IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, VOL. PAs-87, NO. 2, FEBRUARY 1968

The authors would consider three to four percent as a low perunit winding-to-winding impedance. Large high-voltage trans-formers most always possess a higher per unit winding-to-windingimpedance than do low-voltage transformers. The increase is dueprimarily to the differences in design of high-voltage transformers.Values of 15 to 20 percent per unit impedance are not uncommonfor high-voltage transformers. Since voltage balance is of far greaterimportance in a high-voltage transmission line than in a distributionsystem, the T-T connected transformer will find little use as a high-voltage power transformer. Also, another undesirable feature ofhigh-voltage application is that the low impedance of the T-Tconnected transformer would permit the flow of large fault currentsin the event of a short circuit.

The resultant per unit terminal voltages at the low-voltage (load)side of the transformer in Fig. 2 are tabulated as follows:

Case I Case II

Load Impedance = 1.0 + jO.0 0.8 + j0.6Va = 0.988 0.990Vb = 0.988 0.986V,= 1.025 1.018

We are pleased to see that our calculations are in agreement withMr. Goodman's results.

Resin-Bonded Paper Bushings for EHV SystemsHANS KAPPELER, MEMBER, IEEE

Abstract-The development of resin-bonded paper bushings forextra-high voltages is described. The problems of thermal stability,internal partial discharges, breakdown along laminae, and themanufacture of large insulating bodies are discussed. An evaluationof the merits of resin-bonded and oil-impregnated paper bushing ismade. The suitability of new bushing designs is shown by reportingthe experiences in operational and experimental networks up tosystem voltages of 1050 kV.

INTRODUCTION

AMONG the many outstanding insulating materials used inIhigh-voltage equipment, only a few are suitable for use in

the construction of HV bushings. Porcelain housings and variousfiller materials, which are only used as protection against externaleffects, will be disregarded. If attention is confined to the maininsulation proper, the capacitor body, there are only two di-electrics at present which can be used for extra-high voltages.These two are oil-impregnated paper and resin-bonded paper.Although both of these materials have to perform the same

duties, their range of properties differ considerably. Both ma-terials have their positive and negative features, with theresult that there are natural differences between the performancesof bushings in service. If an acceptance specification is drawn upwith the properties of an oil-impregnated bushing in mind, thismay make the use of the otherwise excellent resin-bonded bush-ing impossible.Owing to its widespread use in all kinds of high-voltage equip-

ment, oil-impregnated paper is very well known. Less has beenpublished on resin-bonded paper for high voltages. The objectiveof this paper is to draw attention to the special features of resin-bonded paper which make it ideal for bushings and to show thatthere are no fundamental difficulties standing in the way of its

Paper 31 TP 67-123, recommended and approved by theTransformers Committee of the IEEE Power Group for presenta-tion at the IEEE Winter Power Meeting, New York, N. Y., January29-February 3, 1967. Manuscript submitted October 27, 1966; madeavailable for printing November 6, 1967.The author is with Micafil Ltd., Zurich, Switzerland.

use at extra-high voltages and, furthermore, that such bushingsexhibit considerable advantages in design and operation.

Resin-bonded paper bushings have been firmly established formany years for system voltages up to 220 kV. They are oftenpreferred, particularly in Europe, to oil-impregnated paper bush-ings because of their reliability. At higher voltages it wasfound that such questions as the thermal stability, ionization,breakdown along laminae, and the manufacture of large insulat-ing elements needed reconsideration. The solutions to theseproblems have meanwhile yielded entirely new conceptions.

THERMAL STABILITY

The theory of thermal breakdown states the following: atelevated operating temperatures, stable thermal equilibrium isassured only when a maximum value of the sustained voltage,characteristic of the particular bushing, is not exceeded. Themagnitude of this voltage serves as a representative measure ofthe thermal stability. The magnitude depends solely on thequality of the dielectric, its ambient temperature, and the mannerin which it is internally cooled. The dimensions of the insulat-ing body do not enter into the calculation.[] 13]

These conditions can be represented by a simple relationship,the most general form of which is (in SI units)

U = m * VX/2irf *e - (tan 6) te .a. (1)

In this equation U is the maximum voltage for thermal stability;m is a nondimensional coefficient indicative of the quality of theconstruction as regards the dissipation of heat. The expressionunder the root sign depends only on the quality of the dielectricat a given frequency f. It is determined by the thermal conduc-tivity A, the absolute permittivity E, the insulation power factoror dissipation factor tan a at the temperature te of the surround-ing medium, and the exponential rise o- in the dielectric losseswith the temperature above ambient. The following expressionapplies:

(tan 8)t = (tan 6) ze. e 'e) ( 2)

394

KAPPELER: RESIN-BONDED PAPER BUSHINGS

Since the dimensions do not appear in (1), it implies that theproblem of stability cannot be solved simply by enlarging theinsulating body. The means of achieving higher stability, as hasto be stipulated for extra-high voltages, are therefore the reduc-tion of the specific losses and improvement of the internal coolingby appropriate design measures.

Dielectric Losses

The principal factors governing the dielectric losses in resin-bonded paper are the quality of the resin and the manner inwhich it is processed. Today there is a greater choice of low-lossresins. In addition to the well-known phenol- and cresol-form-aldehyde resins, there are now available the epoxy resins andvarious combinations thereof with very low dissipation factors.The minimum losses, however, can only be obtained when theresin is processed in the right manner. It has been found byexperience that when curing phenolic and cresolic resins, theresin film has to be condensed and polymerized on the paperbefore it runs into the body of the winding core. Today resin-bonded papers for use in bushings have reached such a highstandard that the values for dielectric losses-both as regardstheir absolute height and their dependence on temperature (lowa)-are almost as good as those of oil-impregnated paper. Ell

The quality of a dielectric is expressed not so much by theabsolute magnitude of the losses as by their constancy withrespect to time. Therefore, if the behavior resulting from agingat elevated temperature is taken into consideration, the firstimportant advantage of resin-bonded paper becomes apparent.Measurements on dry and uncontaminated bushings have shownthat even after service of 20 years and more no significantchange has taken place in the dielectric properties.

In contrast, the risk of aging is considerable with oil-impreg-nated paper. The oil molecule itself does not possess a very highresistance and it is particularly sensitive to high temperatures.Moreover, the low viscosity of the oil allows particles of foreignmatter and aging products to migrate to the points at which thefield concentration is greatest, in an irreversible process. Thisgradually lowers the electric strength and shortens the life.Progress has been made in the conservation of oil and aging canbe retarded by means of inhibitors. However, it is a difficultmatter to maintain the properties of the new state continuously.

Constructional Measures

The second method of improving the thermal stability isbetter internal cooling as characterized by the coefficient m in(1). This method has been found to be much more effective thangoing to extremes to reduce the losses. The fact that resin-bonded paper bushings can be used for very high voltages maylargely be attributed to the success of these efforts.

Least favorable, from the thermal aspect, are long, one-pieceinsulator cores completely immersed in hot oil, the heat fromwhich can only flow radially outward, as in a cable (m - 1.2).The thermal stability is roughly doubled when such bushings

are given very short conical ends, which allows some of the heatto be dissipated axially when provision is made for oil to circulateinside the tubular conductor (m - 2.5). The heat runs per-formed on such bodies have proved that they can be safely usedat system voltages up to 525 kV. Fig. 1 shows an example of acompletely immersed bushing of this kind.Transformer bushings where only the bottom end enters the

oil are better from the thermal aspect. If this section is madeshort and steps are taken to prevent the heat from traveling

Fig. 1. 420-kV resin-bonded paper bushing with short conical endsimmersed entirely in oil (for transformers with cable boxes).

through the transformer oil to the upper part, then one-pieceresin-bonded paper bodies can be employed for system voltagesup to 750 kV.The most effective measure, however, is the subdivision of the

insulator body into several sections with oil-filled gaps between.This enables the thermal stability to be raised considerablyhigher (m > 5). In such cases, though, it is very difficult toestablish the maximum voltage of thermal stability. Thus one

must draw a conclusion from a heat run at a lower voltage tosuit the circumstances. For example, on a bushing for a systemvoltage of 1000 kV, with its bottom end immersed in oil at 900C,a four-day heat run was performed at 700 kV. During the course

of the heat run it was observed that the power factor remainedpractically at the same level, both when the voltage was appliedand when it was not. This indicates that the maximum voltagefor thermal stability must be considerably higher than the testvoltage, because the latter's contribution to the rise of tempera-ture was almost nil. According to the calculation, the risk ofthermal instability in this case is no greater than that of a one-

piece bushing with a rated voltage of 300 kV.Thus the problem of thermal stability of resin-bonded paper

bushings may be regarded as solved, even for the highest possiblesystem voltages.

INTERNAL CORONA

There are two aspects of ionization inside bushings whichmust be considered separately. Firstly, corona discharge attacksthe dielectric and thus weakens the bushing electrically. Secondly,the presence of such discharges may prove an obstacle to thedetection of partial discharges inside a transformer.

The Effect of Corona Discharges on the Dielectric

Different dielectrics may behave quite differently whenexposed to corona. Here too, as with thermal stability, the resin-bonded paper bushing occupies a favorable position. Its solid

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, FEBRUARY 1968

dielectric, though containing finely dispersed air, exhibits a veryhigh resistance to partial discharges. The resistance to corona isattributed to the fact that the residues of decomposition producedby the action of the discharges are nonconductive and there-fore do not accelerate the process. Decomposition takes placein the form of a slow but steady erosion which may go on formany years without doing much harm to the insulation. Forinstance, in resin-bonded paper bushings in which the partialdischarges had an intensity of several hundred picocoulombs perhalf-cycle, the insulation showed hardly any deterioration aftermore than 30 years service. [4]

In spite of this, it is customary now to go one step further inprecautions to prevent ionization. At the highest service voltageit is stipulated that no discharge whatsoever may occur, evenassuming air inclusions. The dimensions of the insulation arethen made such that the corona inception voltage is not lowerthan the operating voltage. Thus, even if test voltages and over-voltages give rise to brief discharges, one can no longer speak ofaging and of endangering the resin-bonded paper bushing byinternal discharges, even after many years of service.

Quite different, however, is the behavior of the oil-impregnatedpaper bushing, whose dielectric is extremely sensitive to corona.The mechanism of deterioration is different from that of resin-bonded paper. The corona discharges crack the oil molecule.Thisproduces flammable gasesand unsaturated molecular residueswhich accelerate the deterioration process. Even low dischargeintensities can result in breakdown after only a short time.Therefore, for the oil-impregnated paper bushing it is absolutelyessential for corona not to persist for any length of time.

This can be achieved in two ways. With the oil-impregnatedpaper bushing containing gas, the radial voltage gradient must bereduced until the operating voltage is lower than the coronaextinction voltage of the filler gas. If the saturated oil is ionizedby test voltages or overvoltages of short duration, no harm willresult as a rule. The reason it is not harmful is that the process isimmediately interrupted as operation continues at the operatingvoltage. Since such bushings have to be made unduly large, theydo not offer any advantages over resin-bonded paper.With gas-free oil-impregnated paper bushings, higher radial

gradients are permissible. But absolute freedom from dischargeup to the maximum overvoltages must be stipulated. Once adischarge had commenced, it would persist at the operatingvoltage, which would now be above the extinction voltage of thegas. Ionization will only cease if the voltage is interrupted for aperiod of regeneration. Further requirements are that bellowsmust be provided to allow the oil to expand and also that mea-sures must be taken to ensure that the oil-impregnated paperremains free from gas indefinitely.

This comparison illustrates the simplicity and the freedomfrom problems of resin-bonded paper bushings in relation to thecorona hazard.

The Disturbing Effect of Corona on Transformer TestingThe fact that a properly designed resin-bonded paper bushing

shows coronla above its operating voltage proves an obstacle inthose cases where tests at higher voltages have to be performedon a transformer insulation system to demonstrate its freedomfrom ionization. Therefore, a search was made for a means ofraising the corona inception voltage without changing thedimenisions.The inception of corona discharge at the layer edges of a

condenser bushing is a well-known phenomenon.[2l The mag-nitude of the inception voltage Uk of a partial capacitor depends

on the thickness d of the insulating layer and on the quality ofthe edges of the layers, according to the empirical relationship

Uk = k*d045 (3)

where Uk is in kV and d in mm; k is 1.5 for metal foil in airand 2.2 for graphite coatings in air.On the basis of this relationship, considerable progress has

been made by substituting conducting layers for metal foil.These layers no longer have to be placed in position, but areapplied in the right length and radial spacing directly on thepaper by an automatic mechanism while the capacitor body isbeing wound.

This manufacturing procedure offers the following advantages:1) The conducting graphite coating raises the corona inception

voltage by about 50 percent (k = 2.2 instead of 1.5).2) Owing to the fact that the coating is infinitesimally thin,

the number of coatings can be considerably increased and thethickness d of the partial capacitors can be correspondinglyreduced. Thus, according to (3), the radial gradient Uk/d isincreased still further.

3) The thin coatings no longer act as a foreign body, as did themetal foil; the result is a uniform insulation structure with betteradhesion between the layers.

4) Automatic application results in greater neatness of thelayer edges and high precision at the overlaps. Electrically over-stressed edge zones are thus avoided.The partial or complete application of the measures described

results in a corresponding improvement in the corona inceptionvoltage of the conventional resin-bonded paper bushing. Today,when freedom from ionization of up to 10-20 percent above theoperating voltage is stipulated for transformers, this can befulfilled without increasing dimensions to an extent that isuneconomical. If freedom from corona is requested at high in-duced voltages, this can prove disadvantageous as specialmeasures have to be taken to fulfill this requirement. A techniquealready in use can be recommended whereby corona in trans-formers is tested at operating voltage immediately after theinduced voltage test. This procedure gives a sure indication of theformation of gas bubbles inside the transformator insulation.

FLASHOVER AND BREAKDOWN ALONG LAMINAE

The greatest weakness of every laminated insulating materialis its low electric strength in the direction of lamination, which isusually only a fraction of the strength perpendicular to the layer.This applies to both resin-bonded and oil-impregnated paper.Flashover from the embedded edge of a capacitor layer along thepaper laminae represents a very serious problem, especially inthe lower part of a transformer bushing. As curve 1 in Fig. 2shows, the rise in breakdown voltage along the laminae is no-where near proportional to the increase in the flashover distance.Thus to test EHV bushings, the bottom part would have to bedisproportionately long.

In this respect the resin-bonded paper bushing offers a further,inestimable advantage for many transformer designs, in that itslength can be appreciably shortened by simple means, in additionto which the longitudinal electric strength is improved. This isdone by machining away the resin-bonded paper down to thecapacitor layers, so that the edges of the latter are situated atthe paper-oil interface.The effect of this can be seen in curve 2 of Fig. 2 where a

proportional rise in the flashover voltage with the length isapparent. The extraordinarily high electric strength is accounted

396

RAPPELER: RESIN-BONDED PAPER BUSHINGS

LL0

;5-J

w0

I

LL

zwdwcr-LL

0

1 200

L- -

600/ ~~~~~~~~~~~~~1

400C

-L

200 A

., ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 .

20 40 60LENGTH OF INSULATION- CENTIMETERS

Fig. 2. Low-frequency flashover under oil of resin-bonded paperbushings. Curve 1-bushing with embedded condenser layers.Curve 2-bushing with free edges of condenser layers.

for by the fact that the fine subdivision of the insulating surfacCby the capacitor layers allows full advantage to be taken of thewell-known high strength of small oil-filled gaps. Fig. 2 alsoshows that the gain is particularly pronounced at very highsystem voltages.

In contrast to the success achieved at the lower end of thebushing, little can be done by controlling the capacitor bodyat the exposed end. Moreover, at very high voltages quite un-pleasant anomalies may be experienced.

In Fig. 3 values of the flashover voltage measured in airalong condenser bushings are plotted against the flashoverdistance. Whereas the impulse withstand voltage increases inproportion to the distance, the electric strength with respect tothe power-frequency voltage diminishes appreciably. The samesaturation phenomenon is observed with switching surges,whose positive flashover voltages are even somewhat lower thanthe peak values of the power-frequency flashover voltage.

All these phenomena indicate that there is a limit to the in-crease in system voltage, determined by the considerable growthin flashover distance and the wide dispersion of the measuredvalues. Flashover voltages with an rms value of 1600 kV arealmost impossible to attain with a reasonably tolerable length.System voltages well above the 1000-kV limit can only beachieved by a substantial reduction of the power-frequency andswitching surge test levels. Thus it is the air and not the resin-bonded paper which imposes the upper limit on system voltages.

DESIGNS AND EXPERIENCES

The manufacture of resin-bonded paper bushings has alwayskept pace with the development of system voltages. Experiencehas been gained with many hundreds of transformer and reactorbushings for a rated voltage of 400 kY.A feature of the design of such bushings is their extreme

simplicity and robustness, both of which contribute to reli-ability. The resin-bonded paper bushing does not need a specialenclosure. The simplest form merely has a shrunk-on flange.

w

0lx

w0

I

4Li.cr

L)

1C1

1 2 3 4 5 6FLASHOVER DISTANCE - METERS

Fig. 3. Flashover of bushings in air at standard at-mospheriq,conditions.

Fig. i shows an example of a bushing used on a transformerfor a rated voltage of 420 kV, connected to-a cable termination,where the bare insulator body is immersed in oil both inside thetransformer tank and in -the -eable endbox. The controlledtapered ends are only 65 cm long at each end. During the typetests they withstood a power-frequency voltage of 950 kV(rms, 1 minute) and an impulse voltage of 1900 kV (crest, 1.5 by40 ,s).For installation outdoors a porcelain skirt is attached to the

flange and the space inside filled with oil. This oil filling is sub-jected to quite low electric stresses; therefore it does not requireany special treatment or attention. The interior of the fitting atthe top end acts as the expansion vessel.The simplicity of the design has proved most useful in the

event of any mechanical damage in transportation, during erec-tion, or in service. Breakage of the porcelain skirt, resulting inleakage of the oil filling, does not mean that the bushing must bereplaced. A new skirt can be fitted on site, or the old one can beresealed, since replacement of the oil is admissible.

In addition to the 420-kV bushings there are several for 735kV in service. They have proved perfectly satisfactory, thoughthey have been in operation for only about a year.Bushings of resin-bonded paper for 700 kV and higher are

assembled from a number of sections, for thermal and productionreasons. This reduces the risk that has to be borne by the manu-facturer, as each section can be tested to its full voltage beforeassembly. When the sections are put together, oil gaps are leftwhich are dielectrically short-circuited, so that the oil is notsubjected to any electrical stresses.

Fig. 4 shows a transformer bushing for a system voltage of1050 kV which, in addition to withstanding the power-frequencyvoltage of 1200 kV (rms, 1 minute), was also subjected to full-wave standard impulses of 3050 kV and to chopped waves of3500 kV. These stresses, which are about 20-30 percent abovethe appropriate levels, were withstood by the bushing withoutdamage.

397

.

801-

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, FEBRUARY 1968

Fig. 4. Transformer bushing for 1050-kV systems. Multicore resin-paper body with short conical lower end. Length above flange 730cm, length below flange 150 cm.

CONCLUSIONS

1) Resin-bonded paper bushings are ideal for extra-high volt-ages. They are already successfully in service in operationaland experimental networks with voltages up to 1050 kV.

2) Through advances in process engineering and constructionalmeasures, the thermal stability of resin-bonded paper bushingshas been improved to such an extent that there is no obstacleto its use at extra-high voltages.

3) Resin-bonded paper bushings are notable for their highresistance to aging and internal discharges. They are dimen-sioned in such a way that no corona exists at operating voltage.Therefore they work practically without aging.

4) Higher corona inception can be achieved to a limited degreewithout a change in dimensions. Thus corona tests can besuccessfully performed on transformers at a slightly increasedoperating voltage immediately after the induced voltage test.Freedom from corona at high induced voltages may lead touneconomical dimensions.

5) Extremely short lower sections of resin-bonded paperbushings immersed in oil exhibit a very high flashover value.This opens up interesting possibilities in the design of trans-formers.

6) By dividing the insulator body into several sections, it ispossible to construct bushings of any size. The upper voltagelimit is determined solely by the flashover in air.

7) Features of resin-bonded paper bushings are their simplicityand robustness, both of which contribute to their reliability.Mechanical defects can be corrected on site.

8) When drawing up acceptance specifications, it is advisableto take the special characteristics of these bushings into account.Failure to observe this rule hampers technical progress.

REFERENCESI'] L. Dreyfus, "Mathernatische Theorien fur den Durchschlag

fester Isoliermaterialien," Bull. SEV, vol. 15, pp. 321-344, 1924.12] H. Kappeler, "Progress in the construction of condenser-type

bushings," CIGRE paper 208, 1946.[3] ,"Hartpapierdurchfuihrung fur Hochstspannungen," Bull.

SEV, pp. 807-816, 1949.(1] H. E. W. Jolley, "Methods and techniques for obtaining

significant discharge measurements on high-voltage bushings,"Proc. IEE (London), vol. 112, pp. 1061-1070, 1965.

[5] W. J. Brown, H. W. Kerr, D. E. Singer, and L. C. Walshe,"Accessories and parts for transformers," CIGRE paper 101, 1966.

Discussion

E. J. Grimmer (Westinghouse Electric Corporation, Sharon, Pa.):The author has made a valiant defense of resin-bonded paper bush-ings and has giYen some interesting arguments to establish theiradequacy for application in EHV systems. Oil-impregnated bushingsfor HV and EHV have been uniformly accepted in this countrybecause of the record of failure-free operation that has been estab-lished in the 27 years that they have been used, as against the lessthan satisfactory record of resin-bonded paper bushings.The author's theory that aging of oil-impregnated paper is a greater

risk than that of resin-bonded paper cannot be accepted. The oppositeconclusion would be expected since oil-impregnated paper has alower dielectric loss at elevated temperature than resin-bondedpaper; the impregnating oil has a higher viscosity than the air in thedry paper and resin laminate; and any gas that might be generatedin the oil would be ejected from the high-stress point because thedielectric constant of gas is much less than that of oil. Our experiencehas borne this out, for we have had resin-bonded paper bushings,especially those applied at reduced BIL, that have developed areasof localized corona deterioration between condenser layers after 15to 30 years of service, but we have not found this in oil-impregnatedbushings, although the latter are worked at higher voltage stress.The author is to be congratulated on developing a method by which

an EHV resin-bonded paper condenser can be assembled in sectionsto permit oil to circulate in the body of the condenser but still have itsealed so that the oil in the bushing does not leak into the trans-former, and to have the assembled sections develop sufficient me-chanical strength in the bushing. In oil-impregnated bushings, theoil is sealed into the bushing by the flange and the porcelain shellsand oil ducts through the condenser are quite easily added to permitthe bushing oil to circulate to provide thermosiphon cooling. Thesebushings develop all their mechanical strength through the top andbottom porcelain cones which are held together by the centralbushing conductor and a spring assembly in the expansion chamber,thus taking all mechanical strain off the condenser.The short lower end of the resin-bonded paper bushings is a require-

ment in transformers that have oil expansion tanks, but obviouslythis length would have to be increased if the transformer has a gasspace above the oil, as is the practice in this country.We also have reduced the lower end length of some of our lower-

voltage resin-bonded paper bushings by cutting the lower end of thecondensers so that the edge of the foil comes at the paper surface.This foil edge is then immersed in high-quality insulating varnishwhen the lower end of the condenser is sealed, and is then in contactwith the transformer oil. The dry paper is thus eliminated at theedge of the foil. This is quite unnecessary with oil-impregnatedcondenser bushings because all the foil edges are embedded in paperand thoroughly impregnated in oil and laminar voids are eliminated.Because of the very small flange thickness and C.T. pocket and no

flange extension below the cover in Fig. 4, the ground layer of thecondenser must extend a considerable distance into the top porcelain.This is also indicated in the sections shown in Fig. 2. If this is doneto get sufficient length in the ground layer so as to have a near-

Manuscript received February 24, 1967.

1EEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, VOL PAS-87, NO. 2, FEBRUARY 1968

uniform voltage gradient in the radial direction, does not this longground extension above the flange and cover cause very high stressat the top edge of the ground layer and poor axial voltage distributionalong the outer porcelain? A metal flange extension through thegas space on American bushings provides sufficient ground layerlength so that the top edge of the ground layer is almost flush withthe top edge of the flange and uniform axial voltage grading over theentire top porcelain can be achieved.

H. Kappeler: The author wishes to thank Mr. Grimmer for his veryvaluable comments resulting from a long experience in the field ofbushing design. Judging from his remarks about the behavior ofresin-bonded paper bushings it seems that the dielectric materialused in the bushings mentioned by him must have been quite dif-ferent from those described in the paper. Without knowing thedetails it will be difficult to indicate the cause of the unsatisfactoryresults. It can only be said that the technique known by the authorand used by many manufacturers of resin-bonded paper has yieldedexcellent results over more than 30 years.The aging of an oil-paper dielectric system as a function of tem-

perature and electric stress is fairly well known. Life expectancy

Manuscript received July 10, 1967.

decreases markedly with higher temperatures. The author agreesthat in general the aging of an oil-impregnated paper bushing isslow and can be neglected as long as the temperature does notexceed about 70°C. At higher values up to the highest admissible oiltemperature in transformers (95°C), the system, according to theexperience of the author, is likely to increase more rapidly in dielectriclosses than can be tolerated.

Concerning the short oil ends, it is true to say that in an oil-impregnated paper bushing the edges of the condenser layers arealready in contact with oil and therefore offer the same advantagesas the conical ends of a resin-bonded paper bushing. However, thedifficulties lie in finding a short end porcelain which will hold alongits surfaces in oil the breakdown voltages indicated in curve 2 ofFig. 2. A resin-bonded paper bushing does not need such a porcelain.The question about the length of the ground layer is an interesting

one. To have a favorable distribution of the radial stresses a suf-ficient length of the ground layer is required. According to our ex-perience, however, a certain extension of the ground layer above theflange results in a higher flashover voltage than can be achieved bysecuring a uniform axial grading along the top porcelain. Thisextension may be quite considerable and to prevent overstressingthe top edge of the ground layer must sometimes be protected by aninternal guard ring.The author would like to add that since the date the paper was

submitted further progress has been made in improving the inceptionvoltage of partial discharges in resin-bonded paper bushings.Today the limitations hitherto existing in conjunction with trans-former testing have mainly been overcome.

Calculation of Electrical Field Strength Around

Transformer Winding CornersLASZLO FOGARAS AND WOLFGANG LAMPE

Abstract-A method is described for determining the electro-static field strength with the aid of a high-speed computer. Themethod is based on the conformal mapping according to Schwarz-Christoffel, and it is suitable for the calculation of voltage gradientsin the vicinity of bare or insulated rounded boundaries governed bythree potentials, particularly with reference to transformers.

INTRODUCTION

THE DEVELOPMENT of high-speed computers withlarge rapid-access storage capacity has made it more and

more attractive to treat plane or cylindrical electromagneticfield problems by means of relaxation techniques rather than byanalytical approximations of different kinds. In special cases,however, such methods require an enormous degree of sub-division of the network of relaxation points, or a rather elaborate

Paper 31 TP 67-129, recommended and approved by the Trans-formers Committee of the IEEE Power Group for presentation at theIEEE Winter Power Meeting, New York, N. Y., January 29-Febru-ary 3, 1967. Manuscript submitted August 22, 1966; made availablefor printing October 4, 1967.

L. Fogaras is with ASEA, Vasteras, Sweden.W. Lampe is with ASEA, Ludvika, Sweden.

administration which is difficult to generalize. This is especiallytrue when accurate information is sought about the field quan-tities in the vicinity of convex contours of small radii. Thispaper describes a case from transformer engineering where con-formal mapping according to the Schwarz-Christoffel analyticalmethod has been applied to an example having a higher degreeof complexity than can be handled by manual calculation.The transformation leads to a set of four transcendental equa-tions for the determination of intermediate parameters. Thisset of equations is then solved by a multidimensional Newtoninterpolation.The example studied contains, as special cases, a number of

previously known and published simpler patterns.

STATEMENT OF THE EXAMPLE STUDIEDIn transformer engineering a frequent problem concerns the

determination of maximum electrostatic field strength in theimmediate vicinity of insulated or bare conductors. The con-figurations often possess circular symmetry, or can be regardedas plane cases, and a cross section shows a convex corner with asmall, but finiite, radius. It is known, a priori, that the point ofmaximum stress is located somewhere along this portion of thecontour.

399