zero flux ct

attainable at the point on the curvewhere TI/Tmax is unity (see Figure 5).The Z in this case is 0.14.

UNSTRESSED LENGTH FACTOR

Once Z for the loaded condition isknown, finding the unstressed length fac-tor is an easy matter. The calculationsare straightforward and are tabulated inTable IV. It should be noted that thisunstressed length factor is based on the Lfor the loaded condition. It is necessaryto refer all unstressed length factors to theunloaded condition. To accomplish this,the unstressed length factor calculated in

Table IV is multiplied by a factor which isL/L'. The permanent set, 0.000316, issubtracted from this unstressed lengthfactor to get the initial unstressed lengthfactor for 0 degrees Fahrenheit.The unstressed length factors for the

other temperatures are calculated fromthe equation lt = Zl [1 +-0(t-t) 1. Fromthe resultant unstressed length factors,the auxiliary C curves for the specifiedrange of temperatures are plotted, seeFigure 1. The intersection of theseauxiliary curves with the basic C curvewill give the values of Z for temperaturesranging from 0 to 120 degrees Fahrenheit.

The results are shown in Figure 1.The tensions have been calculated

for 0 degrees and 60 degrees and are,respectively, 4763.6 and 4303.7 poundsfor the upper support and 4722.9 and4263.1 pounds for the lower supports.The sags for the different temperaturesare recorded in Figure 1.

References1. TRANSMISSION LINE CATENARY CALCULATIONS,D. 0. Ehrenberg. AIEE Transacltonzs (ElectricalEngineerinzg), vol. 34, July 1935 pp. 719-28.

2. ELECTRIC POWER TRANSMISSION, L. F. Wood-ruff. John Wiley and Sons, Inc., New- York, N. Y.,2nd ed., fourth lprinting., Feb. 1946, pp. 201-05.

No Discussion

Synopsis: A method is described of re-ducing the core flux of a current transformerby supplying the necessary voltage to thesecondary circuit. For one load current,the flux may be eliminated, giving zeroerrors, and at other loads the ratio andphase angle are so small as to be difficult todetect in many cases. Applied to reason-ably good transformers, extremely highaccuracies are obtained, with small weightand bulk. The scope of low ratio bushing-type transformers is also increased, but theaddition of triple-frequency auxiliary fluxstill further extends the use of the method,and test results are given for ratios down to20/5 amperes.

N A PERFECT current transformer,the primary and secondary ampere-

turns would be exactly equal in magni-tude and precisely opposite in phaseposition for all conditions of service.

In practice, the ideal is never attainedbecause a voltage must be induced in thesecondary winding to overcome the im-pedance of the circuit. This gives rise toa corresponding magnetic flux in the core,and it is the ampere-turns needed tomaintain the flux which constitute theerror of the transformer. They subtract7ectorially from the input ampere-turns,and the result is that the secondary cur-rent is a little less than it ought to be andnot quite in its proper phase position.When considering how to make a trans-

former without errors, the obvious line ofattack seems to try and make up for themagnetising losses by supplying correc-tive ampere-turns to the transformer.

This is a most difficult task. A currenttransformer has to work over a fairlywide range of current. The magnetisingand iron-loss ampere-turns vary in a mostcomplicated manner as the primary cur-rent changes, and while it mav be feasibleto correct for one particular condition, itis too much to hope that a complex curvecan be followed with accuracy.

Nevertheless, a number of attemptshave been made in the past, but the suc-cess attained has been limited because ofthe extreme difficulties involved. Inmost of these and other methods, effortshave been made to secure a flat character-istic by balancing the upper and lowerhalves of the magnetising curve againsteach other, using saturated cores for thepurpose. In thisway, someinventorshaveimproved the ratio error, some the phaseangle, and some both, but in all cases thebenefit has been achieved by makingcritical adjustments on the individualtransformers. It has not been possibleto predetermine the results by ordinarydesign methods.A more reasonable approach to the

problem is to consider supplying thenecessary voltage to the secondary cir-cuit. If this is done properlv there is no

Paper 53-194, recommended by the AIEE Trans-formers Committee and approved by the AIEECommittee on Technical Operations for presenta-tion at the AIEE Southern District NMeeting,Louisville, Ky., April 22-24, 1953. -Manuscriptsubmitted October 24, 1932; made available forprinting March 16, 19.3.A. HoBsoN is with Smith Hobson Limited, Kings-ton, Surry, England.

need for anv voltage to be induced in thesecondary winding consequently thecore flux is zero and the transformer oper-ates with neither ratio nor phase-angleerror. In other words, the current trans-former is no longer obliged to supplyenergy and is able to concentrate fully onits proper task of measuring the current.

Moreover, a current transformer gen-erally works into a fixed impedance sothat the secondary voltage is not onl-proportional to the current, but alsokeeps the same phase position with re-

spect to it, offering a much simpler prob-lem than the provision of a whole mag-netising curve.

Principle of Operation

In the method to be described here, thevoltage source is a second current trans-former, which mav be called a compensa-tor, worked by the same primary currentas the first one. The diagram in Fig. 1

shows one suitable arrangement for a

500/5 ampere-ring-tvpe current trans-former. The explanation will be simpli-

CURRENT - IVvvYTVWVVTRANSFORMER COMPENSATOR

Fig. 1. 500/5 compensated transformer

608THobson-The Zero-Flux Current Transformer

The Zero-Flux Current TransrormerA. HOBSONNONMEMBER AIEE

AI7GUIST 1953608

fied by ignoring magnetising losses forthe time being and assigning numericalvalues to the various quantities.

Since the transformer has a bar pri-mary, the secondary has 100 turns. Forconvenience coils B and C on the compen-sator are each given 50 turns, althoughthey may in fact have many other values.The 1-ohm resistance represents thelumped impendance of the whole second-ary circuit, comprising coils A and B,together with the load.

Consider the conditions with 500 am-peres in the primary bar. The secondarycircuit carries 5 amperes. This currentis decided solely by the 100 secondaryturns, since the presence of the closedwinding C on the compensator core pre-vents B from acting as a choke in the pathof the secondary current. Another cur-rent of 5 amperes flows in C and the vari-able resistance R to make up the ampere-turn balance on this core.

Clearly a voltage equal to 5R must beinduced in C to send the current throughR. The resulting core flux is also em-braced by coil B, and an identical voltageappears across this winding, because bothcoils have the same number of turns.By varying R, therefore, any voltagechosen can be injected into the secondarycircuit.The drop across the 1-ohm load is 5

volts, and this cannot change as long asthe current remains constant. It followsthat the vector sum of the electromotiveforces in A and B must total 5 volts, inphase with the current for this noninduc-tive burden. If one of the coils is some-how made to supply a particular voltage,then the other will automatically adjustits output so that the total is 5 volts, inthe proper direction.When R is zero, for instance, coil B

contributes nothing and the full voltageis induced in A, in which case the currenttransformer behaves normally and has itscustomary errors. The compensator fluxis zero for this condition. If R is nowsteadily increased there is a gradual trans-fer of flux from one core to the other,since B generates more and more voltage,less and less being required from A.When R is I ohm, B supplies all the volt-age, none is induced in A, and the flux inthe main core is zero. All the work inboth circuits is now done by the compen-sator, and the current transformer hasneither ratio nor phase-angle error.

Should R be still further increased so asto exceed 1 ohm, more than 5 volts will besupplied, and under this condition Aactually provides a reverse voltage tobring the total down to 5 volts. The cur-rent transformer would then show errors

CURRENTTRANSFORMER COMPENSATOR

Fig. 2. Alternative connection

of the opposite sign to those usually ex-perienced, that is, it would have a posi-tive ratio and a lagging phase error.

It is apparent that simply by varyingR, a very flexible control may be exer-cised over the transformer, which canbe made to have a whole series of errorcurves at will. Using an impedance ofvariable magnitude and power factor inplace of R extends the control still fur-ther, since the phase position of the coreflux may also be varied.

In Fig. 2 another method of connectionis shown which achieves the same effect.Comparing it with Fig. 1, coils B and Care now combined into a single 50-turnwinding carrying 10 amperes. The resist-ance R now bypasses the difference be-tween this current and the secondary 5amperes, the resultant being 5 amperes inthe opposite direction to the secondarycurrent. Because of this reversal, thevoltage drop across R actually becomes aboost in the secondary circuit, and servesto reduce the flux in the main core; inother words, helping to compensate thetransformer. When R is 1 ohm completecompensation is obtained, as before.A moment's thought shows that in both

diagrams the compensation is correct notonly for 500 amperes, but also for anyother line current, since all the voltagesand currents change in proportion. Ifthe impedance of the secondary circuithad some other value and power factor,the zero-flux condition would be restoredby replacing R with an equal impedance.

Full Compensation

From the theory as so far explained, itwould seem possible to construct a cur-rent transformer having perfect accuracyover the whole range of primary current.Indeed, it might appear that the maincore, since it carries no flux, could be dis-

pensed with altogether. Actually, ofcourse, this core has a very important partto play, and a practical transformer wouldbe of little use without it.

Tables of test results, given later in thep-aper, show that the ideal condition maybe approached verv closely on occasion.Generally, however, it is difficult to elim-inate the flux entirely over the wholerange of current, although simple to re-duce it to a fraction of its normal value.The reason is that the compensator, beinga kind of current transformer. has errorsof its own. The current in coil C of Fig.1 is really a little less than a amperes, andR would in practice have to be madeslightly more than 1 ohm to produce thefull 5 volts. Assuming this adjustmentwere accurately made, the main-coreflux wotuld indeed be zero, but when theline current changed, so also would thecompensator errors, and the new valueof voltage would not be exactly right. Asmall flux would then appear in the maincore and the current transformer wouldhave corresponding errors.

Losses in Compensator

In the examples used so far, the volt-amperes consumed in the compensatingload have been equal to those in thesecondary circuit. The additional loss isnot important, considering the benefitobtained, but it is good practice to keepit as small as possible, compatible withsatisfactory performance. Its value maybe lessened by having more turns on coilB, which means that the compensationworks on fewer ampere-turns, and has asomewhat poorer performance.

In practice the loss varies from about 5per cent, up to 100 per cent of the totalvolt-amperes in the secondary circuit,depending on the type of transformerunder consideration. If it has a largenumber of ampere-turns, such as a high-precision laboratory transformer wouldhave, the loss can be made very small withscarcely and reduction in accurac-.

Change in Load and Frequency

To obtain the lowest errors the compen-sating load should match that of thesecondary circuit. It is often convenientto supply a transformer with a fixed com-pensation, chosen to give best performanceat some stated load, probably that of aparticular instrument. If a differentload is used, either in magnitude or powerfactor, errors will appear, depending onhow much voltage has to be induced inthe main secondary, and this is clearly afunction of the fractional change in the

9Hobson-The Zero-Flux Current TransformerAUGUST 1953 609

Table 1. Ring-Type Current Transformer (500 Ampere-Turns)

Mumetal Core: 3 Inches Total Depth, 3-Inch Inside Diameter, 41/2-Inch Outside Diameter

5-Volt-Ampere LoadPlain Transformer CompensatedRatio Ratio

Nominal Error, Phase Error, PhaseSecondary Per Angle, Per Angle,Amperes Cent Minutes Cent Minutes

5 ..

3 . ......

I .......

0.5... ...-

25-Volt-Ampere LoadPlain Transformer CompensatedRatio RatioError, Phase Error, PhasePer Angle, Per Angle,Cent Minutes Cent Minutes

-0.042 ... +4.0 ... 0.000.... 0.00 ... -0.297.... + 6.8.... +0.005... 0.00-0.053 ... +4.9... 0.000.... 0.00... -0.320.. + 8.1.... +0.003... 0.00-0.068... +5.6... +0.001 ... +0.04... -0.318. .. . +13.7.... +0.013. .. +0.21-0.077... +7.3... +0.002 .. . +0.06... -0.273. ... +19..2. +0.021. .. +0.35

Table IL. Ring-Type Current Transformer (500/5 Amperes)

Silicon-Iron Core: 4 Inches Total Depth, 5-Inch Inside Diameter, 7-Inch Outside Diameter

5-Volt-Ampere LoadPlain Transformer CompensatedRatio Ratio

Nominal Error, Phase Error, PhaseSecondary Per Angle, Per Angle,Amperes Cent Minutes Cent Minutes


5 - 0.27... +18. 0.00 ... 0. -0.50... +22. 0.00. -13 .....0.-0.30 ...+25....+0.02 '. .0. .-0.55 ... +30..+.+0.02 . 01 ..... - 0.33 .. +42. +0.13 ....i+2. -0.62... +54. +0.19 +50.5... -0.37. +60 +0.25 o5.. -0.65. +78... +0.45 +13

Table Ill. 100 !5-Ampere Bushing Transformer

Mumetal Core: 8 Inches Total Depth, 5-Inch Inside Diameter, 7-Inch Outside Didmeter

5-Volt-Ampere LoadPlain Transformer CompensatRatio Ratio

Nominal Error, Phase Error, P.Secondary Per Angle, Per A:Amperes Cent Minutes Cent Mi

5 ....... - 0.40 .... + 17 ...... +0 .03 .....

3 -0.40... +22. .+ 0:31 -0.35......+32. +0.070.5 - 0.30... +36. +0.10

total impedance of the secondary circuit.An increased load means that the trans-

former is under-compensated and has anegative ratio error and a leading phaseangle. Similarly a reduction results inovercompensation, and the errors are re-versed in sign.At all reasonable loads, the performance

should still be a good deal better than forthe equivalent plain-current transformer.A considerable part of the secondary cir-cuit is located in the transformer itself,and changes in the external-instrumentload often have only a relatively minoreffect on the total. Change of operatingfrequency, to a first approximation, hasno effect on the performance of a fullycompensated transformer.

In practice, the compensator flux variesin inverse proportion to the frequency,and the errors of the compensator changeaccordingly. The current transformerconsequently shows errors which are of the


.0-0.85 ... +24 ... +0.04.... +10. -0.90... +33.. -0 20.... -I0... 0.83 +55... 006. +3.0 .. 0.75.... 72.. -0.14 .... +5

second order of magnitude when com-pared with those of a plain transformer.

Test Results

Tables I and II give test figures show-ing the effect of compensation on tworing current transformers. For a truecomparison between plain and compensa-ted transformers, the same total amountof core should be used in both cases, ifpossible the identical core itself. Ac-cordingly each transformer was firstwound in the normal way and its naturalerrors measured. Then it was strippeddown and the core divided into two pack-ets. one of which was used for the maincore and the other for the compensator.Finally it was rewound with compensa-tion, and the required tests were carriedout.

All the measurements were made on anArnold-type testing equipment which is

the kind used at the National PhysicalLaboratory in Teddington, England.On the coarse range, the largest errorswhich can be measured are 5-per-centratio and 250-minutes phase angle. Themost sensitive range will detect differ-ences of 0.001-per-cent ratio and 0.01-min-ute phase angle, and in Table I some re-sults are given to these limits. This isdone only for comparison; it is not claimedthat the final figure is accurate.The standard transformer used had a

ratio error of about 0.01 per cent and aphase angle of about 0.5 minute. Theseerrors, small in themselves, were too largeto enable the compensated transformerin Table I to be tested by a comparisonmethod. This transformer was thereforewound for a ratio of 5/5 amperes, and thespill current between primary and second-ary measured directly by the methodshown in Dr Arnold's paper.1The transformer in Table I, uncompen-

sated, would be considered a good one formetering but not so good when judged asa precision unit for a test room. The ad-dition of compensation causes the errorsvirtually to disappear. On 25 volt-amperes, the compensator core flux ap-proached saturation, yet the degree ofcorrection obtained was still very re-

markable. With silicon-iron, see TableII, the improvement is also considerable,but here the effect can be seen of thechange in the compensator performance asthe line current falls.To bring this point out more clearlv,

the compensation was in each case ad-justed to give minimum errors at fullrated current. The figures could havebeen made superficially more impressiveby using another value of compensation,which would have miade the errors smallerby balancing them about the zero line.

Practical Applications

PRECISION TRANSFORMERS

The better a transformer is to startwith, the more easilv and effectivelv canit be compensated. For this reason, themethod is extremelv useful in "perfect-ing" reasonably good transformers, suchas are used in test rooms and labora-tories. The compensator needs onlv asmall core section, it will work well on asfew as 100 ampere-turns, and the extraloss may be less than 1 watt.On high precision standard trans-

formers, the lowest errors obtainable bynormal design are about 0.01-per-centratio, and 0.5-minute phase angle. Sucha transformer is very bulky and expen-sive. It must have a heavy nickel-ironcore, wound with up to 5,000 ampere-

610THobson-The Zero-Flux Current Transformer610 AUGUST 19053

turns, and of sufficient diameter to ac-commodate the large amount of copperrequired. It is very difficult to reducethese errors much, even if the core sectionand ampere-turns are made greater, be-cause the increasing copper loss and corediameter both react unfavorably, whileother factors such as internal capacitancesuddenly begin to upset the calculations.

In Table 1, a Mumetal core weighing7 pounds, wound with only 500 ampere-turns, is made to have errors almost im-measurably small. True, this trans-former is more susceptible to change ofload than would be a laboratory standard,but with 1,000 or 2,000 ampere-turns,excellent performance may be obtainedover a fairly wide range of load, using afixed compensation, with a loss of perhaps1 watt. Moreover the difference in theerrors as the operating frequency ischanged from 25 to 100 cycles is verysmall indeed.A multirange transformer for use with

an electronic wattmeter was compensatedto have maximum errors of 0.1 per centand 2 minutes, over a frequency range of50 to 500 cycles. It was wound with 30ampere-turns, and measured 8 cubicinches.

It is possible to make compensatorsas separate units to work with existingcurrent transformers. This involves nopractical difficulty; the two primaries andsecondaries being connected in series.

BUSHING TRANSFORMERS OF Low RATIO

It is well known that current trans-formers of the bushing type offer immenseadvantages in cost, safety, and simplicity,but that their use on low ratios is severelylimited because the inherent accuracy isvery poor. It is not surprising that, inthe past, many engineers have endeavoredto improve their performance sufficientlyto render them suitable for metering.The main difficulty is that the primary isonly a single turn carrying the line currentof the system. In the author's opinionthe full implication of this fact is not fullyappreciated by many engineers.To demonstrate what the designer is

really up against on the lower ratios, letus consider the weight of core needed fora 100/5 transformer, when comparedwith one of ratio 200/5 amperes, havingthe same errors and output.

First, there must be only half as manyampere-turns lost in the core. Because ofthe unfavorable shape of the magnetisingcurve, however, the flux density could notbe more than one third that in the 200/5unit. Next, since there are only half thenumber of secondary turns, the total fluxmust be doubled to obtain the same in-

Table IV. 100/5-Ampere Bushing TransFormer

Silicon-iron Core: 8 Inches Total Depth, 5-Inch Inside Didmeter, 7-Inch Outside Diameter

5-Volt-Ampere Load

NominalSecondaryAmperes

PlainTransformer

PhaseRatio Error, Angle,Per Cent Minutes

Plus TripleFrequency


Plus TripleFrequency andCompensation


5.-2.35... +115.. -0.80... +20.......... -0.13......... +23 .-2.60... +155.. -0.75... +19......... -0.11. .+2

1 .-3.4.. +280.. -0.70... +17........ 0 .. -10.5 ..off scale -0.55..5 +17 .. +0.15 ... 0

15-Volt-Ampere Load5 .-4.2 .. +145.. -1.7 .. +40.. 0 03 .-4.9 .. +210.. -1.7. +40.. ...0 -11 off scale .. -1.5 ....... +38 .. +0.15 00.5 .off scale.. -1.5 .... +35. +0.30 ......... -1

Table V. 50/5-Ampere Bushing Transformer

Two Cores: One, Mumetdl; One, Silicon-Iron. Edch Core: 4 Inches Deep, 5-Inch InsideDidmeter, 7-Inch Outside Didmeter

7.5-Volt-Ampere LoadCompensated Plus

Plain Transformer Plus Triple Frequency Triple FrequencyNominal Phase Phase PhaseSecondary Ratio Error, Angle, Ratio Error, Angle, Ratio Error, Angle,Amperes Per Cent Minutes Per Cent Minutes Per Cent Minutes

5 -2.65... + 75... -2.20... +73 .......... 0 ....... +13.-2.90... + 82... -2.05... +60. -0.05......... -11 .-3.25.... +153 ... -2.00 ... +48 ......... 0 ........ -1

0.5. -3.20... +210... -2.00... +40. +0.03.. -2

Table VI. 30/5-Ampere Bushing Transformer

Core-See Table V

2.5-Volt-Ampere Load 7.5-Volt-Ampere LoadPlain Compensated Plus Plain Compensated Plus

Transformer Triple Frequency Transformer Triple FrequencyRatio Ratio Ratio Ratio

Nominal Error, Phase Error, Phase Error, Phase Error, PhaseSecondary Per Angle, Per Angle, Per Angle, Per Angle,Amperes Cent Minutes Cent Minutes Cent Minutes Cent Minutes

5. -3.2... + 78... +0.02.... 0. off scale..... +0.35..... +93 ....... -3.5 ...... + 112 ..... +0.04 ...... 0............ off scale ......... +0.02..... -21. -3.6... +225... +0.12.... -1. off scale..... +0.05..... +50.5. -3.6... +280... +0.15.... -3.off scale..... -0.06..... +15

duced voltage. It follows that the core

weight must be about six times greaterwhen the ratio is halved. On this basis a

50/5 would have more than thirty times,and a 20/5 more than three hundredtimes the weight of a 200/5-ampere trans-former.Even these figures, formidable as they

are, do not fully represent the difficultiesinvolved because they assume that themean core diameter is the same for allratios. If this were so, the transformerswould have to be ridiculously long to

obtain the full core section, and the onlyremedy is to make the outside diametergreater, which not only increases the mag-netic path, but also the weight, to an

enormous degree.Table III shows the improvement

made by compensating a 100/5 bushingtransformer which had a poor inherentaccuracy. It is apparent without furthercomment that the simple application ofthis device considerably widens the scopefor this type of transformer.There is still, however, a limitation.

The duty of the compensator is to providea voltage proportional to the line current.and of constant phase position; unless itsperformance is reasonably good to startwith, it will not do its job sufficiently well,on the low ratios being considered, tomake the complete transformer suffi-ciently accurate.

AUUT 3Hobson-The Zero-Flux Current Transformer 611AUGUST 1953

USE OF TRIPLE-FREQUENCY FLUX

The possibilities of compensated-bush-ing transformers ma- be considerably in-creased by applying triple-frequeneyauxiliary excitation in a manner similar tothat described by Bovajian and Camilli.2They have shown that the addition of thehigher frequency flux reduces the errorsto a fraction of their original values. Butthat is not all: more striking still, in theopinion of the present author, the mag-netising and iron-loss curves for the nor-mal-frequency flux are rendered remark-ably straight, so that the ratio and phaseerrors are practically- constant for all linecurrents. The triple frequency is easilyobtained from a 3-phase bank of smallsingle-phase transformers, with primariesin start and secondaries in open delta.The device i! well known and needs nofurther comment.The author has carried out tests on this

method using silicon-iron and Mumetalcores, and has found that by far thegreatest benefit is obtained with the sili-con-iron. Numetal was not improvednearly so much, nor was the resultingperformance so linear. For this reasonthe use of the orthomagnetic principle,used in the manner shown by Boyajianand Camilli, appears to be limited totransformers tor moderately low currents.The performance of, say, a 50/5 silicon-iron bushing transformer would be sopoor inherently, that even the utmostbenefit of triple-frequency flux would failto reduce the errors to the limits requiredfor metering. On the other hand, anickel-iron core could not be improvedsufficientlv to justifv the extra trouble in-volved. It seemns to the present author,however, that orthomagnetism might wellbe applied with advantage to the zero-fluxtransformer.

Since the dolcduty of the compensator

DiscussionC. K. Duff V Hydro-Electric Power Com-mission of Ontario, Toronto, Ontario,Canada): The remarkable improvementsin current transformer accuracy attainableby Mr. Hobson's method of compensation,and especially when Boyajian and Camilli'sorthomagnetic principle is combined there-with, speak for themselves. Test frequencyused is not stated, but if 50 cycles is assumedequally good results could be expected at60 cycles.

Mr. Hobson follows recommended prac-tice of the International ElectrotechnicalCommission in stating percentage ratioerror, wherein ratio error is positive whensecondary current multiplied by the nom-inal ratio exceeds the primary current. Onthis continent the sign is reversed, pre-sumably because the thought is concen-

Table VII. 20/5-Ampere Bushing Transformer

Core See Table V

2.5-Volt-Ampere LoadCompensated

Plain Plus TripleTransformer Frequency

Ratio RatioNominal Error, Phase Error, PhaseSecondary Per Angle, Per Angle,Amperes Cent Minutes Cent Minutes

0 ......

3 ......

I ......O .5a ..I...

off scale..... +0. 10 . + 3.off scale ..... 00 + 4.off scale....... +0 10. . . +18,off scale .... 0 17. +28

is to provide a linear voltage, the magni-tudes of its errors, considered from thecurrent transformer angle, are of no im-portance, provided that they remain con-stant for all line currents. It wasthought, therefore, that the results ob-tainable with a silicon-iron compensator,rendered linear by triple-frequency flux,might even be superior to those with aMumetal core. A further advantagewould be that the working flux densitycould be twice that in the Mumetal, thushalving the core weight and bulk.The main core would probably be

Mumetal, at least on the very low ratios.Although the relative benefit of triple-frequency flux on this alloy is less, itsultimate performance is still considerablvbetter than that of silicon-iron. Further-more, since the compensator was in anycase to be rendered orthomagnetic, itwould be a simple matter to excite theMumetal from the same source. To testthis reasoning, a 100/5 transformer wasbuilt having the same core size as the oneof Table III, but using silicon-iron in-stead of Mumetal. The main and com-pensator cores were each divided into twoequal parts and supplied with triple-fre-quency excitation.

trated on the ratio correction factor (RCF)which is high when the secondary currentis too low and vice versa. Section 13.032of the American Standards AssociationStandard C57.13 states:

Per cent ratio error = 100 (RCF 1)

Tabulation of ratio correction factors in-stead of per ceilt ratio errors would eliminateany ambiguity.

REFERENCE1. INSTRUMENT TRANSFORMERS. ASA C57.13-1948, American Standard Association, New York,N. Y., 1948.

Harold P. Knopp (Electrical Facilities, Inc.,Oakland, Calif.): The content of the paperwith its interesting and revealing test re-sults on various types and capacities of

Results are given in Table IV. Thenatural errors are very large, but it isinteresting to see that triple-frequencyflux alone reduces the phase angle to thesame order of magnitude as that of theplain Mumetal transformer of Table III,with the extra advantage that it is con-stant. The further addition of compensa-tion makes the performance equal to thecompensated Mumetal transformer.

Table V, VI, and V'II give the results ofsimilar tests on 30/5, 30/5, and 20, 3ampere bushing-type transformers. Thesame core was employed in each case. Itwas first wound for 50/5 amperes, andturns were taken off as the ratio was re-duced. The silicon-iron was, of course,the compensator core. The triple-fre-quency excitation was supplied to bothcores, but at different flux densities. Onthe 20/5 transformer the main core hadfour, and the compensator two secondarvturns. The latter was thus working ononly 10 ampere-turns at full current, and1 ampere-turn at 10 per cent of full cur-rent. Its working flux density approached33,000 lines per square inch, and abouthalf its input was lost in magnetisation.

It is interesting to note that for equalperformance with a plain design, thistransformer would have to be about 50feet long, using a solid Mumetal coreweighing more than 1 ton.

References

1. CURRENT TRANSFORMER TESTING, A. H. M.Arnold. Journal, institution of Electrical Engi-neers, London, England, vol. 74, 1934, pp. 424-44.

2. ORTHOMAGNETIC CURRENT TRANSFORMERS FORMETERING, A. Boyajian, G. Camilli. AIEETransactions (Electrical Engineering), vol. 64,March 1945, pp. 137-40.

3. INSTRUMENT TRANSFORMERS, A. Hobson.Journal, Institution of Electrical Engineers, Lon-don, England, vol. 91, part II, April 1944.

4. INSTRUMENT TRANSFORMERS (book), B. HagueSir Issac Pitman and Sons, London, England, 1936-

transformers is, in the writer's opinion, aworth-while further contribution to thework done and being done toward develop-ing practical current transformers withnegligible ratio and phase-angle errors.The author's work seems to follow andextend that of Boyajian and Camilli ofthis country, to which the author makesreference.

In reading this paper it occurred to methat it would be interesting to have furtherinformation from the author as to theeffect of his compensating method on theleakage fluxes in various transformer de-signs. Was it Mr. Hobson's experiencefrom test results that errors resulting fromthe placement of the primary winding asfound by Dr. Arnold' were reduced oreliminated?

It would seem that one of the main prac-tical benefits obtained from the author's

612THobson-The Zero-Flux Current Transformer AUGUST 195)3612

compensating method is that the ratio andphase-angle performance is improved so asto give excellent accuracy over a wide rangeof load current. This advantage should beparticularly valuable in metering applica-tions such as where bushing-type currenttransformers are employed and where theload current fluctuates and should bemeasured with equal accuracy regardless ofload.On the other hand, I think that the fore-

going advantage of Mr. Hobson's compen-sating method becomes relatively unim-portant when considering multirange trans-formers which, because of their multiplicityof ranges, need not be used over a widerange of load current but are used primarilybetween 60 and 100 per cent of full-loadcurrent. It is possible and very practical todesign and build transformers of the labo-ratory type employing a fractional-turnratio-compensating method and a separatephase-angle compensation which have negli-gible ratio and phase-angle errors over theforegoing range of load and ampere-turnsthat do not have to exceed 800 to 1,200, de-pending upon the secondary burden. It istrue it would seem that the author's com-pensating method would make possible areduction in the ampere-turn value, but ifthis is done, the values of primary currentranges would be limited, and also, as theauthor pointed out, the transformer, as aresult, would be more susceptible to changeof burden.

It was of particular interest to me to notethat Mr. Hobson, in order to test thecompensated transformer of Table I ofthe paper with sufficient sensitivity, used amethod described by Dr. Arnold2 wherebythe difference between the primary andsecondary currents was measured directlyon the 5/5-ampere range, or the 1-to-I ratio.This method, except for a difference in thetype of detector employed, has been used inthis country in connection with the current(and also potential) transformers manu-factured by the firm with which the writeris associated.

This test method, known in this countryas the Knopp one-to-one method or, morebriefly, the one-to-one method, was de-veloped and used by Otto A. Knopp in1912.3 Knopp employed two watt-hourmeters as the detector to determine thedifference between the primary and second-ary. Later, for this purpose, he developedthe torsion-head detector wattmeter.4 Theuse of this detector wattmeter in the one-to-one method was further dlscussed in anAIEE paper.5

Because of my experience with the one-to-one method, I can fully understand andappreciate why the author employed thismethod where it was necessary for him tomeasure very small ratio and phase-angleerrors and with the most direct meansavailable so as to eliminate the need ofapplying correction factors to the measuredresults.

4. TORSION HEAD OVERCOMES WATTMETER ERROR,0. A. Knopp. Electrical World, New York, N. Y.,vol. 89, Feb. 19, 1927, p. 407.

O. SOME APPLICATIONS OF INSTRUMENT TRANS-FORMERS, 0. A. Knopp. Electrical Engineering,vol. 55, May 1936, pp. 480-89.

G. Camilli and L. W. Marks (General Elec-tric Company, Pittsfield, Mass.): Thispaper represents another worth-while addi-tion to the long list of the methods whichhave been developed for the improvementsof bushing-type current transformers. Theunderlying principles incorporated in themethod of compensation described in thispaper may be better appreciated by brieflyreviewing the nature of the problem in-volved in improving the accuracy of thebushing-type current transformer.

In a current transformer, the inaccuracyis caused by the exciting current required tomagnetize the core. Operating at a reason-able flux density, a transformer requires acertain number of ampere-turns so that themore the turns the less the current will be.As the bushing-type current transformer hasonly one primary turn, its exciting currenthas to be larger than that of units withmany turns. But this is not the onlydifficulty. The exciting current varies non-linearly with the load and thus resists simple

corrective measures such as compensationby modification of turn ratio.

It may be appreciated on reflection thatthe magnitude of the ratio correction factorwould be of little or no consequence if it wereconstant through the range of the currentvalues to be measured. The case of phaseangle is more complicated because, even ifthe phase-angle shift were constant, theultimate correction would differ for differentpower factor of the load to be measured.The problem, therefore, is to make the ratioerror at least constant and the phase angleas small as possible.

In the scheme described in this paper theexciting current is 1. reduced to a verysmall value by the help of an auxiliary ex-citing transformer'; 2. minimized in somecases by the use of low-loss, high-permea-bility material such as Mumetall; and 3.straightened by the use of the orthomagneticprinciple.3 The results obtained are cer-tainly startling when compared with non-compensated bushing-type current trans-formers. Since the most accurate resultswere obtained by the combination of threeschemes, it may be well to discuss the con-tribution of each scheme to the total per-formance.

1. Compensation by the use of an auxil-iary core (zero flux current transformer).

Table I. Test Data

Bushing Current Transformer; Cores Mdde of Silicon Steel. Two Cores Edch 93/4-Inch InsideDiameter by 11 /4-lnch Outside Diameter by 4 Inches High. Burden 12.5 Volt-Amperes dt

90-Per-Cent Power Fdctor

Nominal Secondary,Amperes

Uncompensated Transformer

Phase Angle,RCF Minutes

Zero Flux Compensation

RCFPhase Angle,

Minutes

0. .1.0175... +97 ..... 0.9927 ... +465.0 .1.0076... +24 ..... 0.9990 ... - 5

Table II. Effect of Burden Change Using Zero Flux Method

Bushing-Type Current Transformer, 300/5 Amperes, 2 Cores of Silicon Steel Each 93/4-InchInside Diameter by 113/4-Inch Outside Diameter by 4 Inches High. Transformer Compensatedby the Zero Flux Method for a Burden of 12.5 Volt-Amperes at 90-Per-Cent Power Factor

Secondary Amperes RCF Phase Angle, Minutes

0 0.0. 9927...+465.0 .... 0.9990 . - 5

Test results at 2.5 volt-amperes 90-per-cent power factor0.5 .... 0.9673 . -765.0 0.9885 . -30

Table Ill. Comparison of Zero Flux and Biased-Core Compensation

300/5 Amperes, Two Cores Each 93/4-Inch Inside Diameter by 113/4-lnch Outside Diameter by4 Inches High. Burden 12.5 Volt-Amperes at 90-Per-Cent Power Factor

REFERENCES1. LEAKAGE PHENOMENA IN RING-TYPE CURRENTTRANSFORMERS, A. H. M. Arnold. Journal, Insti-tution of Electrical Engineers, London, England,vol. 74, 1934, pp. 413-23.

2. See reference I of the paper.

3. COMMERCIAL STANDARDIZATION OF INSTRUMENTTRANSFORMERS, 0. A. Knopp. Electrical World,New York, N. Y., vol. 67, Jan. 8, 1916, pp. 92-93.

Secondary Amperes

Zero-Flux Compensation

RCF Phase Angle

Biased-Core Compensation

RCF Phase Angle

0.5 . 0.9927.... +46 .. 1.0095.... +415.0 .0.9990 .... - 5 ...1 .0044.... - 1

Burden changed to 2.5 volt-amperes without change in compensation0.5 .0.9673 .... -76.1.0041.... +355.0 .0.9983 .... -30. 1 0021 ....0

Hobson The Zero-Flux Current TransformerAUGUST 1 953 613

Using a silicon iron core: Comparative re-sults between the compensated and un-compensated transformer are shown inTable II of the paper.The scheme seems particularly effective

in reducing the phase-angle error. Theslope of the ratio error is increased over theuncompensated transformer. Some testdata shown in Table I of the discussionwere also obtained by the authors of thepresent discussion on a 300/5 bushing cur-rent transformer with the same trend inaccuracy.

2. Using Mumetal cores. As expected(see Tables I and III of the paper) the errorswith this type of core material are muchsmaller. Again the zero-flux compensationis very effective in reducing the phase angle.

3. By the orthomagnetic principle.Table IV of the paper shows that the ortho-magnetic scheme reduces both the ratio andphase-angle error to a small fraction of theoriginal errors.

Table IV. Metering Performance at 60 Cycles on a 300-5 Biased-Core Bushing Current Trans-former for 1 38-Ky Oil Circuit Breaker

Secondary Burdens and Power Factor

2.5 Volt-Amperes,90 Per Cent

Nominal Secondary Phase Angle,Current, Amperes RCF Minutes

5 Volt-Amperes,90 Per Cent


12.5 Volt-Amperes,90 Per Cent


a ...... 0.9996. -3......... 0.9998 -3. 1.0005... - 33 .... .... 0. 9996 . - 2......... 0.9998 .-2 1.0005... - 11 ......... 1.0002....-.1.. ......... 1.0004 ...+2. 1.0012... + 40.5... 1.0006. +4... 1.0011 ....+6. 1.0023. +14

5 Volt-Amperes, 100 Per Cent 12.5 Volt-Amperes, 100 Per Cent

Phase Angle, Phase Angle,RCF Minutes RCF Minutes

5 0.9998 .-3.1.0005 . - 23 ................ 0.9998 .-1.1.0005 .. 01 ................ 1.0002 .+2. 1.0012. + 80.1 1.0005 ...... ... +8. .1.0015 ... +15

GENERAL COMMENTSThe data presented in the paper seem to

indicate that excellent results can be obtainedby the simultaneous use of a special materialfor the core, the zero-flux compensation andthe orthomagnetic excitation.

It should be noted, however, that suchgood results could have been obtained bythe use of the orthomagnetic scheme aloneif the author had taken advantage of thefine adjustments which have been incor-porated in the scheme.3,4

It should also be noted that the zero-fluxcompensation is only effective at the par-ticular burden to which the transformer hasbeen compensated. This is shown in TableII of the discussion.

COMPARISON WITH BIASED-CORECOMPENSATION

In Table III of the discussion the ratioand phase-angle error of the transformershown in Table I of this discussion are givenfor both the zero-flux and the biased-corecompensation.From Table III of the discussion it will

be seen that the biased-core compensationleads to accuracy which compares veryfavorably with the zero-flux compensationwhen this latter has been adjusted to theparticular burden at which the test is made.The superiority of the biased-core com-pensation is evident when the burden ischanged to other values without modifyingthe compensation.

It should also be mentioned that for anequivalent total cross section of the core thebiased-core transformer will saturate atmuch higher overloads than the zero-flux-compensated current transformer.

REFERENCES1. See reference 3 of the paper.

2. CURRENT TRANSFORMERS WITH NICKEL-IRONCORES, Thomas Spooner. AIEE Journal, vol. 45,June 1926, pages 540-45.

3. See reference 2 of the paper.

4. A NEW LINE OF ORTHOMAGNETIC BUSHING-TYPE CURRENT TRANSFORMERS, John W. Farr.AIEE Transactions, vol. 69, pt. I, 1950, pp. 424-28.

C. A. Woods, Jr. (Westinghouse ElectricCorporation, East Pittsburgh, Pa.): Thezero-flux current transformer described in

this paper is an ingenious addition to thevarious schemes which have been devisedto improve the metering accuracy of currenttransformers over a wide range of loadcurrents and secondary burden impedances. 1

The principal applications of this schemeare to current transformers used for labora-tory test standards and low-ratio bushingcurrent transformers. In the latter case,the principal disadvantage of the scheme isthe complications of added equipment andinstallation adjustments; this is the samedisadvantage encountered in most othermethods devised for the improvement inmetering accuracy of bushing currenttransformers.

In commercial applications of low-ratiobushing current transformers for billingmetering there is a desire for the simplicity,ruggedness, and economy of bushing trans-formers having the accuracy and minimumsecondary wiring of wound-type currenttransformers. Any attempt to meet thisdesire presents major difficulties, as isclearly illustrated by the author in his de-scription of the sizes that would be requiredto obtain the same accuracy performanceon various ratings of usual design low-ratiobushing transformers. The maximum sim-plicity commensurate with accuracy andsecondary burden requirements often maybe obtained without auxiliary adjustingdevices. Bushing current transformersusing special alloy core materials such asHipernik and/or simple compensatingschemes such as the biased-core2 design,where auxiliary devices and wiring are notrequired, will usually have adequate billingmetering accuracy over the primary currentranges encountered on present-day systems.

In the interests of reducing the numberof auxiliary devices, and further evaluationof the zero-flux compensating scheme, thetest results given in Tables IV to VII ofthe paper would be enhanced if data weremade available on the performance of thesetransformers with the compensating schememinus triple frequency excitation. Againfrom the data given it appears that thecompensator was adjusted for best per-formance at rated current for each burden.It would be of interest to know what theperformance would be for a single com-p)eisator adjustment when used with afairly wide range of burdens. For example,Table IV of the discussion shows the 60-

cycle performance of a biased-core 300-5bushing current transformer suitable foruse on a 138-kv oil circuit breaker. Thetransformer was compensated for a second-ary burden of 5 volt-amperes at 90-per-centpower factor lagging and tests at all otherburdens were made without any change incompensation.

REFERENCES1. A SURVEY OF BUSHING-TYPE CURRENT TRANS-FORMERS FOR METERING PURPOSES, G. Camilli.AIEE Trantsactionzs, vol. 69, pt. I, 1950, pp. 429-40.

2. BIASED-CORE-CURRENT-TRANSFORMER DESIGNMETHOD, Theodore Specht. AIEE Tranisactio'ts(Electrical Engineering), vol. 64, Sept. 1945, pp.635-40.

A. Hobson: Mr. Duff's kind remarks onthe efficacy of my method are much appre-ciated. I agree that the term "ratio cor-rection factor" avoids confusion of signi,but think that in estimating the effect ofinstrument transformers on meter readingsit may be simpler to deal with the per-centage ratio error.Mr. Knopp remarks that my work seems

to follow that of Boyajian and Camilli.This is true only for the latter part of thepaper. The zero-flux transformer representsa totally different approach, and furtherwork is being done in England which, it ishoped, will extend the use of the methodto still lower ratios and at the same timerender the errors independent of the burden.The effects of magnetic leakage on the

errors are much smaller when compensationis used, providing the cores are not satu-rated.

Multirange transformers may be com-peusated very simply with very little extramaterial. What is more, the performance ispredetermined by normal design methods,and a number of similar units will have thesame errors even though the individual coresdiffer in quality. Fractional turn-ratio andcapacitor phase-angle compensation wereformerly used by me. They serve only toraise or lower the whole curve and do notreduce its slope.

I was most interested in Mr. Knopp'saccount of the one-to-one method of testing,which was so useful to me.Mr. Camilli and Mr. Marks seek to show

that the orthomagnetic design gives thesuperior performance, and for this purpose

64Hobson The Zero-Flux Current Transformer AUGUST 1953614

have chosen the particular conditions Nwhichsuit the method best-a fairly high ratio of300/5 arid a silicon steel core. Evenl thenthe results are not really good enough formetering and recourse must be made to thefine adjustments to which he refers, adjust-ments which are extremely complicated ifone is to judge by J. W. Farr's paper on thesubject.Much better figures could have been ob-

tained with a Mumetal core of the samesize using zero-flux compensation alone.The total cost would be little or no greatersince no triple frequency transformer wouldbe needed, and the extra trouble of a sepa-rate source of supply would be avoided.

It is impossible to judge the merits ofMr. Woods' biased-core tranisformer from

his test results since no information is giveneither about the core size and material orthe performance of an equivalent plaintransformer. His wording seems to suggestthat Hipernik may have been the core usedin the tests. If this is so, then zero-fluxcompensation would undoubtedly havegiven better figures, while the change inerror with burden would not have beenappreciably greater.

I am familiar with the paper by Mr.Specht referred to by Mr. Woods and Ijust do not see how the biased-core designcan be considered as either simpler or morerugged than the zero-flux transformer,which does not require any installationadjustment as he suggests.

Strictly speaking, of course, the two

biased-core methods quoted by Mr. Camilliand Mr. Marks and by Mr. Woods shouldbe compared with each other, but not withmy transformer which is totally different incharacter and conception. Both theirschemes aim at an artificial improvement ofthe core material, and although the ortho-magnetic transformer gives the better resultsit is much more trouble to apply.On the other haiid the zero-flux trans-

former aims at eliminating the core flux, andin difficult conditions the addition of biasflux helps it to do its job more effectively.Used separately then, each method has its

merits. Used side by side, the zero-flux aridbiased-core principles form a powerful toolin the difficult task of constructing low-ratiobushing transformers of high accuracy.

A Negative-Phase-Sequence-O vercurrent Relay ror Generator

Protection

withstand unbalanced faults has beenexpressed as a function of 12 and of timet, present relay practices should be ex-amined to determine whether they pro-vide adequate generator protection.

Present Relaying

W. C. MORRISASSOCIATE MEMBER AIEE

R ECENT investigations,'-' includingtests and theoretical considerations,

by the manufacturers of synchronousmachines, have indicated that a revisionin the ASA Standard C50, paragraph3.1301 is desirable.The reference papers show that when a

generator is sutbjected to an unbalancedfault, the stator current inclucdes a nega-tive-phase-sequence component whichcauses a double-frequency current to flowin the rotor iron, slot wedges, and amortis-seur windings, resulting in local heating.This heating has been expressed by thefollowing relationship

f,122dt=Kwhere

12 = negative-ph;ase-sequence currenitt = timeK = a constant

A revised clause has been suggestedwhich takes inito account the factorsinfluencing the magnitude of the nega-tive-phase-sequence current, and whichtakes advantao-e of the fact that rotor

Paper 53-178, recommended by the AIEE RelaysCommittee and alpproved by the AIEE Committeeon Technical Operations for presentation at theAIEE North Eastern District Meeting. Boston,Mass., April 29-May 1, 1953. Mianuscript sub-mitted Februars 2, 1953; made available forprinting March 2, 1953.

M;. C. MORRIS and L. E. GOFF are wvitli the GeneralElectric Companv, Philadelphia, Pa.

L. E. GOFFASSOCIATE MEMBER AIEE

heating is proportional to aclause is:

"A machine shall be capable ofing, without injury, a 30-second, tshort circuit at its terminals whetat rated kva and power factor,excitation at 5 per cent overvoltmachine shall also be capable ofing without injury any other shorits terminals, provided the maclcurrents under fault conditionsthat the negative-phase-sequencemachine per unit stator currenthe duration of the fault in secolimited to values which give anproduct 122t of values equal to othose shown in the accompanyAlso the maximum value of insphase current shall be limited b3suitable reactance or resistancewhich does not exceed the maxircurrent obtained from the three-p

Type of Synchronous Machine

Turbine generators..................Hydraulic-turbine- driven generators ..

Engine-driven generators............Synchronous condensers.............Frequency-changer sets..............

* "Machines subjected to faults fallingabove limits and 200 per cent of thessuffer varying degrees of damage andspection of the rotor surface is recomifor faults in excess of 200 per centlimits, serious damage should be expe

Now that the capability of m

I,(t. IThiis

withstand-:hree-phase1 operatinlgwith fixedtage. Thewithstand-

\When a generator is connected to asystem in which all elements have pri-mary and backup protection such thatany fault is cleared before the ]22t charac-teristic of the machine is exceeded, thereis no need for additional backup relayingat the generator. In many instancesthis desirable condition is not realized andhence additional relaying is necessary to

p)rovide adequate protection of the genera-tor against unbalanced faults. Some ofthe relays now used for this purpose are

t circuit at time-overcurrent relays, time-overcurrenthine phase relays with voltage restraint, single-zoneare such distance relays, and phase-balance relavs.current in

t(1c2) and W"hen time-overcurrent relays are used,nnds (t) are their application is limited by the require-integrated ment that they be adjusted for sufficient

Ir less than time delay to co-ordinate with the otherring table, relays on the system, and for high enoughtantaneousy means of pickup to prevent operation on antici-to a value pated overloads. Frequently the sus-num phase tained fault current is too low to operate)hase fault, such a relay reliably. The addition of

voltage restraint to the overcurrent relayPermissible overcomes the problem of sensitivity but

12t* requires that the voltage at the generatorbe determined for the various fault condi-

30 tions. Furthermore, after the voltages... .40.. 40 have been calculated, it is still necessary

30 to determine whether a time setting can....30be made which will co-ordinate with other

between the relays on the system and still provide ade-;e limits mayan early in- quate generator protection.mended, and Single-zone distance relays have beenct:ed." used to back up the generator bus and

part of the system. However, such re-lachines to lays are instantaneous in operation, and

Morris, Goff Relay for Generator Protection6AUGUST 1953 610-

zero flux ct

Documents