steinmetz cp discussion on 'the effect of iron in distorting alternating-current wave-form

From these complex currents he produces a hysteresis loop, noting whether thishysteresisloopis areasonableone ornot, andderiving there-from relations regarding the relative intensity and

DISCUSSION ON "THE EFFECT OF IRON IN DISTORTING

ALTER-NATING-CURRENT WAVE-FORM" AT NEW YORK, SEPTEMBER

28, 1906

Charles Proteus Steinmetz: This paper deals with the

wave-shape distortion produced in alternating-current

cir-cuits by the introduction of iron It is a theoretical paper,

and while of scientific interest appears at first of rather little

practical value to the electrical engineer There is, however,

to-day only a very short step between pure scientific

investiga-tion and engineering practice; and I hope to show youi that the

phenomena dealtwithinthis paper, and similar phenomena, are

of very great practical importance in alternating-current

FIG I tribution; thatis,wave-shape distortionmay lead to effectsnot

only very marked and pronounced but occasionally disastrous

In general, in investigating the effect of iron in

alternating-current circuits, the curveof excitingcurrent is calculated from

the hysteresis cycle of the iron Dr Bedell proceeds inversely

by superposing different harmonics of current. From these

complex currents he produces a hysteresis loop, noting whether

thishysteresisloopis areasonableone ornot, andderiving

there-from relations regarding the relative intensity and phase of the

triple harmonic in the wave of exciting current. As far as the

investigation goes, itextends only to the fundamental andtriple

harmonics;theinvestigationofhigherharmonics is leftto afuture

occasion

19(6] DISCUSSION AT NEW YORK 693

These higher harmonics obviouslv modify to a certain extent

the conclusions arrived at by assuming merely the fundamental

and triple harmonic as present For instance, by superposing

atriple harmonicuponthefundamental wave, one gets a waveof

the shape shown in Fig 1., with a hump on the rising side anda

hollow onthe decreasing side Introducing a triple harmonic of

higher amplitude causesthe hump to developinto a double peak

asin Fig 2 It is obvious that a double peak cannotexist,because

whatever relation may exist between the magnetism and the

magnetizing current,thec urrentnmust rise as long as the

magnet-ism rises; an(d therefore the maximum possible value of the

triple harmonic is that value which (does not yet give a

A

downwarcl bend, buit merely flattens the current wave on

the rising side This maximum amplitude of the third

harmonic can, however, be exceeded if higher harmonics

are present Assume for instance a fifth harrnonic which has

sucha phaserelation as to beneo,ative atA Fig 2, and positive

at B, and then superpose this fifth harmonic on the

double-peaked wave; it wvillbeseen that it cutsofif thepeak and fillsup

the hollow, and gives a wavTe which represents a possible

hy-steresis cvcle,as seeninFig 3 Theeiffectof the fifthharmonic,

then, is to permitthe existence ofa tripleharmonic, largerthan

couldexist intheabsenceofthefifthlharmonic It isquite

prob-able that not ilifrequently in the exciting current there occur

triple-harmonlic culrrenlts higher than the rnaximum value

cal-culated in Dr Bedell's paper, and the double peak is cut off by

the fifth harmonic The fifth harmonic beinginphase,

approxi-mately, at the maximum value of magnetism, is approximately

in opposition at the zero of magnetism, where the double peak

tends to form This brings up the question of the desirability

of extending Dr Bedell's investigation to still higher

har-monics, the fifth, seventh, ninth, etc

An interesting investigation ofthe wave-shape distortion of the

exciting current is given in a paper presented to the Institute

May 1896 by C K Huguet It was this: let there be a sine

wave of electromotiveforce, producingasinewave ofmagnetism,

FiG 3 andfromthe hysteresis cycleconstruct thewave ofexcilting

cur-rent. Thisexcitingcurrent canberesolvedintotwocomponents:

onecomponentsymmetricalwithregardtothewaveofmagnetism,

or wattless current; the other symnmetrical with regard to the

wave of electromotive force, -representing power The

com-ponent inphasewith themagnetismwill befound to be greatly

disto-rted, while the component in phase with the electromotive

force is practically a sine wave, as shown in Fig. 4 I have

checked this in quite a number of cases and it agrees nicely,

except that there always are some small very high harmonics

in the energy wave which makes this curve horizontal at the

1906] DLICUSSION AT NEW YORK 695

zero value That is, the harmonics symmetrical with regard to

the electromotive force arenoticeable only at the zero point, asa

flatteningout Themagnetism curve at this point ishorizontal,

so that the resultant current curve must be horizontal also

This could be expressedby stating that the distortion of thewave

of the exciting current is due, not to the energy lost in theiron,

but to the magnetic characteristic or the bending of the

satura-tioncurve, andtherefore it is this curve which weshouldendeavor

toconstruct, themagnetic characteristic as it would be givenby

a magnetic cycle, in theabsence of hysteresisloss This would

probably give approximately the higher harmonics in the

ex-citing curve wave

Sometime in 1881 or 1882 Dr Froehlich noticed that the

magnetic characteristic of the dynamo machine could be

ap-proximatelyv represented by a parabolic curve. Dr Kennelly

showed, in`1891*, that the B Hcurve, ormagneticcharacteristic

of iron, for the higher values, could beexpressed by a parabolic

curve,an~equationof theseconddegree Usingthis equation ofa

parabola for therelationbetween B andH,therecould be founda

strictly mathematical curve, about like B in Fig 5,.which

combined witha sinewaverepresentingthehysteresisloss,would

fairly closely represent the distorted wave of exciting current

In dealing withhysteresiswehavetokeepinmindthedifference

between magnetic hysteresis and the energy lost in the iron.

If iron is exposed to an alternating magnetic field, the loss of

energy that takes place in the iron, by some form of magnetic

*Magnetic Reluctance, byA E. Kennelly, TRANSACTIONS A I E E.

Vol 8, page 485.

friction, is usually expressed as "molecular magnetic friction."

This loss seems to be constant, independent of the frequency or

wave-shape, depending only on the maximum values of the

magnetic induction If the alternating electrical circuit is the

only source of power, and no power is consumed outside of the

iron, then the power consumed by molecular magnetic friction

mustbesuppliedby thealternating circuit,andissupplied inthe

form of a hysteresis cycle In this case molecular magnetic

friction and magnetic hysteresis coincide, or rather themagnetic

hysteresis measures the molecular magnetic friction As soon,

however, as there is another source of power present, or power

can be consumed elsewhere, this coincidence disappears and

there isnoinherent relation betweenmolecularmagneticfriction

and magnetic hysteresis This was shown first by the

experi-ments of Gerosa and Finzi 1891, recorded by Ewing in his work

tt - ,t _

FIG 5.

on magnetism If an alternating current is sent through, the

magnetic circuit parallel to the lines of magnetic force, at a

frequency which is high compared with the frequency of the

magnetic cycle, then thehysteresis loop moreorless completely

collapses; but the molecularmagnetic friction still remains, only

that now the longitudinal alternating current supplies all or

nearly all the power The reverse is the case where there are

loose laminations in a transformer It will be found that the

hvsteresisloop is extended and the electric circuitinthe formofa

hysteresisloop supplyingmorepowerthan isconsumedin the iron

by molecular magnetic friction; the difference is consumed in

the vibration of the laminations, resulting in noise Where

energy issupplied fromanoutside source, it may go sofaras not

only to make the hysteresis loop disappear, but to make it

1906j DISCUSSION AT NVEW YORK 697

negative Some interesting conditions wvhere the hysteresis

loop could be flattened out or turned over were investigated by

Mr Eickemeyer an(d myself in 1891, on a magnetic circuit

of the shape of that of a shell-type transformer, shown irn

Fig 6, in which the central core could be rotated We found

that such an arrangement when running at synchronism would

givre all kinds of hysteresis loops; forinstance,thatthemorethe

apparatus as motor was loaded the fatter became thehysteresis

loop Whenever the friction is supplied by an outside source

the hysteresis loop collapses, and reTerses by driving the rotor

by power Some hysteresis loops of this apparatus are given

inmy second paper on the Law of Hysteresis.*

These overturn.ed magnetic cycles differed considerably from

the typical hysteresis cycle, Fig 5 A typical hysteresis cycle,

FIG 6.

however, can be madeto contract, disappear, and reverse in the

following manner:

Two equal exciting coils) A and B, in Fig. 7, at right angles

with each other in space, are energized by two equlalsinu-soidal

quarterphasee.mf's sogivingoauniformly rotatingmagneticfield

In the center of this field is a movable iron disc, C With this

disc at standstill, the line of resultant magnetism in the disc

Yf Yl1,lagsbehindthelineof resultantrotatingm.m.f XXm ofthe

exciting coils, bythe angleof hystereticleada, and the relation of

impressed e.m.f and soof magnetic flux, and of exciting current

in thecoils A and B givesthetvpical hysteresis cycle, Curvei,

Fig 8

With thediscCrotatingbelowsynchronism,theangle X 0 Y= (

remains the same, the hysteresis cycle, and thereby the power

consumed in the exciting coils, is the same; but the molecular

*TRANSACTIONS, A. I E E., 1892, vol 9, p 3.

magnetic friction inthedisc, while the same per cycle, decreases

with increasing speed, proportional to the decreasing frequency

of slip The difference in the power consumedby hysteresis in

thee.xcitingcoils,and thepower consumed by molectularmagnetic

friction in thedisc,is convertedinto mechanical work, and such

an apparatus, which I called"hysteresis motor," so gives

con-stant torque at all speeds, tup to synchronism If this torque is

more than the friction torque, the disc accelerates up to

syn-chronism At synchroni-sm, molecular magnetic friction

dis-appears, and the line of resultant magnetic flux retains a

con-stant position with regard to the iron, and all the power given

by the exciting currents in the form of the hysteresis loop is

convertedintomechanicalpower If this is more than the power

consumed by mechanical friction, theline ofmagnetization runs

ahead by the acceleration of the disc, to Y2 Y21, the angle of

hysteretic advance X 0 Y decreases, and the hysteresis cycle of

FIG 7.

theexciting coils so contracts, to Curve II, Fig 8, givingan area

corresponding to the friction toique only If now thefriction

torque is supplied by amechanical driving force, and the disc

Cnotcalled upo-n to do anymechanicalwork, it runs ahead until

its lineof magnetization Y Y1z coincides with theline of

result-antm.m.f X XI; that is, the hysteresis angle (y disappears, and

the curve of magnetism is symmetrical with the curve o)f

exciting current, or the hysteresis loop collapses to Curve III,

Fig S

Still greater driving force impressed upon the disc C, sends the

lineof resultantmagnetizationahead of XXi, to Y4 V41 theangle

of hvsteretic advance a becomes negative,and the hysteresis

loopopens up again, toCurveIV, Fig 5,but istraversed now in

opposite direction, or overturned, representing production of

electric power In this case, the curve of exciting current in

A orB hasthereverse shape; ahollow on the rising, a humpon

the decreasing side

1906] DISCUSSION AT NEW YORK 699

With increasing driving power, the overturned hysteresis

loop IV fattens, until it reaches the same shape as I, but traversed

oppositely, and then synchronism is broken, and disc C speeds

up Above synchronism, the hysteresis cycle has the normal

shape I, but is overturned, the angle of hysteretic advance of

phase has reversed its sign, and molecular magnetic friction

again consumes power in the disc; but this power is now given

by the mechanical driving power, and notby the electric circuit

Below synchronism, a constant amount of electric poweris

consumed; above synchronism, a constant amount of electric

powerisgenerated inthe excitingcoils, irrespective of the speed,

while thepowerconsumed by molecularmagnetic friction in the

disc varies proportional to the slip from synchronism, but is

the same above asbelow synchronism.

The bearingy of these wave-shape phenomena on practical

engineering will now be considered

If there be a sine wave of impressed electromotive force,

E, Fig 9, or rather of counter electromotive force, it produces a

sine wave of magnetic flux B This sine wave of magnetic flux

causes an excitingcurrent to flow which is distortedby hysteresis,

or rather, as wemay say, by the magnetic characteristic, and is

givenby Curve I if, however, the transformer is traversedbya

sinewave ofexcitingcurrent, I in Fig.10,we getbythehysteresis

loop a wave of magnetism, which is not a sine wave, but which

ishollow on the rising side, rises very rapidly and decreases very

slowly, at first, and then very rapidly That is, the wave of

magnetism has a pronounced flat top, and the wave of e.m.f

induced therebvis very low for a considerable partof the period,

then rises very sharply to a high triangular peak, and falls off

just as rapidlyN, as shown by E in Fig 10 This peak rises to

nearly twice the maxim-um value of the fundamental sinewave,

El Fig 10 That is, with a sine wave of current traversing an

ironclad magnetic circuit, thee.m.f wave is greatlydistorted,and

the magnetic circuitgenerates higher harmonics of e"m.f.mainly

of triple frequency.*

Very interesting phenomena result from this wave-shape

FIG 9.

tortionby themagnetic cycle,if transformersaregroupedin such

a mannerthat certain harmonics can not develop

In a three-phase system with three transformers connected in

delta or ring connection,and a sinewaveofimpressed e.m.f, the

excitingcurrentinthetransformers has the usualshape, I in Fig.9,

containing apronounced third harmonic, which is showln

separ-ately as I,in Fig 9, together with all its higher harmonics or

*For instance with the hysteresis cycle Fig 5, and a current I 10

sin (l + 30), the e.m.f is approximated by the equation: E =-11.67 cos

(+ ± 2.50) + 6.64 cos (3- 3 40) + 3.24 cos (5(b-11.9') + 1.8 cos

(7(5-10.70) + 1.16 cos (95 -4.50) + 0.80 cos (11L 5-220) + 0.53 cos

(13sb-260 ) + 0.19 cos (150 -150)+

1906] DISCUSSION AT NEW YORK 701

"overtunes." Thecurrent irn the three-phase lines can not

con-tain any third harmonic: the current in line 1 is the resultant

of the currents flowing from line 1 to 2, and Erom 1 to 3, and since

these two currents are 60 degrees apart inphase,their third

har-monics are 180 degreesapart, or in opposition, hence cancel That

is, thetriple-harmoniccomponentofthe excitingcurrentcirculates

in a local circuit through the transformertriangle, without

reach-ing the three-phase lines All the other harmonics of exciting

current appear in the line current

If the primary coils of the transformers are connected in Y or

star connection, the secondaries in delta, the primary exciting

current does not contain any third harmonic, but the triple

FIG 10

harmonic of excitation circulates in the secondary transformer

triangle in localcircuit

Perhaps still more interestingis the case of three transformers,

connected with their primaries and secondaries in Y or star

connection ina three-phase system with sinusoidal e.m.f

im-pressed upon the lines

In athree-phase system, thethreee.m.f's from thelinesto the

neutral are 120degrees apartand so are thethree currents With

a sine wave of impressed e.m.f., if the e.m.f's between lines

and neutralwere sine waves also, the three exciting currents

wouldcontain strong third harmonics Since these currents

are 120 degrees apart, their third harmonics would be

3x 120= 360 degrees apart, or in phase; that is, all three

flow simultaneously toward the neutral If now the