o 1.. .Oee. Ito .00. .‘ ......t 0"°' '1 I C e..."“’ O I i I 3 o 0-0. s s,- 4 04+.-- . o o IIIIIIIo. Ito. s, I. .o I . .v _ a e e .. s o e . . — “...—‘5‘ -..—eqfi e 4 M .\ 7 Ir; OLLEGE \— MICHICAN STAT! 4.1 1 4 I I I I 1 IIII 1 A.“ 0.0%....00... . .. ..Io»...o‘.. Actovo I. . voIIIoIécm... . ...“...I. . ......OIOAII. . III40369090IVA 40... n . .. V...¢..oc.. .. .N... .. . ..vno‘m. I. . .... . ..-..oo.vIW ... oI..oOo¢ov.oo.. ‘uooo..u . .9. ... ...... c . .6 v. . o. . ..... .....o... .0 I . b. ..00- ac. - O. Q...a-..l .... . ... . . . o...o.. .. ...; o .....W.I.I'oooo~ go. ....9.6. 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Q 7A I . r I. . o T OoI . .V. 9 000 .0 9 I.Y‘lov «II . . v 0‘. f . I. 7.! ‘0! Y. i . ca «4.1 .. v.9; .Lo 6, l. .24. v ova' v 4 0 1‘“ ., v W‘Iv F9. M .. .g 4... 94.9 4+ V‘ 1H 4 I I I» 1 ¢~ v1 .L w 4 «a . u. IS I . . .4wm o 441.9.Lym.ko.o f o9I I fifi< . VleVAv AVJT'A o, if I W Iffi JJH. ..ITITWII 37:1. . t K HH HIP 7H1. . 111le r o. HAW .1 H H 1111 4rIFrI4I § “1%. H v vWI.‘ at z 1...}... . z 3W 1 Y..I I I? 2F. W Iofi . . . Lfi .H II o +. VvW 1.. ‘H110. L: M H94 74 Ar.vOHrTfi»1IOVH..4 Pl” H4“ tho W Ot..o+ +‘ »> 73. 4 9ro0.‘0 464W .9’ 44. 9¢f45‘ .+ L 4 4‘? o..&. » 90. oo o o ;; .:#L?:w 4 *.“ ......vz ...». . m1 .. : L..¢I.o.+..v»fl. » .II T ..H: .. ...... 7W .2 + I . I HM. .W...1. 1.4%,... 46”.?" p . I .»Y« oww....VVJH .0 o o II. v 0’} 9 IV. ffllofITHoA F o .. .... .... O. . .. ... v C. M t vaOIH 1.....IIco. .. .L. r“.,.f ... j.:u:.f9..o . :.. .9: : ..- .7 . . ...0 VI .045.‘ “0.... 9.. .v‘fi990.9 r6IQoo‘... I.. .. . . . . 9v .OIAI.... .91..... o........ ....‘f... .II. o. . .I on .- ..uvooo‘..... no.9n4Oo9 .07. ..."......Qoo ... A. . . I o...r. ... ...Io...0~tv.oc0v..v‘ Oo.o~ Iv“.....vI.. VI UH . .v. .0 I. o. .0“. ”novo.I.OYOOVov‘-- o;£.o..o. .0..O6O.O~HAVHJ. 9.. ‘Ir.‘|IOI.IITIII£ [It '0" I . Iv... I ovv..§‘o o.tto....o.. no.0 . '9 . .... ..w .o ....._ . .HINIWIOIIJIP m {It}... If ...... . .ooo ..M.....¢o -...0¢ro.*. cooIOOY O...oo.... .¢OI0.¢.. .0. I. . ... . . . .Io‘oo... .oot¢v.L v.0.I .«QIaqon o ... .. . . .poo . .avoa... o. ... . ......u. ... oo o .. . . ... -.. .u .. 99. I . .. ... c . .o .... . w ... I. 1. . . ....... ... .. .... .. ... .. ~o o .. . . .. o .. _. ... . ... h . . .-. . . o. . . . . . _ .l. ‘ u . -\ ' MA THEMATIC! ()F UFPARTM ‘.H r ‘ Y—TV v v . V - V ‘ z W" hid-4mg: : * w “W [.W mir‘r‘fl‘m“ sém 1.3:: -Hz. . no ...“..‘OOO‘ODMVA' ¢ A A f: a ‘OO- O .0 $ N ‘ QCW . b .3. '-‘ . - ......... 0-. ..-.owro I. A: A; A V A A...4;¢.. Honouo§ o*&§ . . ‘j. d H I °"‘ ' f‘ 1‘ V 17‘ J- . ¢ ...-0 v. 9H 0 -O 0 .- ....-.“ 55%; 7"; v 'fi4 ‘t ' ’4“. 4’ >.: ‘ . . . . .‘ . . .- H". '05-. ~«OQWO‘ ‘fi: v 'v 7 v4 91». C“* - 4 .0. ...r v c”. ,4 .- -- . - - o 1. o o vb O“v?oQOO< .‘.. >‘m.r'..'l ‘ - h . OOH» ' . " 3:361?erJ -Q~L~OO.JN ..- -o¢ooq. - -.-4p..To—.3... .4 9.“. ”f- 0 uy .1? oofi-oo ; o 900‘. ooO-Q-ul- ‘::,2 .I.- - “I ' “.. .00. >90. 1: - 0-0 — o O .0 d... t 00 It; MICHIGAN STATE COLLEGE .,-;... ."1’V. J; ‘;-;1:1 *I'tt 5.. 0390‘. o y ~Q§002 h..!—o ... 3‘; .-~ E1 ..ITZI... .’ 4‘ '49-. . tbi‘IO-v °v - 00:1 go !. 4 V .‘_.o..- T . -9. .i pop-04 “O0.0.... . .,‘ r.“ ..- n.......9.gb.oOQ «.5 ., ... - .‘ ‘bol—o-o >19 - .-. , ..-M‘x {‘r H ‘ . .«3‘ Xi. { o .4 . .....‘ " A A LA ‘ 3' ‘ M v‘ .ot-bt! b* 1 a. .0 »+ -4 3 , 6v. ' 'OOOaO“: ' ~‘.’*" , ‘ AAAA ;. 31‘.” g I 6‘ r.".1A;12 'f vV Y‘ .40 "+j co .2 I-OO o o ‘ 0 . _ ”"EII1’+ i ' n.00...’ P . . ‘5.-L - ...; WA Y 36109. "’ —tH'° "fl ‘ 9" C . .1 .vvbr9 - H H’b—f‘ _ . P ‘A x .11 ’- szjv .{1 ~;; * ‘ 4! 'f‘ ~~- T.. ..-... '5- ... w—o3ouflr‘ ' " .“.Q ;--2_.... -‘fiouo ’4' .... .‘ b 1‘ \ -0 ‘00 V - 0 .. 1 . o~ -6 ‘ O _' Q—J a _ ’ .. fl . 4 ' _ .‘r ‘ ._ -‘ ~ Afi .o-‘ .... .‘_. .3 ‘oO-O Q‘t” $.. A #L W: Ax‘L.."‘?. o... o ..,-, ‘ ~"O— W”? °"‘ «‘90: ‘ .0 -nQ-\——.. .....-ahdbyd - vv ii ‘5“ 0". oo » 0- .94 b‘Jo. MA .vv'L vfi; ‘fl‘nd ‘ ‘ ~§ '0 “I t ”01‘. (r. VAVVA L L Q" " - ~ ‘.00- — 6o Jofi‘4»¢’o 50““ H. t .. . .- -% V #9 v v A“ -5 9“ ~ -- ...-i..,.._- .-:,:. :LJ ...“ 4 -¢-- {o9”09‘-vlo§ro‘lr04 ' 0 ‘ G .}-QQ—$ c§0‘-O-l. l. n .. m ‘. o. O‘ ~ - . ..‘o '404‘ 1‘0o.~'>t~ ~. . oo.'a..-tl;o‘9r0-yo“1 .o' . --[ ..¢ .1 p“"« -oO - g. 1 .15'0.”O- 0-. o- 0.. a96'1&6 - . 6-.-..-.‘ 6'90- — 0".“— -‘ fi‘ ’ ~ . .o -o . ‘ .-l .. 0.7.0:>. o6 o-ov-a.-¢ -H'J.“o-Q .. |oo¢ . ...-4o. 9 o§‘ ' "I.’Q-“.Q‘. ‘ o 5-. ‘ &- -..~ -o. '6‘ . . I n. ..r ‘g.9OOQt I .- at ‘ ..,._ -.I..c _. - ‘ .. - - .9 <0 . ... W r” ... . v— - ° ‘ ‘ ' ' ‘ o - 0— ‘ >'~—- ‘ ’ - - c . 9 0. A. ‘0’0“‘ ' ". o. . . .9“ uofl:. a. ' . . -.~ - ‘. " ' ' " " u ‘ ‘. ' - .' . _ ...‘. ' l . . - '. u...--OO -- . - . A .0- . 2 ‘V"..; ‘ f:.’h‘.i. :' . .. 0.3-0.0o‘ O -. ‘ :4 n- A. .1. o .>. ‘ _7 u‘. ..._ o ‘-f 0:;094‘. - .,", ~ I o;;.. " ' . f . -o-o .. ..g .- , ' . ...... I. ' - I . . . . .z ’-.0 " ‘0 O. .. . . ‘.,. '. 9‘99 .. .. . -' . ---.. -.. ‘ F-. ,‘ t 9- . . ‘. “—.-.‘_.,..~ ‘0 ‘ - . - ‘0. ~p~*‘.- 1". ' .“ . ..... 3- - g. c v u '} ‘o-v.» ' u o , — “ ... , 0 . _ ‘ . . . o ‘9 -~ ‘ t o . 4.- " ‘ ' ‘ ., ...‘ 0‘. 0- . ‘ ' ‘ . .“ ‘ru '9 _' . , . . ... oo--' . so 0 —. tn. . . .. '1’ ". -. .. . . .l- .0. - ~'- ‘0 o} . - v Q ‘ :0. .: “ A. . ... .. ..‘-'. . :0 -o o: --o¢>.0 ’ I...‘ u u o . 0 -° ‘ O l.’ 0 "' " .l . ..lo. ‘ . . 1 -Ooo- .... .voott""|" ' .. .' '. ‘ ' ‘ 'QI‘OO- , . .. I....... v ' - 90-0 ¥ _ -- ‘.‘--.--; fio‘dfltgAt-—_‘- _o.—-Joc--_o..-‘ - 1 )rpaquFNY or MAYHEMAIIC‘. 71. DETERITINATTC???" FOR 6-7 and (3-8 BY VAR! CUS ICETTKODS: Open circuit and short circuit cuz'vvs were dr'vm for 6-7 and for 6-8. These are included in diagrams £10. 3-2 911d 53. Th. curves for the two machines are so nenrly identical that the "gala- tion cwlmtations are carried thru for only one mhino. Remlation was also determ‘ned by actual test for unity pow“- factor and for .7 lead andfl lag. the following table cox'taira the rqaaufits of the different metloc‘m of determining rermlation tomether with the actual values obtained 6 perimentally. Wm Egzhod gt geteminat‘og g 2, 2: Machine ‘5 Rgflluflg 3. Mo F. 100 6-7; 6—8 24.10 I. no 3. 100 ditto 1Q90 A. I. E. E. 100 ditto 12.30 Actual test 0-? 100 GP? 12.60 Actual tc t . 100 a—a 12.80 x. m. r. 70 he 0-736-8 48.60 A. I. E. E. 70 1088 M 23050 mum 17991; 70 leg 0-? 25.10 Actual test 70 lag (H: 24.90 E. M. ,- 70W183d $.73” “25.95 n. K. P. 70 168d d1“. "26000 A. I. E. E. 70 lead. “”0 ‘21070 Actual test 70 lead. 6-7 -23.20 Actual test '70 1634 0-8 435.70 1'11-III‘I IIII‘III‘II . 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I .O I.“ I Q . .I . ~ . g . . . N M . 3 I I Q. I.’ 9| . o . . o O _ 0‘ . p 1 . _ .».. . . I. _. I~._. II <. I I ... o O. I .~ . u«A I. . I I. II; I .u . I I O _. I It I! . . I . . o I . . . . I .. .L .1! ‘6 III .1I. III‘I .. ‘II- .. . . . ‘A .s . . . fl. '0‘ . O I _, .A w. 7. It. . I.-.I IIIII . ~. . . . . . . ~ . _ . h A -. I I *I l 4 . u . u w. I . . . o . a C — . o I! _. O. I o. ov ”O. .. I I . . 'YI . 'I I.I . I. I. .I4 I o '1 . .. .g4v-A.‘ 8.0 2.0 2.3 mammal. 0 O O I 1 1.5 ‘ '.. .a _ 5 C o I I - ..f.‘ I r ') .L_~4AYII‘ 74. W0! 3'! EJJ‘. mom htod mt cm 18.8 m. Iran to w circuit CI. this current comm to a £1.14 mltntluu at short circuit on tho gratin. at 1.3!! up»... an m siren tor-1nd "lug. ”tum to this ulna of field Inn-rant ml- 158 volts. a» rum-mu m1 lantmt :- am mauuomu. It. oqulo We". 158118.83 and. 4.85 obi. OI W impedance pot plan. as insulatln oqulo 100a. 1088 "lap-m1 18“ vol”)! 8:11 10.11 Outta. Lot m1 1nd voltqo 0M: 2‘ and I. led volmomlloummmmnsmw pm. equal to 1. ma 1'. Win11. Calm nag-ale. fl. pm '0. 5‘0 analog pluf(!plujx.) Mbmhctwunlw i. m1. (188.08 pm .10) pm. 18.8 (.2“ pm .1 4.88 ) equal (138.3451U),,Ae§m. 188 alts . an s «suntan m1- 100 (165 dam/133 oqull 24.0 s A .‘_. When pour factor equals .7 1.35:. ml- (133 x.7 plus J .711”) pm 18.8 (.284 plnl J 4.88 ) equals 98.34. p1u J 188.1 oquh an effect!" 1:111. of voltage of 208 volts. m: s "nation ml. (288 43:) 100 [138 equa- 4.8.8 as. 75. mm W fnctor 011115-18 .7 19341;. oqull 1s: (.7 - 1.7) p1u 18.8 (.2“ pm 1 4.85 ) eqmdml - 393.1 ) pm (5.36 pm 91.2) oqnnls 98.45 - 51.9 . I. equi- 98.5 “It: . % romantics: null 100 (90.5 «43311:: equals -25.95 s . Diagram lo. 66 cm! 56 inflonto the npplienticn of th- o.n.f.dzvd m.m- methods“! r factors of l I lweim and India: reapectinh. "DI-gran No.56. 3W?!” BY IJIJ'. mom to ”native fore. nothodnud n8 as follows. 8. cu obtained inthonmwu for the 9.913. mtbodandvu Mus- 91nd mmwamaummmn. 54-56. no fioli curl-anti Wag to in voltage- 08 an! «I an attain“! Ira the open circuit m and '91-. and tutu-1:11: 76. to ebtsin s value 1,. me voltage corresponding to :1 field current 1"” dotsrninedfran the open circuit curvesndnsusolss file no load voltage I. in the «termination of regulation. Fox-unity power factor. e' equals 118 and e" equals 116 men from he open circuit curve 1!) equals 1.8 anperes mile If" equals 1.8 smperos. 1! equals 2.58 smperes. E. corresponding to n field current of 2.54 mores equals 147.5 volts. ‘5 regulation equals 100(147.5-1351153 equals 10.9 98. When power factor equals .7 ha. 8' equals 98.54 while 0" equals 188.1 . 1: equals 1.5 «spores shile I" equals 8.2 mnpeus. 1, equals 4.46 snperos. E. corrospmding to s field current of 4.86 snpsres equals 188.5 volts. mentors % regulation equals 100(188.5-1ss)/158 oqusls 41.7%., men the poser factor equals .7 lend. e' equls 98.45 while e" equals 4.9.11. equals 1.5 If” equals practically em 1, Therefore equals 1:5 amperos which corropoondl to a voltage of 98.45. lease ‘5 regulation equals 10d”.45-133)1133 oqusls 28%. RW‘MON BY L.I.E.E. man: be sore power factor ourvo no constructed fran the Open oimitcumbymmingfruitutsllpointsthefullloodl 2. drop. Per aw given field excitation snd sore poser footer the ”mag. that would be induced on open circuit referring to diagr- lo. 58 is 0-: and the apparent internal drOp under load is on. as i regulation is thus mots/ca. 'i'he tominol veltege for other pour factors is found by drawing e.m.f. diagram similar to diagr- 10.5.. he line b-f is dran st the power factor eagle 6 has the 77. theistic. 111.12 drop is dmvm front as chm. andthens-cas total from the curve is drawn intersecting f-t at s. e-b is than the teninal voltage at the poser factor equal teen 6 . e-h is then laid off «1 the curve of ding-s- Ho. 57 m locating the point d. W repeating this process for several field excitations. the can load saturation curve m be obtained for my desired pm factor. The regulation from his curve for a given poser factor is tb 100 d'alca . in flush d‘ is the point of intersectim bctlssn the nomal voltage line and the saturation curve. For unity power factor. ‘5 regulation equals 1811001150 equals 12.: For poser factor of .7 log 96 regulation equals “11001250 equals 23.3 For poser factor of .7 load 5 regulation equals ~50x10012w or ~21.7 IISWSSIOE OF RESULTS! 'ihe conclusion to be drawn from the above calculation/at fiat as far as the machines considered are concerned is clear cutand definite. 'lhe 1.1.EE method in each instance gives excellent results which check very sell with those actually obtained in in laboratory. Both the n.m.f. mirthod and the e.n.f. method give values in each case shich do not check against no actual. The above calculations. do not bear out the WOW fact that the moon of the mmf. nethod and the e.m.f. methods gives about the correct values. Wile the results obtained in this comotien may not be general. it can hardly be said that these conclusions are aural. However. it could certainly be much safer in view of those results to advocate the AJ 3.1:. nethod in preference to either of fine other two as far as accuracy is concerned. 78. Diagra- le. 57- 1.1.3.3. Isthed of Main le‘lstia. MICHIGAN STATE COLLEGE t w“ -“.r9 d. i \ "~WY "" s DB’ARTM EN? or H ATHIHAT'OI mm H ‘ v5 4’, e11"... (3n. 80. WEE-.9.- swam CGI'ERCIAL WAVE FORE: In cull plants operating at comparatively low potentials the current and voltage saves are it of great importance. is this use the lost cannon condition in the earlier devcpoent of the elstrical industry. little attention was then given to wave form. Recover. the vast extensions of electrical systems of distribution and the necessity 1"" operating long distance transmission lines at higx potentials demd very careful attention to all factors that may produce save distfltin.‘ here are too fundamental requisites of the save fern in constant potential system: (1) In parallel operation. the waves should be equal at all inst‘s. to prevent cross curruts. (2) The differentials and integrals of the curve should have the some shape as the generated voltagevave. Per alternating currents mated by rotating nachinery both requirenents are not by simple sine saves. The principle unavecidable faster in proacing distortion in nve for-s is the variable permeability of iron. “Other causes are due to femlty design or constructin. line generated voltage save of a properly designed alternator shoull approach very clr‘sely the standard sinusoidal fern. Of course in many cases. the inherent characteristics of the load load to a distorted current wave which would be ncoml under a nor-cl load. 81. louse care not be enroised in large interemnected out. to mid such conditions shit would lead to distention in parts of the network. In the liait of the above amoral observations it some advise-file to consider at least brief]: the save ferns of the synchronous generators “.7 ad 8e Diagrule. Mohenflsenveferleffieenrrentsupplied by 6—8 under a heavy moire load. Disgr- leJO indiea‘be the some condition for arm a sliatly different shunt was used to actuate the oscillegrapn slalom. it new be readily son that these waves are practically six-Isoidal. Q o. ' I- : ... L9-n . A I ‘ u” '04 .L‘O I Dagrani No.60» five Fan of 0-? o -’: . Diagra- lo 01 iadieates equal voltages of 6-7 and 6-8 in phase opposition. his corresponds to a sore phase rotation setting 82. of the 0-7 rotor. It may be sen-What the machines are properlyaligbéd on the shaft for their voltages are oorresmdingiy Just 180. out of phase at all times. Likewise when the two voltages were cemented in lilacs they appeared identical. i'his investigation was carried thru for each phase though only one pair of phases is considered in tin diagru. Diagrn lo. 62 shows the currmts of each phase of 6-? viii a balanced resistance load such as to give rated current. Diagram lo.” indicates starting conditions of armature voltage. current. and field current. It may he soon that for starting. reused armature coltsge is applied and a high armatare mt of irregular fora fleas . in alternating field current also flows due to the fact that the lines of force of the rotating field cut the field coils first at a big: rate thereby inducing a my; voltage across the terminals of to field which canoes an alternating current to ‘ flow. i'hd resistance is provided ocrees the field for starting to i prevent mange to insulation due to the high voltage induced . } thnthemachinehasreached synchronous speed. itmaybe seenthat the field current is sore because the field structure is traveling at the same rate as the field. hence no lines of force out the field windings. At this point. he d.c. switch is closed exciting file field. As the machine pulls into stop there is a transitory M of current asshcen by the irregularity of the armature current vars. the am armature voltage as then applied and after a t-porary Wane surge of field current and armature mt. all values settled down to those of nouns). operation. _ a .a . 3 . c; » Enema 4, a .. a y H. arm H haven «Hob coma «on . ago» 356.3» egg can pack—fie H. cdemulpaoahne cage—Fun wanton.» mange uganuemo Tau—ac» egg flashy—sac go: 6.6% eon—533m E5 cornea 3357095.?» egg wagon J .. . U s'H inf... 1....— ..— _ A. . .. , .... .... , _ _ L . . . . a an a..___...=.§i§§§§§.§3== ......zss... ...... .53............................_..............................;....§3..................................... 3%.... ......g............ ............_......._.. ....3......3.........53.2.............3......2....2...................................................3........_...._...... law . __ , _, _ . , _ _ . _ .._._.._:.,.:..::::........:_..;::.52..........z::_::::....: .. ... ....___,...:.=.;:..=.:=. _ ...:z...::.: ,_:_.:_ ._ . ...:r......._......_.55:i.at:z.._r...:tifigg-EZ5.2:.....:.... : _. E ...: _ ::. ... .. ._ , t _. E _:_., 2:... :5: . ......._:..::: ........x..........:.......::::_ - I . I o I 'l C es Ill 0' . . 9"? e f...“ . . -u . v . - a e O t ‘ mmmmawmnmwmmm iris:£&1l=!&ii Speed held constant at 1800 r.p.m. Field Current of d.c. machine constant at .26 amps lo Load Power Input d.c. machine 1‘ 1 watts d.c. alternator no head .. 145 1.00 0.0 Priction—‘Hindage of , 6-7: 0-8; l—7 1045 7.00 0.0 Priction—Windage for all machines Iren‘loes for 0-8 1297 8.78 6.0 Ditto as above but iron loss for different ex- citation 1157 7.80 2.0 Ditto as above 1208 8.20 4.0 W Friction-Windage for g all machines and Iron loss for 0-7 1310 7.75 6.0 Ditto as aboVe for different excitation 1214 8.20 4.0 Ditto as above 1150 0.75 2.0 Prictionda'indage for all machines and iron loss for 11.7 2100 13.70 10.0 Ditto as above for different excitation. 1714 11.50 6.0 Ditto as above 1413 8.50 3.1 Priction-Windage of A 0-8 alone 400 2.60 0.0 isnuuunnssanalsufazgnclalsazuunz I ,g.oz 2.50 3.00 E 3.95 5.10 5.82 R 4'95 1.95 1.94 JEHHIlfliflflfififlilkflEUflEfiflfllEflflalflulafié.°hma manual-b 1:22.: 2-1- rriction-Vindage of all [achinos plus lo Load Losses of d.c. mm. mm... Wag-.9.- rield Current Total watts input to d.c. Cu. Loss in Watts Iron W a 0 1 u 9 0.0 V 1297 150 200 4.0 1208 151 130 2.0 1157 . 119 91 Win-z- 6.0 1510 150 210 4.0 1214 ' 131 154 2.0 ' 1150 117 as Wmn-l- 10.0 2100 330 823 6.0 1714 B75 610 3.1 1415 141 325 .. é alifiiflipm“ Lapses friction-Windsge Loss of Generator 30.7. 285 watts Driction-Windage Loss of Generator no.8. 244 watts Friction-Windage Loss of Hater Ie.7. - 275 vatts Dots: It is of interest t6 note in the above tabulation of friction- windage losses. the machine 0-7 has a somewhat larger loss than the machine 0-0 while their construction is to all appearances identical. This is due.howeversto the fact that the stator of 0-7 is actually suspended from the shaft. thus cruising a greater friction loss. MWMME‘IIHH 1 52.1 r 5 1 5 5 5 f 8'7 3-1 8-5 1' 8-! I-w 2-5 .50 5515 50.0 59.5 .50 55.0 55.0 55.0 .50 51.0 52.0 51.5 .50 57.5 50.0 57.5 .50 75.0 75.0 75.5 . r 51.0 52.2 51.5 .70 55.0 55.5 55.5 .50 71.5 75.0 72.2 .50 95.0 99.0 95.5 .70 55.5 55.5 55.0 .90 109.5 110.5 110.0 .50 97.2 95.0 97.5 1.00 125.0 125.5 125.0 .90 109.5 110.5 110.0 1 .10 152.0 155.0 152.5 1.00 121.5 122.5 121.5 1 .50 155.0 155.0 155.0 1 .10 152.0 152.5 152.0 1 .50 155.0 155.0 155.0 1.20 155.5 155.2 155.5 1.50 177.0 175.0 177.0 1.50 155.0 155.0 155.0 1 .50 155.0 155.0 155.0 1.50 155.5 155.0 155.0 1 .70 197.0 195.0 197.0 1.50 175.0 175.0 175.0 1.90 205.0 205.0 205.0 1.50 155.0 155.0 155.0 2 .00 220.0 219.0 220.0 1.70 195.0 195.0 195.0 2.22 255.0 255.0 255.0 1.50 205.0 205.0 205.0 2.50 252.0 252.0 252.0 2.00 220.0 219.0 220.0 2.70 255.0 252.0 255.0 2.20 255.0 255.0 255.0 2.90 275.0 272.0 275.0 .2.50 255.0 255.0 255.0 5.20 255.0 255.0 255.0 2.50 255.0 257.0 255.0 5.00 275.0 275.0 277.0 1f 1‘ 1’ 1‘ It 1! 1y I. .25 5.0 5.0 5.0 .27 5.0 5.0 5.0 .50 5.2 5.2 5.2 .40 5.2 5.2 5.2 .55 7.5 7.2 7.5 .50 5.7 5.5 5.5 .50 7.9 7.5 7.5 .50 5.0 7.5 7.5 .70 9.5 9.5 9.5 .70 9.5 9.2 9.5 .50 10.7 10.7 10.7 .50 10.7 10.5 10.5 .90 12.2 12.2 12.2 .90 12.5 12.2 12.2 1.10 15.2 15.5 15.5 1.00 15.7 . 15.7 15.7 1.20 15.50 15.5 15.2 1.10 15.0 V 15.0 15.0 1 .50 17.7 17.5 17.7 1.20 15.5 15.5 15.5 1.50 19.2 19.2 19.1 1.50 17.7 17.7 17.7 1.50 20.5 20.5 20.3 1.50 19.1 19.2 19.1 1 .50 21.9 22.0 21.5 1.50 20.5 20.7 20.5 1.70 25.5 25.5 25.2 1.50 22.0 22.0 21.5 1.70 25.5 25.5 25.5 £19.21 W M 1.52 5522 .91: 2a KJF. Input 00. Loss Input-1.05555 Efficiency-45 I P .F.-% watts 5.5. ampere: 6.65 170 6.15 92.6 20.0 80.0 6.43 110 5.00 92.2 16.4 79.6 5.10 73 3.70 90.4 13.2 74.7 3.52 6‘ 3.13 89.5 12.1 70.0 5.00 55 2.55 85.5 10.5 59.5 ' In the above calculations, constant Friction-01116530 Lees - 326 watts WW :Wmm m: H WM 3&mnm 7.90 155 7.55 95.2 19.0 95.5 7.50 155 5.95 95.0 17.5 99.5 7.05 119 5.55 92.5 15.7 99.5 5.95 50 5.59 92.5 15.5 100.0 5 .55 59 5.99 91.7 12.7 100.0 5.92 55 5.55 90.5 11.5 100.0 5.55 55 5.99 90.0 10.2 100.0 5.95 55 5.52 59.5 9.5 99.9 5.29 25 2.55 57.5 5.1 99.5 2.77 20 2.55 55.5 5.5 95.5 In the above calculat ___—“WW ims.Conste.nt Friction-Winding! Less - 387 watt .222222525221552521552925519551. Figlg Excitajggn M 3:599515551E525 KM. Input 00. L055 hunt-1.05555 Efficiency-‘5 1 PJ.-% - ' watts 1.1. amperu 7.20 153 6.70 93.0 19.0 5 91.6 6 .45 125 5 .97 92 . 6 17.1 90. 9 5.22 ’ 91 4.79 92.1 16.5 86.5 4 .15 64 3.75 90.0 12.2 82.0 3.45 54 3.05 88.6 11.3 '_ 73.6 2.78 46 2.38 85.6 10.0 66.8 In the above 55155119515515.0511555115 Priofla-Wlndage 1055 - 552 “5:5 W1”. .Iislsuilniseillnusaaéll 3552159595551595 5.50 157 5.00 91.0 15.0 75.5 5.52 121 5.55 99.5 15.9 59.5 5.55 105 4.02 59.5 15.7 55.5 5.00 59 5.55 55.7 15.5 55.2 5.00 55 2.55 55.5 15.0 51.7 In the above calculatiue. Constant Friction-#:1115535 L055 - 560 watts W m 7.85 153 7&3 m n 1%.9 19.0 99.5 7.26 1.6 6.79 93.6 17.5 100.0 5.66 82 5.“ 92.6 16.1 100.0 4. 75 56 6.36 92.0 11 .2 100 . O 3.70 36 3.61 90.2 9.3 98.5 2.62 20 2.27 86.7 6.7 96.6 In the above calculations. cenntnnt Friction-7717151585 Leas - 353 watte W m WMMMi-l WWW . .1-2 m 3:. & LI. Input On. 1055 Input-1.55555 Efficiency-56 1 P .1" .46 vatte K. . amperee 6.65 170 6.10 91.7 20.0 60.0 5 .00 155 5.59 91.5 17.5 51.5 5.55 112 5.95 91.2 15.2 51.5 6.20 71 3.75 89.6 13.0 77.5 3.55 62 3.09 85.5 18.1 70.5 2.90 57 2.58 85.6 10.5 6625 in the above 55151115515115. Constant Friction-91114539 Lou - 375 ntte WM ‘ 51515 W 9.95519. 32.9 m a: 195 7.15 151 6.62 92.5 18.8 91.7 6.47 126 6.00 92.7 17.2 90.6 5.91 109 5.43 92.0 15.9 69.6 5.25 92 5.75 91.2 15.7 55.5 5.75 77 5.27 90.5 15.5 55.0 5.15 55 5.71 59.5 12.5 51.5 3.42 55 3.00 87.2 I 11.2 75.7 2 .80 46 2.38 85.0 10.2 66.2 111 the above 55151115515115.0th hifilen—flndage 105e- 595 nttl WW WWW 5.5 mu m 5.50 155 5.75 17.5 5597 75.7 5.75 120 5.50 15.5 91.0 57.5 Cont'd on next pegs. mummy; 11mm my. .2»; my. .1: 1% LI. Input 011 Loan lung-Loss» mm“ I , P.l".-$ M m...— 5.30 133 4.75 r 89.7 17.. 75.7 4 .73 120 4.30 91.0 16.8 67. 0 4.50 105 3.99 88.0 15.. 64.5 4.10 94 3.58 87.5 14.8 62.5 3.02 81 2.53 83.8 13.8 53.2 In the 317019 05101111131011. Conqtant Friltim-Uindagv Losses - 415 watts t 2 ts Iron mmmmE-z WWW 3.113131% 2.05 31 2.10 01.2 1.22 52.4 4.10 65 3.47 84.5 1.01 61.4 5.74 05 5.09 80.7 2.00 69.3 7.35 110 6.00 90.0 2.84 75.0 0.90 154 0.17 91.0 2.70 79.4 10.57 204 9.79 92.5 5.11 81.9 12.80 303 12.00 93.2 3.00 81.7 15.60 430 14.60 93.5 14.50 04.7 17.53 500 10.22 93.70 5.00 04.7 19.44 001 10.41 93.9 5.60 04.7 In the 30m calculation. Constant Friction-Hindus. Lou" — 070 7. MW 01m Wmmmu 11.913 W 393%: 32-3. 1522 .22 1922 1.1. Input 011. L955 Input-1.05595 522151...” I P .P .4 M m... 22.30 650 21.05 94.5 5.5 100.0 17.40 590 16.50 “.5 4.5 100.0 13.40 222 12.57 93.0 3.0 99.4 8.75 102 8.05 92.0 2.8 98.2 4.90 28 4.27 87.5 1.3 98.7 In the above calculationfionatnnt Friction-Windago 5 1.95555- 505 watts W 11215 mm Li manna 15.97 551 17.50 ‘ 95.9 5.1 91.9 17.15 425 15.10 95.9 4.5 91.5 15.15 540 14.22 95.5 5.0 91.5 15.50 275 12.50 95.5 5.50 90.5 12.52 255 11.75 95.2 5.52 91.7 10.51 175 9.51 92.5 2.91 55.1 7.72 104 5.99 90.5 2.22 95.0 5.55 75 5.15 55.1 1.92 75.5 4.20 50 5.55 54.1 1.55 55.7 2.55 27 2.00 75.5 1.12 57.0 In the above 55101115510115. Constant Friofiwfndagu Lou - 625 watts E ‘3 33m: n 2520 a In JEESBHJIIEHzShHEELIE£h§JEleEfiL Priotian—Windago WM WWW iémnlm 15.5. 1111's 011. 1.955 Butt-1.05559 527151-1054 I P.P.% ~54 155551____._11.11: 5.50 170 2.85 75.8 2.74 50.4 4.98 180 4.15 82.8 2.80 42.4 6.75 225 5.85 88.8 5.20 50.8 8.15 254 7.22 88.8 5.58 57.8 9.52 278 8.57 90.0 5.54 84.2 11.00 552 10.09 91.8 5.74 70.0 15.55 575 12.51 95.2 " 4.20 75.5 15.52 428 14.22 95.4 4.50 82.0 17.59 510 15.51 95.5 5.90 55.0 I 19.99 594 18.72 95.9 5.50 89.7 In the than 0515111551051. 0011588175 Friction-81114539 ....__JiJ3uMEEaELJdL35&9____._.J1JD3211888111 5§Z§122130 21215 mm mm. 259.193.312.123 4.04 255 2.97~ 75.5 3.54 27.2 5.85 284 4.58 80.8 _ 5.87 56.8 7.34 296 8.24 85.1 5.75 46.5 8 .80 330 7.87 87.5 5.95 55.0 10.10 860 8.94 88.5 4.15 58.4 11.40 590 10.27 90.0 4.50 85.5 15.68 551 14.52 91.5 5.10 75.2 19.12 711 17.80 92.0 5.80 78.8 In the above 85101115519515.00115t5nt - 805 tutti m1! If 1. If 1‘ 4m... ___..EQLM .25 20.80 .25 23.40 .50 18.00 .50 20.80 .75 15.20 .75 18.00 1.00 12.80 1.00 15.50 1.25 10.00 1.25 12.50 1.50 7.20 1.50 9.80 1.75 4.50 1.75 7.50 2.00 2.30 2.00 4.60 2.25 1.20 2.1. l 1 2.25 3.70 PJ. I 1 2.50 2.10 2.50 8.80 2.75 4.70 2.75 7.50 5.00 7.70 5.00 9.80 5.25 10.70 5.25 12.50 3.50 13.50 3.50 14.70 5.75 15.80 3.75 18.80 8.00 17.80 8.00 18.00 "rm 9.80 P.P. 221% If 1‘ 1f 1‘ :‘QEHIQEQ §0%»Lg§§ .50 23.70 .75 24.00 .75 21.00 1.00 21.30 1.00 18.40 1.25 18.50 1.25 15.60 1.50 17.70 1.50 13.00 1.75 13.20 1.75 10.30 2.00 11.00 2.00 8.80 2.29 2.27 7.30 PJ'. I 1 2.50 10.40 2.50 8.00 2.75 12.20 2.75 10.00 5.00 14.00 5.00 12.30 5.25 18.00 5.25 14.40 3.50 17.80 5.50 18.30 5.75 19.00 5.75 18.00 4.00 20.80 4.00 19.80 for 0—8 If 1‘ I! 1. mm___ ”W 1.00 24.00 1.25 24.10 1.25 21.60 1.50 22.00 1.50 19.00 1.75 20.50 1.75 16.80 2.00 17.30 2.00 15.50 2.25 18.40 2.25 14.10 2.55 18.00 2.42 14.50 Pd". 3 .1 2.75 18.20 2.50 14.60 3.00 19.00 2.75 15.60 3.25 10.30 5.00 10.70 3.50 20.40 5.25 17.90 3.75 21.50 5.50 19.00 4.00 22.10 5.75 20.10 4.00 21.10 5.60 P.1'. 8 1 1921-1. If 1‘ If I. ____mm___ ___—W .25 20.40 .25 23.00 .50 18.00 .50 20.30 .75 15.10 .75 17.80 1.00 12-30 1.00 15.00 1 .25 9-0 1.25 12.10 1.50 7.00 1.50 9.60 1.15 «40 1.75 7.00 2.00 2.50 2.00 4.00 2 .20 2.00 r.r.- 1 2.25 2.50 2.70 2.50 4.40 2.70 4-80 2.70 . 7.40 3.00 0.00 5.00 10.00 3.25 10.90 3.25 12.00 3.00 13.30 3.50 14.90 3.75 15.30 3.75 15.00 4.00 15-90 4.00 10.30 Tm £8. 51!. It 1. If I. ...—m...— M .25 5.55 .50 5.20 .50 5.15 .75 5.55 .75 4.65 1.00 5.15 1.00 4.15 1.25 4.50 1.25 5.50 1.50 4.10 1.50 5.05 1.75 5.50 1.75 2.55 2.00 5.00 2.00 2.00 2.50 2.00 2.25 1.50 2.75 1.40 2.50 1.00 5.00 1.10 P.! 5.00 .40 m m m 5.25 1.55 5.25 .65 5.50 1.95 5.50 1.25 5.75 2. 50 5.75 1.90 4.00 5.00 4.00 2.50 ‘4.25 3.50 4.25 5.00 4.50 5.95 4.50 5.50 4.75 4.25 4.75 5.85 5.00 4.55 5.00 4.51 1 Tm 1221-1 1f 1‘ 1f 1‘ mm... 5031425....— 1.00 6.20 1.30 6.20 1.23 6.60 1.75 3.60 1.50 3.13 2.00 5.10 1.73 4.63 2 .25 4.50 2.00 4.10 2.50 4.10 2.25 3.50 2.73 3.30 2.50- 3.00 3.00 3.30 2.73 2.50 3.25 3.50 3.05. 2.23 14.1. = 1 3.50 3.70 3.23 2.33 3.73 4.00 3.30 2.73 4.00 4.30 3.73 3 .20 4 .26 4.60 4.00 3.60 4.50 4.80 4.23 4.00 4.75 5.00 4.60 4.30 3.00 5.20 4.73 3.63 3.00 3.90 Tm 5.!) 7.7.3 1213-1. 1f 1'I 1: 1. ___—W 4am... 1.23 6.70 2.23 6.73 1.30 6.23 2.30 6.20 1.73 3.70 2.73 3.33 2.00 3.13 3.00 3.60 2.23 4.63 3.23 2.30 4.13 3.30 3.33 2.73 3.30 3.73 3.37 3.00 3.30 4.00 3.61 3.03 4.33 7.7. 3 1 4.23 3.63 3.23 4.40 4.30 3.71 3.30 4.60 4.73 3.73 3.73 4.73 3.00 3.60 4.00 4.90 4.23 3.03 4.30 3.23 4.76 6.40 5.00 3.33 MWWMH 5 14! 2.75 4.77 .577 1 . 125 7.80 13.70 .570 2 IEZ 5.00 8.55 .578 5 152 2.80 4.85 .578 2 Y‘Z ‘ .90 a.“ .558 W 12612235.: 1.1.27.8 8 mm: Monom 13322-21224 IF! .5751 .2881 135 .5707 .2853 late: Each of the 171-1316 1710134534 111 the above tabulation of 11313531106 03.53. 13 111 turn the mean of throo 3641416331 ”1313. mmnmmfi m1 3 E x-r 7.00 13.70 .070 0 1:4 2 .00 0.00 . 570 1 x-a 7.70 10.40 .070 z x-z 0.00 0.00 .070 0 1.7. 2.70 4.77 .577 1 7—0 7.00 10.00 .570 2 2.2 4.90 0.02 .270 W W 1110 mm 01.101.an 11mm x-t .5730 .2070 A 1.2 .0700 .2000 r-z .0700 .2070 Iota: 3.01. of tho 121.10 10010.0» 1n 01. 0'03" 0.101.010. d mistmce 0003.. 13 111 turn the 103011 of tin-33 0001110001 ”1013. mmmmz—z 0 X.Y 4630 3325 1‘310 2 1-1 50.0 3.50 14.10 1 :02 45.0 0.20 14.12 2 1.7. 00.7 0.00 14.10 0 1-2 00.0 4.00 14.15 1 1-2 40.7 0.00 14.10 2 r-z 51.0 0.02 14.17. W 3211110220 10111.91 mm 11121411001001 11.891.221.221 1.! 1‘315 ’30‘ x-z 14.12 7.00 1.2 . 14.10 7.00 Iota Each of the 1.71013 11111303341 1n tho 311373 tabulatim 3f "datum. 041.. 10 111 turn tho man of tin. Mtiml triula. mamas 1212-31-1. l 1.1 “:1: I. 1’ 2.201 mm 71m. $0120 electrical dope” W 229 0.00 0.00 2.10 0 0 200 0.00 0.00 2.10 050 0 220 .70 .00 2.10 1050 10 229 1.00 1.00 2.10 2500 10 200 1.00 1.00 2.20 0000 20 231 2.25 2.23 2.26 4460 25 202 2.70 2.70 2.20 0000 00 202 0.90 0.90 2.00 7050 05 202 4.50 4.00 2.70 9000 40 1:2 m1. 200 0.00 0.00 2.10 . o o 200 0.00 0.00 2.10 410 0 200 .00 .00 2.10 4000 10 200 1.20 1.20 2.20 .2490 15 230 1.75 1.78 2.18 4520 20 200 2.10 2.22 2.02 4070 25 200 2.70 2.70 2.07 -0440 00 200 0.00 0.91 2.00 .7700 05 200 4.47 4.49 2.70 .0040 40 lote: In the above tan-1.21.0. when pour 00.11130 are 1116.130”! 00 neg-3173. this 13 interpreted to mean this the power 13 fleeing tram the 1000111110 with such 3 01¢. .mnmmmm 2.919.: m M 1111:0211. + 21.0. 05170 7.001 W03 00 1’3 5 1 Penn 7400030 W W... 10 1500 1550 1.000 15 2550 2775 .740 20 0500 0505 .977 25 4450 4400 .997 00 5500 5550 1.000 05 7050 7070 .977 40 9000 9050 .997 .2.-fl. M 1- 10 1550 1590 .790 1 0 2490 2490 1.000 20 0520 0500 .790 25 4070 4000 .797 00 5445 5500 .700 05 0410 0020 .970 40 7700 7900 .975 9:! 20:1 3.0. 0 2100 2240 .970 5 0270 0200 .779 10 4200 4270 .705 15 5150 5225 .907 20 0200 0240 .770 2 5 7100 7200 .702 00 0150 0040 .770 WWM M37 Inthenbeve ataxrhenpuermnea mwwnmfln 31511. 1t 10 mum to lean flat power 10 1n mh 1n3t03333 (1331115 from the 1300111110 undu- 00113th1771. .931 2211 El. 2 I I I Watt. 13:11:03 Shift WM 229 1.15 1.10 2.20 2100 o 229 1.05 1.05 2.20 0275 5 229 2.10 2.11 2.20 4200 10 229 2.05 2.01 2.25 5150 10 250 0.15 0.10 2.00 0200 20 250 0.07 0.05 2.40 7150 20 250 4.20 4.10 2.50 0150 00 200 4.74 4.70 2.51 9205 00 319. 2.07.1 3&7 200 1.44 1.44 2.20 2000 o 250 .75 .75 2.20 1775 5 250 .15 .10 2.27 020 10 250 .00 .00 2.00 .90 15 230 .40 .40 2.00 -7 00 20 200 1.15 1.10 2.42 4720 25 200 1.05 1.05 2.51 .2920 00 77.230 2.20 2.20 2.50 -3950 35 .122702011 13031200 100000005912221122 x I I 'Watte Phase Sh1ft W W 220 1.20 1.20 5100 0 220 1.20 1.20 5140 5 227 1.25 1.25 5100 10 227 1.25 1.25 5100 15 227 ‘1.27 1.20 5100 20 220 1.20 1.25 5110 00 227 1.25 1.25 2000 05 12031515 227 1.20 1.25 . 5000 220 1.252 1.240 5040 220 1.25 1.24 5040 220 1.20 1.24 5040 220 1.25 1.241 5000 227 1.25 1.24. 5000 227 1.25 1.24. 5000 220 1.20 1.24 5040 0000: In the above “1111.01“.an great 33:3 113: bun enrolled to record enct current and voltage 77.11133. thm the power 70.1330 Indicated are 30 aeom-ate 33 could he obtdnod. 11110 accounts for the fact that though tho 1030 333 we mintanoein each 0333. the prodlmt of volts and 010113733 111 33513 1n3tanceo. 1033 not check aoonratoly 31th the 751113 1511040» for power. 9113 actual power 7511133 shown are 11301 33 the u1t1nate 7311133. mum m 25219; 2515 33.1 22:1 3&- Phue Shift Total Watte' T3 E 1 Pen:- Footer W 0 2550 2550 1.000 5 1775 1750 .999 10 520 500 .990 15 error error error 20 950 950 1.000 25 1920 2150 .900 30 2925 5250 .590 55 5950 4550 .910 1-1 an 31- w 2500 2770 .920 2500 5210 .512 2550 5590 .793 3100 44:0 .700 5550 5230 .540 5525 5550 .590 5870 0040 . 560 4000 7440 .555 "5:2 2:1 .21- 2530 2770 .914 2040 2590 .510 2155 8160 .502 1890 2890 .51? 1710 4220 .005 1490 4520 .309 1250 5550 .222 WM. Elm Eh- ! 11 13 fimtts I, ..__.JUIIEI__.__JBEEIEEE____£EEEEEELL_ :EIIIIIIL.__. 22! 1.40 1.00 2500 2.60 228 1.62 1.60 2600 2.60 228 1.90 1.75 2850 2.70 228 2.26 2 .20 3100 2 .’5 228 2.00 2.61 3350 2.15 228 2.98 2.95 3525 3.50 228 3.05 5.39 3870 3.50 228 3.77 3.70 4000 3.70 1'11 an 5.1. 230 1.40 1.00 2530 2.00 229 1.45 1.46 2340 _1.07 230 1.58 1.60 2156 1.72 230 1.81 1.85 1890 1.52 229 2.12 2.18 1710 1.36 250 2.00 2.45 1490 1.20 230 2.80 2.83 1230 1.02 229 5.10 3.13 1005 .88 A1temtoro.oouotrnotion and theory of. — Anetta-e fiction. 5 Burke [-0 ”Analytic: ma plot!!!“ ef. le-Leed 1eooee. 000111533... A 26 - 28.‘2. 35.3,. 80 - “O Open-dronit teete. ‘ 23.71.73. Par-11d operotiou. 35.61 - 79. rerfon-noe ammo. :7 - 50 . Begohtiu. 5 71 - 79.53.35. Rotating mgnetle f1e1do.# w 4 - 7. Synchronous mm. 9 - 19. 8mm note”. 'I - 0. “081113 methods. 14 - 16. hating... 15 - 16. limping. —_ —_ 15 - 17. Synchronous counters.- 1 — 17 - 18. W415; «mat.- *- 10 - 11. Symhronlslngm of. —— 11 - 13. 8110" oironlt “hr 290720730 but duh. ‘ w 04 - 113. "V" Curves. 1 _ 28.83.“ - ‘6. Home tor-i. fl ~84. . v“ .-‘ “30'4— u-a: 3 In yr, -,~u- Vr , 1 \ € ‘jLN‘PFTSN’ 3 03177 99 3 129 .. {'9'er F‘ 07 ‘ . o . u‘ x ‘ l . ~ fi K e' . b . O \ \ . . . VI Q . ‘ -\ - ' .'I . .‘ .i - ' _. 1 4 .