everything else. I agree that instancesdo occur where a graduate student has e xcitation o n uction otorsturned out to be a poor teacher. This.however, is a fault of the individual con-cerned rather than of the system of usinggraduate students as assistants. As to By C. F. WAGNERcomputations, I am positively in favor of MEMBER AIEEthem and have used them in connection withmy courses. But I attempt to make mycomputation not 'slide-rule" or "formula- Synopsis: It has been known for some subject. However, the increased usesubstitution" problems but rather problems time that an induction machine whose rotor during the past few years, of capacitorswhich stimulate thought. Computing is driven mechanically may become self- f pest fection, of paced a

periods should, in my opinion, be periods excited if capacitors are connected across for power-factor correction, has placed ain which the habit of straight thinking is its terminals. The present paper is con- new aspect upon this problem. If therequired under competent supervision. cerned with the predetermination of the power supply to an induction motor isNims seems to favor "slide-rule pushing" machine characteristics when operating disconnected, the inertia of the connected

and "graph plotting" as showing the student under such conditions. The- frequency of"relationships which he otherwise might not excitation is very close to the synchronous rotating load tends to continue the rota-grasp." I am sure the "graphs" themselves frequeney corresponding to the speed of tion of the armature. The extent todo reveal such relationships but I question the rotor. The voltage to which the ma- which this occurs is dependent upon thewhether the actual plotting of these graphs chine will excite is dependent upon its no- nature of the load and in certain cases thedoes! In order to illustrate what I mean load excitation characteristics at that fre- armature may continue to rotate forlet us assume that one laboratory course is quency, the criterion to be satisfied being seconds or minutes. In addition, appli-run by two different instructors as follows: that the lagging volt-amperes of excitation

equal the leading volt-amperes of the cations are known in which gas or gaso-Instructor A requires his students to run capacitors. line motors are connected to the same

the equipment, take data, and when the ex- Under load, similar criteria must be satis- shaft with the induction motor and theperiment is over gives his instructions as fied. Voltage conditions are determined utilization device, so that, in the event offollows: by a cut-and-try solution such that the a

r

(a) Compute only one point on each curve or summation of reactive volt-amperes equals the removal of the electric-power source,perhaps only one curve, thus reducing slide-rule zero. The slip is then obtained from the the armature can actually increase inpushing to a minimum. relation that the summation of the real speed and remain at the increased speed(b) Blue prints of all curves are given to each power equals zero. These relations have until manual readjustments are made.student. You do not have to plot any curves but! been applied to various types of loads, such With capacitors connected across the(c) Give a complete and adequate discussion of as pure resistance and inductive resistance,the why, how, wherefore, of all the results that the single-phase and three-phase and also to terminals of induction machines whichcurves reveal. induction-motor load. Excellent checks have been disconnected from the electri-(d) Answer the following pertinent questions between test and calculated results have cal source and in which the armature con-(which require thinking) regarding the results of been obtained.your experiment. tinues to rotate, the value to which

This is the instructor who does not care the terminal voltage will rise due to self-to have his student waste time on curve HE general impression appears to exist excitation is dependent upon the speed,plotting and slide-rule pushing. He would th r * * value of the capacitor, and load. Withrather have them use their time in forming at for an iductionmachine to oper- the regulatory function of the powercorrect habits of thought. ate either as a motor or as a generator a

source of alternating potential is always vInstructor B requires his students to run . , I the excit rise to dangerously high voltagesan-

the equipment, take data, and when the ex- n.ecesrirder to suppl the ca-P gerous with regard to human life or dan-periment is over gives his instructions as tiongerous with regard tohumatnl ore -follows: for under certain conditions, an induction gosw i vregrtoinsulati break

(a) Compute all points on each curve (maximum machine may supply power as a generatordown. P l ted lights ight* x . . *. r *,*pygeeratr also burn out with but a nominal increaseslide-rule pushing). without a source of alternating potential,

(b). Make neat plots of all curves using india ink the magnetizing current being supplied by in voltage. It may be seen, therefore,(maximum curve plotting). static itsttccapacitors. It S the purpose of(c) Discuss curves (by this he generally means say Paper number 38-106, recommended by the AIEEthat this curve runs this way and that curve runs this paper to discuss the circumstances committee on electrical machinery and presented atthat way, which of course is obvious from the curve under which such operation becomes pos- the AIEE Pacific Coast convention, Portland, Ore.,itself). August 9-12, 1938. Manuscript submitted May 16,

sible. 1938; made available for preprinting July 7, 1938.This is the instructor who requires The fact that such operation is possible C. F. WAGNERis consulting transmission engineer of

"1curve plotting" and "slide-rule puhn" the Westinghouse Electric and Manufacturingand is the preponderant type in pushing, has' been known for some time, but very Company, East Pittsburgh, Pa.neering colleges. little has been written upon the subject The author wishes to acknowledge the assistance ofNow I ask who turns out better engineers, until recently. The reason for this pau- R. P. Shimp in making the necessary computations

instructor A or instructor B? city of papers and articles lies in the rela- incident to writing this paper.Del Mar puts his finger on the right spot tively minor practical importance of the 1. For all numbered references, see list at end of

when he states that our present plight is pdue to mass education in engineering. Nowit so happens that other professions havesolved this problem of mass education bylimiting enrollment. This is true of themedical, dental, and legal professions. teachers. Thank God there are high-grade instituted whereby a large number of engi-Engineering as a profession has, so far, not teachers scattered throughout this land. neering teachers throughout the countryseen fit to take this step which, in my It is these who would and could educate are afforded a chance to spend their sum-opinion, is the only solution to the problem. better ones along the lines suggested. mers in industrial concerns. I also com-

Coover raises the question of how the Manning and I are in full agreement. mend Manning's statements that mathe-present teachers can educate better ones The value of co-operation between industry matics and physics are valuable to theif they are not so good themselves. My and the universities is unquestionable. engineer not perhaps so much because ofanswer is that Coover begs the question. They both have something to offer to each their subject matter but because of theI nleither did condemn nor even had the other and a mutual exchange is extremely training they afford him in logical reasoningintention of condemning all engineering desirable. I should like to see a plan and in correct processes of thought.

FEBRUARY 1939, VOL. 58 Wagner-Self-Excitation of Motors TRANSACTIONS 47

that this problem has been removed from power, three-phase 60-cycle 220-volt the range for which the data overlap, theone of purely academic interest to one of 1,770-rpm type CS Westinghouse motor test data checks with that obtained bypractical importance. of conventional design. The constants, the application of an alternating voltage.

In 1935, Bassett and Potter' presented obtained from test data, are Referring to the equivalent circuit oftest results showing the performance of egenerators under capacitive and combina rs = 0.151 ohm per phase to neutral figure 3 it may be seen that the ratiogenerators u r cp rr = 0.145 ohm per phase to neutral ntions of resistance and capacitive loading. x - 0.394 ohm per phase to neutral for any point on the no-load excitationThe present article considers simllar xm (air-gap line) = 19.8 ohms per phase to curve must equal (xm + x) or x,. Inproblems and further shows that the per- neutral order that the reactive kilovolt-amperesformance under such conditions, including sum up to zero, xc must equal (xm + x).both balanced and unbalanced operation, The no-load saturation curve is given in Thus the slope of a straight line drawncan be precalculated quite accurately. figure 2. The lower portion of this from the origin of the curve of figure 2

curve, indicated by circles, was obtained to any point on the curve gives the capaci-

rby impressing a three-phase alternating tive'reactance of the capacitor required tor~~~~~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~tvvoltaanetothemacin terminal and'r t

,u h < voltage to the machine terminals and produce that voltage at no load. As thegr {1z; IC ijx varving the speed by means of a connected= I-S JX xe T-~~xc I condenser capacity decreases the slope>S rr / ea e I 4 d-c motor so that the power input fromI R representing its capacitive reactance in-

INOUCTION MOTOR LOAD the a-c end was zero. creases and the terminal voltage de-Figure 1. Equivalent circuit of induction creases. When finally the slope equalsgenerator with three-phase load of capacitors No-Load Excitation the air-gap line, an infinite number of-Jxc in paralle with induction load R + jX solutions are possible. Beyond this point

A three-phase bank of static condensers the machine is inoperative. Therefore,was connected (without the a-c supply) there exists a certain minimum amount

With known conditions the characteristics across the terminals of the machine and of capacitors which will still produce self-of the machine can be predicted by the the rotor driven at a speed corresponding excitation. In this regard the inductionmethods presented here. to normal synchronous speed by means of generator performs in a manner quite

the d-c motor. Since only the losses of analogous to a shunt-excited d-c gen-General Considerations the machine must be supplied, the quan- erator.

tity, rri I (figure 1) which represents In what follows it will be necessary toThe conventional equivalent diagram s rpent know the volt-ampere characteristics of

of the induction motor will be used with the shaft input, will be very small. This the xm branch alone. This is obtainedthe exception that the magnetizing branchwill not be regarded as constant but must Figure 2. No-load 1 [ _ _ _vary in the manner dictated by the saturation curve of 5 00 - _zsaturation characteristics of the particular 15-horsepower 220- NO-LOAD EXCITATION .-machine. This circuit is shown in figure volt 60-cycle in- 400 CURVE, _ - - I

duction motor ~~~~~~~~~~~AIRGAP1 for one phase. The symbols will have duction motor ---__VOLTAGE __the following significance: o=motor connected o 300 - - / - - - -

to a-c source >-r= Stator resistance in ohms per phaseto neutral x = motor excited z 200 A

rr = Rotor resistance in ohms per phase to through capacitors - - I - uneutral F TERMINAL VOLTAGE- Vneutral w~~~~~~~~~~CPCIOKACUV STATOR REACTANCE DROP

x = Stator and rotor leakage reactancesin ohms per phase to neutral

x, = Reactance of branch representing < _ 20 30 40 5 D 0 70 80 90magnetizing current in ohms per imn-MAGNETIZ4NG CURRENT IN AMPERESphase to neutral 0 2 4 8 8 10 12 14 18 18CAPACITOR KVA. AT 220V.,60 CYCLES NECESSARY TO PRODUCE

s = Slip expressed as a fraction of syn- NO-LOAD VOLTAGE GIVEN BY ORDINATE.chronous speed

The slip is referred to the frequency of condition requires that s be very small and from the dotted line in figure 2 by sub-the stator voltages and currents and, consequently that 1- r be large and i7 tracting the xi drop giving the curvewhen operating as an induction genera- s shown by the full line and marked "air-tor, is, of course, negative. small. The equivalent network for this gap voltage."The general considerations which will operating condition for all practical pur- A further demonstration of the truth of

be applied in determining the solutions poses reduces to that shown in figure 3 the above theory is offered by the mannerare that the summation of the real power in which r8 of figure 1 has also been neg- in which the terminal voltage changesand the summation of the reactive volt- lected. Because s is small the generated with change in frequency. The full linesamperes throughout the entire circuit, frequency corresponds to that of the shaft in the insert of figure 4 show the magnetiz-including that of the load, must each equal which in this case is normal frequency. ing characteristic and the capacitorzero. Because of the presence of satura- U3pon varying the magnitude of the capaci- characteristics for normal frequency. Astion phenomenon, resort will be had to a tors the test points, indicated by crosses the frequency is increased the terminalgraphical or a cut-and-try method of solu- in figure 2, were obtained, extending the voltage for a given magnetizing currenttion. no-load excitation curve to more than increases proportionately with the fre-Most of the tests which are described in ten times normal excitation current. It quency. On the other hand, the capaci-

what follows were made on a 15-horse- will be observed that over the portion of tor current varies inversely proportional

48 TRANSACTIONS Wagnzer-Self-Excitation of Motors ELECTRICAL ENGINEERING

to the frequency. These characteristics under consideration is shown complete in The series reactance in the load for theare shown by the dotted lines for an in- figure 1. To calculate the performance former case, although only 8.3 per cent,crease in frequency of about 20 per cent. while keeping the capacitor fixed the fol- exerted considerable influence upon theThe new terminal voltage is then given lowing steps are involved. An arbitrary terminal voltage.by the intersection of the dotted lines. value of R and its corresponding value of An interesting condition exists for theThe comparison between test and calcu- X are chosen for which it is desired to de- range of operation indicated by the dottedlated results using this method is shown termine the terminal voltage, e. Esti- lines in figure 6. Note that for this rangeby the circles and crosses in figure 4, mate the value of e. This fixes iL and i.. there is no appreciable saturation so thatwhich indicate a very close agreement. The current is is the sum of ic and iL. Xm can be represented by a constant. It

Knowing is the drop through r8 + jx is is possible, therefore, to determine theJ x found which determines ea. The magne- impedance of all that portion of the cir-

tizing current i,,, is obtained from the fullL0 I X r line of figure 2. And, finally, ir is the 400 -

sum of im and i,. At this point all the 380ti 13T-JX~ currents are determined for the estimated 360 XI A54 RHMS 741KVOAGE^ 3J Xm l cne values ofe. All of thoseopvrationsare,eAllot operations are,

of course, vector operations. If the esti- 9 - - -|mated value of e is the solution the follow- 9 280

9_ &,4 VA)_ing relation should be satisfied. 260Figure 3. Equivalent single-line diagram for ' 1

no-load excitation condition XiL2 +xis,+e-i- , + Xi 2-X,i,2 = 0 (1) z 2240200

Figure4. Effect of a8c -400 { change in frequency 160

,, 30 _No load-constant -6 120_1-120C .~~~~~~~~~~~~~shuntcapacitor= '40 >2 001 Z -5 VE010V t6CCe Og g ;>O //CITAOTIO5N 2URR2EN 1<1C l j x CdlCU§dte PO;ntS V10.6kv at60cycles IC e ea: 4 80-_ _400 IOC..u ao=test points ~ 6

0 5 10l 20 25 l x=clculated points 2EXCITATION lJRRENT c p l lt

300 I I IL40.. 0 20 30 40

FR YLOAD CURRNT(NOT INCLUDINGICAPACITOR CURRENT) IN AMP

t>h200 -s -Figure 5. Characteristics of a 15-horsepower-JThis curve gives the terminal voltageas calculatedresultsfortwovalues a induction generator under three-phase resist-

a funtin f te ilvol-apees f he tor ae how i fgur 5 g30011)SKA.anceload having 8.3 per cent reactanceg. x = calculated pointso = experimental results

c55 5 6 8 = terminal voltage40e42 44 46 48 Ti52 54 5- mh60 62 64 66 6 7

slipFREQtUENCY IN CYCLES PER SECOND ~si

In order to provide a better quantita- if, however, this summation is not satis-tive perspective of the values involved, fled a different value of e should be tried 36C - _ AT NORMAL(4LTAGE -the dashed line in figure 2 was calculated. The comparisons between the test and 34This curve gives the terminal voltage as calculated results for two values of capaci- 32( -a function of the kilovolt-amperes of the tors are shown in figure 5. 5030C-capacitors at normal frequency and volt- The slip for this particular value of R is o i by ti mtoa--eage. It will be seen that for a capacitor determined by summing up the power .jwhose kilovolt-amperes is equal numeri- quantities for the solution obtained from o 2 _ __td -cally to the horsepower rating of the ma- the summation of reactive volt-amperes -220.chine the terminal voltage reaches a value and equating this sum to zero. No cut- OCequal to twice normal. This will vary and-try method is necessary. Thus [OC5- -within limits for different motors, depend- 7C- - /-'ing upon their excitation characteristics. - r0i,2 4 r,i02 + r.i82 + iL2R = 0 .61..

-5 IOCr - 'I3Three-Phase Impedance Loading or, combining the first two terms and c~ c -4 . 80SA ~Asolving .3C /60rf-I .[

cuit in figure 1 which lies to the right of a. satisfied by this equation. Actual opera- to \/3 times the current in R and arma-A solution exists when this impedance is tion is impossible at any of these values as t opurely real, there being no imaginary an attempt to operate on the straight age across Rvpart. Since for pure resistance load of part of the curve results in instability. fge lods adfigure 6, X is zero, then R and-fc in For values of R slightly smaller than this If the load IS an impedance instead of a

pure resistance, it is only necessary to re-parallel become which will be critical value the machine loses voltage, is placeR by R +jX whereX represents theR-iXc unstable. A self-excited induction ma- reactance of the load. Tests and calcula-designated by R' + jX', in which chine cannot, therefore, supply a sus- tions upon the foregoing basis have been

tained short-circuit current. A similarx 2R made on the previously used induction

R2 (3) motor excited with capacitors acrossR2+Xc2 dotted lines in figure 5, the slope of whichX ,_~~three terminals and loaded with a resist-and r,/n3 e ance rack across two terminals. The

r t iR2 -\/R2+X2 rack possessed 8.3 per cent reactance.X 2 +- ,2 (4) which still permits operation as a genera-

tor.The impedance to the right of a then be- - -

320lcomesSingle-Phase Impedance Loading 300

jxm((R' + rs) + j(x + X')) 2--_(R' + rs) + j(x + X' + xm) ± i For this case let it be assumed that a v26 e

resistance R is placed across phases b and >220The condition that the imaginary com- c o 224.-_ -c of the induction generator, the capaci- Z2 _ _ponent of this expression equals zero, re- .20'.J 2tors still being connected across all three ° 18Osults in the following equation: . .flowngephases. This is analogous to the short- z 160._

(x + X' + Xm) [xm(X + X') + circuit of a three-phase system through a 140-x(x + X' + xm) ] + resistance R, a case treated frequently in -3120_(R' + rs)(xm + x) = 0 (5) the literature.2 For this case the posi- |.

Z-2.tive- and negative-sequence networks are 6_Upon substituting (3) and (4) into (5), a IS60fourth degree equation in R results, which connected together as shown in figure 7. kfi0--permits the determination of R. The TheactualcurrentthroughtheresistorR -1 is V13 times the positive- or negative- 0°quantity R is equal to X times the slope sequence current flowing through R in the LOAD CURRENT(NOT INCLUDING CAPACIrOR CURRENT IN AMP

of the dotted lines in figure 6. The signi- diagram. This procedure tacitly assumes Figure 10. Characteristics of a 15 -horsepowerficance of this expression is that there are the justifiability of superposition in the induction generator under single-phase resist-an infinitely large number of solutions for presence of saturation phenomenon. It ance load having 8.3 per cent reactance and athe terminal voltage when R has the value will be assumed that saturation effects in- three-phase capacitor equal to 10.3 ohms per

fluence only the positive-sequence net- phase to neutral (4.7 kva)work and not the negative-sequence net- = calculatedwork. The checks obtained by compari- o = experimentalson between the calculated and test values = terminal voltage

rPOS. SEQ.||NEG. SEQ~ 1justify these assumptions. The positive- = slipNETWORK NETWORK sequence network of the machine is the

R same as has been considered previously in The results of these tests and calculationsthis paper and the negative-sequence net- are plotted in figure 10, which shows very

Figure 7. Method of connecting sequence work, with the exception of the capaci- close agreement.networks tors, has been treated previously in the If a capacitor is connected across the

literature.3 This network is reproduced load only then the two capacitors -ixer, -Jx Jx in figure 8. Since s is usually small, a of figure 9 must be removed and a singlegood approximation is to assume s equal capacitor having the impedance of the

to zero and to combine r, and 1-sr

actual capacitor must be connected across2-S FrmJXs 2-s the load impedance.

0 making the sum equal r. It will be as-Figure 8. Negative-sequence network of in- s Load Characteristicsduction motor with three-phase capacitor sumed that xm can be replaced by a con-

across its terminals stant term determined by the air-gap line. Under certain conditions an inductionIt is thus possible to replace the negative- generator driven by an engine or othersequence network of figure 8 by a simple equivalent motive power might havre con-

r.JX JX r, R impedance independent of saturation and nected to it other induction machines5 _ UUt 1 Ut ~~~slip. The resultant combined network which had also been connected to theu ~sr ,jeIIeaL.L R for the positive- and negative-sequence is source of supply. At the time of failureS S *JXX I a TJSXT JX therefore that shown in figure 9; R2 + of the a-c source of supply the engine-

1 j-1L7 .X2 iS the impedance to which the net- connected induction motor tends to driveFigure 9. Equivalent circuit for induction work of figure 8 has been reduced neg- the other induction machines at a fre-generator and three-phase capacitor loasded lecting the impedance of the capacitors quency determined by the speed charac-

single-phase by resistance R - jxc. The current in the load is equal teristics of the motive power and at a

50 TRANSACTIONS Wagner-Self-Excitation of Motors ELECTRICAL ENGINEERING

340 .___ __. _l __ 10 - be supplied from the decrease in volt- of the generator and the starting laggingCy320-_ _ _-_ _ a, = = _ _ C _, _ amperes required by the excitation. At kilovolt-amperes required by the station-

10-30L0___ _ -_ _ _ _ _ _ _ _ the higher voltages produced by the ary motor.

I__IjA ~~~~larger condenser capacity the machine isRzzs0 _ _ _ _ _ . t_ _ _ 5 operating at a higher saturation and, Wave Shape24 '

2! 4 6 7 8 91,I° 2 therefore, more reactive volt-amperes is

LOAD IN HORSEPOWER AT TERMINALS OF GENERATOR released for a given change in excitation Oscillograms of terminal voltage under

voltage. either no load (figure 12) or load (figureDRI 7 8-t For the particular values of condenser 13) indicate a very close approximation

CAWACITORSTIUcITRoN wCTHRESISTANCE capacity used in these tests, it was neces- to sine wave. The current wave formsGENERATOR MOTOR LOAD. S sary to bring the driven induction motor are distorted to some extent.

Figure 11. Self-excitation characterisucs of up to speed by its d-c machine in ordertwo 15-horsepower induction motors, one of to make the sets excite themselves and Conclusionwhich is driven as an induction generator feed- carry load. However, at the no-loading the other as an induction motor. Figures condition discussed previously, the ma- Calculations have been made for severalon curves represent capacitor kilovolt-amperes chine came up to voltage very rapidly conditions, both at no load and under

at 220 volts, 60 cycles provided there was sufficient capacitor load and the results agree closely with the

kilovolt-amperes to provide the excita- test results. These checks include both

voltage determined by the shunt-con- tion. In the loaded case, the capacitor balanced and unbalanced operating condi-

nected condensers. In figure nis-shown kilovolt-amperes was too low to supply tions. It is felt from this that, given thea test setup to determine the characteris- motor characteristics, the self-excitationtics of an induction motor when operatingunder such conditions. The setup con-sists of two of the above-mentionedmotor-generator sets, the induction ma-chines having the characteristics of thosedescribed previously. One of the d-c ma-chines acted as a motor to drive one of theinduction machines as an induction gen-erator and the other induction machinedrove the second d-c machine which was Figure 12. Wave forms for a 15-horsepower,loaded upon a resistance rack. The two 220-volt three-phase induction motor operat-induction motors were connected in ing at no load and excited by a five-kilovolt-parallel and a bank of condensers con- ampere static capacitornected across their terminals. Under Upper curve-terminal-to-terminal voltage =this type of operation, theory dictates that 320.4 volts Figure 13. Wave forms for a 15-horsepowerthe capacitors supply not only the excita- Lower curve-armature current = 18.3 am- 220-volt three-phase loaded induction motortion requirements of both induction peres excited by static capacitorsmotors but also the leakage reactancevolt-amperes of the two machines. The both the excitation requirements and thecurves of this figure show the characteris- leakage reactance volt-amperes of the effects can be predicted in advance to thetics at 60 cycles for constant values of machine. Subsequent tests in which a same degree of accuracy as that of thecapacitors as the load is increased on the five-horsepower 550-volt induction motor information.induction generator. The no-load values was used for the load both sets were ex-of the voltage correspond to the values cited very nicely by either bringing the Bibliographyobtained previously for the no-load condi- two machines up to speed simultaneouslytion. It will be observed that the upper by the one driving motor or by first excit- 1. CAPACMVBEXCITATION FOR INDUCTION GEN-

BRAToRs, E. D. Bassett and F. M. Potter. ELBC-of these curves is much flatter than the ing the induction generator and then con- TRICAL ENGINEBRING (AIEE TRANSACTIONS), May,lower one. The reason for this is appar- necting the five-horsepower machine. 1935, page 540.ent when it is considered that as the load The question merely resolves itself into 2. SYMMETRICAL COMPONENTS (a book), C. F. Wag-is increased, the increase in leakage reac- one of whether a given capacitor can sup- 3. SYnMETRICAL COMPONENTS (a book), C. 4.tance volt-amperes of the machine must ply both the excitation kilovolt-amperes Wagner and R. D. Evans. Page 349.

FEBRUARY 1939, VOL. 58 Wagner-Self-Excitation of Motors TRANSAcTIONS 51