b7

MlnHU Herbel'\ llopldn1, h. /)/

The•ia eutaitte4 t.o the Qracluate Panlt.7 ot th9

Yirginia roqteohlde Inat.lwte

IWIDB rl SCDICI 1n

ll.Htl'ioal ln&iMerinc

APPIOYID1

MaJor PNte11or

Febra&17, 19'8

-77

I. Introduction • • • • • • • • • • • • • • • • • • II. • • • • • • • • • • • •

III. The lnveatigatieth • • • • • • • • • • • • • • •

A. Object ot Inveetipticm • • • • • • • • • •

• • • • • • • • • • • •

• • • • • • • • • • • • • • • • • • • • • • • • • •

c. beult.a ••••••••••••••••••

IV. Di•euaaion of Results • • • • • • • • • • • • • V. Conoluaiona • • • • • • • • • • • • • • • • • •

VI. Svmrnar.r • • • • • • • • • • • • • • • • • • • • VII. Aoknowledgementa •• , •••••••••••••

VIII. B1bl1ographT • • • • • • • • , , • • • • • • • •

II. Vita •••• • • • • • • • • • • • • • • • • • •

l

2

8 9

9

26

30

31 .'.32

LIST Of TABl&1

1. Mea8Ul"en\fm\ ot Neptive-leqwmee Curnnta for Unbal-anoed Three-Phue-Resistive Load• \laing a Weston

P.AGB

Hodel 43.3 Zero-to-Fin-Ampere Ammeter tor Hu.euring 12 • 12

2. .._~t ot legativa-Bequence Currents tor Unbal-anced 'l'hree-Ph&H-lesiative LoachJ Ul.ing a Weston Model 4.3j Zero-to-One-Ampere A.meter for Meaaurhtg 12. • l3

s. Meas~t. ot legative-&.quenee Current.a tor a Three-Phase Induction Motor Openting cm Unbalanced Voltages Vi~ Ia laad on Weston Model 1.33 Z.PO-to-five-Ampere Amat.er. • • • • • • • • • • • • • • • • • • • • • • • • lS

4. Meas~t ot Megative~ce Current• tor a ~ Pba•• Induction Motor Open.ting on Unbal&nced Voltages With l.2_Baad on Weston Model 904 Amm.Gter Zero-to-0.ne-.Ampere Benge • • • • • • • • • • • • • • • • • • • • • • 19

2. Calibration Circuit • • • • • • • • • • • • • • • • • • 10

3. Measured Ya.lwts Vema Calculated Values !or a thrM-Phaae-Beei•ti~ Load • • • • • • • • • • • • • • • • • • l4

4. Reasured Yal.uN feraus Ca.lcula:ted Yalu•• tor a Th.Ne-Pbase -Res1at1ve Load • • • • • • • • • • • • • • • • • lS

s. Dif'ferenee Between M8&e'IU"9d and Calculated Values for Three~Ptia .. ~BesistJ."¥9 Load • • • • • • • • • • • • • • • 16

6. Dif!erenetl Bet.wen Measured and Calculated Value• tor 'fhrree·Phase-Beaiative Load • • • • • • • • • • • • • • • l?

7• ~Values Versu Calculated Values for a Three· PhAH 'Iitduet1on Motor Operating on Unbalanced Voltages • 20

LIST OF FIGURIS (continued)

s. MH.&Ul"ed Values Versu Calculated Values tor a Th.l"ee-Phaae Induction Motor Operating on Unbal ...

PAGI

a.need Voltages • • • • • • • • • • • • • • • • • • • 2l

9. Difference Bet.ween X.&8\U"ed and Caleu.lated Val\148 tor & Three-Phase Induction Motor O,.nting on t1nbalanced Yo1tap8 ·• • • • • • • • • • • • • • • • 22

10. DU'f erence Bew.en Jleuured u.d Calculated Values tor· a fiu"ee-Pbaao l'nduction Motor Operating cm Un~ Voltas-e • • • • • • • • • • • • • • • • 23

ll. Ditterene• Betve•n Corrected and Calculated Yalas tv a Three-Phau ResiaUw Load • • • • • • • • • •

12. D1ff•J'ene• Between Corrected and Cal~ulated. Value• tor a i'hre......rhue Induction Motor O,.rating on

· ~•cl Voltage• • • • • • • • • • • • • • • • • 25

The aolut.iona ot msbal••tMI ~ .. oirn1\a can be grea\l.J

a1apl1tled thro\1gb the ue ot \he Mthocl ot a,_etrl.eal c.,._u.

In a tJlree-pb&ae qat.m the pNHDO• ot neptift-pb&H•Hq11.enM eunut.

1a an inc11ea\lon of Ubal&ao• ill tJae oiftllit. 81no• ... , thNe-plaaM

•chima baft balanced oiro11.iu, the preaenoe ot a neptiw-pba•-

MqUDee CVNnt 1a --~ an iladication ot an almelMl oondiU.• ill

tile circuit.. The Mpi:t.ude ot the nepU.w-pbaae-Mquw• oVNnt. 1a

an 1nclicatioa ot tile UIOUllt. ot unbalance.

At. the pnaent UM Y&ri.ou pl'OteoU.w de'Wlo•• &N in ue wbiob

operate due t.o the pnaenoe ot aepU.ft-phaff-aequaoe OU'ftllU, bat.

ftJ7 little 1a be1n& done t.ward diNot, accra.rate .....,..\a ot

aepU.w-Hquenoe eurnnta.

2

The •11.hod ot QWVioal o_,__ta u applied to tbe aollaUcln

ot unbalanced J»l1pbue netwva w.a tint. int.roctuced b7 c. L. r~aoue

(3) in 1918. At \hia t1M no mat.1• w.a Mde ot •11hoda tor aotualll'

•an.ring the omponent.a ill a oirnit.. In 1923 Porte••• (4) pruent.ed

a paper t.o The .Aml"1oan lnatit.ute ot llect.rioal ~ ... ,,.. entitlff,

........_t ot Power in PolJpbaH Cirnit.a•. Kr. Porte••• at.at.eel

t.bat. the ala'U.q power rates wen not equitable ader wm-ltnoed oon-,

d1t.1ona and aqpatecl t.bat. a new at.hod ot ~ power, based on

the •11hod ot QWVical • .,..t.e be ...... Kr. '·~-··· paper alao eqpated netvom wtd.oh WRld be capable of aeaam1.n& poaltiw-

and neptiw- nquenee W>lt.apa and ov.nnt.a.

Also in 192) an art.iole w.a pa.bliahed b7 Kr. L D. IYana (2)

•t.lill1n& •1ihocla ot •tering powr in unbalanoed poqptaue qat.a.

Kr. ..._ at.at.eel •- ot the ad't'ant.apa ot aequnoe •tering and aaw cd.reuit dJ&gNU ot a.tworb oapal:>le ot •tering pu1tiw- and nept.1w-

nqu.noe ocaponuit. ot W>lt.ap and ourrent.. After t.be poa1t.1w- and

neptiw-aequenoe o_,_.nte of Yolt.ap and current an ffp&raW, it

w.a ahcnm t.hat. 1t. waa poaaible to omabine \bea to muun powr, N-

aot.1w power, and power fact.or.

Other writ.en n.oh •• ll&J'W&l"d ( S), Slmck (6), and Borden and

Behar (1) baw preeented. d11ouaaiona ot \be aubJeot, tnat. w17 little

.... adclecl to the work ot rort.eaoue and l'naa.

~ J

I i

• l i

~

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! ~

i I I

E f

~

E

~ l

~ ~

• I

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f a

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f I !

§

l ! f

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·.'

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l •

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i s

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.. Jr:·

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= '·

t!'

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c ..

1 "'l

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~ ~

.... 0

..

11

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I +

i I!

-f~ 5

f . [·

ff J ~

;

l = ..

I ·=

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&

. .

i Si"

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p f I

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1 •

( ~

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f j l £

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f tllt

1 ii

Di

f ~

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...

M i::: B I i

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4

C.7.

c. T. :r. --ii'"

+ -

Figure 1 CIRCUIT FOR MEASURING NEGATIVE PHASE SEQUENCE CURHENTS

when (a) ia the ompla operator, 1lJa!f! • Werring t.o tlguN l,

1t all vindinp ot the CUl"NDt trantltormer bl.ft the .... amber ot

t,vu, the ._.t.r will nad the OOl'N8t T&l.1ae of MpUft-Mq•DCe

cnarnnt when tbe following condiU... an aat.i.&tiedt

l. The cvnnt in windin& w ie one-t.bil"d ot Ia and 11 in

phu• vi\h Ia· 2. The hJ'J'Ut, in wiDdSng two 11 one-third ot ll> amt 1a 1b1ttecl

in pbue by an anal- ot 240 dearH"• vi'Ul NlpM\ t.o It.• 3. !be ovrent in w1nd1ng thne 11 one-w.N ot lo and. 11 1hitt.e4

in phue b7 an anal- ot 120 degrH• vi'Ul re1peet, t.o lo•

It \he impedanoe ot the amwtnc ournnt tru.atomer vindinga

and ._.ter an negleotecl, a relatJ:well' 11aple •\bed can M ued to

oalculate the impedanoea z, Za, z.,, and f.a• The ai•• ot the impldano•

of the load• to be plaeed on \he main cvrent. t.rautomera dwpeDda on

the volt......,.re capaclt.J' ot the ClU"Nnt tnu.toraen uecl. In 'Ul1a

inft1Ug&Uon the illpedanMa wen cboaen 10 tbat the nlt-ellpt.N lN.rden

an current tranetomer A. vu 15 volt-apena at a aeconcla17 OUl'ftnt

ot 5 &mpeN9, and the 1111dn1nc iapedancea wre caloulated nah tbat

the ._.ter ....U nad tbe nepti~• ovrent directlJ'• ~ ealnlAlU.. &N llhown Ml.ow•

In order to bl.ft a bvden ot 15 TOlt-apere1 en V.Utoiw• .l,

the tollAMla& equation bad t.o l>e aatiatt.d.

z.. z (l) Za. z • o.6&!.,. o1ma

6

(2) z Za. z • 0.333 LJf! ...

t.beretore frm equii• (l)

0.333 LR! z. • o.6 JJt. and z.. • i.a JJe. -..

lol'f'ina tor Zt

z. • z z • 0.333 L!t. •

tfdnc tbe ft1- calcl&laW for z. the &kn eq•ti• oan be 1olftd te

z, whi•h s.. toad to be 0.9 L!J! .... TM olU'NDt throqb wiadtna two S.. to be ..-tJdrcl ot Ii, and S..

to be shifted in phaH b7 240 decz-e with reapeet to lb• TM pbue

ahitt ot 240 dqree• can b4t obtainecl lt7 pttina a nnut that laadll

tlae line cvrent bJ an aqle ot 60 •er-• and \ha N'fWlinc U. acm-

neoUona to t.be OUl'ftllt tftuf _._r wiading. Thi• gift• t.be .._ etteet. u a 240-deSZ"M pbaH lhitt. The calclllatiou are u toll.,.

,9 {ff • o.,,, '111!. obu, Zt>·• ,9£J!

t,_ whiall ~ • 2.38 /-12,1° or 0.4, - .12•34 -..

The ovrut \bJ'oqh winding tlmte .. t be ..-t.hbd ot le and

-.at baw a 120-dqNe phaae aldtt. Thia •7 b4t obtained in a armer

7

similar to the previous ease except that a minus 60° J>h&•• shitt must

be used. In this manner Z0 was found to be 2.'8 a9.•lo or 0.4; +

j2.34 ohms.

fB!AA!•mt The summing current transtol"latU" was constructed u•ing the core

of a Westinghouse Type PC JJ.S current tranatormer rated at two and

one-halt volt....ampens. four windings were placed on the core, each

winding consiating of two sections connected in parallel. The sections

consisted ot 50 tu.ms ot number 17 B & S gauge enameled copper w1re.

In the phase-shitt network the resistances were eonatructed

tram number 22 advance metal wire, a eopper--nickel-chromiua &Uoy.

This wire was chosen because of its low temperature coefficient of

resistance.

The capacitance for the pha.ae-shitt network was obt.aimJd by

connecting a number ot capacitors in parallel and adJusting the caa-

bination of capacitances tor the proper im~ce. As waa thcwn pre-

viousl,Jr, the calculated capacitive reactance required was 2.34 oms •

.At a frequency of 60 c;ycles per second the capacitance required would

o. llJ4 microtarada. Thia is a rather large capacitance, but it should

be ~red that it th• a7stem were designed tor a pr:lmary current

tnmatonner having a higher volt-ampere ratinc, the capacitance required

could o. reduced. Another method of reducing th• required ca.pae1t.anc•

would be to design the circuit so that the current thro~h the summing

transformer could be leas than one-third or the line current.

An att.apt vas made to wind a.n air core inductance coil to be

uaed in the inductive part of the circuit, but ditticult.y was experi-

enced in keeping the resistance low enough to satisfy the circuit re-

qui.rementa and still have enough inductance.

The posaibllity of using an induction voltage regulator connected

•• a variable inductance was investigated, and it was found that the

correct value of reeiatance and reactance could be obtained in thia

manner. The next step was to determine it the :presence of iron in

the inductance would cause any objectionable distortion in the current

wave form. It was found through uae of a cathode-ray oacillograph

that the current wave torm. did not deviate appreciabl.j" from a eine

wave, and, it was therefore concluded that under the range ot currents

used, the distortion present in tho current wave was not large enough

to appreciabzy &tf ect the accuracy of the network.

Calibra\ion

It was found that the ~ce of the s~ transtonar

windings and the reflected impedance of the ammeter could not be neg-

lec\ed, and, there! ore, that the impedances Z,v zb, and Zc in the

circuit of :figur-e l ware n.ot exactly thos• calculated. It then became

noeeeaaey t.o calibrate the network with the current transformer and

I2 aneter connected. The calibration was carried out by mald.ng the

assumption that the effect of mutual coupl.ing between the three circuits

connected to the summing current trans.t"ormer was negligible and then

maldng neceeaaey adjustments to obtain the impedances ;, zb, and Zc

which now represent, respective~, the total impedance of ea.eh branch

of the network. The shunt impedance, z, which was placed in ea.ch line

9

was lef't at o. 9 ohms as was cal.culat.ed. Impedance measurements were

made using the voltmete~ter-wattmeter method. Thia method, al-

though not extremei, accurate bec&UH ot the low values of current,

voltage, and power that. had to be read, was choHn beeause it. was felt

that the impedance should be measured un.der cond.i tiona as near au

pcssible to the operating conditicm1t. The network was then connected

&s •hO'Wn in figure 2 in order to ch•ck the ca.librat.ion.

Referrin& to r~ 2, with a current I flowing in the circuit

and \dt.h either ot the switchee cloaed, the ameter shoW.d read 1/J

amperes. With Si and 82 closed and S, open, the current in the auneter

should be tbe vector aum of I/3 {. 00 . and I/3 lf'!O" alae I/3 in ma4-

nitude. 81milariJ.1' with any two ot the thrw switches cl.o&ed the

Mfmeter should read IiJ amperes. With all three lritches closed ti.

current in the a.nneter ehould be the wet.or sum of I/J LJt., It:; /?Jit!, and I/J /16.00, which is equal to zero. When each ot theM ebecka was

ma.de the impedances were adjusted to elim:.inate as far as possible acy

error notieed.

ifau;its

With t.he network thu calibrated it ·waa then conneoted so aa

to meaaure the ugative-aequence cttl"ntnt. in an unbalanced three"'"1!d.re

reahtiw load. Headings were taan ot z.., It,, le• and 12, and the

value ot Ia calculated wd.ng z., l\, 1 and Io was compared with the

value or I 2 rod on the meter. The reaulta are Bhown in tables l aad

21 and curves of I2 (measured) versus I2 (calculated) an plotted in

tipns l and 4. Figu.rea S and 6 are plota of the difterence bet.ween

10

z z i!

Figure 2 CALIBRATICJI CIRCUIT

ll

the calculated and measured values of Ia expree-.d aa percesat.aps ot

the measured values.

'l'h• circuit was next ueed to measure th4' neptive-eequence

current drawn b7 a three-phase induction motor. In this case unbalance

was caused by placing a Yariable red.stance in aeries with one or \he

line conductors connected to t.he motor. The de~ of unbal.Anoe vaa

varied from nro u.nb&.l&ne• to the otl"elle condition where one conductor

wu open. lto&dinga were taka.n at various degrees et load on the mot.or

tram. zero to appr<'*imateq full load. !be Nwlte ot this teat. are

shown in tables 3 and 4. Curves ot I2 (measured) verna I2 (calculated)

are plotted in tigu.res 7 and 8. figures 9 and 10 are plot.a ot the

ditterence between the cahul.ated and meaaured values of I2 mcpnsaed

as pe:ree.ntape or the measured values.

Table l

.......__t. ot legatiYe-leq•no• Currea\a tor Vnbalanoed Dlne-Pb&M-le•18t4w Loau U.in& a V.awn lledel 43) lero-~w-Allpere -..i.r for Jllluur1ng Ia•

,.,. Ca.tr I.l Ia re Ia I2(oalc11lated) Ditterenoe Ditt•nm:•

4.54 1.40 4.71 l.97 1.97 0 0 1.30 .3.32 3.31 l.20 l.u -o.aa -1.64 4.02 ?.lS .... a.61. a.'6 •0.08 3.03 ••• ••• 9.31 4.20 4.aa +0.18 4.lQ 2.32 9.34 9.92 4.so 4.42 +0.08 i.ao '·" 14.41 l?.48 6.68 '·'' •0.12 l.80 6.40 i9.sa 19.76 8.1' 7.96 +0.20 2.50 0 19.16 19.16 ll.20 u.oe +0.14 1.2s

31.00 31.00 12.50 u.90 u.30 +0.60 s.a 3o.40 30.40 0 17.40 17.so -0.lO -o.os1

Table 2

Measurement of tlegative-.Sequence Curnmts for Unbalanced Three-Pbase-Resistive Lo&da Using a Weston Model 433 Z.ro-to-One-Ampere Ammeter tor- Measuring 12•

Per Cent IA Is le I2 l:l(calculated) Ditterenoe Ditf enmce

3.70 'J.74 ,;.65 Def lee- -- -- -tiou 4.06 4.1.) 4.95 0.452 0.570 -O.ll! -26.l J.81 3.96 4.44 0.265 0.379 -o.m -43.0 2.03 J.?6 3.96 o.s;o l.150 -o.)00 -35.3 2.os J.95 4.27 0.960 1.410 -0.450 '*'47.0 l.96 2.9:; J.).2 0.545 0.840 -0.295 -51..0

lf(correeted) Per. Celt I2 x 1.45) I2(calculated.) Ditf erence Difterence

o.648 o.;70 o.01s u.o o.;;79 0.379 0 0 l.220 l.lSO 0.070 5.7 i.370 1.410 -0.040 - 2.a 0.780 0.840 ...o.060 - 7.7

20

18

/6

'"' ., • ~ 12 J ~JO N'

t-f

'; 8 • ::1

~ 6 'O

~ 4 "' ., t>

::II

2

/ I/cf

/ /

U/ /0

_/ 0/

I/

/ "'" -

..P/ ~ ..

0 /' 2 8 /0 12 14 16 18 20

Calculated Value of I 2 in Amperes

Figure 3 MEASURED VAUJES VERSUS CALCULATED VALUES FOR A THREE-PHASE

RESISTIVE LOAD

.., • ,..

2.0

1.8

/.6

1.4

! /.Z

0.2

lS

v v ~

/ / v

/ v t>

9-

i/ / v ·~ v ~

lh v / "'

o.z o.'/ 0.6 0.8 /.O /.Z 14 /.6 /.8 2.0 Calculated Value of I2 in Amperes

Figure 4 MEASURED VALUES VERSUS CALCULATED VALUES FOR A THREE-PHASE

RESISTIVE LOAD

6

s

3

z

_z

-3

16

~

...

~ I\ I \ \

\ / :>' \ \ _/ .........

~I \ o- 0 \

- \ l v

j

4 6 8 10 12 ,,,,. ,, 18 20 Measured Value of I2 in Amperes

Figure 5 DIFFERETlCE BETWEEN MEASURED AND CALCULATED VALUES FOR

THREE-PHASE RESISTIVE LOAD

-60

17

Measured Value.or I2 in Amperes ~I 42 ~3 ~4 ~5 a6 ~7 ~8 ~9 lO

/q

/ \ ,,,Vo, cl \ /

v ,0 './ .. 0

Figure 6 DIFFER.PMCE BETi'lEBN MEASURED AND CALCULATID VAWES FOR

THREE-PHASE RESISTIVE LOAD

18

Measurement ot hgative-s.quence C\u-nnt.s for a Three .. Phaoe Induction Motor Opttra\ing on Unbalanced Voltaps With ~ had on West.on Model 4-'3 Zero-to-live-Ampere Ammeter.

Per Cent. IA Ia Ic Ia la(e&lculated) Dif terenco Ditterence

0 10.76 l0.76 6.24 6.20 0.04 o.64 o.s 14.08 u.oo 7.00 7.16 -0.16 ""2.28 0 llo40 14.40 8.40 s.:;2 o.os 0.95 s.20 J.S.48 14.$2 6 .. 60 7.20 ... 0.60 -9,.l 6.56 19.20 12.72 1.16 8.80 -o.64 -7.84 0 20•40 20.40 llt.SO u.ao -0.30 -2.6

14.00 19.00 13.76 5.76 5.76 () 0 0 ,1.00 :n.oo lS.00 17.9 0.10 o.s.s

10.00 21.00 20.80 10.S:O u.;o -o.so -4.85

19

........_..\ ot lept1~•• Cvrent.. tor a Three-Pbue Inchlot1on lloWr Operatiq on UnMlaneeci Yol\ape Wit.h 12 lead • W.•tcm lladel 90ft, Am.ter Z.ro-W-«ne-Allpere lanp.

Per Ceat. i, Ia le I2 12(calculated) Ditt•ren•• m.tt•reao•

6.40 a.16 6.60 0.92 i.as -o.)J ... ,, .. 6.oo 9.00 6.ao 1.51 l.'9 -0.31 -25.2 4.20 '·" 7.00 2.30 2.as -o.ss -2).9 4.00 10.40 1.ao ,.ao ,3.88 ...o.'8 -u.2 , ... 9.14 1.20 l.~ l.24 ...0.20 -19.J 7.40 10.44 8.0f. 1.62 1.97 -o.,, -U.6 6.60 11.28 a.20 2.42 2.86 -0.44 -lS.2 4.IO 11.16 9.40 ).86 4.88 -1.02 -26.4

10.00 12.60 10.36 l.'6 l.64 -o.u -20.9

'·" 14.84 11.72 3.24 4.0f. -o.eo -14.1 12.44 u.60 12.92 1.6S 1.93 -o.28 -11.0 ia.oo 16.40 12.80 a.'4 2.79 ...0.4, -19,2 11.36 1?.IO 1S.l2 '·" 3.70 -0.32 -,., 14.60 11.12 15.08 1.92 2.26 -0.34 -1?.? 13.88 19.44 lS.l.6 2.88 3.57 -o.69 -23.9

lf (oorreot.ecl) Per C.n\ Ia • 1.23) Iz(eal.nlateci) DUf erenee DU'f ennee

i.u 1.2, .... 12 -10.60 1.16 1.89 -0.03 - 1.60 2.1) 2.as -0.02 .. 0.70 '

3.94 , .• o.06 l.SJ i.aa 1.24 o.<V. . 3.13 1.91 1.91 0.01 o.si 2.91 2.86 0.12 4.os 1+.1s 4.88 -0.13 - 2.74 1 .. 6? 1.64 0.03 1.80 3.91 4.at. -o.06 • l.Sl 2.0'J 1.93 0.10 4.94 2.18 2.19 0.09 3.12 4.16 3.70 o.46 u.oo 2.36 2.26 0.10 4.24 3.54 ).S? -0.03 - o •• ,

18

/6

14

2

-v-[7

/ l~c

o( _/ -

h/8

l/L I/

[7 I

2 f 6 8 10 IZ 14 16 18 Calculated Value of I2 in Allperes

Figure 7 MEASURED VALUES VERSUS CALCULATED VALUES FOR A THREE-PHASE

INDUCTION MOTOR OPERATING ON UNBALANCED VOLTAGES

4.0

3.6

3.2

2.8

Ill

f Z.4

! rt 2.0

orf

N H

~ /.G 0

C> ::1 ~ /.2 'O f <;jo.8 Ill .. :! 0.4

I I I I '-- I I I I I I I I I I I --,

- I/ I

- I I /I · ./ ~ I I/ I ' 1/0 _ I/ o _/ -

- I I/ rv- I -

I/I~~ - -~ - ~ I -.. 1/: f-+---1-~ I '--r-H';4=-//_o L _.___ I -l/~O I I

I /lo/ ' I - . -- VA> I -1-1-'-L~v --1-- -i--t--+_J-.. r--1-t--t-_J v, I -1-1----'-- -I ¥· -

I I I I I I I . l I -0.4 0.8 /.2. /.f, 2.0 2.4 z.8 .J.2 9.6 "f-.O 4.f 4.8 5.2

Calculated Value ot I2 in Amperes

Figure 8 MEASURED VALUES VERSUS CALCULATED VAWES FOR A THREE-PHASE INDUCTION

MOTOR OPERATING ON UNBALANCF.D VOLTAGES

flJ ....

I

0

_, - 2.

-3

-8

-9

-...... 0 \ /()

..J - 1 12. 14 / 2 4 ~ 8 /0 18 \ \ v

/ 0 \ o'

v I

I ,/ \I ·O

1h

-v

Measured Value ot I2 in Amperes

Figure 9 DIFFERENCE BE'IWEEN MEASURED AND CALClJLATED VAWES FOR A THREE-PHASE INDUCTION MOTOR OPERATING CB UNBALANCFD VOLTAGES

Keaaured 'Y&l_ye ot 12 in ~res 0.5 /. O /.5 z.o Z..5 3.0 .1.5 4.0

.. /IJ ("';

I' ")_ 1-q ~ ,rf ~ \

'O 0 \~ '\,. \ -20

• ~ . :! -25 t "" .., .. 30

' -I ., -35 !

-4tJ

0

' I /\ 0 n ' 'If b

c

Fi8UN 10 DIFFERENCE BETREN :MEASURED AND CALCULATED VALUES PCB 1 THB.1-PHASE INDUCTION MOTOR OPERATING Cfi UNBALANCED VCLTA~

12

JO

8

4

«

-8

,,.....

1 j

I I u

/\ I I \ I I \ I -

0.2 o.4 ~6 .o.8 /Jf /.2. \'.4 /.G

~

I t

I I

<..

Corrected Value of I2 in Amperes

Figure 11 DIFFERENCE BETWEEN CORR&!TED AND CALCULATED VALUES

FOR A THREE-PHASE RESISTIVE LOAD

12

0 /() ' ' 8

6

t> 4 ! I) ,... I) z ~ '-i ..... Q I) 0 b() <'(!

~ I)

,, '() ,

o" ' J I\ ~ \ ' ' u\ (~ \ \ ;1 1

\ (J.5 J.o /.5 \Fo 2.S 'Q.t.o ~~ 1\1!'~

0 0 s.. -2 I)

., 0 -

ll..

-4

-" -8

-10 0

·~

Cerrected Value of I2 ia Amperes

Figure 12

0

DIFFERENCE BETWEEN CORRECTED AND CALCULATED VALUES FOR A THREE-PHASE INDUCTION MOTOR CPERATI~ ON UNBALANCED VOLTAGES

26

If DDCVlllCll tll IDUL!I

The Nnlt.tl of t.lsia inw•tJ.ptJMa •laow that 1t 18 po88ibJAI t..

INil4 a napt.1~ ~tor ueva\e _....._t.. at

-.u.,....._. CUTenu. The nnlk alM point •' ... ot \he

d1tt1"111U.. and 11ait.aUoaa of ihia •tJlocl.

The netvvk-. oalibaW fer ue wit.b a V..\on lfode1433,

sero-t.o-ti'N .,.. ... wter, aad nattnp taken vi\b tlda Mt.er wN

found to he nuon&bq aoourate. In aoat .... , \be ditferenoe be-.

tbl ealnl&Md ...itae ot Ia and. the ftl.u read frca the L,a •\er, •-prnee4 .. a ,.l'Mllt.lp ot tM L,a -'er nadin&, _. well uder tiw ,.......,.

line• \M netwn: •• cleaipM fer epuatia vit.h Pl'!a.17 OV'l"ent

tl'uultorMN wbOle OVND\ au.a -. lift ..,. .... , a rat.Mr Mrieu

t&Jran. tb1e -. tJWt belaue readtnp flWl Hl'O to .. ..,. ... o..U

not be aoevateq tuma with \he •tw uect. !bu tor tbl 1-•• Ml'ieu

cue• ot .U.lanoe wMN \he I2 •tw ovrent bees•• i.n \lau w ..,. ... , \he NOO.N.iJtC mt... bad \o be Cbanpd in eJ'der to ol>t.aia &

N'Mltnc. llae etteat. ot ohangtnc tm •tw -. '° in~• error1 int.o \he N•d.il'CI •inM 'the network vaa callbraW tor \be aen-t.o-

ti..........,_. wt.er. WJ.t.b a uro-to ... 111pU9 w\er .__.w, tlMI per cet clittweao• betwNn t.be oaleulated and -RNCI ftlu8

ot Ia ._. 1n ... oaM• .. ach .. 35 or 40 perwceni. ot t.be Mal8Nd

ftlu. In all ..... t.be MUUNd ftllae ot Ia .. 1-r \ban tile

Mlnlatecl w.J.u. 'nd8 error _..,, \M\ the partinlar •ircndt anuce-_, ued in t.b18 in'fUU&atien •-.1.d ~ lHt ued to obtain aoovate

readtnp of Ia tor llicb\11' 11DMlanoe4 l.el.d9. An att.mpt, -. _. to NG'15ltriate tAe o!rnit for ue with

a Ml"O-to-Gne•PD!pl.N Miel' Wt du to \119 tact tat the •all.er Wier

bad a mob higber Nd8t&lse• \bu t.be orSci»l •ta it. -. 1"9""lble

t.o rM*UbRie the olrcnait, wit.heat olllmglnc t.he eircuit et1NJi. Jn

~ 'tfOl'd8, t.be proper ~to-N&Otano• ratio cev.14 not be

ob\ISmci.. !hU o-14 perbapa be r1m1died b7' inorea11nc the YOlt-e..,....

ttvden 111 t.be pr1mq OU"Nllt tranat ... n 1n order to allow a MaMr

tllpedanee to be uecl in tbe pbt.M-llh1tt net.won. In \Id.a W7. it. m1g)lt,

be pouible te ob~ tJae preper Ntiaanoe-to-reutarace •ti• in tJle

pbt.M-llh1tt network.

la all ..... \he read1qa taJata wit.h tbe Hre-to - .......

._ta ..,.,_ low an41 at ahown in tipna 4 and 8, the wlU of I2

re..s tnm tltAI Ia •ter 'tVied JSnearq vit.h tM oalc\llatecl ftl:u, wt. w.a ooutatant.1¥ low. 9a1a ftl'ia\icm ngpa\ed t.hat. it upt be pM•iblA

to ue a OOl'N8t1• tact.or to obtain 'f'&lua reaaOllQq oloff to \be

•enMt ftlM of Ia• ror ID one with• W.etm llOdel 43.3, •n-to-

••.....,.n wter, a oorncU. tutor of l.43 vu UMdl ter lml tw.,

with a W.t.a .-1 9Qf., MrO-t.o - nwpere Wier a oorNOt.icm tutor

ot 1.0 w.a--. 'lhe renlta inoorporaUnc t.he oorreeU.• futon

lift .... in \lbl.111 2 and 4 an4 t1pna 11 and 12. In ... , ..... \hi

.. et \heM eorneU. tao\uw pw Yalua oloM to \hi talnlated

wJ.u ot 12·

•

Pl"m t.be w.-u.cm aat.beNct 1a th18 1t.8Q' u, ~ be eww t.bat. ..,...., ot -..u.,....,...-eeq.no• ~" wit.la aonru7

o_.11'-8t wit.la ct-Nial ~- 11 polllil>JAI• fte .. t. 41tt1-

01ilt probla 1D the d9eip ot a oil'01d.t tor .aaviq ..,.u~·

c~ utna tide •tbod 11 t.bat. ot b4lp1Da t.be TOl.w.,... bvdea

cm the prDar:r C\U'Nll\ truatomen lw 79t. at.ill bnina a •t.wvk

........ 1llpeclanlel .,.. in a ranae t.hat oan be ••:117 ... v.w and

oalibraw.

iltllcN&b ne ....,_.. wv. tUm et .. •aaU~

..,...\a 1a a t.brM-pbue, t~ o1rnlt., it. tan be MU t.bat. the

•tllocl ued 1a tlda 1DwaUpU. -1d be Jat u applieablAI tor tile

t~ o1"1d.t. •1ao• the deli»itJm ot the ..,.u..,. ......... CVNl'lt.

rrnS•• thew no •t.ter •t.Mr the tbrM- or t.......nr. oirn.1t.

11 .....

in. Q'8t. .-t be Ml.lbrated. tor t.be ~ mter t.bat. u lolna to be ued, maeh t.be .- u t.be llmnt tor a diNot-IVNl'lt.

-• .n be aalibrat.ed tor ue wit.ll a p&rt,inlar •ter. Dml U

a ob&np 1n Hale readtna 11 ctuiNd, t.be o1""'1t. wt. be r1Hl:lltraW

u ordeJo ,..,. t.be rea':lnp t.o be cornet..

29

This inveatigation ws.a set up tor the purpose of ~rfeeting a

method of :measuring the negativ•-s•quemce current in an unbalanced

three-phase circuit.. A four1iading current tranaform1n•,, in eonjunetien

with & phase shift network and an alternating current ammeter, was

used for obtainillg a current proportional to, and in phase with, the

mega ti ve-phtll!Ht-eequence eurMnt.

Atter calibration of the circuit, reading• w•re taken of the

three line currents in a. three-ph&M th:ree-w.1re circuit and of the

current in the a.mmeter.us•d for mea.surir4' the negative-sequeMe current.

The value of the negative-sequence current was calculated frca the

line currents and was compared with the ~ter reading. 'fhe ditterence

bet.ween the two readings in most cases was less t.han five per cent ot

the urneter readJ.n&. When an attempt was made to change the range o!

readings b)" changing the meter used tor fMS.suring the negati..-e-eequence

current., it. was found to atfect the calibratiora. Thus it wou.ld be

ne<:esaa.ry to calibrate the circuit for each type ot amme.ter u.sed.

It ldUJ concluded that direct nadin,ga ot msgative-aequenee

cur.rents can be made with accuracy consistent wi:~h commercial reqtaire-

ments.

)0

The author wishee to express hia appreciation to Prof eseor

Geerge c. Ba.mes of the ll.ectrio.al Engineering Department for hi1

gu.idanoe a.mi encouragement: to Profes•or B. M. Widener, Head o:t the

Electrical :Bngineering Department, for mald.n& available tacilit.ies in

the !l.eetrieal Engineering labontory; &Lnd to Professor w. A. Murra.7

!or his inwreat.

The ~ut.hor also wishes to «>epres& hie appreciation to

and tor their

assistance.

Gntitude is al.so Q:pNSsed to Professor L. :a. Melllchamp or

t.mr Jmgllih Jlepartment tor bis suggestions and to

tor her typing.

Finally, the author wishes to expNsa his gratitude to hie wUe1

, tor her inspiration, cooperation, and patieno~t.

ll

1. Borden, P. A. &nd Behar, M. r., "19!N!J!!Btl !n Jl!W!H!o~

Qutraca,1- sut,m•• I Instruments 7J 19 I PP• 185-191, Sept. 1934.

2. :mvan.,. a. n., "I.I! ~' fll!H! ~ f!kRha•ff Maten"• §!;

6, PP• 33.31 1923.

:;. Forteeo.e, c. L., "Method !£. 8Eftf!oal ~9!J!!!!!nts Anli•d

.!! h*9,tipn 9l,. rfJ.n?b!fMt let:!!dt•", tranuct1ona A.I.5.E.

Volum.o 37, 1918

4. Fortescue, o. L., "Me&&.Ff!!nt !Jl. Power !!J. tgb:ptl!.ge ~,!rc!it•"•

'.tranAction• A.1.s.1. lt!J PP• .3.$1, 192.3.

s. Ha~, A. P., ~t !! S.l!!!l!tf&1~4r C@pgmmts•, The

llectric Journal !ti 6, PJh 3Sl, 1931.

6. Shuck, G. R., "Mlt.trtz:!& !?!'. Sl!!!tid:!!l C~t••, llectrical

~ering .St 8, PP• 536-543, August, 1933·

1. Wagner, c. '· &rld lhana, a. o., "bmftrl.ot,l ~""• lat

Id., (MeOraw Hill), PP• 271 .... ,;os, 19.'.33, .Hew York.

s. &rem.rt' a. I!. and Corcoran, G. F,, "Alt•£9!tip& 0!£r.st c*-nst,a•, 3rd Id., (Wiley), PP• 347 ... 3;3, 19S51 New York.

The vita has been removed from the scanned document

A METHOD OF JWSURDIG tH!DATIVE-PHASE-SBQlT&iCE Ctmli.ENTS DJ A

THREE-PHASE .SYS~

Manaell Herbert Hopkins

Virgin1A Po~ohnic Inatitute

Department ot Electrical Engineering

MASTD OF 'SCIENCE THESIS

Abstract, 19.58

A method ot measuring the neptive-nquence current in an un-

balanced three-phase circuit. A tour-winding ourrent tranatormer, 1n

conjuction with a phaee abi.ft. network and an alternating our.rent ammeter,

was used tor obtaining a current proportional to, and in phase with,

the negative-sequence current.

After calibration, readinp were taken ot the three line currents

in a. tbree-phaae th:roe-wire cil'Cluit and of th& current in the negative-

aequenee aJ:mD1ter. The negative-sequence current. was calculated trom

the lir.e current.a and cmpared with the ammeter reading. The dif'terence

between the two values, 1n moat cane, waa lass than five per cent ot the anmeter reading. It was tound that. the circuit had to be calibrated

tor each type of ammeter uaed.

It was concluded that direct readings of negative-sequence

currents can be made with accuracy consistent with ccmaeroial require-

ments.