Transformer Noise

Transformer Basics

Westinghouse Lecture Series

Transformer Sound Issues [.pdf]

Transformer Noise White Paper [.doc]

Transformer Noise White Paper [.pdf]

These documents were developed to sent to customers asking questions about transformer noise. Feel free to send them to anyone.

Wes Patterson Seminar

Feb 1992 Transformer Seminar by Wes Patterson

This document is also sent to customers asking for basic information about transformer design

1) Transformer Types and Applications

2) How a Transformer Works

3) Power Transformer Windings

4) Distribution of Impulse Voltages in Power Transformer Windings

5) Methods of Controlling Impulse Voltages

6) Insulating Materials, Stresses, Breakdown

7) Transformer Insulation Structures

8) Paper & Oil Insulation

9&10) Cores, Structure, Properties

11) Resistance, Reactance, Regulation

12) Calculation of Transformer Reactance

NOTE: This is proprietary information and should not be circulated outside of the company.

This is a series of lectures on the Basics of Transformers provided to Westinghouse employees in 1966, back in the good ole days of typewriters and slide rules. They appear to contain some good basic information on transformer function.

Page 1 of 3Basics of Transformer Design

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From SHARON. WORKS, ML-57

DatI July 15, 1966

SUDject Transformer Fundamental Course

We are now ready to complete the final arrangements of the Transformer Fundamental Course announced to you in May, 1966. The original response to this program was large and, as a result) several adjustments in the procedure and contents have now been made to accomodate the wishes and needs of the participants.

1. The program will start on Tuesday, September 20, 1966 from 4-6:00 P.M. in the Auditorium and continue each consecutive week for two terms of 12 weeks (24 in total). See the attached list for subject, instructor, and dates.

2. Participation is being restricted to those who have technical back­ground~ (E.E.; M.E.; I.E.; Math; Physics) since the course material will be on a graduate level basis of understanding.

3. Extensive readings, home study and final examinations are scheduled so a. scholarly atmospher~ and tempo can be anticipated.

4. Regular and prompt attendance will be expected because the instructors will be presenting course material necess.itating the full utilization of the two-hour period. In many cases, time will have to be spent filling in the information gaps through outside reading and research.

5. We plan to record all the sessions on tape and then make the tapes available, on a scheduled basis. for those who must be out of town on business trips,. etc. We plan to keep these tapes on permanent file for future use and. reference.

6. Extensive notes, diagrams, instruction materials, etc. are being developed by eacn instructor and will be given to each participant. Additional copfes will be made availabfe in the Engineering Library for anyone:wfshing to. use'. this inaterial.

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.. ' ;",.\tisable-':.to; limi.t.p.~cip-atiou'·~o this program to those who plan. to enrGtI on .. f"fUII.?artfc:ipaticn st~usrt·~. We' will, however, be receptive ~o' an. occasional" visitor':'wncr has-·a,.. p.articular interest in !!. specific session. r£: you' areim this. category J; we do ~ need the. enclosed questionnaire .. returned~ . < .-

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Transformer Fundamental Course Page 2.

8. ·It woulJ be advisable to equip yourself with a three-ring binder and note paper prior to the ficst session.

9. " The sessions will start promptly at 4 P.M., and it is our intention to stop at 6 P.M. or as the class dictates; you can plan your rides accordingly.

10. Mr. E. C. Wentz has been retained as a consultant to administer this program and he is now working with each instructor in the preparation of the course material. Mr. Wentz will be available on a scheduled basis after September 15 for private consultation on any matter relative to· the contents or problems associated with this educational program.

11. If you meet the general requirements outlined in the aforegoing

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.material and wish to participate fully and contribute to this program to the best of your ability, you are invited to return the enclosed questionnaire by September 3, 1966. There is no charge for this program; it represents a beginning series of educational programs for the personnel of the Transformer Division. You will be notified by bulletin board or direct notices as soon as final plans have been completed on other educational programs.

Mark your calendar -.!l2!. - using the accompanying schedule of pr.esentations as your guide.

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Westinghouse Lecture Series

1) Transformer Types and Applications 2) How a Transformer Works 3) Power Transformer Windings 4) Distribution of Impulse Voltages in Power Transformer Windings 5) Methods of Controlling Impulse Voltages 6) Insulating Materials, Stresses, Breakdown 7) Transformer Insulation Structures 8) Paper & Oil Insulation 9&10) Cores, Structure, Properties 11) Resistance, Reactance, Regulation 12) Calculation of Transformer Reactance 13) Losses and Stray Losses in Transformer Cores and Coils 14) Losses & Efficiency 15) Mechanical Forces On Short Circuit 16) Insulation Aging and Thermal Evaluation 17&18) Heat Transfer Theory 19&20) Application of Heat Transfer Principles to Transformer Cooling 21) Transformer Oil 22) Protection Against Overloads, Hot Oil, & Hot Spot Devices 23&24) Insulation Coordination 25) Detection of Faults in Transformer Equipment 26) Symmetrical Components 27) Equivalent Circuits of Transformers 28) Taps in Transformer Windings 29&30) Methods of Load Tap Changing 31) Designs of Preventive Auto Transformers 32) Design of Windings for Load Tap Changers 33) Regulating Transformers 34) Instrument Transformers 35) Testing ASA: Test Code, Test Schedule, and Equipment 36) Loss Measurement 37) Temperature Testing 38) Power Factor Tests of Oil Immersed Transformers 39&40) Economics of Transformer Application 43) Packing and Shipping 44) Installation of Power Transformers in the Field

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LECTURE 1:.

TRANSFORMER TYPES AND APPLICATIONS

by

W. T. Duboc

TABLE OF CONTENTS

Transformer Types and Applications ------------------------ Pages 1 to 4

Figure 1 Substation Transformer ------------------------- Page .5

Fi?ure 2 Substation Transformer with LTC ---------------- Page .5

Figure 3 Regulating Transformer (Small KVA) ------------- Page 6

Figure 4 Large Generator Transformer -------------------- Page 6

Figure 5 Autotransformer with LTC for Tie Between Lines - Page .7

Figure ·6 Furnace Transformer --------------~------------- Page 8

Figure 7 Rectiformer -------------------------.---------- Page 8

Figure 8 Ventilated ASL ------------------------------~-- Page .9

Figure· 9 Sealed ASL ------------------------------------- Page 10

Figure 10 Network Transformer -------------------------~ Page 10 ...

Figure 11 Cutatvay of Core Form Transformer --------------- Page 11

Figure 12 Cutaway of Shell Form Transformer -------------- Page 12 "

Figure 13 Past Developments in Shell Form Transformers --- Page 13

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TRI\..1\1SI'OR~ER TYPES AND APPLICATIONS

Since. the introduction of transformers in the first commercial alternating current syste~ at Great Barrington, Massachusetts in 1886, the power industry has grown to its present proportions. And it can be expected to continue to grow at its historical rate of doubling every 8 to 10 y~ars indefinitely. In the process, the need for specialized transformer types and chan:cteristics has also expanded and concurrently the requirement for more creative engineering and ingenuity has likewise expanded in order to s2.tisfy part:'cular specifications for each appli­cation.

There is little point in dwelling at length on the details of all the particular applications since many texts are available on this subject. I would refer you particularly to Chapter 5 of the "Transmission and Distribution" reference bookl and to Chapter 2 of Mr. ~ventz I s book2. It is worth,,,hile, however, to examine a feT

" of these applications with respect to their present limitations and the parameters which govern further development.

As discussed in the preceding l~cture, power is fed to the ultimate user of relatively small amour.ts through distr~bution transformers. The supply (high voltage) side of these units varies but is typicallY of'the order of 13 kv though thare are still a number of 2400 and 4160 volt systems in operation and a few at higher voltages. To feed these multiple distribution loads requireS a more centrally located substation transformer, such as sh,~wn in Figure 1, whi::h transforms power from transmission line voltag~s to distribution feeders in blocks of perhaps 1 to 20 or 30 mva, depending on the concentration of lOads. Quite frequently the practical aspects of load variation are such that voltage variation is required in this process to compensate for system impedance so the substation trans­former is sometimes equipped with a load tap changer (Figure 2) on the lines themselves, '...rith s.!:!parate regulating transformers (Figure 3) - the choice depands on economics, personsl preference on the part of the customer, tow the system has grown and the characteristics of the various types of loeds served.

The transmission lines serving the substations typically operate at voltages of 34.5 kv to 138 kv though occasionally isolated substations

lCentral Station Engineers of the Westinghouse Electric Corporation, East Pittsburgh, Pennsylvania,. Electrical "Transmission and Distr;i..bution" Reference Book, R:~ R;~. D"onnelley &. SonS' Comp3ny~ Chicago and Crawfordsville,. rndiana~ 1964 (fourth edition) o.

2Richard L~ Bean~ Nicholas Chackan, Harold R. Moore and Edward C. Wentz, nTransformerst~ for: the Electric Power Industry, HcGraw-HiIl Book Company, Inc." New York, 1959

Lecture 1: - Page 1

m<"!y be fed from higher voltages. In some cases, too, there may be a double stage reduction from a main high line voltage of say 345 kv to Several sub.- transmission voltages of perhaps 115 kv or 69 kv.

At the higher voltages, the blocks of power are, of course, somewhat greater with consequent increase in transformer kva, as well as kv, ratings. Generator transformers have been built as high as 725 mva, three phase, with larger units on order. As a rule, these units (Figure 4) are simple two-winding transformers directly connected through isolated phase bus duct to the generator. Voltage regulation is accomplished by generator excitation together with LTC equipment (if necessary) at the receiving end of the line and no circuit breakers are used between trans­former and generator because the additional flexibility is not worth the price for breakers which could handle fault currents in the event generators of the size in use today were bussed.

The foregoing has described a simple radial system independent of any others, which is seldom the case. In order to increase reliability and minimize margin requirements in total generating capability compared to peak load, many generating stations are tied together and, indeed, neighboring systems are also tied together. The characteristics of such tie transformers must be very carefully specified in order to effectively control both reactive and real power flow and-maintain system stability under possible fault conditions. These complications lead to all sorts of voltage and phase angle control requirements,. both of which require sophisticated load tap changer schemes. As a rule, too, these trans­formers are autotransformers. Since the ratio of nominal voltages typically varies from 1 to 1 (that is, phase angle regulator) to seldom more than 3 to 1, the use of an autotransformer permits greater power flow with a smaller unit in physi.cal size - see Figure 5.

There are also a number of' even more specialized applications in the power transformer field~ Electric arc furnaces require huge amounts of. current at quite~low __ voltages and this imposes unusual design require­ments. on the transformer (Figure 6) which supplies them. The aluminum. and chemical industries frequently require large blocks of direct current power at voltages of 1000- volts or less so the rectiformer (Figure 7) has been developed.where the transformer and associated silicon recifiers are packaged together. The transformer in this case usually has multiple windings in various combinations of wye, delta and/or zigzag connections to provide 6, 12 (or even more) phase voltage so that ripple will be minimized and they must also be extremely rugged mechanically.

Finally .. there: are the transformers used in special situations at the low end of the power transformer scale~ Industrial plants,. such as the- Sha-roru, Transformer Plant,. reqUire substantial quantities' of power for machine tools,., cranes, heating, elements, etc. Most 0 f these loads require voltages of 440 volts or less. Since it is highly uneconomic to distribute large blocks- of power at this voltage with acceptable line droIt,.: transformers (typically 4160 to- 440 -or 208) are strategically

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located throughout the Plant. Safety considerations rule out the use of oil-filled units (interestingly, this is true in this ~ountry but not 1~ Europe) so the dry type, either ventilated (Figure 8) or sealed (Figure 9) is frequently used. The same application holds for office and apartment buildings. Another special application is the network transformer (Figure 10) which is really different only in its application to a network system which provides the ultimate in continuity of power supply.

So much for the application of transformers, what about the forms and methods of construction? There are ttvO basic forms 'of construction in use though variations of each tend to make it difficult to distinguish which is used in some cases. These two, however, are core form (Figure 11) in which the windings surround the magnetic circui~d~ll form (Figure 12) in which the reverse is basically true. As will be developed later in this course, the core form construction is usually applied in a fashion such that the various windings are concentric with each other as well as the core, while the windings of the shell form - while concentric with each other - are usually interleaved with each other. There is no fundamental reason, however, why the high and low voltage windings cannot be interleaved on a core form transformer. Then too, the core form coils are generally (though not necessarily) circular in cross section while shell form are generally (again not necessarily) essentially rectangular. These considerations, though seemingly simple; have profound implications in the ease with which design requirements can be met and on shop con­struction practices.

Before proceeding to discuss these implications, the basic ground rules for transformer design and manufacture should be examined. There are just three fundamental considerations which must be kep·t in mind at all times:

1. Of' overriding importance is the matter of reliability. Power supply to the nation is accepted as being almost 100% reliable - when power is interrupted on any significant scale (that is, the Northeast blackout) serious disruptions iq essential services, even defense of the c0ll:ntry~ and massive inconvenience result. It follows that transformers, particularly the larger units~ which are an integral part of the power supply system must be built for mean times between failure of tens or even hundreds of years ••

z.. With reliability in mind, it. is,. of course, necessary that the system requirements (that" is, voltage, kva, impedance, LTC, etc.) must be met.

3. Once reliability and performance requirements are met,. it. follows that: these must. be: accomp-li'shed at: minimum cost if the manufacturer is to· stay. in: business.

UnfortunatelYr none. of: these. three basic philosophies can' be considered independently •. 'thus, while one desi'gn may have 1000%.. margin

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and is, th~r-=:fore, conceivably more reliable thun on,;: with 200/0 margin, it should probCibly be rej;;ctE.d if it is significantly moroe costly since the additional ~argin would most likely buy nothing in the way of increase~ life and woul<.l have no incremental value.

With the above discussion in mind, the application of shell and core form construction can be considered. Until the introduction of the interleaved (Hisercap) winding about 15 years ago, the core form winding clearly had less i~pulse voltage strength than did shell form. It also had (and probably has) less inherent mechanical strength to withstand short circ~i~ forces and the tricks that were necessary to solve the impulse voltage problem usually made the mechanical situation worse. On the oth:r hand, in the lower ratings- both voltage and kva - where sufficient nargin could be obtained, its inherently simpler insulation structure and resultant cost advantage dictated its use in these appli­cations. The shell form was thus reserved for those large units where its inherently good me~henical structure and good impulse distribution were particularly valuable.

Reliability, in this Cdse only mechanical strength to withstand short circu:"t stresses, hCiS also dictated the limits on the use of core form trans~o~ers with coils (and cere) of rectangular cross section. The leakage flux in this type of transformer is such that it tends to force the coils into a circle and if the coils are in some other con­figura~ion, they must be braced to withstand this force. Gradually, ways have been f~und to do this with osufficient margin so that the cost advantage arising fron the better, insulation space factor can reliably be used ~o advantage.

From a philosophic,al point of vieN~ the' foregoing very briefly describes the need for sound, engineering applied without. preconceived ideas yet wi~h mature judgnent and thorough attention to detail - the latter twc cannet be over-emphas~zed when it is remembered that the final proof of reliability is the fi~ld service record and no really significant data can be acquired in this respect fer 2 to 5 years after a basic design change is ~de. It follows t~at compiete; and if necessary elaborate, tests must be substituted to assure that no subtle problem has been over­looked in the development of a n~TN method or process.

Admittedly, e'lolutio!1ary dE:velop!Ilent of this nature is difficult but it can be dene as evidenced by the curve in Figure 13 and it must be conti!lued if this org=rnization is tc retain its leadership in the power transfcr:ner fi~ld. It is the purpose of this course to enhance your capability to do it. .

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DISTRIBUTION AND INSTRUME~~ TRANSFORMERS

TYPES AND APPLICATIONS

L. L. Wright Engineering Manager, D & I Engineering

CONTENTS

r--.-. J DISTRIBUTION TRANSFORMERS

Introduction

Types

Application

New Design Concepts

INSTRUMENT TRANSFORMERS

Introduction

Funct.ions

Potential Transformers

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Sharon, Pa. September, 1966

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DISTRIBUTION TRANSFORMERS

Introduction

The last link between the power-generation-complex and the ultimate consumer of power is a relatively small and inconspicuous device called a distribution transformer.

Yet for all its modest appearance, it is truly an unusual machine in almost every aspect.

Reliability, for example, is taken for granted: One utility company engineer: commented that "we hang them up and forget them: if they break down or falloff the pole before 20 years, that's too soon!"

Efficiency must be near perfect: for the iron loss goes on day and night continuously, and the "copper--loss" (or aluminum loss) rises as the square of the load that is carried. So the typical figure of 98% or better at full load is nO.ne too good .

Stamina~ the ability to withstand abuse; must be phenomenal. The various units on the system are scattered and unattended, they are sub­ject to sun and wind, to rain and sleet and hail, to heat storms and snow storms and sometimes to sandstorms; they are attacked by salt, fog and by corrosive: fumes from industrial smokestacks. Electrically they are subject to swings of voltage-level, to surges caused by switching or to direct strokes of lightning; and the load may be anything from zero to short-circuit. Mechanically they fare little better; in fact some line crews. have been known to unload them on site by kicking them off the t~il­gate of the truck!

Cost, nevertheless, must be kept to a competitive level. All of the features that make a distribution transformer last for 20 years or more must be built in, but not at the sacrifice of profitability.

AlL this must be in the thinking of the engineer who designs these devices--all this,· plus the technical problems of electrical and mechanical functioning. The engineer must be more than a technician; he must" be knowledgeable in many fields; .. perhaps even an artist!

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To understand the different kinds of distribution transformers, we break them down by type, depending on the choice of variable that is to be considered. For example, ,ve may refer to anyone of the following type classifications:

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Kind of AC Circuit

a. Single Phase--The most commonly used by far in the United States, both in urban and rural areas.

b. Th~ee Phase--Used mostly for industrial loads, or rural loads where large AC motors are required.

Hethod of Cooling and Insulating

a. ,Oil-filled. This is still the most commonly used" type. (Fig. 1) The oil has excellent insul~ting qualit~es; it penetrates into the fibrous sheet m~terials and improve> their.- electrical strength, and it flows by natural convection, thus transferring hea~ from coil to tank.

[fr. Dry TyPe-. The electrical components may be filled· " with a. solid material designed to exclude air, dirt and moisture. This results in'a simple design; easy' t·o handle~ sturdy mechanically, and free from any explosion hazard, Fig •. 2.. This is the fore-runner of th~ cast-solid coil design, to be described later.

3. Method of Protection

a. The "conventional" type. This has' no internar-protective gear ~ When installed, it may be connected to lightning arrester or fuse· cut-out, or both. Approximately half of aLL:. units made- _a:re of. this type._

br.;.>nie. '"self~prot.ected''' t:ype. This may include::

Lecture I-A

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2. A circuit breaker, for cutting off overloads before they can burn-out of the transformer. (To avoid customer outages as much as possible, a warning light is usually provided, which turns on well in advance of breaker trip-out.)

3. A specially-designed fuse called a "protective link", that clears any fault that may occur within the transformer itself. This link is, of course, not to protect the· transformer, but to protect the HV line against lock-out.

Tlle "Completely Self Protected" (CSP2. transformer includes all these devices. (Fig. 3)

Forerunner of "beautification", this transformer enabled users " to clean up the pole". (See Fig. 4) This took place 25 years before

public demand caused a.lot of excitement ab()ut this s.ubject. It is still one of the b.est ways available to the user to improve appearance of overhead!

4. Other types. Certain designations such as kind of magnetic circuit (shell-form or core-form) and electric-curr.ent-cir­cuit (Low-High, or Low-High-Low) will not be discussed here because they are part of specific design detail.

Athens designations relate to the kind of service that is expected of the transformer. These types will be covered in the section below.

Application

Pole Mounted

In the past~ the most common application by far, was the pole­mounte~unit which formed a. part of the overhead-line distribution system. In spite of the exposure to weather, to lightning, and to storm damage, this was long considered to be the only practical way, because it was the only way that_ was acceptable in cost_

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However~ within the past few years, new insulating materials have been-developed and new methods of trenching invented, that bring the cost of buried HVcircuits-within reasonable limits. Now we have a rapidly growing market for transformers to be used with this underground system. These have taken many different forms.

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One of the first to be used was "Pad Mounted Transformer ll• This

consists ofa 2-part steel' box, one part of which is closed and oil tight, to contain the core-coil assembly; the other part that is fitted with access doors, to contain the cables, bushings and all auxiliary equipment. (Fig., 5) The whole structure is mounted on a concrete II Pad" , with cables passing down into the ground through an opening in the pad. Such a con­struction keeps the transformer above grade level, so there is no require­ment for o?eration: \vhen submerged. It must be "kid-proof" since these units are not enclosed with a fence as our conventional substations.

A more recent design is the combination of a transformer with a street-light installation. The heavy concrete base for the light pole is made in the form of a hollow vault, in which the transformer is mounted. (Fig. 6) Above is a tapered section, which has window opening on the sides

'to afford ventilation, and a flat top to support the pole. This effectively conceals the transfurmer, makes it safe against tampering, and yet provides some cooling air. A new HV Bushing design, ,of plastic and rubber, makes pos'sible a plug-in connection that is so well sealed tllat it can operate when_s~b~erged under 10 feet of water.

Another variation of this installation is the Vault-mounted transformer. (Fig. 7) Here the hole in the earth is lined with a cylindrical tube made of asphalted paper or the like, and covered with a grating held b'y penta-headed bolts. (The 5-sided shape ia used to discourage tampering)._ Tarcper 'shields 'are used under the grating to help control the flow of air, and to prevent, ~ticks or wires from being inserted.

Most recent of a-lI,' and still in the planning stage', is the "Service­Unit ll design. Here the concept is to bring the HV circuit. literally to the, doors'tep: making the transformer either a build-in part of the wall, or mounted on an outside floor just a few feet from the wall. For compactness and convenience, the unit would contain part or all of the LV accessory equipment, such as the Watt-hour meter and the LV Switches. (Fig. 8) For safety it would contain no oil, but. would preferably be made with the cast-solid coil design (see below).

Such a design overcomes many of the problems of underground distribution,. eliminating secondary runs and the related voltage drop. It places- the transformer in an accessible location and in, an environment which is not detrementalto the' unit~

Since each unit:: serves: ana house il: does. not take advantage of the: load, diversity which a: unit that serves several homes can do.

Lectur.e I-A 4

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New Design Concepts

Not only the enclosing structure, but also the basic transformer core-and-coil assembly has been changed recently by new concepts. A few of the more important examples are as follows.

Capaciformer. The idea of using a capacitor in series with a transformer winding, to produce a phase-shift which will regulate voltage, is very old. But in the past, it was never ve~ practical to do this in actual installations, mostly because of the difficulty of protecting the capacitor. The trouble comes from the fact that voltage builds up across the capacitor in direct proportion to the current, so that even a momentary surge of current may break down the insulation. And if the capacitor is built as part of the transformer, then a failure in this one part makes the whole unit defective.

So this problem, and many others, had to be solved before it was possible to build the combination that we now call the"Capaciformer".

In this new design, the capacitor is wound directly into the HV coil~ so thac these turns serve both the function of producing voltage and providing capacitance. A diagram of the circuit is shown in Fig. 9. This makes it clear that there is no metallic circuit through the HV coil. Instead, this protion of the winding (a strip of aluminum foil) overlaps with another strip of foil, with a sheet of insulation between. The capacitance obtained in this way is sufficient to carry the normal load current of the transformer.

. As was mentioned before, the voltage that appears across the capacitor insulation may become high enough to puncture it. This will happen iI the current exceeds about 4 times normal for even a fraction of a cycle. To by-pass this current instantly, it is possible to design electronic gear that will work, but the cost is prohibitive. Instead of this, another device was developed of surprising simplicity. It consists of a closely­controlled air gap. about .020" long, formed between the edges of heavy copper bars, in combination with a strong field produced by permanent magnets·.. Such a gap will break down at about 1850 volts. The are, once formed, oscillates rapidly because of the alternating current direction, and this~ plus the- effective coaling of the arc terminals by the copper "heat sink.'" "" keeps .. the- arc voltage up- high enough so that it is self-extinguishing at about 1500 volts. This cut-off action, 'of course, is just as important as: the breakdown action; the combination makes this simple device an ideal protector for this particular application

Lecture l-A - 5 -~ . _____ ._______ ____ __ . ,.."1If:;.:"_ ."._ ... _

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Cast-Solid Coils The problem of encapsulating a coil in a solid material is simple mechanically; but electrical it is most difficult. This is because of the requirement to exclude eve~y particle of air, and to accomodate. the changing dimensions of the conductor as it expands with increasing temperature. It requires also adequate insulation at every turn and at the outer areas; and it requires means for making terminations and means for dissipating heat. All these problems are part of the development of a coil wound wi~h enameled aluminum foil and then impregnated and encapsulated in a special type of Epoxy resin. The appearance is shown in Fig. 10.

Ne~., Appearance Design. Although the underground system is the ultimate in improved appearance, yet much can be done to alleviate the .unsightliness of the overhead system. The clutter of crossarms, fuse cut-outs, lightning arresters, guy 'dires, and conductors at all angles accounts for much of the trouble. If this situation is cleaned up, and if the transformer is modified to blend in with the surroundings, a striking_ improvement can be obtained. One such proposed improvement is shown in Fig. 11.

Future Possibilities. When the coil design is perfected, it may be quita immune to the effects of water, .s~ it may be operated when sub­merged in water. To use water as a coolins medium wou~d greatly improve the cooling effect and thus further increase the permissible rating.

If we can. then combine this coil design with the new "die-formed" precision core~ the assembly could be made to include its own terminations. Then it could be slipped into a form-fit box, the cover welded on, and the

" .. transformer would then be complete. The name "ULTRAN 70" (Fig. 12) suggests a goal and a date for the long-range development. objective.

Lecture I-A - 6 -

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INSTRU}lliNT TRANSFORMERS

Introduction

Electric utilities derive revenue from the sale of electric power. This power is sold to customer~ at various voltage levels and for various periods of time according to the customers needs. In order to sell this power, the utilities must be able to measure accurately and simultaneously the power used and the duration of its use. Thus what utilities actually sell is electrical energy measured in kilowatthours by watthour meters.

Watthour - meter technology has advanced to a point where up to 200 amperes at 480 volts can be measured directly from the line.

But where current and voltages above 200 amperes or 480 volts must be measured, instrument transformers must first reduce the current and voltage to a safe metering level.

The policy of the particular utility will dictate the maximum voltage and current for direct metering. Some utilities, for example, will limit direct metering to 100 amperes at 240 volts and requir~ instrument transformers for all metering applications above these values.

Instrument transformers are needed for use with ammeters or voltmeters if the line current or voltage is higher than the instrument rating, and they are also used in connection with r~laying in control and protective circuits.

Thus the main applications of instrument transformers are in metering and relaying.

Functions of Instrument Transformers

Instrument transformers, both current and potential, perform two primary functions:

1. They provide secondary current or volta'ge in values suitable for standard instruments and meters. These' are normally 5 amperes and 12.0 voltsw

Z... They insulate the instruments and meters from the line voltage.

Lectqre l-A

FoX" the: safety of both the instrument and operating personnell the secondary circuit must be grounded.

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Po:e~tial Transformers

Voltage or potential transformers are connected in parallel with, or across the line, in order to transform line voltages down to the standard meter or relay ratings, 120 volts. A voltage transformer core and coil is practically the same as a small distribution transformer 1 Distribution transformers are sometimes used as potential transformers in the lOlver voltage

-classes, but the principal reason for wing a potential transformer generally is that it costs less, and because it is not actually as large a transformer.

The exact measurement of power requires that the secondary voltage be proportional to and 180 degrees out of phase with the primary voltage. Actually this relation is never exactly obtained; the secondary voltage is slightly less than would be predicated from the turns ratio, and is slightly. out of correct phase position. The deviation from correct magnitude is called ratio error; and the deviation from correct phase position, phase angle. These errors are caused by the voltage drop across the through impedance of the windings; which in turn is determined both by the magnitude of the winding impedance and the load current through the impedance.

The best design for small errors in a potential transformer will be that wi\:h low through impedance. This means ~ow winding resistance and reactance, which can be achieved by designing for a relatively high volts per turn to minumize the number of turns required.

.Westinghouse produces potential transformers from 10 l<.v BIL' (Basic Insulation Level) through 1300 BIL for use on circuit voltages from 120 volts through 345 KV. Potential transformers through 150 BIL are butyl molded, and the high ratings utilize an oil paper insulation system. Figures 1 & 2 show potential transformers typical of these two types of construction.

Current Transformers

Current transformers in order to step down line currents to values suitable for use with standard meters must be connected in series with the lines. Consequently, current transformers are independent of line voltage insofar as their turns ratio (primary to secondary) is concerned. This ratio is determined entirely by the relation of line current to standard meter or

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relay currents - almost universally 5 amperes. . .....

The exact. measurement of power- requires that the secondary current be proportional to and 180 degrees out of phase with.the primary current. As in f;he p<>tential transformer, this'relation is never exactly obtained. The secondary current is slightly less than would be predicted ,from the turns

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ratio and is slightly out of phase. These deviations are termed ratio error and phase angle respectively, but in the current transformer they are due to the fact that the secondary current output is deficient because of the ampere­turns lost in magnetizing the core.

A current transformer is entirely different in its operation than a potential t~ansformer. The primary current in a current transformer is whatever is flowing in the line. The secondary winding tries to put out the same ampere turns that the primary winding puts in, and the secondary voltage rises qccordingly to whatever is needed to force this current out through the meters and leads connected to the secondary. The reason the secondary winding, tries to put out the same ampere - turns is that if it falls below, the surplus ampere -turns in the primary winding induce a magnetic flux in the core which induces a voltage in the secondary in the proper direction to produce the ampere - turns. This phenomenon is described as Lenz J s la,.,1 T.vhich states that if a voltage is induced in any coil by a magnetic flux the current produced by the voltage tends to flow in a direction so that the ampere turns oppose the change in magnetic fl'ux.

But if a magnetic flux does have to flow in the core to induce the secondary voltage required to circulate the secondary current out through the meter, t.hen there will have to be some surplus of primary ampere - turns over the secondary ampere - turns to produce this flux. This surplus of , primary over secondary ampere - turns actually appears as a deficit in the secondary, and' we do everything we can to make this deficit as small as possible, because a current transforme~-approaches perfection when the secondary ampere-turns, representing current output, approach most nearly to the primary ampere turns, representing input.

In order to reduce the ampere - turns required to magnetize the core to the lowest possible value current transformers are designed with a.low volts/turn to keep the core induction low. A high quality core is most impQrtant, and the resistance and reactance of the windings, which are of major importance in causing the drop in voltage in a potential transformer, have relatively little to do with the error in a current transformer.

Westinghouse produces cu~rent transformers from 10 KV BIL through 1800 BIL for use on circuit voltages from 120 volts through 500 KV. Current transformers through 150 BIL are butyl molded, and the higher ratings utilize an oil paper insulation system. Figures 3, 4, & 5 show a 10 KV BIL through type current transformer, a 60 BIL outdoor butyl molded wound type, and an 650 BIL oil insulated unit respectively.

Lecture I-A - 13 -

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Through Type Current Transformer

Figure 3 is an example of a through type current transformer. This transformer doesn' 't have any primary winding at all, simply a hole for the customer to pass the primary cable through with the magnetic circuit carrying the secondary winding surrounding Jt. It might seem that a straight conductor through the core is only half a turn, but it mlS t be remembered that the primary conductor comes back to the source some~vhere, however far removed from the core, and eventually forms a complete turn around the core. This is such a handy arrangement we wonder at once why we don't use it for all current transformers.

The limitations of through type current transformers will be explained more throughly in the section on Instrument Transformers. For our purpose .it will be enough to intutively accept that the smaller the input ampere -turns to the transformer, the more difficult it is to reduce the core magnetizing ampere - turns (error) to any given percent of the input ampere -turns. Since the through type has only one primary turn, the input ampere turns are dictated by the current rating. In general through type transformers are not used below 200 primary amperes for typical metering burdens. This does not mean that through type transformers cannot be built for low primary current because they have been. If the impedance of the burden is low, the errors will be low. A through type transformer will work at any low current. if the burden is low enough.

In this brief. introduction t.o Instrument Transformers we have seen that the primary reason for their use is that meters to measure high voltage or current directly would waste more energy and would cost more to buy and use than the present. combination of transformers plus meters. Instrument transformers are such handy devices, and relatively so cheap that they are used everywher~.

Lecture I-A 14

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DE.::-:·7ITIONS AND NOHENCLAT"uRE

I; TRANSFORHER - ::. electric device, without continuously­moving parIJs., .... :,ch by electrcm2.;;netlc induotion trans­forms electric 6~~~gy £rom one or more circuits to one or more other ci::·::,·..:.iJc;s at the same frequency" usually with changed values of voltage and current.

2. DISTRIBUTIONTRANSFOR£iSR - any transformer having a ratangoe'c;\ieen j ana ?UU KVA inclusive" and all net­work transfor~ers.

3. pmmR TRANSFORrvIER - any transformer having a rating aoove ";X50KVA., except ne'c~'iork transi'or .. ,·ers.

4. AUTOTRANSFO.R:>:ER - a transi'ormer in \':hich part of the Vll.noJ.ng is COlT'~'1:0:l to both prir.-.a.ry and secondary circuits. A single-winding transi'orr:er.

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NET'tTORK TRA.'l-ISFOru.'fER - a distribution transformer suitable for use in a vau~~ to feed a variable capacity system of interconnected secondarles~

SUBSTATION TP~NSFOR!ljER - a transformer of the free-stand-ing type" a'"S""dl.i'i'eren_ciated from Unit substation Transformer. The terms substation and Power are very often used inter­changeably ..

T. .UNIT SUBSTATION TRANSFOF~mR - a transformer which is part ----~or_a_unit-subs_cat1.on ana mechanically- and electrically­

connected to and coordinated in design with one or mor~ switchgear or motor-control assemblies. or c'ombinations~ thereof.

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a. Secondary Unit-Substation Transformer - a transformer which 1.5 useO in a unl ~-st.:osta'i:;lon and has a low-vol t­age rating of 1500 volts or'below.

b .. , Primary Unit-Substation Transformer - a transrormer Which ia useO Ln a. w~~£-subs~aYlon and has a low-volt­aglarating of 1501 volts or above.

POLC-TYP& TRANSFOru·ffiR - is a transrormer with 125 KV BIL (18 KV busning volt;age rating) or less l 167 KVA and smaller" sing~e-phase" 150 KVA. and sma11er~ three-phase" \'Thlch is

·su1.table· ror- mounting on a pole or similar structure.

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DEFINITIONS AND NO~mNCLATURE (continued)

10. EIL - Basic Impulse Level (also referred .to as full-vlave impulse test) is reference insulation level, expressed as the impulse crest voltage of the nominal 1.5 x 40 micro­second I.'lave.

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(1st number is the time from start of the '.'lave to the instant of crest value, and the second number is the time from the start to the instant of half-crest value on the tail of the via ve. )

LOAD-TAP-CHANGTNG TRANSFORi·IER - (LTC) or (TCUL) - a pO\'ler trans:rormer wnicn incorporates a step regulator as an integral part of the unit and normally maintains a con­stant low-voltage with system variation of i 10%.

TRANFO UNIT - I-T-E trade mark for an integral.secondary unit su~tion, norrrally utilizing a molded-case circuit­breaker panel on the secondary side. A T&R division product.

13. NEMA - National Electrical 11anufacturers I Association -a:ilOrganization ot: electrical-equipment manufacturers whose object is to promote the standardization of electrical apparatus.

14. ASA'- American Standards Association - a national organiza­tlOn made up of a composite ot: committees from other standard associations; such as, N~~, National Bur~au or Standards, AIEE, etc.

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'0

LECTURE 2

TRANSFORMER FUNDA..~NTALS

by

E. C. Wentz

(1) How a Transformer Works Page 2

(2) Performance Characteristics Page 6

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TRANSFORMER FUNDA!~ENTALS

This isa course of study written for the express benefit of engineers working in the field of transformer design. However, it is not essentially a textbook on how to design transformers. It has been prepared to give the engineers a coordinated, unified, technical background in the fundamental principles \Vhich include the design and operation of. transformers.

As an introduction to the material\Vhich will follow, \Ve might first consider \Vhat a transformer is. The user of a simple transformer may well consider it to be a "black box" with t\Vo input terminals and two output terminals. The input terminals are connected to a source of a-c power at one voltage, and the output terminals are connected to a load which is to operate at a different voltage. The black box with the connected load is shown in Figure 1. The user's principal interest is in the po\Ver delivered, and in the voltage at which it is delivered. He is also interested in the reliability of his black box in with­standing all of the assaults of time, \Veather, overloads, and over­voltages. He has no apparent interest in what is inside the box.

Figure 1. An idealized external view of a transformer. The user is primarily concerned with the transformer as seen from the outside, while the designer is concerned with the inside of .the Hblack box".

The designer of the transformer, on the other hand, thinks of the transformer as the structure inside the box, as_ shown schematically in Figure 2. He sees the input terminals which he calls the "primary" connected to a coil of wire wound around a core of iron, and a second coil logically called the "secondary'" wound around the same core. He directs his: attention toward designing these elements so that the maximum power will be transformed from the primary to the secondary coil and delivered to the secondary terminals,. remembering that they must perform this- function reliably during continuous assaults by the condi'-­tions mentioned above. He has no--apparent interest in the origin of the external conditions, but he must know what they are if he is to make a satisfactory design.

Lecture 2~ page 1

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Figure 2. The transformer as seen from the inside. The simple transformer consists of an iron core with t~"o

separate windings that are wound around the core. When the voltage EI is applied to the turns of the primary winding, the voltage E2 is induced in the secondary turns by electromagnetic induction. If the voltage induced in the primary winding at any instant is directed from H2 to HI, the voltage in the secondary winding will be directed from X2 ·to Xl, because the winding from X2 to Xl goes around the core in the same direction as the winding from HZ to HI. We say that HI and Xl have the same polarity, and the designations HI and Xl are assigned. according to the ASA Standards to these terminals because they have the same polarity.

The actual conditions of design and use of a transformer are not nearly as simple as has been implied. Both user and designer will benefit from mutual knowledge of both the internal and external condi­tions governing operation of a transformer.

1. HOW A TRANSFORMER WORKS

The answers to the current and voltage relationships in a trans­former and to other simple questions are taken for granted by many engineers, but a real understanding of the answers to these apparently simple questions is basic to the understanding of transformers in general. Many engineers consider that such questions need not even be asked~. much less. answered. The· importance of a clear understanding of these basic concepts,. however,. justifies. a detailed discussion and clarifi.cation.

a_ Equilibrium between Magnetic Flux, Induced Voltage and Exciting Current_ When a voltage is applied to the primary terminals of the transformer of Figure 2, a current will flow in the primary winding, and a vol~age will be induced in the secondary winding. The current that flows in the primary ,,,inding is mysteriously limited by the presence of the iron core. If a load is connected to the secondary

......

terminals, a current will ,flO\~ in the secondary winding. The' primary current will increase at ,the inst~nt that tpe secondary current begins to flow. Th'e-'reas6n fc)t~,,-th~'s' ac't~on is' riot' apparent.

h. The Transformer with D-C Voltage Applied. It is easier to follow the r,~lation 'be~e~).'1 current and voltage in the windings if we first study what happenswhen'w;e apply a continuous direct voltage to the primary terminals rather' than 'the usual alternating voltage. This will also help to explain the:'more comp~icated transient relations which will be discussed later. :

When a voltage is C:pplied to the'pr'finary termina~s, current starts to flow in the primary winding. CufrJent~ "flowing, in the' winding produ~_es_a_I)Jg_gnetic flux in the i~on cor~-J/

..... - .-- .--- _._----- --~;.-.~/

The flux in the core will increase until the ~urrent has reached its steady~state d-c value •. , Tb.e'fa~t'that tIre flux is increasing means that a v~ltage is induced in the turns of the winding by electro­magnetic induction. By Lenz's law, the induced voltage is in a direction opposing the current that causes it,i~, the first place. This opposing effect ~~1l let toe'current increase just en-otigh ,to" keep the flux increasing sufficiently to induce the opposing voltage ,to balance the applied voltage. Figure·3 shows the four quantities that are in a four­way equilibrium:, 0) ,applied v?ltag~~,; (2) curr.ent, (3) rate of increase of flux due to the .. cu;rrene, and; (4) ~onsequent induced vol tage. ' :-. . ': ..: ~

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When a d-c yolta'ge is first applied to the coil terminals, onIy' a small current i~' ,,~·eq4J..red to' produce enough flux to induce the counter voltage equal to the applied voltage. After the current has increased sufficiently, the voltage required by the ohmic resistance of the winding will become appreciable'.' ,When- the flux has' increased to approach the saturation value,of the core,' the- current required to cause further increase of the flux will be mUch'larger; somewhat as shown by the curve in Figure 3. After the maximum flux, ';'(almos't, the saturation point) has been established, the induced voltage disappears ,and' the current will be equal to the applied Vol tage- divided b~ the ohmic resistance 'of ·the primary winding. ,T~e magnetic. pro'perties of the core and the mathemat­ical relations of flux, .current,.. turns~ and voltage will be covered in more detail in. la ter: lec~res. . - , ,; "

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f c. Equilibrium with A,lternating Voltage Appliecf.' Now it will be I easier to see What happens ,if an.·;:rl.ternating ,voltage, is applied. Again I a curren't sta~ts. ~o ,f~~w»' _~~jshown~,ino Figure 4, and again the ·rate of

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. (lrt· is assumed'that:, the- reader understands the! basic ideas of electro-'irur(netism; how current flowing in a coil produces magnetic flux, and how this increasing magnetic flux induces a voltage in that coil. The ideas expounded here a,re in. some respects. over-simplified' in order to make a beginning. " >

~. . '" .. . - ,Lecture 2, Page 3

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Figure 3. Four-way equilibrium when. direct current ~s applied to the primary terminals., A small current is required to produce the flux to induce the co~nter voltage equal. to the applied voltage when the direct current is first applied to the primary terminals. Aftel! some tima tt the flux :tn the core approaches the saturation value,. and at time tz the current has., , increased several times. At time t3 the core is nearly

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curren~ isc limited:, only by the ohmi.c- resi$.tance of the­primary winding.. trp ta time tl the' current is limited' principally by the induced voltage. Afte~ t2 the current is limited' principally by the ohmic resistance of the winding~ _

8-. Current-flux- saturation curve b. Induced voltage = rate of change of flux x 15 x 0.8

(for this problem) c. Resistive volts = IR = current x 0.15 ohm

(for this problem) .dr Magnetic flux:

j e. Induced'voltage plus resistive voltage = (::.

applied vol tage.·

Lecture ~ ~ page' 4.',

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iQcrease in magnetic flux induces an opposing voltage. The applied voltage, the current, the rate of change of flux, and the consequent induced voltage are again in four-way equilibrium. The difference between the a-c and the d-c condition is the flux reversal. Although the flux continues to increase as long as the a-c voltage acts in the same direction, it starts to decrease as soon as the a-c voltage reverses, because the rate of change of flux corresponds to induced voltage. Thus, the flux is also alternating, as shown in Figure 4, but is 900 out of phase with the voltage. Transformers are always designed so that the flux never saturates the core, and the no-load or exciting curre!F is ,_~.

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,ts Figure~. Equilibrium between current, flux, induced voltage, and -applied voltage when alternating current is applied to the primary winding. In this figure the resistance in the winding

. is· aS8~ed to be negligible, an assumption justified by the facts in .ill transformers used i~ the electric power industry~ The applied a-c'voltage is balanced by the voltage induced by the flux in. the. windings.

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Lecture 2~ Page 5

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d. Iguilibrium when the Transformer Is Loaded. 'Closing 0 f the switch in Figure 5 will conn~ct a load to the secondary. A current will tend to flow in the secondary circuit, corresponding to the secondary voltage divided by the impedance of the s~condary circuit. However, the current flowing in the secondary coil tends to produce a flux of its own in the core. We have seen that the primary circuit will supply any current necessary to ITLqintain the flux in the primary coil of a value sufficient to induce the primary voltage. Therefore, the primary coil in effect 3ens~s the current flowing in the secondary coil because the secondary current t~nds to change the flux in the core, permitting primary curr~nt to flow in suffici~nt amounts to maintain the primary coil flux 2t substantially the original value. The result is that additional ~urrent flows into the primary whan the secondary is connected to a load.

Th~ primary current then increases until it is greater than the secondary current ~y such a value that the difference in ampere turns is able to maintain the same magnetic flux. There still exists a four-way equilibrium; the primary ampere turns are greater than the secondary :lmpere turns by an amount that the difference between primary and se~ondary ampEre turns will force snough magnetic flux through the core to induce sufficient voltage in the primary (with the ohmic resistance voltage drop in the primary) to balance the applied voltage. Figure 5 shows this Equilibriu..'Il. This t::quilibrium explains ~.,hy the transformer will draw additional primary current only ~.,hen the secondary is connec­ted to a load.

2.. PERFOR."A.fANCE CF..ARACTERISTICS

Many other things !:ire happening within the transformer at the same time. Tlie vortage is stressing the insulation on the turns of the winding. The core expands and contracts ever so slightly each time it is magnetized. This expansion and contract~on produces the audible hum associated with transformers., Currents are induced in the iron of the core itself and cause part of the input power to be lost as eddy-current loss which adds

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to the hysteresis loss; the surne of which is known as iron loss or no-load loss. The currents flow through the resistances of the windings to produce copper foss~ or load loss, and the magnetically opposing nature of the currents, as. in Figure 5, causes some of the magnetic flux to leave­the core as leakage flux which in turn causes, stray losses in both core and windings. The leakage fl~x also is lost to the secondary coil and does not induce voltage in all its turns, having the same effect as if a reactor were introduced into the circuit. This leakage reactance together with the resistances of the windings cause a loss in voltage at the secondary terminals known as regulation.l Current flow in the 'windings causes then ta repel,eaen other by electromagnetic force.

lFigure 5 is oversiniplified in: that it does not show the leakage flux or any drop' in secondary voltage when the load is connected.

Lecture 2~ Page 6

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Figure 5~ Variation of current and voltage when the secondary switch is closed. When the secondary current starts to flow, the primary current increases. The primary current is greater than the secondary current so tha_t the difference in ampere turns is able to maintain the same magnetic flux in the core.

Because of all the losses the windings and the core both begin to heat. Care must be taken to dissipate this heat and to design the insulation so that it will not be damaged by the temperature rise which finally results. -

All these performance characteristics must be understood by the user if he is to specify them correctly and obtain a transformer which will adequately supply power to his load. They must be even better understood by the designer if he is to design transformers which will have adequate characteristics.

The changes in temperature, the mechanical forces, the vibration, and the natural influences such as lightning and all types of weather tend to cause deterioration of one or more elements of the structure.-The characteristic which might be called serviceability is difficult to measure, but it is of utmost importance. All these charac-teristics are discussed in more detail in subseque~t lecturea. They are discussed by transformer designers,. but the intent is to aid the users of transformers in understanding what goes on inside the transformers they use_

Lecture 2, Page 7

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PROBLEHS FOR LECTURE

ELEHENTARY THEORY

(1) Assuming that you know what a transformer is', make a list of

the service conditions which you think will be important for the desig~er

to cons ider.

(Check later in the course to see that they are all covered.)

(2) Make a list of the performance characteristics which you

would specify for the designer to work to assuming nothing to be

standard.

(Check later in this course to see that they are all covered.)

(Check later in the course to see how many were covered that you

didn't even think of.)

'. Lecture 2, page 8

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TRANSFORMER FUNDAMENTALS COURSE

Lecture 2 Elementary Theory

Answers to Questions

Service a. The

l. 2. 3. 4. 5.

Conditions line to be connected to the Voltage, rated or nominal. Frequency. Phases. Grounding. Possible overvoltages. (a) Rated frequency. (b) Switching surges. (c) Lightning.

primary:

b. The load to be connected to the secondary: 1. Voltage, rated or nominal. 2. Frequency. 3. Phases. 4. Grounding. 5. Possible overvoltages.

(a) Rated frequency. (b) Switching surges. (c) Lightning.

6. Loading and duty cycle.

c. Tertiary - same factors.

d. Location and environment: 1. Pole-top, surface, underground, underwater, etc. 2. Atmospheric condition, indoor, outdoor, altitude, ambient

temperature, etc.

e. The cost of power.

(2) Performance Characteristics to be Specified

If the service conditions are specified, and if there are no standards, about all you can do is to tell the designer to design for maximum economy in light of service conditions. You can't specify KVA, temperature rise, noise level, BIL, losses, impedance, or anything unless you have standards. You must specify wye or delta, neutral grounding, and taps.

Not many people got this idea but perhaps the questions were not too clear.

The indifference to the number of phases is amazing.

E. C. Wentz 11-8-66

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TRANSFOru'lliR FU~Ufu~NTALS COURSE

LECTURE NO. 3 Earl W. Tipton

POWER TRANSFOR}lliR WINDINGS

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TABLE OF CONTENTS

I Defini tions ...........•••.....•...••••.••••.•...........•... II Primary and Secondary Functions .......•..•••.............•..

III Types .....•.•................•.............................. A. Classification by Coupling Configuration .............. . B. Classification by Shape ......•......................... C. Classification by Turn Arrangement .................•...

IV Winding Design ....•.•.....•..•.•...••.••....•................ A. Round Concentric Layer Wound Windings ........•.••.•..•.

1. Cylindrical .•.....•.....••.•..............•.•..... 2. Lowgrocap ...•..........•.............•............ 3. High Vol tage Layer ............................... . 4. Pozaryski .•............•....•.....................

B. Round Concentric Disc Windings ........................ . 1. Continuous ....................................... . 2. Double Section .......... : ........................ . 3. Hisercap .•...........•..••...•...................•

I. Twin Interleaved ...•.•..• -..•...............•. II. Single Interleaved •.•...•.••.......•......•..

III. Daub Ie Inter leaved •••.••.••...••.•.•.•....•.• IV. Mutually Twin Interleaved ••.....•..•.••..•... V. Mutually Twin Mixed Interleaved •.••..........

VI. Mutually Single Mixed Interleaved ........... . C. Round Concentric Spiral Windings .•..........••••...•••.

1. Heli tran Daub Ie Group •.•••.••••.....••••.•••••.•.• 2. Helitran Single Group ••••.••.•••••....••• ~ •.•.....

D. Round Concentric Combination Layer-Disc Windings ...... . 1. Round Wire Would Coi Is ••••••.••.•••.•••.•.......•. -2. Basket Windings •. _ •..••••••• ~ •.••............•...•••.

E. Rectangular Concentric Layer Windings ..•••..•..•...•... , 1. Strap Wound ..•.••.••...••••••••.•••••.••.....•.•..

2. Sheet or Foil Windings ............................ . F. Rectangular Interleaved Windings .•• ~ .•.............•..•

1. S trap Wound •.•......•...••.•..•.•....••...•.•..... 2. Sheet or Plate ••..•...•..••••.•.....•.•..•......•.. 3. Spiral •.•••.••.••.••••••••.•.•••.••.•••..•..•....• 4.. Roebel ••••••••..••.•.•••.••••..•••..•.••...........

G. Round Interleaved Windings •.•.•.••••••.•.•••.•...•..•.• 1. Core Form •••••••••••••••••••••••••.•.••..••.•..••. 2_ Shell Form ••••••••••••••••.•••••••.••.••••••...•••

V. Photographs (Figures No. 1 to 20)-•••••••••••••••.•..•••••• VI. Appendixes •••••••• _ .-••••••• ~ ••••••••• ~ •••••••. ' .•.•••..•••••

VII. VIII •

1. Surge Voltage Distribution Continuous Windings .• _2~ Surge Voltage Distribution - Lowgrocap Windings .•.

3. Surge,Voltage Distribution - Hisercap Windings ••.• Bibliography ..••••••••••••••••• _ ••••.•••••••••••••••••.•••• Prob 1 ems ................... ' ......................................................... .

Page No.

1 1 2 2 3 4 5 5 5

16 18 21 24 24 28 29 29 32 33 34 36 37 38 38

- .. 42 .-:>:

44 44 46 49 49 51 53 53 61 62 63 68 68 69 71 75 75 77 78 80 82

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Transformer Windings

I Defini tions

A brief review of transformer fundamentals will be useful in intro­ducing the subject of transformer windings. In its simplest form, a transformer consists of a magnetic circuit closed on itself into a loop, which is capable of containing a strong magnetic field. Linking the magnetic loop are two coils of current conducting material. The Odd Fellows Lodge three link emblem is also a good transformer diagram \vith the center link being magnetic material and the two outer ones being electrical conductors. The two loops of current conducting material are called the transformer windings or coils. One of the two windings is connected to a source of voltage supply and this is called the primary winding. The second winding is connected to a load and this is the se­condary winding.

II Primary and Secondary Functions of Windin~s

A transformer winding has two primary functions:

1. To carry current. 2. The primary winding to induce a magnetic field in the magnetic

circuit with an induction proportional to the supply circuit voltage and to the number of turns in the primary winding. The secondary winding to have induced a terminal voltage pro­portional to the induction in the magnetic circuit and to the number of turns in the winding.

The second of these two functions although expressed differently for the primary and seco~dary windings ~s really the same function, since 'the transformer is capable of operation in reverse with the functions of the two windings interchanged •

A transformer winding has a number of important secondary functions, which must be successfully performed to enable it to perform its primary functions. The more important of these secondary functions include:

1. The winding must maintain electrical insulation between turns, sections, laye~s, other coils and to ground. This insulation must be good enough for manufacturer's test voltages at power frequencies, operacing voltages at power frequencies, and also for high frequency voltage disturbances, which occur in service because of lightning or switching operations.

2. Windings have electrical resistance to current flow and are loss generators when carrying current. The winding must dissipate these losses with a temperature rise limited to a value which will

. not damage the electrical insulating materials.

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3. Transformer windings operate in a strong magnetic field when loaded. This field causes losses due to eddy currents and circulating currents over and above the losses due to the d.c. resistance of the conductor material. The coils must be de­signed to have an economical minimum loss.

4" When one ,,,inding of a transformer is short circuited, the windings may be subjected to very high mechanical forces. Windings must have sufficient mechanical strength to withstand these forces without dama~efor a time long enough to permit protective equipment to operate. In practice, this means that the coils as a ,,,hole and all its parts individually must not move nor distort under the short circuit forces.

III Types of Windings

There are a great many ,vays of classifying transformer winding. The one which will be used here is distinguished chiefly by the fact that it is just one of the many 'vays. A fundame-ntal classification can be based on the method use to obtain close magnetic coupling bet,veen the primary and secondary windings.

A Classification by Coupling Configuration

1.· Concentric Windings. 2. Interleaved Windings.

Figure No. 21 Figure No. 22

Concentric windings, as the name implies, are those in which one winding fits inside the other and is coaxial with it. Figure No. 21 shows a typical example with round low voltage coil placed around a leg of the magnetic circuit or core and a round high voltage coil located around the low voltage coil. The term is used also for rectangular coils where one coil fi ts inside the other. Concentric ,vi ndings are typical of the core form construction although interleaved windings are also used to a limited extent. With few exceptions, only one group of high voltage and one group of low voltage coils per core leg are used in power trans­formers .

Interleaved windings are characterized by a single s~,ck of coils with alternate ·groups of high voltage and low voltage coils as sho\o/TI in Figure No. 22. These windings are typical of the shell form of construc­tion, al.though concentric wind ings- are used to a I imi ted exten t. The more groups used per w~ding, the better the coupling and the lmver the reactance of the transformer.

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FIG. NO. 22 - INTERL~1yt1~~frp.I~G

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B. Classification by Shape

1. Round 2. Rectangular 3. Oval 4. D-Shaped

, Transformer coils have been wound on moulds of many different shapes

and the list above is not all inclusive. The great majority of windings, however, are either round or rectangular. In Westinghouse, power trans­former practice rectangular interleaved windings are used for shell form transformers, which is the standard design for transformers rated 30 MVA or larger. Round concentric coils are used for core form power trans­formers in the size range from 2.5 to 30 MVA. Smaller core form power transformers, up to 2.5 MVA, use concentric rectangular coils.

At one time a line of single phase transformers were made with D­shaped concentric windings. When two such windings were located back to back on opposite legs of the core, the transformer fitted well into a round tank.

C. Classification by Turn Arrangement

1. Layer Windings 2. Disc Windings 3'. Spiral Windings 4. Combination Layer-Disc Windings.

In a layer winding the conductor turns are wound side by side in a tight spiral on a mould. Over the first layer of wire is placed a layer of insulation and then a second layer of conductors as in a bobbin, A coil may consist of from 1 to 20 or more layers of wire. Some specific kinds of winding of this classification are cylindrical, Lowgrocap, Pozaryski, and high voltage layer windings. These will be described in detail later.

Disc windings consist of a stack of disc shaped ,vinding sections separated by spacers. Each section is a flat spiral winding made with a rectangular conductor wound in a tight spiral, like a watch spring. The' thickness of the disc being the same as the insulated width of the conductor. The complete winding may consist of from one to 100 or more discs. Windings, which fall in this classification are the continuous panc~ke. basket.and Hisercap windings •

.In external appearance, spiral windings look like disc windings in . which each section has. a slight pitch. The conductor consists of a rec­tangular group of rectangular straps, all of which are in parallel. The group of conductors is wound on edge in a spiral with the turns separated by spacers.

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Each turn is shaped like a spring lock washer. Windings of this type are the single and double group Helitran coils.

Some windings consist of a combination of the 1ay~r and disc type windings. A small coil of the layer type is wound in which the axial dimension is small compared to t~8 mean radius. The conductor may be either a round wire or a small rectangu1£r wire. The complete winding consists of a sta:k of these coils in which each coil is separated from the adjacent

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one by spacers. Examples are round wire coils and part coils used in rec­tangular windings.

IV Winding Design

In the following discussion the various types of ~vinding ~vill be con­sidered one by one from the design view point. The design problems and appropriate solutions for each type of winding will be given under the headings:

a. Construction b. Current and Voltage Limits c. Insulation

Voltage Stresses Minor Insulation Major Insulation

d. Limitation of Losses e. Transpositions

f. Taps g. Cooling h. Mechanical Strength 1. Advantages j. Disadvantages

ARound Concentric Layer-Wound Windings

1. Cylindrical Figure No. 4

a. Construction

Cylindrical coils are wound with from one to sixty or more flat copper or aluminum straps arranged in a rectangular cross section from one to three straps thick and from one to twenty straps wide. The turn dimen­sions vary between 1/32 and 1/2 inches in thickness and from l/a to 5 or 6 inches in width. The turn is a butted spiral wound on a cylindrical insulating tube with from 1 to 6 or more layers. Commonly, the coils have two or four layers so that both leads come out at the top of the coil. Since the winding is spiraled, the axial length of a layer is equal to (n + l)W., where n is the turns per layer and W the insulated

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Figure No. 23

width of one turn. If the turn becomes quite wide, o~ it does for heavy currents, the lead may be split so that one half is taken off on one side of the coil and the other on-the'side diametrically opposite.the first.' By thi,smeans, the axial length of the coil becomes (n + 1/2)W. The two halves of the lead are than connected outside the coil •

b. Current and Voltage Limits

Cylindrical coils do not have any serious limitation because of current rating. Turns may vary in size from a single round wire to a turn 1/2 x 6 inches. The width may go up to perhaps 10 inches with a split lead. Current may vary from about 2 to 5000 amperes per turn.

Westinghouse practice limits the use of simple cylindrical coils to a maximum of 15 KV with a basic impulse level of 110 KV full wave impulse test. Because of the electrostatically induced voltage on the end of a low voltage coil when the high voltage coil is impulse tested, the cy­lindrical coil is not used when the high voltage exceeds the 69 KV class.

In service transformer windings are subjected not only to the low frequency (60 cycle) power voltages but also to impulse voltages due to lightning and switching. Lightning voltages are high frequency pheno­mena. The standard test voltage for defining a transformer's resistance to lightning is a wave rising to crest value in 1 1/2 micro - seconds and falling to half value in 40 micro seconds. The basic impulse level is the maximum crest value E, which the transformer is designed to withstand when tested with such a wave.

Unlike the power frequency 'voltages, which are uniformly distributed across all turns of the winding, impulse voltages are non-uniformly distributed. The inductance of the winding acts like an open circuit or

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infinite impedance to an impulse wave because the inductive reactance is equal to 2nfL, and in comparison to the 60 cycle wave an impulse represents a frequency at least 2000 times as great. As a result, an impulse wave distributes across the winding in accordance with a hyperbolic function of a.constant:

ex = -..JCG/CS Where:

CG = The winding capacitance to ground.

Cs. = The series capacitance through the winding.

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The higher the value of a the greater the proportion o£ the voltage that is concentrated across the turns near the end of the winding. It can be seen that it is desirable to keep CG as low as possible and Cs as high as possible. These last two paragraphs are included here because impulse strength is a primary factor in coil design. These facts should be ac­cepted on faith until the mathematical and physical development is made later in the course.

There are a number of mechanical limitations on cylindrical coils required for manufacturing reasons:

Maximum single conductor strand .182 inches thick Maximum width of single conductor .580 inches Minumum square wire .091 Conductors on edge: minimum thickness .144 and not more than two sizes from square When the conductor is more than one strand thick the width of each

strap must be a't least t\vice the thickness and not less than .204 inches. The width of the narrQ1;vest strap not more than t\VO sizes less than the widest one.

c. Insulation

In discussing coil insulation, 'it is convenient to refer to minor insulation covering insulation between the internal parts of the coil, such as turns, layers~ sections, and to major insulation referring to the insulation fro~ ground and other windings.

There are three minor stresses to consider in cylindrical coils: strand to strand; turn to turn and layer to layer. Considering power fre­quencies, all windings are tested by an induced voltage of twice the nor­mal volts per turn. Even in the largest cylindrical coil this would seldom exceed 100 volts. The layer to layer, stress is equal to:

2n x 2' VT = 4nVT Where

n = turns per layer VT = normal volts per turn of the winding

Stres's between strands of the conductor is very low being only that due to eddy currents.

When impulse voltages are considered, the coil capacitances become important_ The capacitance of a condenser formed by two metal plates:

- 7 -

C = .224 A K d

C = capacitance A = area of the d = Separation

where

in micro-micro farads plates in Sq. In.

in In. K = SIC of the material between the plates

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capacitance turn to turn along the first layer is quite low. Figure No. 25 The area of the plates is small since only the edges of the turn are ad­jacent. Also all the turns capacitances are in series so that the series ~ capacitance through the layer is inversely proportional to the number of turns in the layer. From layer to layer the area of the condenser is large and all the capacitances add since they are in parallel.

When impulse voltages are applied, the stress across the first layer is non- uniform and the turns at the line end may have several times their proportional share of the voltage applied~ The voltage between strands of the conductor may be considerable but will be less than the turn to turn stress.

From layer to layer, the insulation is usually made strong enough for the total impulse voltage applied to the winding.

The major stresses to ground are equal to the applied test voltages both impulse and power frequency.

The turn to turn insulation in cylindrical coils consists of layers of paper tape applied to the individual conductor strands. For mechanical rea­sons a minimum of .018 paper is used between turns and strands, ea~h con­ductor being taped with three butted layers of paper tape .003 inches thick.

_This insulation has a breakdown strength of 8.5 KV at. 60 cycles and an im­pulse strength of 25 KV~ which is more than adequate for transformers :1.1'1 the 8.7 KV class.

Layer insulation consists of sheets of pressboard, which are wrapped around the. coil between layers. At each end of the layer is placed a collar of insulating ma'terial which fits ,the pitch of the winding and. is's'quare "at the other end~ This collar is made long enough to stand the major stress to ground. Layer insulation is wide enough to extend to the outer end of the collar. This provides a strength against creep around the layer insulation from layer to

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layer at least equal to the puncture strength of the layer insulation.

d. Losses

In coil design,the losses which are a problem are the stray or eddy losses, which are due to the leakage flux which cuts through the conductor; or, to circulating currents in parallel paths through the winding. The size of the individual conductors is limited by the forces required to wind it into the coil. As a result, several strands in parallel must be. used for heavy currents. Each of these strands must have the same impedance if the current is to divide equally~ Consider a cylindrical low voltage coil wi th a lo~.; vol tage turn made up of two layers of wire in parallel. The reactance of the winding is proportional to its distance from the high voltage winding. It can be run then that the layer next to the high voltage has a lower impedance then the second layer and hence, will carry more than its share of the load •. To correct this situatio~, the strands of the conductor must be transposed so that each has the same average spacing to t~e high voltage.

Methods of Transposing

Figure No. 27

To reduce eddy losses the turns in cylindrical coils are made up of individual strands which usually are not over .182 thick. The total turn may be made up of from one to four of these strands, one over the other. IQ order to be effective the turn must be transposed so that each layer of strands has the same average spacing to the other windings. There are many ways of doing so in cylindrical coils:

1. By paralleling layers 2. By paralleling section of layers 3. By twisting conductors at the center of layers. 4. By turning the conductor over between layers. 5. By a Helitran transposition between layers.

(1) Paralleling layers

Figure No. 28 illustrates this method. The coil consists of four layers of conductor only one strand deep. By connecting at the layers end between layers I and 4, and layers 2 and 3, then layers Land 3 can be para­lleled with layers I and 4 because the average spacing to the high is equal. OQ single phase transformers a similar effect is given by paralleling the two legs.

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(2) Paralleling Sections of Layers

In Figure No. 29, a two layer coil is illustrated. Each layer is but one conductor high. Half the first layer is wound then a lead is brought out through a slot in a collar between the two halves and the turn is cut. A se­cond layer is wound over the first and at the center of the coil it drops down and forms the lower half of the first layer. Finally the conductor is welded to the finish of the upper half of the first layer and another half layer is

.wound on top of the bottom half of the first layer. When completed, the two layers can be paralleled.

(3) By Twisting Conductors at Center of Layers

This type of transposition is made in two ways depending on the dimen­sions of the conductor. When the thickness of the two strands is about equal to the width of each Figure No. 30 applies. The transposition is made at the center of each layer by twisting the turn 1800 so that the top strand becomes the bottom. Allowance must be made for a thickness equal to the diagonal of the conductor.

If the two strand turn is wide compared to its thickness the transposil:ion is ·made by bending the top strand o~t a~d. down, then under the bottom one. Allowance, must be- made for an extra strand width in the length of the coil. See Figure No. 31.

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(4) Turning Conductor Over Between Layers

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This transposition illustrated in Figure No. 32 is a very good one, but rather expensive since the'wires must be cut after the transposition and re­brazed. As shown, after the last turn of the first layer is wound the con­ductor is bent out parallel to the axis of the coil, folded back on its sel£, again bent at 90° and the next layer started. The inner strands of the first layer become the outer strands of the second layer.

This transposition can be used for turns with any number of strands in thickness and width. It has a mechanical advantage in that when the second layer starts the conductor is already raised to the proper level and there is no scissors action tending to cut the conductor insulation.

b a

Figure No. 32

- 11 -

3

Position of strands before and after transposition

(5) He'litran Transposition

A B C

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A B C

Figure No. 33

The helitran transposition is made at or near the crossover between layers. Two strands wide and t,-lO high are illustrated in Figure No. 33. Mechanically, each transposition is made by shifting the top strand from one group to the adjacent group and at the same time moving the bottom wire of the second under the first. When this is done twice, the top strands have been moved to the bottom. The strands of _the conductor must be arranged so that they can be divided in groups of t,-lO or/ and three in width and all strands within a group must be of the same width.

This is a good- low cost transposition. It requires an allowance for one extra strand in thickness. Conductora do not have to be cut.

f. Taps

When the. cyliiidtical coil is an outside winding,- the taps are most conveniently taken out at the center of the outside layer., With transposition: made at the end of the layer taps always partially short out: the transposition. If taken in the outside layer this effect is minimized since this layer is in the weakest part of the leakage field~ This location for taps alsa has the least effect on the tt:ansformer impedance. It permits the taps to be taken directly to the tap changer or terminal board.

For inside coils the best location for taps is at the center of the first layer. They then can be brought out in a duct between the insulatirig tube and the first layer to the end of the coil. Since they must thus cross the line turns of the coil they must be taped sufficiently to withstand the full surge voltage of the winding.

- 12 -

.. ~ . j "' ...

NI

~ f I I I I :

I I I .

LV

g. Cooling

T A

p

S

Figure No. 34

· . -.. -. . ,. t·-¢..j·e"' ., 4¥r,--':"-··§tt4amztrl"e rt?tft :" ·:,,£'a .. ;;t ""M

It is not good practice to bring the taps out of the layer adjacent to the high low space since this in­creases the space high to low required by the thickness of the tap. Also as taps are taken out in operation the impedance increases because the ef­fective space high to low becomes larger.

There are two 105$ sources in a transformer ,.;inding, one due to the 12& loss calculated with the dc resistance of the winding, and one due to stray losses from circulating currents caused by voltages generated by the leakage flux. These losses must be transferred to the cooling oil and the temperature rise of the winding must be limited to a value which does not damage either the winding or its insulation. To accomplish this the coil mus-t be ventilated to limit the watts per square inch of coil surface. In cylindrical coLIs the ventilation consists of providing oil ducts between layers of the winding. Normally one side of each winding layer is exposed to an oLl duct •.

Ventilation ducts are formed by using strips of pressboard about S/S wide, by the duct thickness. These strips called vertical spacers-are the same length as the completed coil and are located parallel to the coil axis

"at equal spacings around the inside perimeter of the duct.

Figure No. 35

h-. Mechanical Strength

In a transformer which is subjected to a short circuit the windings' are subjected to high mechanical forces. The ASA standards for power trans­formers require the transformer to be capable of withstanding a bolted three phase short circuit on one winding with full voltage maintained on the other winding and for a length of time based on the transrcinner impedance. The

- l~ --

·, " • '7 "= "d ," "-d'

maximum mechanical faeces are exerted on the first loop of short c~rcuit current, which is nearly always displaced from the neutral axis.

Transformer windings must be designed with adequate consideration for these mechanical forces. The principal force if one of repulsion between the primary and secondary windings. Since taps and building variations re­sult in vertical displacement of the electrical centers of the windings, there are components of these forces which tend to move one winding up and the other down.

Consider a cylindrical low voltage coil which is located inside the circular high voltage winding. During a short circuit the repulsion force between windings subjects the coil toa uniform radial load directed in­ward. The winding is s tressed like a submerged cylindrical submarine. This makes it necessary to space the vertical spacers forming a duct close enough together to prevent the coil layer failing as a beam and collapsing into the duct. It also puts limits on the amount of subdivision of the conductor which can be used. If the copper is wound in one conduc tor "w" wide by .'I.t" thick, its strength·as abeam=K t 2 W. 1<- W -1 r-=-W-j-L However, if it is wound with t,vo cor:- -r CJ E3 -I.)IN ductors W x t/2 the area will be the ~ f same, but the .Ream strength is reduced i to K2 {}:(t/2)2..J = Kt2W.

2 Figure No. 36

The vertical forces, which tend to move the Winding. either up or down., make it important to wind the coil under high tensionr Cylindrical coils are wound with flat strap conductors with the thin edges of one turn adjacent to the edge of the next turn. If one turn is loose, it can be seen that it would be easy for it to climb over the adjacent one when subjected to'a vertical force. This is even more apparent when it is considered

Figure No. 37 that ~e edge of straps .062 and less in thickness is made half round in shape. So, it is important to wind tightly and to moderate the amount of radial sub-division of the conductor. To help counteract this tendency for turns to te1esc9pe the outside layer is taped with glass tape covered with a B stage epoxy. When the toil is dried out, the epoxy sets up and serves as a strong. circumferential bond.

Vertical forces in these coils may become quite high, up to 10000 psi between turns. alld the end collars _. It .is Wes.tinghouse practice to make the collars at the edge of each layer of a high strength material such as micarta. The to~ collars are made oversize in width. After the coil is wound, it is clamped between steel plates with steel tie rods.

- 14 -

~~ ____ ~~.~.~. ~ __ ~~~ __ ~ __________ ~~ __ ~-'~~~_P-.~P_._~~~ ______ .~_-~'~~~E~'«'_'~' ___ ~ ________ ~~~~~~~~ -":;;-~~Jh'~~~\~:.

-~ -; -.~';:;~~:.~.~'~~.:,i'" .- .... -. . : ... :;":" .:.-.

.\

f\1IUH'i'iA C l-!..AR

;V·. ,) I IV (.

Figure No. 38

1. Advantages

k' e ',i,

On each tie rod a heavy steel spring is placed and the tie rod bolts are pulled down until half the spring compression is used up. These plates remain in place when the coil is oven dried and the springs take up any slack between turns to make

. the winding tight in the axial direction. After the coil comes out of the oven, the excess collar is sawed off even with the winding tube.

The cylindrical coil is low in cost and easy to wind. It has the advantage of being very flexible in arrangement for series-parallel windings. It can be made to almost exactly the length desired by choosing the proper combination of wires. It is suitable for almost any current rating. Cylin­drical coils. are easily made with both leads at the top so that they do not have to come up from the bottom paSt the high voltage coiL The vertical cooling ducts are efficient and cylindrical coils have low gradients. Trana­position is effective and simple so that eddy losses are low.

j. Disadvantages

In the past, these coils were considered weak against mechanical forces. However,tne methods now used as described above have resulted in coils with adeq~ate stx:ength. In larger transformers forced oil cooling is used with the oil being mechanically pumped through the coil ducts. Up to the present time~ no method has been found to make cylindrical coils, which will cool in this manner. Apparently, the oil flows freely through the smooth coil ducts in laminar flow without the required turbulance for good cooling.

If the high voltage winding is for a voltage over 69 KV, the low voltage winding is not made to use cylindrical coils. When the high voltage winding is impulse tested, the electrostatic potential induced in the low voltage coiL results in high stresses dn the thin square corner of the cylindrical coil end~ This condition can be improved by the use of shields in the cy­lindrical coil but these must be of high resis'tance material to reduce heating: caused by· the transformer leakage flux.

- 15 -

.. "~,,

.. - ,,' . .. :~ .... Ff "%r22"t' ... • bi _. , »

Line

In cylindrical coils the impulse voltage distrib~tion across the first layer may be very non-uniform and the stresses between turns near the line is quite high. For high voltages the number of layers required to keep the layer to: layer stress down becomes excessive and results in a coil with a poor space factor.

2. Lowgrocap Winding a. Construction

Lowgrocap is a coined word formed from the initial letters of the phrase, "low ground capacity." The coil construction is the same as described for cylindrical coil with one exception. Next to the line layers of the coil. is placed a shield separated from the layer by the same insulation that is used between layers. The shield is a sheet of metal

Line

Foil aper Filler'

Line

Shield

Line

Shield

Cylindrical Coil Figure No. 39

Lowgrocap Coil

foil backed up by a sheet of pressboard. It is cut back at the top and bottom edges to be slightly narrower than ··the coil layer so that the sharp edges of the foil are shielded. 'In addition, a piece of paper is folded to form a channel over the top and bottom edges of the foil. A gap in the foil is provided to prevent it from being a short circuited turn. The metal f0.1.l is connected to the line lead of the coil.

- 16 -

~.

)

n I .•.. J

b. Current and Voltage Limits

Lowgrocap coils have the same current limits as cylindrical coils.

Shielding the line layers improves the impulse voltage distribution and permits the use of the Lowgrocap winding for voltage classes through 46 KV (250 BIL). With the shield this type of winding has very nearly a linear distribution of impulse voltages.

All the mechanical limitations given for cylindrical coils apply to Lowgrocap coils also, as do the limitations on the maximum voltage of the high voltage winding used.with it.

Use of the Lowgrocap winding for voltages above 15 KV has been limited because the large number of layers required tends to make it un­economical.

c. Insulation

Turn to turn insulation is .018 minimum for mechanical reasons the same as in cylindrical coils.

Layer insulation is applied in the same way as in cylindrical coil. The thickness of insulation is chosen to have a breakdown stength equal to 1.5 x 2 xUnp~e test voltage. This corresponds to 1.5 times the stress

NL . if the voltage distribution were uniform.

Major insulation is the same as in cylindrical coils.

Use of the shield eliminates the piling up of impulse voltages be­tween the end turns of the line layer. A glance at Figure No. 39'will show that the charging curr.ent for the ground capacitances CG are supplied from the shields and do not flow in the coil turns. The series capacitance Cc is large because each shield and each layer acts as a condenser plate with a large area.

d. Losses e. Transpositions

See write Ull for cylindrical coils.

f... Taps

The tap problem is the same in Lowgrocap windings as it is in cylindrical windings. There is one small complication. If the taps. are

- 17 --_________ ",.....,~_"........o_._~=,,_---.-... -... ? .... _""""' ____ ...... ~~ , __ ~ ___ ~~.~~~_"_

"~ .. ~,. . . - : .. ;;. .:~~~, .... ~ r-.·~.'. .~".. ... :.: ... :~ ':'-~ .. _ .. ~.,.;:::--.' .

. ,:.;6~&4\~~~~~-.-·~~~~*:~i~:~;k~~k~~!mii~Wt~~~~:**::~,Cc.;!'~:~c. ,' .. ~"."J.·A1:C'0"$.fh'~ .;,;5;.,."'~.,?'t.,.SfJ~,P,i.,~~~;~l;Zft

. '0; " c 'i'b't"""; ····P5Ctriiee Y"Yd*'· ,--' • " "#' r· "c' ' .... 0···

located in a line layer then a circumferential gap must be left in the shield to bring them out. .

g. 1.

Cooling h. Advantages j.

Mechanical Strength Disadvantages

In general there are no differences between the Lowgrocap and cylin­drical coils except that the Lowgrocap winding has a near linear surge voltage distribution and can be used with less insulation and for higher voltages.

LV Coil

3. High Voltage Layer Windings

1 b ~ ~ , iI'

~,1

/ ,

~ I k' "

1 Sketch A

:'-

High Voltage Layer Winding

Figure-No. 40

a. Construction

Sketch B

Line

Shield

1.-..1.

Line

Shield

Tlie layer wound high voltage.coil is used by some American and by a number of European manufacturers for high voltage transformers. It is particulary suited for grounded neutral wye connected windings. Normally each layer of the coil is wound on a separate tube or roll of paper insu­lation" then by one means or another- -the tube is flanged out over the ends of the winding. Gee Figure No. 40J There are a number of ways of "doing this. "

- 18

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~.~

"T""' " ."tt"· t ... · "-.. "."" "' i sX" p' "w"" ts )"

1. The tube may be made of turns of paper wh~ch extend beyond the ends of the winding. After the winding is complete,'the paper is slit from its end down to the wi,nding into narrow widths with the slits stag­gered in adjacent layers. The slit portion is then flanged down at right angles to the tube.

2. The -tube may be made of turns of creped paper, which can be flanged down without slitting.

;1".1 3. The tube may be made the same le~th as the winding and a sepa-

rate angle ring used to form the flange. lSee Figure 4lJ

The inner layer is the grounded end of the winding and each layer is then made progressively shorter until the outside or line end layer has sufficient distance to the yoke for the line voltage. Short­ening of successive layers is equivalent to a large corner radius on the winding in relieving voltage stress concentration on the end of the winding.

Angle Rin

Figure No, 41 From high voltage to low voltage, the distance need only be sufficient,

to withstand the voltage at the end of the first layer of the high voltage winding. Since each layer is ventilated, this type of winding is favorable to the use of solid insulation in the pigh to low space.

Connections from layer to layer are usually made from the bottom. of . one layer to the top of the next layer in order to reduce the maximum stress between layers to the voltage of --l2EL... ~ E 1-... one layer. [$ee Figure No. 42~ This - I 1- I 1-may be done by two different methods. T 1 1: The connection can be made ,between the layers as in Figure No. 40, Sketch ' A, or all the connections can be brought E E E E out of the coil ends and the connections 1 1 1 I made outside the coil as tn Sketch B. L

-i o~ -1 E t-Figure No. 42

b. Current and Voltage Limits

By definiti.on,. the· high voltage layer winding has its chief ad­vantage for high voltage transformers, perhaps 138 KV class (650 BIL) and.up~ It is doubtful that it would be suitable for high currents above perhaps 500 amperes. While such a coil could be designed for a delta

- 19 -

'n· z-Yrl± <

connected winding, it would lose many of its special. advantages whLch are peculiarly adapted to wye windings with grounded neutrals.

c. Insulation

Paper normally used. stress •.. A line similar to that

tape on the conductor for the turn to turn insulation is The thickness must be calculated to withstand the impulse layer shield is used and the voltage distribution will be in Lowgrocap coils.

Layer to layer stress consists of a paper or pressboard tube which is flanged over the ends of the layer plus an oil duct. Again the stress layer to layer on impulse must be calculated and the tube plus duct made to withstand the calculated stress. Collars to obtain creep at the ends of the layers are not required.

With a grounded neutral winding the major stress high to low is re­duced to tha.t required for the maximum test vol tage occurring at the un­grounded end of the first layer of the winding. Distance to yoke at the outside layer must be sufficient for the test voltages applied to the winding.

d. Losses

Limitation of stray losses i~ the same problem as in cylindri­cal coils except that the maximum current in much less and there usually will not be parallel paths wi thin the winding.

e. Transpositions

Several of the methods used in cylindrical coils could be used notably methods No.3, No.4 and No.5. The. most suitable might be by u~ing the Helitran (No.5) transposition at the center of each layer. In many cases a single strap conductor will suffice and no transposition would be required.

f. Taps

Taps in the high voltage layer winding are a problem. From an insulation view point, the best location would be at the center of the in­side layer with the leads brought out in the first duct. When this ia done, however, the impedence increases ra pidly as the taps are cut out of the winding. The effect of cutting out turns next to the low voltage winding i~ to increase the effective high to low space and this increases reactance_ All things considered probably the best compromise.is to place the tapS"· in an interior layer between the center and. inside layers. Because of the ease' wt.thwhich the taps can be carried. to the terminals, it is tempting to place them in the outside layer. The objection to this is that it is .too close to the line and a no load tap changer would require full line insulation to ground.

- 20 -

_.~ 0_ .;L..., "7'';'''';' ·tiC··z, Oft ·s··S·d····:· ;",..>-··'WW .... b"~;.*{Wei.( "'n- -"'y'd".'t;l: -w"·

g. Cooling

Cooling of high voltage layer ~vindings is the same problem as­in cylindrical coils. Each layer is exposed on one side to an oil duct ..

h .. Mechanical Strength

These windings would normally be outside windings and the stresses due to horizontal short circuit forces would be taken by tension in the conductors.

To withstand vertical forces, the coil turns should be drifted tightly as they are wound. Each layer can be bound circumferentially with a layer or layers of glass epoxy tape to prevent climbing and telescoping of turns. The angle flanges at the end of each layer must fit tightly against the turns and be made of a high density material. At the ends of the column the flanges 'of the angle ring must be separated by radial blocks of a material such as densite ,vith a high compressive strength.

i. Advantages

This type of winding has many theoretical advantages. For g~ounded neutral windings maximum advantage can be taken of graded insu­lation in which the quantity of insulation is graded from a. minimum at the ground end to full insulation at the line end.

The layer winding is well adapted to the use of solid high to low in~ sulation which permits a minimum separation bet~een windings which has a snowballing effect on reducing. transformer size and cost. Winding costs are low and the winding can be made by winding it directly over the low voltage coil eliminating set up and assembly operations.

A shielded layer winding has good surge voltage distribution and the insulation parts are simple. Only the angle flanges at the layer ends are high in cost.

j. Disadvantages

Maximum advantage' of this type of winding is limited to wye connected windings with a grounded neutral. Bringing out the taps is more­difficult than in disc type windings. Considerable care is required to obtain adequate.. mechanical streng.th against short circuits.

J. PozaryskiWinding See Figure No. 43

a.. Construction

The Pozaryski winding is a layer type winding which can have advantages for auxiliary regulating windings or for low voltage windings with multiple

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,_~ __ • __ ~_~. _oliO ........ _.~ •. ..,.._ .. ''H ==*--=---------=-=~~..;;.~~~_:.,.:; ..

. 7'""",,";"'M.~~~:~~~'~"~'=ri"'"'"H .. e,:;,..~i~~.;,.~<i2:~1ilI

.-"''0,,''

series parallel sections. A rectangular conductor made up of a number of rectangular straps is wound spirally on an insulating tube jU$t as in a cylindrical winding. In this case however, the number of subdivisions in the width of the turn must be the same as the number of tap sections de­sired in the winding. The radial subdivisions may be from 1 to 3 depending on the current required.

~6 'IE E.g '2B I 18 5B 78

\ ~rVl I lA <3 ,lA JE +A4.8 IA £''(3 GIl G} 71"178 ;1'\ PS .9

LJL1LJLJLJLJLJLI

. -----_. L------

Figure No. 43

// . . I .~ •

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I SA 'fA th· d· . 11 . fl' 1 b n many cases, e w~n ~ng w~ cons~st 0 on y one ayer ut more than one can be used. Construction details are the same as for a cylin­drical winding.

If the winding is a regulating winding.all the grGUps of conductors will be connected in series by connecting 2A to 2B, 3A to 3Betc. and taking off a coil lead at each junction. F0r series parallel-use,all the leads. are taken to a terminal board arranged for series and parallel con­nection. The winding as shown in Figure No. 43 has eight sections of 3 turns each. If. each section is for 10 volts, the winding can be connected for 80-40-20 or 10 volts~

b. Current and Voltage Limitations

Current limits are more. severe than for cylindrical cause for really heavy curren.t: the turn would become too wide. heavy currents are not: required since the principal use of the fora regulating winding at about 10% of the main winding K!VA. above 500 amperes would begin to produce problems in design.

- 22 -.

coils be­Normally~

winding is Currents

/7"',' oJ

'Art . t r ~"""') so,,' , -

Voltage limits are also on the low side. Mostly the winding does not apply above the 15 KV class.

c. Insulation

Major insulation is the same as is used for cylindrical ~vindings.

Turn to turn insulation is quite a different problem. For lot., vol­tages, it is not too difficult to insulate each of the turn groups for the full impulse voltage of the winding in one way or another, either by heavily taping each group with paper tape or by winding in a pressboard spacer be­tween groups. Impulse stress between turns can be reduced by placing a static layer next to the winding but separated with wrapped pressboard layer insulation.

d. Loss

The problem of stray losses is identical to that in cylindrical coils.

f. Taps

No taps between leads are used.

g. Cooling

Ventilation problems are solved as in cylindrical coils.

h. Mechanical Strength

Solutions as used for cylindrical coils.

i. Advantages

Pozaryski windings are well adapted to regulating windings in transformers with load tap changers. They make it easy to bring the re-· gulating taps out because they all come at the end of the layers. Also, taking out taps does not unbalance the winding and cause high vertical stresses. No matter how many taps are out, the remaining portion of the winding still occupies a full layer.

j _ Disadvantages

The chief disadvantage is in the various limitations of the con­ductor si~e. The number of strands wide must be a mUltiple of the tap voltage required and of volts per turn.

- 23 -

I,' •

. ~ .. : -.

.~--

f~ 'y

With this width, the thickness is set by the current rating. At the same time, the width and number of turns per tap must be such as to evenly fill out a coil layer in length.

B. Round Concentric Disc Type Windings ~ee Figure Nos. 5-~ 1. Continuous Pancake

a. Construction

Continuous coils are wound with from 1 to 4 or 5 rec­tangular copper straps in parallel. The individual conductors vary from .204 to .580 inches wide and from .025 to .144 thick. Each section of the coil consists of a flat circular disc whose thickness is equal to the con­ductor width. The sections are connected alternately start to start and finish to finish. Like cylindrical coils, continuous coils are wound on a micarta or pressboard winding tube. Over the tube are placed longitu­dinal spacers of pressboard which form a duct between che tube and the coil sections. The complete coil made of from 20 to 60 or more sections is wound of a continuous copper conductor without brazed joints.

The winder first winds one section with the start next to the mould. When the first section is complete, the wire is carried down to the mould and a second section is wound. After completion of the second section the first section is collapsed and reversed by hand which leaves two sections, connected start to start. This process is continued rewinding every other section by hand until the coil is complete. ~ ___ _

Section to section insulation is formed bj oil ducts. The oil ducts are maintained by equally spaced rows of radial spacers. The spacers are

Spacer

Radial Spacer

made of a high density press-board and are keyed to the verti­cal spacers back of the winding. See Figure 44. Major insulation to the core or inside winding is provided by the duct and the insu­lating tube on which the coil is wound. The winding is made shorter than the tube and the space from the end of the winding to the end of the tube is filled with high density pressboard blo cks formed by cementing together coated radial spacers.

-. " ~.

..-..::;'

Figure No. 44 ...... -: .

If the voltage is over- 33 KV a static plate is placed on the end of the column between the winding and the collar.

- 24.-

,­

•......

. ....

'-)'. '7 Y

It serves to distribute impulse voltage stress across the turns of the first section, and because it has a radius surrounded with solid insu­lation, it reduces the concentration of the major stress on the corners of the column. The static plate is made of a 3/8 inch thick pressboard washer covered with copper foil, then taped with a 3/16 inch thickness of paper tape. The foil is connected with a pigtail lead to the line terminal of the transformer and must have a radial gap.

When the voltage is 69 KV or over, angle rings are used at each column end. An angle ring· is flanged cylinder of pressboard. The cylin­drical part fits snugly inside the winding tube and the flange extends out across the ends of the winding just outside the static plate.

b. Current and Voltage Limits

Continuous coils are suitable for currents in a range from about 10 amperes up to 500 amperes. They can be made for voltage classes up to 138 KV 650 BIL although Westinghouse practice is to use inter­leaved Hisercap windings for voltages above 69 KV, 350 BIL

c. Insulation

Turn insulation is obtained by taping the conductor with layers ~ of paper tape. The thickness of tape is determined by calculation. The distribution constant is determined as a function of the series and ground capacitances, and the voltage across the first duct as a function of the distribution constant. The turn to turn stress is then a function of the section to section stress. The turn insulation· is uniform throughout the winding. In practice most coils up to the 69 KV class need only .014 which the minimum permitted for mechanical reasons.

Section to section stress is insulated by means of oil ducts. Th~

thickness is calculated for the stress across the first pair of sections calculated as above. Up to 46 KV, a 3/16 duct, which is the mechanical minimum is sufficient for most designs. At 69 KV, 1/4 ducts usually are required.

High to low insulation is made up of alternate tubes and oil ducts. The stress divides between insu1ation~in series inversely proportion al to the SIC value for the insulation material. In oil and pressboard barriers, the volts per inch in pressboard is about 1/2 of that in the oi·l~ Since the strength of an oil duct in volts per inch increases as the duct size decreases,. it is advantageous to use many thin barriers with small oiL ducts between them.

d~ Losses

s.tray losse;; in continuous coils are low and the conduc·tors usually are subdiVided in the radial direction to keep them low.

- 25 -.. _. ----------------- _. __ ... _ ... '-'-;.-' -

.. -.- . ~- .- -. -, - - -~ . - .-... .~ ---

~ fi) ,

e. Transpositions

The transpositions required are simple. Only one type of trans­position is made at the start to start connection between sections. It re­quires no extra space and costs no more to make than a regular series con­nection. Figure No. 45 looking at the inside circumference of· two sections at the start-start connection shows how the outside conductor in one sec­tion becomes the inside in the next.

Figure No. 45

f. Taps

In continuous windings taps are taken out as nearly at the center of the column as possible. As shown in toe notes, taps at the center have a minimum effect on reactance and on the short circuit forces. The tap is brought across the face of the section to the outside of the column and then extends about 1-1/2 inches to serve as a terminal on outside columns. It is taped and shielded with pieces of pressboard to insula~e it from the sec­tion.

On inside columns the tap may be carried to the duct outside the coil or: to that inside the coil. It then extends up in the duct to the end of

Figure

- 26 -

the coil. Where is passes the end of the column it must be insulated for the full impulse voltage of the insulation class. This requires heavy tnpe and large ducts. As a result, we do not usually make in­side columns with taps for voltage classes over 33 KV.

--.- ----------------:-- --_ .. _-_.- .

The construction of continuous coils is very weIr adapted to good cooling. A vertical duct behind the winding @ee Figure No. 41J and horizontal ducts between sections give good cooling and low gradients above the oil temperature •

Continuous coils also give excellent cooling for forced oil cooled transformers. In such a transformer a pressboard tube or· wrapper is placed around the outside of the coil leaving a duct between the coil and the wrapper. Pressboard boxing at the bottom forces the oil to flow upward around the coil sections between the outside tube and the winding tube. In each section between turns a duct is provided by means of corru­gated pressboard spacers.

II ,I II

II I'

r /'

1\ II ~ ~/

1 II II

II II II

I " " 1/ I

I " , I II I

\7 I :: ::: ~

Oil Flow

Figure No. 47

Oil through the ducts spreads out in the area bet~veen sections then must eddy to enter the duct in the next section. This promotes turbulent flow and gives: excellent cooling.

h. Mechanical Strength

As in. cylindrical coils, continuous coils are subjected toa radial outward and inward force and to an axial force directed upward or downward~

When used as an inside winding, .the horizontal forces are directed ra­dially inward. The strength of the coil- as a circular arch against buckling· must b~ calculated and in some cases it may be necessary to use thicker

. - 27 -

<~1 y

, ......

--," " :'" -4 '&""'1o""-;·,O'w . ','," :.: 'r-

copper strands or less subdivision of the turn to obta~.n the required strength. If used as an outer coil the stress is taken by tension in the conductor material and in moderate sized transformers this is not a problem.

Vertical forces are more troublesome in continuous coils. Normally the coils after winding are clamped axially bet~.,een steel plates and then are thoroughly dried by the vapo-therm process in which the coils are heated by the condensation of a low boiling point vapor in a high vaccuum and then are impregnated with transformer oil. The hot dry coil stack is then loaded in a hydraulic press with a load equal to the calculated short circuit force. Extra radial spacers are added or subtracted to obtain the calculated height at the short circuit load. The coils are then placed on the core and after the core is yoked are again pulled down to the same length as before. Such a man~facturing process makes certain that there will be no further compression on short circuit and hence no motion. High density pressboard must be used for the radial spacers to limit the compression under load.

i. Advantages

The continuous wound coil th-ough slightly more costly than the cylindrical coil is still a low cost winding. It has a good space factor and when removed from the winding machine little coil assembly time is re­quired. Mechanically every turn is locked in place and the coil is strong and 'easily braced for short circuit stresses. Stray losses are low and temp­erature gradients also are low. It gives excellent performance for forced oil cooling.

For voltage classes above 15 KV the. space factor is higher than that of cylindrical coils. Taps are easily brought out.

j. Disadvantages

A'simple continuous coil has a poor surge voltage distribution and requires extensive modifications for voltages over 69 KV. It is limited to currents not over 500 amperes although higher currents can be handled by paralleling sections of the coil.

2. Double Section Pancake Coils

a·. Cons truc t ion

When completed, such a coil appears to be identical to a con­tinuous coil except. that the finish-finish connections instead of being con­tinuous with the winding are brazed.at a coil assembly·operation. In winding, a single'section is wound then the mould· is reversed and the conductor from the reel is brazed to the start of the first section and another section is wound spaced by a. duct from the first section. The pair of sections is then

- 28 -

- <---.... "' ,_~_.~,_,:'~ __ ~:~~~:-.~.:..;.'~~.-c,:. •.

removed from the mould and another pair is wound. ' When enough are completed for a complete coil the coil tube is set up with vertical spacers taped to it. The pairs of coils ar~ then stacked on over the tubes with radial spacers between all sections. After stacking is complete, the finish-finish connections are brazed.

All other details of construction are the same as for continuous coils.

b. Current and Voltage Limits c.' Insulation d. Losses e. Transpositions f. Taps g. Cooling h. Mechanical Strength

All these problems have the same solutions as given for con-tinuous coils.

i. Advantages

There are few advantages as compared to continuous coils and the double section winding is no longer used by Westinghouse. One possible advantage for future use is the possibility of using, it with solid high low insulation. A wrapper can be wound over the low voltage coil and then the. double sections can be assembled over the wrapper without a duct next to the coil sections. With solid' insulation and a small high to low distance it is important not' to have an oil space next to the coil. The solid material (oil soaked pressboard) has high dielectric strength but due to its higher dielectric constant" it shifts the stress to the oil when oil ducts are in series. Failure then occurs in the oil duct. For this reason continuous coils which are wound over spacers forming a duct cannot be used with solid high to low insulation. '

j. Disadvantages

At the present time double section coils used with oil and pressboard barriers in the high low space cannot compete with continuous coils in cost.

3. Hisercap Windings

I. Twin Interleaved ~nglish Electric's Stearn Patent] :..~C· f~G- IJ<: ~l

a.. Construction

After the coil is wound and the end collars put in place~ the winding has the same appearance as a continuous disc type winding. Most of the, construction details are the same. The winding process is, however,

- 29 -

' .. '

quite different. Two reels of wire are set up and two straps are wound into the coil at one time (§ee Figure No. 48 which shows the turn sequence of the winding]. After the first section is wound with a double strap to give half as many turns as finally desireq the conductors are dropped to the mould and a second section is wound. Then the fi~st section is collapsed and .is reversed by hand. At this point one of the straps from the reels is cut ~o. 8 in Figure No, 4~ and the turn is reconnected to one of the two wires at the finish of the first section @o. 9 in Figure No. 48J. This process is then repeated until the desired num­ber of series turns is obtained.

'.

(b) Current and Voltage Limits

I. 1~ 17 -9 6 e.g:

-2- /5 18 /0 7 '2~

.3 14 19 (p 27

Twin Interleaved English Electric Stearn Patent

Figure No. 48

3c. "2.4 2>1

This particular winding is limited to the current rating of the largest single strap which can conveniently be used; in Westinghouse practice about .114 x.S80. This permits currents of 80 to 100 amperes. Higher currents may be used, by paralleling winding sections. One connection which is particularly advantageous for grounded neutral wye windings is to wind the top and bottom halves· of the coil stack in parallel with the line

lead in the center. When this is so: , done, the insula'tion at the end of ~

I"

~ ____________________________ ~ the column has only to be good for the neutral insulation level and the static plate can be om~tted. The line voltage then appears only

=J-----at the center of the column where

;::::::::::::==:= ~ Line the voltage gradient to the low ~ ______________________ ~ voltage is uniform. Improved vol-

~-------------______ Jt;~

tage distribution is obtained and, the current capacity is doubled.

The tower limit for voltage is about 450 BIL because the extra winding labor for the Hise~cap winding costs more -than the gain obtained from better -'voltage distribution. In ~eries.windings, however, the Hisercap winding may

,.

=--"to. , t".' ., ... "

b~ economically used to obtain high series capacitance:for low voltages. So far as is known, there is no upper voltage limit considering present commer­cial voltage systems.

(c) Insulation

Paper tape turn insulation is used as in continuous winding. As can be seen from Figure No. 48, the turn to turn insulation must be good for the 60 cycle test voltage across .the total turns in one section. Turn to turn impulse stress must be calculated from the distribution calculation.

Section to section, the voltage across the start-start connected sections is twice the turn to turn stress and across the finish-finish connections is three times the turn to turn stress. This permits a big re­duction in duct size over the continuous type of coil. In most windings, regardless of voltage class, a 1/4 inch duct is sufficient.

Major insulation is the same as for continuous windings.

d. Losses e. Transpositions f. Taps g. Cooling h. Mechanical Strength

Solutions of these problems are the same as for continuous windings. With only one strap, there are no transpositions required.

i. Advantages

This type of Hisercap is the lowest in winding labor cost of all the interleaved windings. It also has the most ne2rly uniform voltage distribution. For high voltages, it is economical.

j. Disadvantages

Winding labor time is considerably more then for a continuous winding and the winding machine capacity for production is reduced. There have been cases where the turns in the first half of an interleaved group T:e­come so numerous and large and the inductance so high, that their turns do not come up to the surge voltage rapidly enough to permit the interleaving principal to work.

Interleaving the turns of two sections increases the turn tc turn stress and more insulation must be- used on the conductors and this in turn decreases the turn to turn capacitance and consequently increases the turn to turn streSs. This is a snowballing effect.

- 31 -

...

____ -'"-_~,...;;.o.....",.;..;.. ....... .._.._... __ ~~ ____ __ ............... __ T"Z"=;o.F~_ ... - __ ~"'."='_-'o.. '-"-.--:.--". ... '"'~ ... --~~".---~ - ..:-!--;<:~:'S""

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,,-.~. :;

'.

II Single Interleaved (Siemens or Dr. Stein Pate:nSJ [5ee h& NC$ Ie t. lej

a Construction

This winding differs from the preceeding one in that the inter­leaved group includes the turns of one sec-tion instead of two. [See Figure No. 49]

The winding is done as before except. that one strap is cut at the top of the first section and after it is reversed this turn, now at the bottom, is re­connected to the second turn from the top. The sketch shows that a top to bottom connection is required for each section. It must be insulated '-lith paper tape and with tough pressboard channels which protect it from mechani­cally dama~ing either of the adjacent sections~ ~ee Figure No. 50J

Inside Channe 1

.

I l

Inte Co~n

rleaving ection

Outs Chan

.-

ide nel

I~ /2. /5 II

14

J7 2.1 18 G( 19 2.3 2.0 2.4

Single Interleaved Siemens or Dr. Stein

Patent Figure No. 49

b. Current and Voltage Limits

The current and voltage lfmLt~ are the same as for the twin inte~-· leaved winding.

c. Insulation

The 60 cycle turn to turn I r./

·Figure ·No. 50

·stress is reduced to the test voltage across one half the turns in the first section. Section to section stress is uniform and e-

qual to four times the turn stress. voltage classes.

Ducts 3/16 inch thick can be used for all

d. Losses e. g. Cooling - h.

Transpositions f. Mechanical Strength

Taps

Al! these- problems are as descr.ibed for the preceeding winding ..

i. Advantages

While: this winding has theoretically a poorer voleage dis­tribution, .the reduction in turn- to turn stress permits using less insula­tion on the strap and in turn increases the capacitance to the point where

-·32 .~

the winding is comparable to the twin interleaved. It~ performace is ex­cellent. The reduction in turn to turn, and section to section stress im­proves the space factor and the material saving more than offsets the in­crease in winding labor cost. It appears that interleaving the turns of only one section is more nearly at the optimum size for an interleaved group.

Disadvantages

The winding time because of the welded interleaving connection is greatly increased)two times that for a twin interleaved)and three times that for a continuous coil. Production per machine hour is materially re­duced and more investment in machines and labor is required for equal pro­duction quantities and times.

III Double Interleaved Hisercao

a Construction

In this type of winding the interleaved group is only half the turns in the first section. Two sets of cross section inter­connections are required an4 two sets of protective channels as described for the preceeding winding. Other features are the same.

b Current and Voltage Limits

These are no differ­ent than in the single interleaved winding.

c Insulation

Turn to turn stress at 60 cycles is only that portion of the test voltage app~aring

15

18

IS 17

J4 '/G

J~ s~ 37

. 'across one· quarter· of Double Interleaved the turns in a section. Figure No. 51

Stress from section to section is uniform and is equal to 8 times the turn to' turn. stress.

d Losses g Cooling

e Transpositions f Taps h Mechanical Strength

- 33 -

'. <··-·r R' ..... -........,... ..

.~.

These problems are unchanged from those in the preceeding types of Hisercap winding.

h Advantages

If taps are located on turns in the center of an interleaved group, the capacitance relationships are changed and high voltages occur on impulses. This means that taps must be taken out only on finish leads. This makes it nec.essary to distort the tap sections to obtain the right number of turns. With double interleaved sections, there are two places per section for taps and less distortion of the turns.

i Disadvantages

The winding time and labor cost become prohibitive and this winding is used only for tap sections.

IV Mutually Twin Finish-Finish Interleaved

a Construction [see Figure No. 52]

~is winding permits winding two conductors in parallel. Two reels of conductor are required. The first section is wound with two straps and then one connection to the reel is cut~ the other conductor is brought down to the mould and wound with a strap from the cut reel to form a second section. Then the first section is reversed by hand and a cross connection made between sections at. the top. Some of the s.tart-start connect~ons must pass under two intermediate sections arid this is done. as shown in Figure No. 53. There are no inter-leaving connections across the faces of the sections but one line lead must be brought out from a coil start. It will be noted that the "An circui t goes through each section like a continuous. winding. The B circuit enters each even numbered section at the bottom then loops back one section.

A - AI Ale.. AI3 A14~' '57 B~ E/~

A2. All AI4 BB 55 1320 A3

I

AID AI~

.B.9 B4 <132.1 A4 AS AI~

BID B3 B'2.Z AS AS AI7

:.811 .. B~· ." ~23.

-A~ A7 . AlB :B 1'2.. "- 81 12.4

I I I ~

Mutually Twin Fin-Fin Interleaved ~ig~re No. 52

- 34·-

. ]3lg A?.'!> ]/7 A~1 BJ(p A'll 'B/S A?.O

.. BJ4 AI9 :313 .-

J B. .

;: " ... ~ -: ."-'.""""."f,;'

,' •. ;., .. ". ""ina:"' ';" aa': ¥ '1¥6,-'ti'q-":': ,)i';..;~.:.:':'; d': '.~ .,,-... 'a+·· 'fs~Sa)t"~\;f-# '=W;-~rl;-h" ~'f#td"'t- ¢,;," ""dVth"-m< 'r:'&"')'·"~#.af ~-_}izi.eL <'~)L,+> : aia.~;;·mb\>fA;.f..-t

[ --~----------------~~~----~} __ .7 ~------=--=Z __ --- __ ; ~.-:--------.. --.-.-- - .-----------------------.-------~

Figure No. 53

b Current and Voltage Limits

Since two straps may be wound in parallel, this winding doubles the current rating of the previously described Hisercap windings.

Voltage limits are not changed.

c Insulation

Sixty cycle turn to turn stress is equal to the test voltage across half the turns in one section. Across alternate ducts, the stress is twice and four times the turn to turn stress.

d Losses g' Cooling

e transpositions f .- h Mechanical Strength

Taps

These require no new solutions over the previous types of Hisercap coils.

i Advantages

_Over the previous types, this winding has the advantage of doubling the current rating~

j D-isadvantages

Winding time and labor are high~

- 35 ·.~=-=]E-~~T·""· ~_~~~~ ~~~=~~ .. --.. ~~ .... ",,-""':

. --."" --_. ---'" ~.- . . .... ·.3i,;;;il

.. , -~.;:~ .: .~ '" .. ... ~ -.:- .

V Mutually Twin Mixed Interleaved 8 A I AI I

B7 : A,-

B8 I I

A3 119 A4 BID AS 1311 AG BIZ-

l, -

AIL A?4~ A 13_ 'Be, B/8 :£>1.9 AII-l A23 AM-]5 J3 )7 B20 AID A '22. AIS B4 BIG, :821 A9 A2/ Alb

B3 B 1,£ :B 22. A8 A 2.0 AJ7 B2. J?14- F23 A7 AlB AI8

i.- E/ :813 '$24-I

Mutually Twin Mixed Interleaved Fi~re No.·. 54

a Construction

A

B

In the mutually twin'Finish-Finish interleaved winding, we have seen that one circuit ~ circuit, Figure No. 5U 'gees str.aight through each section with crossover alternately at the top and at the bottom. The other circuit enters each even numbered section at the bottom and then.loopsback through the odd numbered section preceding •. In the mutually twin mixed interleaved windings, the A circuit Q?igure No. S41goes through tw~ sections in series, skips a section, goes through the fourth section then loops back thro~gh the third. Circuit B enters the second section at the bottom, loops back through section one then goes straight through sections three and four. Each circuit then goes straight through two sections then skips one, enters the next and loops back through the skipped section.

b Current and Voltage Limits

Same as for the previous winding.

c:: Insulati on

Sixty cycle turn to turn stress is equal to the test volta:ge across-half the turns in one section. Across alternate ducts the section to section is equal to twice and then three times the turn to turn stress.

- 36

winding.

d Losses­g Cooling

e Transpositions f Taps h Mechanical Strength

These problems require the same solutions as in the previous

i Advantages

Over the preceeding winding this one has a single advantage: the maximum section to section stress is reduced from four to three times the turn to turn stress.

j Disadvantages

The winding is more difficult and expensive to wind.

VI Hutually Single Mixed Interleaved

B3 - Elc. _]/5 r- :824 AC; - '-- A~ - AlB I- - All B'2. -"Ell Bit 1523 AS A8 AI? A20 BI :B 10 L-.:..- 13 13 1522-

oAf '- A7 It. li.o !-- AI9 B~ '-- B9 ])8 r-I-- o B21

A

A3 BS A 2.. B4- '-

AI

AI~ - .-- Aft B8 1317 All AI4

'"-- 137 B If> ~ '---

AJO f- '- AI3

Mutually Single Mixed:lnterleaved o Figure oNe. 55

.a' Construction

A (,4-"H2O A23 BIS A '2.2-

,.--

1-.

B

A

.

Your-reels of conductClr are needed to wind the mutual single mixed interleaved.'winding but no section has to be reversed after winding. First, two straps:are wound together to fGlrm a half section then sne of the straps is drapped.down- to the mould. A wire from the third reel enters

- 37-... ~-~~~=-~--~~-=======~~==~~~~~~~~~---

.,~"::-:-.;,.;!;:t.~22t1~~~t':~~~:~'.'.L .;; :~; .:, .. .....--. .. _. ... ·c,-:5.~

'~ )

the first section at the center and a wire from the fourth reel enters the second section at the bottom. At this point, the top "half of section one and the bottom half of section two are wound simultaneously. This cycle is then repeated. It will be noticed it has three interlacing connections across the face of the coil.

b. Current and Voltage Limits

This winding has the same limits as the the windings previously described in the preceding paragraphs IV and V.

c. Insulation

Turn to turn stress is equal to the low frequency test vol­tage across 1/4 the turns per section plus one turn.

Section to section stress is equal to the stress across 3/4 the stress across one section

d. Losses g. Cooling

e. Transpositions- - f. Taps h. Mechanical Stresses

These problems are no different than in other mutually inter-­leaved Hisercap windings already described.

C. Round Concentric Spiral Windings

1., Helitran - Double Group [See r,g lA.res /'Ie 7 -a~c{ No 8]

a.- Construction

He-litran coils are wound on a micarta tube with .vertical spacers next to the tube to form a duct between the tube and the inside of the coil. The turn is composed of two groups of rectangular conductors wound side by side. Each turn is spiral wound with a single layer on the tube. The stacked height of the conductors becomes the radial build of the coil. Each turn of the coil forms a spiral disc similar, except for the pitch, to­the sec·tions of the continuous wound coil. Between turns are ducts main­tained by radial spacers keyed to the vertical spacers between winding and tubes. In such a coil column the number of sections must be equal to the number of turns or a multiple of the number of turns.

·The leads on helitran coils are brought out from the winding in an opening in the collar. The collar serves to prevent uncoiling of the wind­ing by bracing the lead. Most leads are brought out vertically, a few on 'outside columns are brought out horizontally.

- 38 -

".. ",

. ~~'~~~"~'~~~*~<;~'~"~#'~' ~'ri~'~~"~~e~y~_~".6~;~~_·~·~:~t.'~~'.'~R~··ftr~'~·;'W.~·'~&%~)·~··~<,~'·dl~'~'~'k~"~~~~~"~'h~'~*~'_'~"~'~'~'~'~~~~'~'~'~)~"'~i~~:'~*/~"~~m~<~"~l~k~t,>~,~~,'i~'3~';b~/~~jW~?M"'a"WH~~'aW~~~":'

r'\, ;;

,r . -

V i-'""'" ~

One Turn

-- - -

Radial

------Spacers

I

I

! y---..

.7 Vertical Spacer

The ~vinding is shorter than the winding tube and heavy collars of micarta are placed at the ends of the winding and are riveted to the winding tube to brace and prevent unwinding of the heavy coil leads .. Leads come out through a gap in the collars and a layer

V//// //L'L//// / .... > .... //j') ~be

of glass epoxy tape circumferentially wound around each collar holds the lead down in the gap between the collar ends.

Figure No. 56

b. Current and Voltage Limits

The helitran coil is limited to windings where the number of turns can be wound in a single layer withQut an excessively long coil. With­in this limitatien it can be used for any current up to about 3000 amperes. It is not limited by voltage although the maximum current in high voltage core form transfermers is not great enough to call for helitran windings ex­cept, perhaps, in series windings.

c. Insulation

Each strand of the conductor is insulated with paper. This paper insulates only for the voltages which produce eddy.currents. Turn to turn insulation consists of oil ducts formed by radial spacers. There is only one layer so no layer insulation is required. Major insulation to the core or tube inside the coil is obtained with the tube on which it is wound. The wind.ing is shorter than the tube and the end insulation consisfs of heavy collars of micarta. When used with a high voltage winding over 115 KV some­times a static plate is used on the end of the column after the pitch of the first turn is leveled off with radial spacers. This static plate serves to reduce the concentration of the major stress on the corners of the coil.

d. Losses

Helitran windings can be effectively transposed and the stray. losses easily controlled. Radial subdivision of the turn usually do not ex­ceed .129 inches to limit the losses.

e. Transposition

Only one type of transposition is used; the helitran trans­position named after the type of winding., This transposition is also used in most cylindrical coils. At each transposition the top conductor of the

- 39 -.. -,.,. ,

,,"~~:i'!!i:~i"~~2!:S£~w~ .. " '

. .J. .... 4,

1

6

5

A

left hand group is moved over to the top of the right hand group: and, at the same place, the bottom conductor of the right hana group is moved OV2r to the bottom of the left hand group. See Figure No. 57, where the solid lines indicate the top two conductors and the dotted lines the bottom two.

This same transposition is made at sufficient equally spaced points so that each strand oc­cupies each radial position in the turn for equal portions of time.

Figure No. 58 represents a coil Figure No. 57 in which each turn is two strands

high. "A" represents the strands before the first transposition at T-l, B after this transposition, etc.

882 BEl tffij4 HE3 ffiB2 43 32 2 1 - l4 43

Tl T2 T3 T4

A B c D E

Figure No. 58

2 6 1 5 6 4 5 3 4 .z 3 1 2

3 5 2 4 1 3 6 2 5 1 4 6 3

4 4 3 3 2 2 1 1 6 6 5 5 1+ tr 1 T2 T3 T4 h' 5 T6

B c D E G

Figure No. 59

Figure No. 59 represents the relative position of the strands when the turn is three strands high.

If we let:

S = No. of strands in each group of the turn T = No. of transpositions N = No. of turns in winding n= No. of turns between transpositions

- 40

It is evident

T = 2S

If each strand is to occupy for equal times every position in the turn the number of turns between transpositions must be equal to (n) where:

N N n='T=is

So if a 15 turn winding is made with a turn 6 strands high the first trans­position must come at the end of 1-1/4 turns (n = N/2S = 15/12 = 1-1/4) and another transposition every 1-1/4 turns thereafter.

The only allowance in dimensions required for the helitran transposition is a radial allowance equal to the thickness of a single strand.

f. Taps

Theheli tran ~·'inding is used for low voltage, heavy current windings and taps are seldom required. Taps can be provided by bringing out the finish of the turn just before the tap and the start of the turn following and brazing both to the tap lead. In such a coil it would be ne­cessary to make a complete transposition between each tap and between each end tap and the line. On inside windings, taps can be provided by brazing on flat copper strap and by bringing it up in a duct between. the winding and the winding tube.

g. Cooling

Helitran coils are well ventilated in the construction des­cribed above and have low temperature gradients.

h. Mechanical Strength

Helitran coils are subjected to the same stresses and con­tinuous disc coils and are processed in the same manner. They are pressed in a hydraulic press after drying with a load equal to the calculated short circuit stress.

i. Advan tages

He1itran windings are particularly suited to windings with heavy current and only a few turns. They have good short circuit strength, low stray losses and low gradients. When forced oil cooling is used they give excellent cooling and may be ventilated by ducts formed with corrugated pressboard wound into the radial build.

- 41 -

j. Disadvantages

Because of the requirement that each section be a turn there is a rigid relation between coil length and number of turns which makes it inflexible to design. The minimum strand width is not less than .144 inches and preferably more. The type of transposition requires a number of in­dividual transpositions which twist the wires between winding machine and wire reel carriers. This requires frequent shifting of the reels. The large number of wires in parallel require many reels of wire and a com­plicated reel strand. Costs are higher than for cylindrical coils.

2. Helitran - Single Group

a. Construction

This type of Helitran coil is wound exactly as was the pre­ceeding winding except that the turn is made up of only one group of con~ ductors all stacked one above the other. All other construction details are as previously described.

r I I I

No. 60

b. Current and Voltage Limits d. Loss Limit Stress

c. Insulation

Same as for double group Helitran.

e. Transposition

Transpositions are made by periodically dropping the top wire of .the turn down to the bottom position in the turn. This is done by making a 90° bend edgewise of the strap then a 90° flat bend at the top then re­peating these operations at the bottom See Figure ~o. 61.

42 -------------~----

" . ..''. ..

-----u--~~:---------:-]

'..---- _. __ ._----..

f------ _. ------

1 2 3 4

3 4 ~--r-----2

3 4 1 2

1 2 3 4 Tl T2. T3 --Figure No· .. 62

Let: S = No.-ofradial strands in the turn T =. No:- of transpesitions N = No. of turns in winding n = No. of turns between trarispositions

Then: T = S

T4

r

2

3

4

If each strand occupies for equal times every position in the turn,the number of turns between transpositions must be equal to (n) where :

n = N N T = S

If a 15 turn winding is made with a turn 6 strands high, the first trans­position must come at the end of turns I n = N/S = 15/6 = 2-1/2 turns and another transposition every 2-1/2 turns. J

This transposition involves a top to bottom connection across the face of the coil which is insulated by pressboard channels as described for single interleaved Hisercap windings.

f. T:ips g. Cooling h. Mechanical Strength

These problems are no different then in the double group Helitran.

- 43 ------ ---------- ~-.=~-------------~-~,--=======

i. Advantages

This winding has all the advantages of the two group Helitran and requires fewer transpositions. Since it is only one strap wide in the axial direction, the turn can be made narrower and more turns can be placed in a given axial length.

j. Disadvantages

The transposition is" more complicated and harder to insulate then that used in the preceeding winding.

D. Round Concentric - Combination Layer-Disc Winding

1. Wire Wound Coils

a. Construction

Wire wound coils are made with single wire conductors of round ,,,ire from . 010 to .102 inches in- diameter. They are disc type coils from 7/8 to 1-1/2 inches thick and from 3/4 to 4 inches in radial build. The coil is wound on a micarta ring with the same length as the coil thickness. Each section is wound individually with several layers back and forth like a bobbin. Bet,,,een layers near the outside of the coil are wound segments of micarta tubes equally spaced around the coil.

After winding, the coils are connected start to start in pairs and the pairs are then assembled into a column over a micarta tube. When all are assembled the· finish connections are made.

Radial spacers of press­board are used between in­dividual coils and one of the segments under the last layer of the winding is located directly in line with each vertical row of radial spacers.

- 44

.~

hG-ure No G3

------" --"-" "-~-----" -" --~-"---...-"--~=--~~====

Segment of Micarta

b. Limits

The current limit for wire wound coils is about 9 amperes. They can be used for any voltage class. Their use is mainly in testing transformers and in high voltage oil insulated potential transformers.

c. Insulation

Turn to turn insulation is in the form of an enamel coating on the wire and or layers of paper tape. The coils have a good voltage distribution because of the high capacitance from layer to layer.

Figure No. 64

Figure No. 65

Two types of layer insulation are used, crimped paper and sleeves. Crimped paper layer insulation consists of strips of paper with the edges folded back and forth to form a collar to hold the turns laterally in ~lace. See Figure No. 64.

Sleeves are also made of strips of paper which are folded over the first and last turn in each layer (as shown in Figure No. 65) to anchor the edge turns.

Coil to coil insulation eonsist$ of oil ducts forme9 with radial spacers keyed to vertical spacersm aduct between the coils and the tube on which they are assembled. The segments in the outer layers are spaced so that they line up with the radial spacer columns and take the clamping pressure off the wires.

Major insulation is provided by the tubes and duct on which the coils are assembled and by collars at the ends just as for continuous coils. For higher voltages static plates and angle rings are used. In addition, the coils near the line end of the column use static rings one on the inside and one on the outside of the coil. This ring distributes the stress across the turns of the first and last layers and also increase the coil to coil strength.

Static Plate .- _. _._- --.

~~ __________________ ~~~~ _____ Line

The inside static ring is connected to the start-start connection. . The outside one to the line.

Figure No. 66

Static. Rings

../~

- 45

d. Loss Limitation

These windings use small conductors and have very low stray losses.

e. Transposition

Windings use only one small strand of wire and no trans~ position are required.

f. Taps

Taps may be placed on any turn and carried out across the layer then radially outward across the coil. Taps and pressboard strips are used for insulation.

g. Cooling

Wire wound coils have many_buried turns and normally have high temperature gradient to the oil. By making the thickness of each coil small and using more coils, some improvement may be made.

h. Mechanical Strength

This type of winding does not have good mechanical strength but in most cases the short circuit forces are low. No hydraulic loading is used. The radial spacers span the coil and form a bridge from winding tube to coil segment which supports the wires.

1. Advantages·

The winding is suited to small current,high voltage'trans­formers with low short circuit forces. They have a good voltage distri­bution of surge voltages and a good space factor.

j. Disadvantages

The temperature gradients in wire wound coils are high and the coils must be worked at low current densities. They are subject to turn to turn faults because of wire defects. Because of the coil assembly time the c()st is high. The small wires required are also high in cost.

2. Basket Windings

s. Construction

- 46 --...... "--,~- 7" --- ------' -=:-~-~--..--==-

A Section l'

y---h Ar-_---.

B

Section 2 r------,v' r-+------.

Basket wound coils are in some ways similar to double section coils ex­cept that each section consists of two discs instead of one. They are wound by t ... V'o different methods. Fig­ure No. 67 shows a single coil of two sections with two discs each. There are 10 turns per section or five in the radial build of each disc. ' Num­bers on each section show the turns in the order in which they are wound. Line from A to B is the path of cur­rent through the coil. This results

Figure No. 67 in an approximation of the layer wound coil with two turns per layer.

A large number of crossovers between discs is involved and each of these requires tape and pressboard strips for mechanical protection. To prevent all this extra insulation piling up and making a big projection on one side of the ceil the distance between crossovers is made less than one turn by the distance between rows of radial spacers. This staggers the cross­overs around the circumference of the coif.

If the current used a modification in the same manner.

is large enough that two conductors in parallel can be of the above procedure will produce the same results

The winding procedure is as follows:

C;

4 3 2 1

1. Section M is wound and the wire cut. 2. Section N is wound over t~e start of section M.

3. Wire is connected to start of A B section N and section R is wound

1 1 5_ 5 4 4 3 3 2 2 1 1

Figure Mo. 68

5 4 3 2 1

over start of section M. 4. Wire is connected to start of

section M and section S .is wound. 5. Sections M and S are connected

in parallel with sections Nand R.

b. Current and Voltage Limits

- 47 -

The current limits may be made as great as 150 amperes by winding three parallels in the manner shown in Figure-No. 68 for two parallels. The winding is uneconomical for voltages below 92 KV and has been largely replaced by Hisercap windings for higher voltages.

c. Insulation

Turn insulation is the same as in continuous wound coils. The insulation between the two discs of one section is an oil duct formed with radial spacers. The size is fixed by mechanical and ventilation considerations since the stress is low. Between sections a large duct must be used because the st~ess corresponds to that across four sections in a continuous winding. The average of two small ducts and one large one is not greater than the equivalent distances in continuous coils. Turn to turn insulation must correspond to the stress of three turns in­stead of one. In the parallel type of basket winding as in Figure No. 68, the turn to turn insulation is the same as in continuous coils ex­cept that surge voltage distribution is better. The section to section stress in the first duct is quite low, and in the second duct corresponds to voltage across twice the turns in one section.

This winding quadruples the series capacitance across the coils. In many cases it can be used by using three or four basket coils at the line ends and then changing to straight continuous sections in the body of the winding.

d. Losses

Same analysis in continuous coils.

e. Transposition

Not used.

f. Taps

Not normally used. Could be applied much as they are in continuous coils. Usually the tap sections are continuous.

g. Cooling h. Mechanical Strength

Same analysis used for continuous coils applies.

i. Advantages

Used at the line end of high voltage coils, the series ca­pacitance is increased and the voltage distribution is improved. Con­sidered as an electrode at line potential the inner end of the first two sections is doubled in thickness. This results in a lower concentration

- 48 -

of stress at the end of the winding.

j. Disadvantages

Hard to wind and high-winding cost.

E. Rectangular Concentric Layer Windings

1. Strap Hound

a. A Construction

The analog between this winding and the cylindrical coil is very close except for the shape. In essence, it is a cylindrical coil wound on rectangular tube.

Winding Tube

,'-___ ---J)

r.-"!....,........,-....-------------.

Figure No. 69

The turn is one or more rectangular straps grouped into a rectangular sec­tion and spirally wound in a tight spiral layer. Pressboard collars fill out the ends of each layer and sheets of pressboard the full length of the coil provide layer insulation. Corrugated pressboard is used to pTovide ducts.Jngeneral ducts are provided only at the ends of the coil which pro­ject outside of the iren eircuit and only a few ducts are used in the por­tion of the coil inside the iron opening.

From one up to 12 or more layers may be used.

The high voltage or outer coil is wound directly over the low voltage coil reducing assembly time. At the corners .where the wire breaks sharply around the corners a strip of pressboard is used to prevent cutting through the layer in­sulation.

- 49 -

Figure No. 70

. .

For voltages above about 15 KV, a static layer is used across the layer at the li~e end as in Lowgrocap windings.

b. Current and Voltage Limits.

Rectangular coils have been developed for voltages through 46 KV. Current limits in strap wound coils are sufficient for the maximum KVA rating for which the construction is used at 2500 KVA, three phase. Mechanical strength is inadequate above this rating.

c. Insulation

Paper tape is used for turn to turn insulation. The minimum thick­ness of .014 is set by mechanical consideration. Layer insulation is of pressboard sheets, or oil ducts formed with corrugated pressboard. Major insulation is the same as in cylindrical or Lowgrocap windings.

d. Losses

Stray losses in this type of winding are not a problem.

e. Transpositions

The types of transpositions used in cylindrical coils can be used.

f. Taps

Normally taps are placed in the center layers of the coil and are brought out at the tap end of the coil.

g. Cooling

Ventilation of the winding is by means of ducts or partial ducts between layers.

h. Mechanical Strength

Rectangular concentric windings are weak against short circuit forces. Normally the low voltage coil is a sheet coil as described in the following section of the notes. In this core the vertical forces are very small. However, the horizontal force of repulsion between the windings causes trouble. The inner winding can be blocked to the iron circuit but the outer coil has no strength against this force and tends to distort to a round shape. The space between phases is blocked with pressboard and across

- 50 -

--------'--~-----~-... -~.<--. --.~

the flat sides of the outside phases is placed a steel brac~ ~hich is bolted or welded to the end frames. The ends of the coils, because of a corner radius on the mould, become roughly semicircular and do not distort.

i. Advantages

Figure No. 71

in the opening metal.

This type of coil is low in cost and has an excellent space factor opening. Space factor is defined ~s the percent of the area of the

through which the windings pass, which is occupied by the winding A high space factor goes with a low cost.

j. Disadvantages

Its inherent weakness to short circuit forces is the chief disadvantage.

2. Sheet Wound [.Re Ftr;.\,M-e Ne 3J

a. Construction

For 1mV' voltages and high currents the rectangular coil is wound with a metal sheet conductor in which the turn extends the full length of the layer except for a collar at the edges. The lead is a bus bar which extends down into the end of the coil. The sheet conductor is brazed

. t , )

1 L

Bus Bar c=====~~==============~~

Conductor

Figure No. 72

i',.' ~ .. t

Co lar

or welded to the edge of the bar as shown in Figure No. 72. Each layer is a turn. Layers are separated by pressboard sheets or oil ducts as in the preceeding winding.

b. Current and Voltage Limits

- 51 -

Current ratings up to 2 or 3 thousand amperes are possible. The voltage rating is usually not over the 1.2 KV class because the number of turns becomes too large.

c. Insulation

The layer insulation of pressboard sheets or oil ducts formed with corrugated spacers forms the turn insulation. Major insulation is no dif­ferent from the preceeding.

d. Losses

Stray losses are high for this type of winding. At the coil ends, the leakage flux cuts across the inner winding into the core. With flux cutting through a wide sheet, the loss which is proportional to the square of the dimension perpendicular to the flux becomes quite high, as

? great as 40 or 50 percent of the l~R.

e. Transpositions

To date no successful method of subdividing and transposing in the axial direction has been found. Radially the conductor is subdivided into sheets not over .040 thick but no transposition is available.

f. Taps

Normally not used.

g. Cooling

Ducts between layers are used.

h. Mechanical Strength

Use of a sheet winding for the low voltage largely eliminates vertical forces because the current distributes itself across the width of the sheet to balance it with the other winding. Otherwise the coil be­haves as does the previous winding.

i. Advantages

Has the advantages of the preceeding winding plus elimination of vertical forces on short circuit.

j. Disadvantages

The chief disadvantage lies in the high stray loss.

F. Rectangular Interleaved Windings

1. Strap Wound SCI: fiGIA~ No. /3

a. Construction

Strap wound interleaved windings are typical of shell form trans­formers. I t should be printed out here that "interleaved" is used in d' different sense. Up to this point, turns within a coil were interleaved. Here we mean that the complete windings are interleaved. The coils are of the disc type but are wound on a rectangular mould with a small radius at the corners. The individual conductors are rectangular in section. In an interleaved type of transformer, the leakage flux direction is perpendicular to the width of the conductor and as a result, the strap is subdivided in the direction of width. Up to four subdivisions are used, however, after they are all taped in­dividually, then the four are taped together to form a rectangular strap as shmm in Figure No. 73. In thickness, any ,number of such subdivided straps may be wound in parallel depending on the current rating. Figure No. 73

Finish

r I

,.' t;=--:;'. -. 1/

Start

A

Figure No. 74

tively larger than in c0ncentric windings.

The coils are all wound individually and then assembled into stacks. Com­pared to concentric windings, only a few coils are used per "iinding. Each individual coil is a tight flat disc rectangu1a~ in shape as shown in Figure No. 74. The thickness of the disc is the same as the 'insulated width of the conductor: W in Figure No. 73. Dimension LB in Figure No. 74 corresponds to the radial build in a circular coil and is called the limiting breadth of the coil. Comparee to the dimensions of the coils used in concentric windings the coils are enormouS in size. The A dimension in Figure No. 74 can be as great as ten feet and the limiting breadth up to 2-1/2 feet. These are extremes but at any rating the coils are rela-

The coils are assembled into phase assemblies with alternate groups of high and low voltage coils. Any number of groups can be used but normally

- 53 -

two or four are used. These are known by the number af spaces high to low as two high-low or four high-low designs. [SeE' FiGvf?eS No JS"-lfP.J

L.V. Coils

H. V. Coils

'___--.. ~ H - L Spaces 7 Figure No. 75

Two High-Low Interleaved Winding

L. V. /i

Coils: H. V. Coils

L.V. Coils

L. V. Coils

The more groups that are- used, the better the magnetic coupling between windings and the lower the impedence. Also, the poorer the space factor and the higher the cost.

H. V. Coils

L.V. Coils

Four High-Low Interleaved Winding Figure No. 76

Normally the low voltage limiting breadth is greater than that of the high voltage. Figure No. 77 illustrates how a two high-low phase assembly fits in, the opening of the magnetic circuit. For the. high voltage the clearance to ground "X"·m1jlst.be greater than the low voltage coil clearance :·"Y". However ;~·,the mould' sizes are selected in such a manner that the mean turn of the two windings is the same. The center lines of the limiting breadths coincide.

- 54 -

Lv. L.V

/ /. /, %, f'

'~, \Xl

:;; -.J

: ~ ~ ;.<:?-'.//</~ ~/7:;f,'/ ~//f>;/:0~.,--:.-=::;.i

Figure No. 77

.. "'"

I

rfrrr ,.... ~ I"l r-r fj iT

t"r~ , ,

II I I

l I! I

""i ........

~ i\ I ~ i'-............

........

" ; u» ~ --- - '-'- '--- -'- '---

Figure No. 78

Figure No. 78 illustrates how the individual coils are stacked and connected into a phase assembly group. The connections are alternately start to start and finish to finish. These connections are made using the wire of the coil which is formed and brazed at assembly. A static place with the same shape as a coil is used next' to the line in the high /./ ( « (I t ( , ~ < '" < < ( ," /' / ' " ... <' 1 '

k

f

II i I

lW

I'~ •• /'."' • ," ,'." ;" . . ' .-

Figure No. 79

." .< .,,'

- 55 -

voltage winding.

Figure No. '79 illustrates two devices which can be used in assembling and winding the coils to reduce the winding size and cost.

When two coils are connected start-start, there is no voltage between the coils on the inside of winding. At the outside, how­ever, there is the stress of two sections. By slightly dishing alternate coils, the space on the inside can be made small and that at the outside equal to the dis­tance required for the stress of two sections. This reduces the average spacing with no loss in insulation distance.

."--~-~~=~-'-'-=:';=- .--~ ...

"

For grounded neutral winding the voltage stress to-ground decreases as the distance from the line increases. At the line coil, full insulation distance "X" is required from the coil to the iron. As the winding progresses less and less distance is required until at the ground end the distance "Y" needs only withstand the test voltage on the neutral. Each coil as one moves from the line end is wound with a greater limiting breadth than the one which preceded it. This type of construction is known as graded insulation.

b. Current and Voltage Limits

This type of winding is used in the largest transformers ever built. The large dimensions of the individual coils and the multiple high 1m·, grouping which permits paralleling coils are favorable to heavy current windings. For furnace transformers, this type of coil has been used in winding for currents up to 80000 amperes.

Interleaved concentric windings are also suitable for any voltage class which has yet been built or seriously proposed. Designs have been made for 345, 500 and 750 KV.

c. Insulation

Surge voltage distribution in this type of winding is in­herently uniform. The large coils and small number of coils in series re­sults in high series capacitance. The analysis of surge voltage distribution is analogous to that in Lowgrocap coils in which the coils represent the layers in Lowgrocap construction. When a static plate is located by the side of the line coil, the impulse is distributed across the turns of the first section and then the- cap-acitance from coil to coil is large.

Turn to turn insulation, as in the preceeding types of coils, consists of' paper tape applied to the conductors. The individual strands of sub­divided turns are insulated with two layers of .002 paper then they all are taped together with tape to stand the calculated 69 cycle and impulse test voltages between turns.

With the rectangular interleaved windings a shell form core is used which surrounds the coils. Consequently, the coil to coil and major insu­lation is made up of pressboard washers, angles, inside and outside, corner channels and inside and outside corner angles, which box each coil and each group, of coils.

Figure No. 81 shows one way that these items are applied to a coil group containing four coils and a static plate. The limiting breadth of the coils is shortened in the figure with a break bet~.,een the inside and out­side channels. Each channel covers or partially covers an area 2 to 2··1/2 wide at each end edge. The turns between the edges of these channels are

- 56 - "

supported by a pattern of pressboard blocks which are-glued to the washers. See Figure No. SO.

Outside Corner Channel

Scarfed Joints

. ------------- l

Inside Corner Channel

- - fifI l~ J ~

Channels

/ I -- -.-------------r-t-~

~ ~ '\

,l Blocks, ,{7 (l

¥I/

____ -4-_______ _

/- . - ----------/

Figure No. SO

Detail construction of the washers with blocks and of inside and out­side corner channels are shown on Figure No. S2.

It will be seen that the channels and angles fold closely around the edges of the coils where the voltage gradient is highest and forms the coil to coil and coil to ground insulating function. The plane of the insulatiol is at right angles to the plane of the principal voltage stresses and this eliminates creepage surfaces.

As with other types of winding the sixty cycle and impulse test voltag are set by the BIL of the winding. Series and ground capacitances are calculated and the voltage distribution is determined and from these calcu­lations, the necessary insulation thicknesses and distances are determined.

d~ Losses

In interleaved winding the direction of the leakage flux is perpendicular to the width of the conductor strap. Since eddy losses are proportional to the square. of the width, the conductors must be subdivided in the width direction. A maximum of four subdivisions are used. To limit

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- 58

'de Corner Outs~

Channel

.'

. "orr" -6'" CENTERS " -ji] WIDE BLOCKS,..t; . Tt.O' 'iUTm: hT. . ISU' P"OIl Co

. '5'-0 MAX Ut I !!l LOIW-JG~8~LO~C~KS~. __ . __ _ ~A ,;, I.I!!!X 2-3-32-4 :.::

USE I ,,2, - 2 ..... I '____ ~ __

AU --- .. - --

Figure No. 82 .

'1 Tvasher CO~ • Wi,th Blocks

'de Corner Ins~

Channel.

the losses there is a tendency to use square wires or eyen to wind the individual straps on edge. Stray losses run from 12 to 25 percent.

e. Transpositions

When conductors are subdivided, they must be transposed in order to benefit in loss. In shell form transformers each subdivided con­ductor is twisted 1800 at a point half way through the coil. Usually tQis is done at the bottom of the coil. When more than one subdivided conductor is used in parallel, the transpositions are staggered to reduce the size of the hump in the coil. Such a twist permits the subdivisions of the strap to reverse from side to side of the coil.

I J i 2.. ! 3 14-1

1'4 i 3 i 21/ i . , . I ,

Figure No. 83

f. Taps

Taps are made from thin,flat straps of copper and brazed to the coil turn at the top of the coil. In very large transformers, it is necessary to carefully transpose the strands of the taps in order to reducing the heating which other~Yise would damage the insu­lation on the taps.

g. Cooling

Figure No. 84

Each coil has an oil duct adjacent to the coil surface. Thes·e are formed by the blocks glued to pressboard washers between the coils. The ducts are vertical and the coils cool excellently by either thermosiphon flow. in"self cooled transformers or by forced oil flow in forced oil cooled ones. When the oil is forced up through the boxing around the coils, the spacer blocks in the ducts interrupt the flow and change the directieu frequently and abruptly. This induces turbulent flow and gives geod coaling.

h. Mechanical Strength

Designing for short circuit forces in interleaved coils is no~ as difficult as in concentric windings. The large coil 'area results in unit stresses only half as great as in a corresponding concentric winding. The principal force is one of repulsion between the high and low voltage windings.

- 60-

Most of the mean turn of the coils is confined in the ~agnetic core and is packed tightly in the opening. The part of the coil outside the iron at

~ top and bottom is braced by a

'\ formed channel welded to the inside Tank Co~lS of the tank wall.

I~----I, A pattern is used for the .. I \

Iron'

" Coil

Figure No. 85

i. Advantages

blocks between coils so that ~very turn is supported at intervals short enough to prevent failure as a beam. Each phase assembly is built up complete and is clamped and dried by vapo-therm process. The iron circuit is then built up tightly around the coil phases.

Rectangular interleaved coils are ideally suited to heavy current designs. By using proper group arrangements, impedances can be con­trolled over a range of values. They have good surge voltage distribution and can be used for the highest voltage classes. With the vertical ducts and block spacers cooling is excellent for both therm0siphon and forced oil cooling. Such coils are. easily and effectively braced for short cir­cuit forces.

j. Disadvantages

For small currents the coils are flimsy and not easily handled. A great deal of formed pressboard insulation is required which is e~pensive.

2. Sheet ~r Plate Coils [S"ec: FIc,.LAr~ NJ 14]

a. Construction

Used mainly in furnace transformers for very high currents, sheet coils are made by welding plates of copper into a coil form as shown. Each coil forms a single winding turn. The width of the plate is the limiting breadth of the coil. Large bus bars extending upward are used for leads.

- 61 -

I I

t I , , ,

Figure No'. 86

b. Current Voltage Limits

This winding is used for high currents up to 80000 amperes with several such coils in parallel. Usually the voltage is low, 600 volts or less.

c. Insulation

Boxed pressboard insulation as described before is used al­though channels and angles are not always necessary between coils.

d. Losses

Usually the thickness of individual coils is kept dmm to 1/8 inch to limit stray loss.

e. Transpositions - f. Taps

Not used.

g. Cooling - h. Mechanical Stength

Not essentially different from the preceeding winding.

i. Advantages

Suitable for high current windings.

j. Disadvantages

Can only be used when the number of turns is small: 1 to perhaps 7 turns.

3. Spiral Strap Coils

a. Construction

As in the plate coil just discussed, a spiral coil forms a single turn. From 1 to 4 or more turns are wound in a spiral like a rec-. tangular Helitran coil. Conductors are formed of rectangular straps and all. the conductors in the limiting breadth are in parallel. This type of coil was once used for moderately heavy currents in small transformers. These windings are now made with concentric windings and the spiral rec­tangular winding is seldom used~

- 62 -

Figure No. 87

b. Current and Voltage

Used for heavy current and 101;<7 voltage in small transformers.

c. Insultaion - d. Losses - e. Transpositions

These problems are no different than in the previously described strap wound rectangular interleaved winding.

f. Taps

Taps are not used in these coils.

g. Cooling - h. Mechanical Strength

See for strap wound coils.

i. Advantages'

For moderatelY.. heavy currents this winding is lower in cost since it eliminates a number of brazed connections and other assembly operationE

j. Disadvantages

Useful only when a one turn coil fits thecurrent.rating desired.

4. Roebel Windings CSn hG-\.4reS /VosJ7f" ,D]

a. Construction

The turn is made up of a rectangular conductor made up of several strands in width and two strands deep. This conductor is wound flat around a rectangular mould and a strip of corrugated preasboard of the same width as the conductor is wound between turns forming a duct. This forms a rec­tangular coil as in the preceeding windings but considerably thicker. See

- 63 -.

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Figures No. 17 to No. 20 and Figure No. 88.

b. Current and Voltage Limits

The winding is used for voLtages up to 250 BIL and for current s requiring 0.4 square inches of conductor or more.

c. Insulation

Strand insulation consists of enamel applied to the conductor strands. Turn insulation is an oil duct formed by strips of corrugated pressboard. Major insulation and coil insulation is by means of washer, channels, angles and blocks of pressboard as previously described.

d. Losses

In the width direction individual strands are kept as small as possible by winding the strands on edge, for example .129 x .182 on edge. Since the coil is wide in the direction perpendicular to the leakage flux strands of the conductor must be carefully transposed.

e. Transpositions

A transposition similar to that used in Helitran coils is necessary as shown in Figures No. 89 and No. 90. Referring to Figure No. 90. The conductor consists of an odd number of wires. The space of one wire is needed to make the bend without bulging. Between the two transpositions this space is filled up with a pressboard strip "P". After each transposi­tion the location of the wires change as shown in Figure 2 (one full trans­pOSition 3600 clockwise). The distance "S" depends on the number of trans­positions needed in a coil. The minimum for "s" is about 3 inches. The . vertical bends and the horizontal bends are made over a short distance and very accurately so that the wire is moved exactly one wire height up or down, or exactly one wire width to one side. This can be done for each vertical and each horizontal bend by using an adjustable pair of bending pliers. The fact that all horizontal bends are identical and all vertical bends are iden­tical, and that the bends are dependent only on the wire size and not on the number of wires used in the conductor, also simplifies the problem of building a transposing machine. By bending each wire exactly, the wires have lost their tendency to spring out of the conductor and a uniform con­ductor is obtained with equal dimensions "A" and "B" (see Sketch 2 Figure 1) across the whole length. Very important is the space "E" between each ver­tical and horizontal transposition to slide back and forth when the conduc­tor is bent flat even over a small 2-inch radius. Thus, no spring tension is created between wires and the transpositions have no tendency to come apart. In addition, the space -"E" insures that two wire edges never cross. This eliminates essentially the d'anger of wire to wire shorts.

_ 66 _

SKETCH SHEE'r \ .' . ,-

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f. Taps

There has as yet been no necessity to try to work up a tapping'design for these coils.

g. Cooling

The ducts through the coil are shown on Figure No. 88 to­gether with the direction of oil flow. The cooling in actual designs has proven to be adequate for both thermosiphon and forced oil cooling.

h. Mechanical Forces

It is important to have a tight winding because the force is parallel to the layer direction and the turns must not climb one over the other and telecope the coil. Also it is necessary that the corrugated duct former be able to withstand sufficient compressive force to prevent it from deflecting and le~v~ng the layers unsupported.

i. Advantages

One of these coils replaces 2 to 4 standard coils. Thus fewer insulation parts and oil ducts are required and a considerable re­duction in winding space results. It is estimated that on 100,200 and 360 MVA generator transformers a savings of 5% in total weight can be made by replacing the standard coils in the low voltage \vinding with Roeble coils~

j. Disadvantages

Its economical use is limited to large transformers.

G.' Round Interleaved Windings

1. Core Form

a. Construction

This type of winding has been used for low voltage core form transformers when complicated impedance relations are required. They are suitable for low voltages only and several high low groups, 6 or more are req~ired to obtain normal reactance.

Coils are wound as double section round coils DS previously described. These are then assembled into alternate groups of high and low voltage coils with the finish-finish coil connections being brazed at assembly. Usually the high and low voltage coils have the same diameter and radial build.

----- ------, .---. -.-------~~~~-~-~--~--=======

b. Current and Voltage Limits

The construction described is limited to a maximum of 15 KV and to current ratings of about 500 amperes.

c. Insulation

Paper tape turn insulation is used. Bet,veen sections an oil duct formed by radial spacers and in the space between windings a com­bination of radial spacers and pres·sboard washers. All coils are assembled on a pressboard tube with a duct between the tube and winding as in double section disc type windings:

d. Losses

Stray loss is a function of the width of the conductor which must be kept as small as possible by. subdivision.

e. Transposition

These are made as in rectangular interleaved strap wound coils by twisting. the conductor

f. Taps - g. Cooling h. Mechanical Strength

These problems are solved as in the double section disc type of winding.

i. Advantages

The large number of high-low groups makes possible transformers with winding to winding reactances to meet special paralleling requirements. Also series parallel windings are easily provided.

j. Disadvantages

Confined to quite low voltage transformers when used in the simple form described.

2. Shell Form

a. Construction

One manufacturer, the Allis Chalmers Company, makes a unique coil design using round coils in an interleaved design which parallels the rectangular interleaved strap windings described above. The principal difference being that the horizontal core leg, which runs through the coils is

- 69 -

. ""

.' .. ..,:, ~:·i·~;;"""":··· .

uniform in shape to fit a round coil. Box type insulation using angles, channels and washers are used but ,made to fit round coils.

This winding will only be mentioned as above since the design problems require the same or similar solutions as for the rectangular counterpart.

- 70 -

. i

I .:

.'

~~ ... --~"'!""---~........, , '., .... 7:U"'~~" ·

\', '~\ ..... ;{.' , '. \ ,,;0 , j ... ,.: ,

,. "," ", ,., \ ' ',: 1\ ' .. " L...-"~ .... " : " \ ," \,-'

f: i\\\ ... --""" I..V.\,.....~ . ' . .1,1" ,... ~ \ .,~

; '., ' . Ij :) \\.\ \ .. " ..... " ... ,r- ::. .,

" .. ' . \ ' "J

r.'.· \ \ ,: ;'.\ t: '

L~ FIG. NO. f RECTANGULAR STRAP

r--····r-~.,.' ... -.-.'~~.'; .. ~.-,.;; .. .,' ..... ~~:~~ ~,~;-,

!;;". .. .... r.. ,/ " t~ . , , ,; o.

f t, I ~, '~~ , I

j., , j . " . ,. ... : '" '" • .j /' ", ' 1

/ '.. ."" I ", .' ..." 1 ./' ~I

--..... ~--------.

l i

"-. ~

...... ~_~_ ......... __ ...... __ ~ .:.. 'lt~.i

FIG. NO. 3 RECTANGULAR SHEET

):

FIG.NO. 2 RECTANGULAR STRAP WITH TAP,

, r"·-----.~-.

I' I., .. , ... ../" "" ,d,

;-". J:, . .'1

~~-_v

, 1

1

1

, " I r :' ,fl; ,',:'('1

, 1_" "d J

':-1

!, R"". .. /

~~_J FIG.NO.4 CYLINDRICAL

CONCENTRIC LAYER WINDINGS

~ I'

~ "

I .:j

",'

l )~

CONTINUOUS PANCAKE WIN DINGS ~ ....... 11\11\ III \11 np )111",;:)1)1,11));))11 \~),WI\,"\\!' ...,.... \PI

':\',i\\!!!\IJllflf 111/r{JlllllmtJI18E) , ',,' \\ ;., ;';~" 'i"., ., ~,~.' .. ' I,: ~J.':.~~.:'~ '. 'l'~~

''')'/.'11 "~'~"rf"'i'" ;"" .':'" JJlII'\1111»}Hl. );) '\ ',\, "\.'\,"'~'", \ .

J[[(ITI' w T\(\'\\I>~r.Jm,)~\\\\\\\)l,~t\~j i, j .\J, \ " <"f·}!I) I r f I w.'1~III'I'I\I\I\I\I\I\I'~I" ': ::il'Li'R · ',' I; "IJh~iV.l, 1/1,1,1,1 I'/.I..ut:'~·'

. ! \ i. l \ -:

" ,; \; 1",\<:: ... ' 'u:L:1

r--~----~ I

I r ' • = , Ii", \ I , : I" ; , 1 , 'I \ .', " '

! I, \ \' \ \; \ ; \! \' \ \ " " iii';' : ; Ii I ' ; I I iI" /' t: til , I: : I: P " r. 'I I I l ' r ; ~ , ! ,I",

) ,'I t ' ' ' J t '!'\ \':\:\ \ ' \ I '\ :!' \;, \": \ ,:' ~:'" "I ,'!J, '. " ,\, I, t, ! ~" .. . ~ 1, ;' ." . '" .\ . . 1

I '. \ ) , i', ,'Ii \:'~ I' , I' i,' ' ;':, Ii I;~';' " l ' , t, I', ,", ,: t, • ,I r

~\ ' " \'", \ " Ie 1 ! ,,'\ ' ,1 .'. \ \ i \. , ... ~. '_ ... --....._....a.....~ ._.to. ' ........... \ .. __ ,."--__ ".~A .............. l ......... __ .. L....L

FIG.NO.5 SINGLE STRAP FIG.NO.6 MULTIPLE STRAP

HELITRAN WINDINGS ' .. " -'-'~l ~.' ,

.. ~- .. - ,

"

. ,.' ,:=::~:~~,~,~'=:---"-. .:. . ".

Li ':,:.,: ;' ~j?":;}~~,;i,~ • "~. ::..,;~:::~ ~ ••• J' ~~ ,,: ,,;. ~ .~\ ~~.:::.~:::-;.:..: !,,':' __ ':':.: I

'~~.:.:..f1'~ ~~8·~::"_ .... ,","~~ ... !:.~~~:--~.~~~

('.~:J ';.." .~;, . ,

"' !"':':'"~--"¥','

"~ ,,' 7' '-..,.! ' ,., C'

... r'----'---- \

'-l , ... ,'.,

r --."i..~.;.>J·' ... '.'I·'-.. ..... -

~ ~ ... ··i---...... ·· ~

""'=- ~ i //

:::::,: : '\,-.:--,-~-.- , .. -._' ::----: .-,---- "--, .. ,,.

:::,===:' '~~-=~;- ::~=:~'~:: ::~~" .',r.~_-,~-:=-:-~.~~_;'~~.

.......... ,.-. ... ---._-.......... ----

~~~~)~-~~~;. __ 1

FIG.NO.7 SINGLE GROUP FIG.NO.S DOUBLE GROUP

,'. ,.;

j

-~.or,;...:. :;:.r. .. ·:'i;'''~:;'':''.l'''. ...-~, :.;"" .. ~~.,,~.,...~ ..

,...----~-:i::(~:::=.:·':.~; !.' ~ ... :,~

--,:::::":::::5:::::~( ... __ .. ~'.: .. ~:-..=~::::;=.'.~' i :

""', ----'-- " ;,--~~--~.-.. " .. ' ~ .. ----~~-~-~ .. ). ,'.

(. -----.... __ . i ~ ........ ~· ............ I_""'.·. i • 'r:----._. -">-

• 4 ............. "".·~~ '"'::'. ~ .... ~­

.<",\:f~.;";' .. h' , .•. >

~,..-... --,-........ ~ ..... ~ .. .,.. ... ~-~' .... ,.. ... i

~::-~:;.;;.:~._---'-=-"';::=. . .::~~. ":''-:.~' .. n ... '''''''· _ ..... _______ _

FIG.NO.9 TWO SECTION INTERLEAVED

r........... ~~ . ~ ..... -::., .. ,:.i~... 'l r //~~.1tt0it;. I l ' " T .

I· "r' ~,/',,;, - j

/ . , ~ " . )'" ,./ .. // .

I / :':,:,>~ ::;;:;, :'1' /

' ~, I./.~';')" "

i ·jlll ;/;'1,' . 1 ( I . 1/1 If, 1

I ~ ,(" ;l/ I ' , ;j .. J.. .. . 1/, ./V .,') It;, ,

t'; -;;:, /! ,c. (,J.t " ! . " l" '/''J..~ . " I "-"1," , ·//i'{1 If ~ • t: ' , " $': ! If ( 1 V l·, k_,";fllir;)t/./;L_~ __ _. . .... _J

FIG. NO.II INTERLEAVING CONNECTION

\ )

,......- ?_t "''I''r':''~'"

.~..<~ I ~~.-, • "rl~j I " 1J} , .•. ,.~ l\~',H~'h)~I~'·I~\'')'ll''\''';'.i!\ .. , .

dllll\I\\\\\\~\\\\\\\'~\\'I\ '\'\:\'\\~\\~~'\~\\'\\\\'''~ , i ,I .\ 1\" t (.,\, \\\ \\\\\\\\\\~;;N'\ "bh ) II/III Ii ,·1 \ \,1 i i; 1,,\,:1;',;,\ \)1. ,:1,1,\ I, ,\\I\I,~\l,~,,~,',\\:.:,\. \' 'I IIII1 \ I \ I \ \ \ I \ I \ II I 1'11\ '\ '.1 [I \ 1\' \ 1\' \ \ \ \ \ \ \', \ \ \ ~ \ \ \ I I,

" \'Ii) \.1\11

1..1,1..1.,11

,1..1,,1, .l.;:,:J\i}:l)'l.l\;.IIi\.:,~;\,i),;\(\:i\ " 1, +1/1)/"'){'"""I"'(,i"'t'I'.';'/' "'i; il~I'l'r:i)r.¥:'r'\' ~O:"~'!'!; ,; "'" II ,: \! '/ I' /1 '1" "I ,if ( 't' f, :Ii"

"li l/:'!I, l!ll.:( '1,1:/ , .ji/(I:' f'lI;t: l! {'Ii j I, \ I I ' ~ I \ ~,~ J, '" 'II , ,', :/!i,"IJ')",/"!(ifl/;ii .ifjliii/jiij~:'J/! :i: ,"/,,:

I I, ( " I, . / /1 . .'I/,,';I/I/~!If/ ,~ ':' "

...... ---------~.~----------.~-----".

FIG.NO.IO SINGLE SECTION INTERLEAVED

--.. ,.,.--~~-"---~~ ....... ---~-",,

' .. ~ ~'"

. :,,' .... . ' .. >," ~

c.~· . '.....' ',:, 'I

"

-~ .. -"';"-"""'-'-'" .

.,. . ~~

<'~'\, . ...... ....:-

. , 'i

".~,:$,\" I ,.~;~.:\~.,.i

. ". (:r~~:;~~~~~\ \'.' \: ,j .;"'::;:'~\ \ \\!

.. ~".~.~":.:i \ \ i --' \ ~

FIG.NO.12 INTERLEAVrNG CONNECTION

HISERCAP· WINDINGS

"

L

I

'j

I 1 I: .~

~ I .,' 1 !

(' ,-, ,,::,' .

/ --~-"_.,,-"- - ._ ... _-_._ ... ')' ,"\ ',:/ -; I I' " I,

' " ,'. ~ .' .' (I < ,

~ , 'j 1\ ':1 " 'i' - iJ ; , , k' "\ j. ;'

\' "' .. ,,~, __ . "., , • "_,, __ , ,,J /

\ ' . J \'

\. ! •

~ ...... ~ ",4;..,.~, .. "." •. ,_ .•

t, _ flli}:I:~~:t~~~

FIGURE NO.13 STRAP COIL

\;".. ~. .. :.' '. '''' '-:--'-.~':"'"

-':::, ~ ~~~.. INNER-COOLED ':.::; ~:::::, ,.:::-. oil -0- ' I ~;::j ~.::;-' , "'-=.-::-:; -.. .... ~

II I" r.,r.!IIT~ jl . -'Ill ~ ,',y, IT:----~~~I~~ ~._-, . "", II] ill

l

, ',I ~! ,', J ;:I1'~ 11'1 ~r :'O~'. "_<,/ 'I I \1! r: J: I I , ~'I' I I ! I'! ' t 1 WI"'" 1,1 :., I j _0ILOUC'5

1", I) lin t~ 1'1 I I) ) I '-..' ", 'I ,

I '"'' I 'I I "', 'i .. I: I "\ i'l Ill. ':' 'J ,I.) Il' I '"./.' , 1 'I I I' /. II ,I I~ ;~, :::',' ·-'i~ ,:',; I' /,E.saoAl"o ! I;) i:<lil! fll

; ;'.'.' ::; ~ , " .' , ,,'I ': ~l , ! ~ •• '. "', " I , " 'd l! ! , ,< ,:

t~'> :::::-:;. . .; . STANDARD

FIGURE NO. 15 INNER COOLING

RECTANGULAR

),

[

."' ........ ,..."..".. ... ..,.·-,.....,r~ .~.~:. '~,,'.. \ ....

~ (~,~;.~: ' h' .~. • .. ~"jA~;i{~ .. >~.,.. \ i':,;~," .. ·"'.,:. ~:~:_::~- ,~~\', :~;:~~~' I.~:. r:-:-:-~ .. " ..... -... ~i,

~ i

., ~, ..

-.:,.-., .,,:,~ ....... ~

)

I

L~--'_""- .... _. " ..... , .. ~ .. ,~.,.....:. .. , .... J FIGURE NO. 14 SHEET COIL

---~w .. ,' "'~--1 -'-.-- _-r-/, '~-::-I /' ~

'. /"{~'" , .~ ' .. \ \> ': '.,' I ' ". I :j

l , :.''. t. \

. " '

.", ,:~'-

, r·' " r.:.. ~

.:" \ .. ...,/

-.... _,-_. ',::.: ..

.,:;;

L· ::<

___ ~.J,' .. _ .. , ~ __ .,_ ...... -' ______ 1

FIGURE NO.16 PHASE ASSEMBLY

INTERL EAVED COIL

I 1

I , I

·1 1 I I .' ,

i' I.~ .

.'

I

I 1

"

I \1' '. :?!

.1]' ",~ ( 1

II

I II il Ii, h Ii I, I:

l

" \.,;

r--'~--' -~-.--'-"-. , r~-~'-~~

I . I

\\ ' I 1\ : I -l \ '" ' .:1

I ,,'i

l . .;-' >;->, ·'7' . I .

J ,_ "'~, : , ,r.,.-, l'I!K~lli'J1IIIII',' 1'''- / _~ \ .. """-

;eii:::.< '~,:. '"'c~:;i;:> 11111 /' ",,' ""'r::" ~'!-;-·1·

[

< :',-"-:'~ i:~:>;5":'" i '. r,';:;.;.::. \ f,·t' '. " . ,,\ I

," I '.1. J ' -,,' ,/ 11 ..-.. ' /,

~ v'" L,.:. ')':":'JW'

, .: ~

I, ,'~~'::~:.;~:<.~.( /~. t." .. ~.. '

.;.,!',.1 ,0" • ,.i)'·, I 'I" ,.:,.~:,:<\\\,\{~\~\-\ ,:,,,. ,.

.i ,;"ill

'/ <~tl~~~~~vj ,/ . . ,,,.,.'.,},,, ~~ .. :~;"., ~

,_. ,_ . ',-V<,,, >.,,»,.> '

I .! \ "~,·"t~:':':: 'C ... " . . j'; .'~~?~;>~>' .'

L''''''-''~': ::-,: .•. -

--"" '~"-' .:.:-~~-_/<"- .' ,_r .. "~ .-..;:$

FIGURE NO.17 WINDING COIL FIGURE NO.IS TURN DETAIL

r'·-- ,-... ,-.~~-'. ~ --, - ~---- 7-' - \ ___ ""\,,' - _.\ : _,'e . ~

I ,\', ',d ,-" ',.,~,,~< 11

! ; I ,I' ",~,~~" 't • ~ • ;. '" \"\\' .,

:\_ \ \ i :' I " -:" '\::~\ H . -, , .... ' I ' . ,\,~.. j . '\'~' .. ""\"\i\"~ 1 , t i: X\i .~.-- t d:,' : ,:;',,\\t:'i~;:qi,'.1

r

~ .. ,' r l \ .... -L .. ~~~.,. ;\;:',,'\\lik\qi\ / I " \'<~<J~.' \ \''';'-:~~'I~;~;:<:<~,i/;~,~'d

'\ . \ "',' i. : ;"):.,.:i,/ 'I~<>~ :~': I \. : . I.': ".:,1, / ,:". "~': I /, J I· . ~.,' >.; 1 Lv; L_.~~ __ ._'_. __ J._~_~ ___ ~. :.. . ..-J

'I !~ I

L -·"1 ,

.' I I .-', .•. ,, __ .1

FIGURE No.I9 COMPLETED COIL FI GURE NO. 20 COIL GROUP

RECTANGULAR INTERLEAVED ROESEL COILS

j

f

f l ~.

t

!

r

I

t r

r

t I

I

i k

... ,,;!

i;\

JL!. .- ......... t!"- .. S"'9_. ~. z .. y " •

" . ~ ... 5 ... 4''' ..

APPEl\TDIX NO 1

, SURGE VOLTAGE DISTRIBUTION - CONTINUOUS DISC WINDING

d /--_-;II-~

I", <..3

~~~--~~~~ ~~ CSL

/----;, /----; I,.. 0' CS3

It- -----=t.--. cf Cs4-

1---1' H-' ---T_ ... __ _ I -.Il - - ----r----' <3 c;-

t-----III-----1 ----~ ~-------------~

F·igure No .... A

] ~I;:=:c,

~1==CS"2.

--r--Co 11-----'----1 ~=C~4

1 =~=Cs.:;

~I=G' I('~--' Figure No. B

- ~--

Consider Figure No. A, a dia­gram of a disc type coil of 6 sec­tions. When a surge voltage comes in on the line it is a high fre­quency voltage and the inductance of the wi~ding acts as an infinite reactance or open circuits to the flow of current. As a result the voltage surge distributes itself through the winding by means of the internal capacitances. The coil for analysis can be replaced with a capacitance network as in Figure No. B. In this figure, the

- capacitances CS1 ' CS2. ' CS3 ----­CS5 represent the capacitance from section to section which are all in series to'ground. Each section also .has a capacitance to ground all of which are in parallel. These are shown as CGl' CG2, CG3 +---- CGG'

Consider now C~l. The charging of all G ground capacitances ·flow . through it causing, lets say, 6 units of voltage drop. Consider now Ca2, it has only 5" units of voltage drop. Like sinc,e CSS' has but one unit of voltage drop. As a result most of the voltage is concentrated between the line sec­tions as shO\vn in Figure No. C. The voltage instead of distributing uniformly across the ~vinding as shown by curve C distributes as at curve D. As shown, approximately 50% of the impulse voltage is im­pressed across 10% of the winding at the line end. The insulation at the end must be designed to with­stand these voltages.

---.. -- ----~----.,~====

-. "._t > . • • ,..; ~

-"' )

,/

,r--. !

)

"'0 c:: :l 0 ....

C,!)

0 .j..l

<II 0.0 co

.j..l

...-I 0 :::-

.j..l

~ <II CJ .... <II ~

1OQ;

90'

80.:

70

60

50

40

30

20.:

YQ-)

0/ 10 20 30 40

Percent of Winding From Line

-llb -

60 70 80 90 100

1· i

?-.~

)

f1! ~

APPENDIX NO. 2

SURGE VOLTAGE DISTRIBUTION - LOWGROCAP WINDING

A lowgrocap winding is a layer wound coil with only a few closely spaced layers. Solid sheets of insulation or a relatively thin oil duct are placed between the layers. The result is that each layer is exposed to the next one over a large area and at a relatively short distance. Since the layer to layer capacitance is proportional to the area and inversely to the separation, this gives a high series capacitance which is what is wanted •. In addition, a static cylinder which is a sheet of metal connected to the line is placed ar~fie ou ts ide<Yf-t-ne-c-o-rr:-"See Figure -Nb-:--n-:The ground capaci nne-es are -t'hentranSferred so that they connect between the static cylinder and ground. With this arrangement, the charging currents for the ground capa­citances are supplied through the static cylinder and do not flow through the winding. This has the effect, so far as voltage distribution is concerned, of cancelling the ground capacitances. The capacitance circuit across which the impulse voltage initially divides is as shown in Figure No. E. As can be seen, the series capacitances are large and the ground capacitances are charged through the static cylinder and the charging current does not flow through the winding. The initial voltage distribution then approximates very closely to Curve C of Figure No. C.

No +r-' -r ___ l.,. ,tv! STATIC.

!-l'Iyr(J.

C6/

Cs'1 C t

("I C'GoS ("1 t-C~4

G4-

-

Figure No. D Figure No. E

- 77 -

-----.'--...,.--~~~--- ----- --~-~ ..... --:--- -;-----:~.-----

./

The lowgrocap windings have the advantage that t-hey give a straight line distribution of surge voltages and eliminate voltage oscillations without complications of the coil structure. The static cylinder is a layer of conducting material wrapped over the outside layer of the coil and separated from it by solid layer material the same as that used be­tween layers. It does not complicate the ventilation of the coil, nor effect the major insulation between high and low voltage coils or from high voltage coils to ground. The mechanical strength and mechanical bracing of the winding are unaffected. These things permit accurate cal­culation of voltage stresses through the coil and insuletion can be applied uniformly throughout the winding. The result is a coil with minimum di­mensions which is simple in structure and which is strong against both, dielectric and mechanical stresses.

APPENDIX NO. 3

SURGE VOLTAGE DISTRIBUTION - HISERCAP WINDINGS

"'---"--~-r---r---'I"-'-.. - --,I J_ r-r========r--,-I_I 1-')

Figure No. F Figure No. G

____ ~ __ 78 -=----~_~=====,

. ::::

/UflN (l-------T"I ~-,., .. ---" --v

I I 2 __________ ~i __________ _

~

3----+£----4--------=r~------­r ----I+--------­C----I+---7 T" S -r

Figure No. H

L Cs = k '8

L = average length of one turn

Cs = Series capacitance of coil

• • pt*

Series Capacitance Equivalent of Arrangement in Figure No. F

Turn 1 2

5 6

3 4

7 8

Figure No. J Cs = k 4L

Series Capacitance Equivalent of Arrangement in Figure No. G

In order to reduce the turn stress and decrease the insulation distances and material required, designers are increasingly making use of interleaved windings to increase the series capacitance. One such winding which shows the turn sequence is illustrated in Figure No. G. This type of winding is in line with U.S. Patent 3090022 issued to Dr. G. M. Stein.

Figures No.. H and No. J illustrate the gain made in series capacitance by use of an interleaved winding. In the interleaved winding the first four turns lie side by side with the second four turns and it has 32 times the capacitance of the straight disc type' winding. Referring back to Figure No. C of Appendix No.1, the Hisercap winding would have a surge voltage distri­bution like Curve E.

- 79 -

" .. x ..•. :. ",f .....

~-"

f • I /

BIBLIOGRAPHY

1. Winding Space Factors Core Form Transformers - Transformer Engineering Memo TEM 1151

2. Insulation Clearances - TEM 218

3. Cross F101v Roeb1e Coil - TEM 1027

4. Basket Coils U.S. Patent 2347009

~. 6.

"Shielded Concentric Cylindrical Windings in High Voltage Power Transformers", by H. D. Stephens, General Electric Revielv, December, 1942.

"360000 - Volt Power Transformer", by J. R. Meader, General Electric Revie,v, December, 1948

"Layer - Type Windings for High-Voltage Transformers", by G. N. Leech, A.E.I. Engineering, March, 1961

8. Static Shielding of Transformer Windings U.S. Patent 2905911

9. "Interleaved Transformer Windings", by J. B. Price, Electrical Review, December, 1959 (British)

10. "Improved. Core Form Transformer Winding", by E. J. Grimmer and W. L. Teague, A.I.E.E. Paper 51-178, Transactions Volume 70,1951.

(11. "Design of Power Transformers to Withstand Surges Due to Lightning, With \ Special Reference to a New type of Winding", by Chadwick Ferguson, Ryder '. and Stearn, British lEE Paper No. 987 Supply Section, December, 1949

12. Transformer Windings U.S. Patent 2725538, E. J. Grimmer

13. U.S. Patent 3,090,022 - G. M. Stein

14. Interleaved Windings U.S. Patents 2453552, 3044031, 3008107, G. F. Stearn

15 .. British Patent 850645- G. F. Stearn

16. Westinghouse Design Manual Pages 1157.02 to 1177.18

17. Westinghouse Insulation Specifications Cylindrical Coils I.S. 61558, I.S. 61564 and I.S; 61579 Basket Coils I.S. 347679

Round Wire Wound I.S. 61568, I.S. 61566 and 1.S.· 347620

- 80 -

(

j

Double Section Pancake I.S. 347618 Continuous I.S. 347610, I.S. 347611 and I.S. 61580 . He1itran I.S. 61594 Hisercap (Twin Interleaved) I.S. 472003 Rectangular Concentric I. S. 553631

- 81 -

-"---"-~-'.-= ~-"--~ -"---=-~=-.-=-'

'. ~-. - -"'--.. ,:.:;:-::-"-""~ .. "-

"(" ./ ..

TRANSFORHER FUNDAMENTALS POWER TRANSFORHER WINDINGS

Problem Assignment

1. Given: 5000 KVA - 3-phase - 60 cycle - transformer high voltage 13800 delta, low voltage 2400 delta. Concentric round­coils. Design a low voltage cylindrical coil using the .following parameters:

Watts per pound l2R in copper at 75°C = 9 to 9.5 Length of coil over collars 39 ins.

2.

Inside diameter of coil tube 14-1/4 ins. Use 4 layers and 68 turns

Design to answer the following: Low voltage current Number and s:ze of rectangular straps in conductor Bare and insulated dimension of turn Conductor cross section area Resistance of winding C3-phases) Weight of copper C3-phases) l2R loss (3-phases) Length of average turn (mean turn) Length of winding including 15 ft. of leads (3-phases) Wound diameter of coil Number, size and location of ducts Thickness, location of solid layer insulation

References: Class notes - D.M. 1100.60 and 1100.61 for wire data. D.M. 1159.10 to 1159.15 for design data D.M. 1500 for general formulas.

What type of high and low voltage coil for each of the following three phase transformers? Why?

A 2000 KVA, 15 KV delta high viltage, 480 volts delta low voltage, self cooled

B 2500 KVA, 69 KV delta high voltage, 2400 delta low voltage, self cooled

C 12000 KVA, 138 KV delta high voltage, 2400 volt delta low voltage, self cooled

D 12000 KVA, l38KV wye high voltage, 2400 volt delta low voltage, Forced oil cooled

E 3750 KVA, 92 KV delta high voltage, 480 volt delta low voltage

82 -

..... :

3. In a cylindrical coil having a winding length ~f 36 In., a mean diameter of 24 whay is the capacitance between two layers separated by a 1/4 in. oil duct. Use a speci~ic inductive capacity of 2.

4. A two group helitran winding has 27 turns, 11 strands per group.

a. How many transpositions? No. of turns between transpositions?

b. Same questions if there is a tap on the 9th turn.

5. In a cylindrical low vol tage coil, why ,vould you prefer not to bring taps out of the outside layer?

- 83 -

Problem 1.

T1' 'lns [()nnel- [lInd ,1IfI~nt.ll:: POT.'er Transfonner Hindings

Lecture No. 3 Solution of rroblcms

KVA Low voltage current 3 x EKv

5000 3 x 2.1:

Copper cress section ~.[at:ts per P'::'.tn,J AL cC'ppe1.- crose:; section

9.25 0.36G Sq. In.

Turn D imens il.)ll S

Coi.l ha'S 68 tllru3 in 4 l:J.ycr-~. 17 turn per L:1),':r. Hinimum co1Lll-, Say 1" DH 1159.11 Coil 1cn,sth = 39" Dimcrl3icn O\7S1' cO[.lper = 39 - 2(1." collaT) 37" Allow [~'l- 18 t'Jrll.S 37/18 2.06 width ()f lm:n HinimTJm cultduc t,_, l' ta.ping .018 IJN 1159.10

Approx. thicknes.s Area _366 .178 ---2.06 Width

Designer used 10 G 102 x .365] all,l .024 tape 2 deep Bare turn .204 x 1.825 IusulateJ turn .252 x 1. 945 Cross section area :;: 10 x .03641 .3641

Layer Arrangl;.ment

- 5

SholllJ have at least Ol,e side each layer exposed to oil.

wide

Should r.ct have a duct directly l!.ndcr layer r..ext to high lo~v space. Designer used 2 dlJcts l/4"thick bet~veell lay<-~rs 1 & 2 and 2 & 3~ Designer used 1 s()lid layer of insulation @ee DM l159.l:U

Material 2(.030)p.n. Allow .076 Duct allow .265

Radial Dimensions Tuhe 14-1/4 ID x 14-3/4 OD

First coil layer First duct Second coil layer Second duct Third coil layer Solid layer insulation Fourth coil layer

2 ~~ 7.375

.252

.265

.252

.265

.252

.076 -252

8.989 x 2 :;: 17.978 a 18-'1/8

, ..

Mean turIl 0.375 + 0.'Ji{C] 11 51.5

Conductor length for 3-phase 3 x 51.5 x 68 = 876 12

Add 15 ft. £0r h:aJs

Resistance L =-- x 1000

89l feet.

.00<1906

AH = .89l x .0091106

.3641 .024 ohms

Weight 3.85 x AL 3.85 x .3641 x 891 1250 pcunds

6942 x 024 = 11GOO watts

Probh'm 2

A. Less 'than 3750 KVA. Cs(.! n:ctdllgular COllccntxic ,:,_,i13. Higb v<.lt:age - Layer \,lL'ullci ~Jith sCrap. Low v()llage - She.e t '-lcun.J.

B. Round coils because vUltage is over 34.5 KV.

c.

High voltage - C'!l1tinuous Low voltage - Cylindrical Round coils

pancake.

.. \ .. .,.

D.

High voltage - Hisercap Low voltagt;! - Helitran

Round coils

[Ahove 69 KV] [Cylindrical I~,O t used for HV over 69 KVJ

E.

High voltage - Hist!rcap Lvw voltage - Helilrall. Round coils

, ~Ylindrical not used for £,=,rccd oil coolin~ High voltage - Hisercap Low voltage - Helitran Dligh C\lrr,,~nt and high high vc 1 tage]

Proulem 3

C .224 A K

= d

A = 36 x rr 24 2720 K = 2 d = 1/4

c = .224 x 2720 x 2 x 4

Problem 4

T = 25 - 1 = 22 - 1 =

Problem 5

21

u =

n =

4875 Pil farads

n =

9 = 21 8 24

2S-1

3/7

6/7

27 21 1 6/21 1-2/7

As taps are taken out high to lC)\Ii,disto.llce incre.:.lses and 'impedance increases. . -,-- .--.--~-~~=== • ....:~.-'-.~-=--.-.:--.-.=.::;;.--:..---- ... ---' _.----'

COMPANY CONFIDENTIAL

., ....

TRANSFORHER FUNDAY!ENTALS COURSE

LECTURES NO.4 & 5 Gerhard M. Stein

DISTRIBUTION or IMPULSE VOLTAGES IN POWER TRANSFORMER WI~TIINGS

... _- .. -._--_ ..... -----------------------_.-... _--_._------_ .. _.-

LecturE 4

Lectures 4 & 5 "Distribution of Impulse Voltages in Pmver Transformer IHndings"

Additional Notes

TABLE OF CONTENTS

Lecture 4. Analysis of Surge Phenomena in Conventional Windings Page No.

A. Introduction............................................. 1

B. Methods for Determining the Impulse Voltage Distribution. 5

1. Impulse Distribution Tes ts of Ac tual Trans formers. . . 5

2. Calculation of an Impulse Voltage Distribution...... 5

a. Core Type Transformers................ ..... .... 6

b. Shell Type Transformers........ ...... .... ...... 6

3. Impulse Distribution Tests of Models................ 7

C. The Initial Surge Distribution in Core Type Windings..... 8

1. General Considerations.............................. 8

2. A Basic Analysis.................................... 8

3. Insulation Grading ................................. . 12

4. Properties of the Impulse Voltage Distribution in a Pancake Winding.............. ..•........ ........... . 12

Lecture 5. Methods of Controlling Impulse Voltages

A. Introduction ..•.......................•.................. 16

B. Shielding ............................................ -.... 16

C. Interleaving of Turns (Hisercap l.Jindings)................ 17

1. General Considerations......... ..................... 17

Z. Surge Calculations .......... ,....................... 19

3. Design Phenomena ...................•.............. ,... 22

Additional References........................................ 24

Figures 1 to 23.......................................... 2S to 27

- 2 -

.-':' /.1'".;: .. ,1: .. :,!,.::ac:5 ___ y. _ :,,,'Yfi-2? . .ci". 4U*?/;! hyq;:: .!l! __ ,+_:::p$gw:s .!pC spt?R .. !b~.~Z;!i!!(!l_;? .

,- -~ ~ ,.... . . - . .,-

ro" .,'

/

I

" ,. ',",

__ ~_ ..... .....,... ...... -~" '-0... .... ' _ ...... w ... · ... '_ ........ , ...... "ioij" ................ .....

Lecture 4

Lecture 1/4 Analysis of Surge Phenomena in Conventional Windings

A. Introduction

Transformers are exposed to lightning surges. Hmvever, this effect is mostly indirect. Actually, lightning may strike first a transmission line and create traveling Haves ,vhich later appear at transformer terminals, enter ",indings and create here elec tric stresses. Traveling ,vaves are like tidal Haves which may be generated by an earthquake in one part of the world and cause great destruction on distant coasts thousands of miles a,vay from their place of origin.

Other disturbances in trans former \vindings ,n:E'! caused by s\vitching surges. These transients are similar to lightning surges, but of longer dura­tion, and shall not be discussed in this lecture any further.

Transformer \vindings are tested for checking their ability to \vithstand lightning surges. The ':!aves applied for this purpose to the transformer terminals have been standardized, as shmm in Figure 1.

The traveling wave is simulated by the so"-called 1-1/2-40 ps full wave ,·,hlch rises to its maximum in 1-1/2fs and decreases .from then on steadily to reach one half its crest value after 40 rs. As a first approximation, this full ,-lave may be mathematically represented by a lfeaviside unit function which rises instantaneously from zero to its maximum value.

Since frequently bushings, ~od gaps or lightning arresters may flash­over while the lightning enters the winding, this condition is also simulated on the test floor. The corresponding standard ,vave is the so-called chopped wave shmm in Figure 1. The flashover occurs a fe,v microseconds after the wave has passed its crest and acts like a second full wave in reverse. This second full wave is, in general, much steepe~ than the first one. Therefore~

the chopping can cause greater stresses in the winding than the original wave but in opposite directions, so that both gl."OUpS of stresses some,-lhat cancel each other after the chopping. Th~ mathematical analogy of the chopped wave is the combination of t\·70 unit functions ~hmm in Figure 1.

If lightning strikes the transmisiiol line close to the transformer ter­minals, the ,"ave appearing at these terminals is less attenuated so that it becomes bigger 'and steeper, and the flashover outside may cccur before the wave has reached its crest. Such a condition is simulated on ~he test floor by the so-called steep front ,.,ave shown in Figure 1.

It may be pointed out that the tes t \Vaves Figure 1 Simulating the effect of lightning surges are measured in microseconds. That are transient phenomena about 1000 to 10000 Eimes as fast than nOL~al op~rating frcquencios so that, also, the response of the windings to these high speed transients is quite

~ different than the response to low fr~quency test"voltages.

* The numbers 1),2),3) etc. refer tr) the h;i)lir)~t"!lphy fur-ni.shed '-lidl the original notes, or at the end of these notes.

-. 3 -

.. t .' ' .. + $i.O::~,. :d6¥._ q ._ • __ y.~. _ _ , .. 4 &.owu ._. 54> .... , j. :;<)>2"'. _ ( .AliU .ki; .&_::S:ZwP.7 .. 9

• "0 __ • c·

Lec tun: 4

The response to the lightning surges, also referred to as impulse voltage distribution, shall be discussed for the concentric or core type winding and for the interleaved pancake of shell type ~"inding ~vhich are the two principal

'windings used in the design of power transformers.

For discussing the impulse voltage distribution in core type coils, the core and coil assembly shown in Figure 2 for a t~.;ro-winding unit shall serve as an example of two principal core type windings, the layer wound or cylin­drical winding appearing on the inside (L.V.) and the pancake or continuous winding found on the outside (H.V.~ Surge voltages may be applied on either one of the two line terminals (1) or (2) of the winding (H.V.) to be tested with the other terminal grounded or also sometimes left open. Both terminals of the other (L.V.) winding are grounded together with the core and tank. "

The corresponding impulse voltage distribution in these windings is actually a function of electric and magnetic fields continuously distributed through the coil space. This field problem has been converted into a circuit 1 problem of lumped capacitances and inductances already in 1915 by K. W. Wagner. ) In a more recent work on this subject 2) to 9)a winding is represented by two separate ne t1;vorks ~.;rhich are a capaci tance ne twork and an induc tance ne twork, as also shmm in Figure 2. In practice, it is difficult to make such an approximation, because :

1. No definite paths can be defined for-capacitance currents and magne­tic fluxes.

2. Extremely high eddy currents in the coils modify resistances and in­ductances.

3. The determination of inside winding stresses requires highly section­alized networks.

A further distjnction has to be made in a surge analysis between the con­ditions appearing in relatively short and long times.

At short times, current flm.;rs much faster into the capacitance network than" into an inductance network so that the capacitance network becomes excited first. Then the voltage distribution in this network will be the same as in an electrostatic field if all winding turns are metalically disconnected from each other. Such a condition could be generated also by a mere D.C. excitation of the network and is in general referred to as the "initial surge distribution".

At longer times current flows also into the inductance pnd resistance net­work so that the surge generates oscillating voltages to ground with D.C. com­ponentsof a straight line distribution usually referred to as "axis of oscilla­tion". Since these oscillations start with the "initial distribution" and have to be symmetrical to their D.C. value, the axis of oscillations together with the initial distribution approximately determines the size of the crest voltages to ground at any point in the winding.

- 4 -

..... : -.r~~;.:'.;"::. ::-;.·:~c-·

.:., .. " .,\11 ., G.-.. O:::Z:;; .....

.. , 01",-:

Lecture 4

B. Methpds for Determining the Impulse Voltag n Distribution

Hm-lever, the above method of determining impulse voltages in _windings from the initial distribution and the axis of o£cillation alone is frequently not accurate enough particularly because it does not include any damping and is confined to the voltages to ground while voltages across ducts and between turns are even more important to know. A more accurate and more complete de­termination of the surge voltage distribution can be obtained either by a test of the complete core and coil assembly, or by calculations, or by testing re­duced scale models of the actual unit.

1. The Impulse Distribution Tests of Actual Transformers.

Such tests were formerly made with high-voltage impulse generators so that their accuracy was limited by the methods available for testing frac­tions of the applied high voltage appearing at different winding points. Use of this technique was further restricted that flashover voltage of a rod gap and the corresponding chopped wave change widely from test to test.

The accuracy of measuring impulse voltages was greatly improved with the introduction of the electronic operated repetitive impulse generator ~'lhich furnishes an applied surge vol tage of only feyl hundred vol ts. The technique has been recently further advanced with the possibtlity of measuring small voltage differences between turns •.

However, all test methods have the disadvantage that the transformer has first to be bui~t before it can b~ tested, and are, therefore, not a complete tool for the design engineer.

2. Calculation of an Impulse Voltage Distribution

For practical purposes, the designer needs methods of calculating impulse stresses before a design is released to the factory. This is a formidable task, as demonstrated,for instant, by the great amount of literature generated on this subject through the years. An example is found in a paper of P.A. Abetti22 ) in which he lisis a total of 69 previous publications on surge voltages with-out even including any contributions of competitors.

The calculation of impulse stresses is the method predominantly used by Westinghouse for the design of high-voltage windings.

The calculation' requires equivalent capacitance and inductance networks, .is shmvn in Figure 2. Their analysis is fundamentally based on the first law of Kirchoff that the sum of the currents at certain selected junction points, called nodes, between the two networks has to be zero. The capacitances and inductances have to be lumped in the parts of the winding lying between each two successive junction points •. The corres12onding linear differential equations are solved by matrix algebra and computers. Z) & 3) .

- 5 -

-. .:vas~.~ .Wi. liE' tl.

.~.

-; " .

Lec tUrE 4

a. Calculation of Impulse Voltage Distribution in Core Type \Hndings

If these principles are applied to the calculation of impulse voltages in core type coils 3)1 winding resistances have to be added to the inductance network, as illustrated in Figure 2 for the outer (H.V.) pancake winding. The ultra high frequencies encountered in the surge transients profoundly in­crease the resistances and decrease the inductances, as compared ~vith the values obtained at operating frequencies 3). The network shown is actually not 'complete, since the mutual inductances between neighb"oring pancakes have to be considered in the calculations. Because of the loose coupling between all pancakes, air coil inductances have to be used.

The capacitance network, on the other hand, is complete as shown in Figure 2, and, therefore, easier to calculate. The other (L.V.) winding is usually, but not necessarily considered as a grounded surface if both terminals of this winding are grounded.

Examples of a calculation of the surge distribution in core type trans­formers under full wave excitation are shown in Figures 3 to 5 taken from TEM #965. 3) The calculated voltages to ground, sho,vn in Figure 3, are in fair agreement with test results if resistances are considered, but exhibit quite different oscillations if resistances are neglected, although the fund­amental frequency became about the same in e{ther calculation. A similar re­sult is obtained in Figure 4 in a comparison between test and calculation of the voltage. across the line duct. Omission of the resistance, however, changes here not only the amplitudes but even more the frequencies of the calculated oscillations.. Figure 5 continues the comparison between tes t and calculation made iu Figure 4 to longer times and only where resistance is included.

b. Calculation of Impulse Voltage Distribution in Shell Type Transformers

The'calculation of the impulse voltage distribution in shell type trans­formers on the basis of equivalent capacitance and inductance networks has be­come the standard method used by Westinghouse for design purposes and has been programmed for use with computers 2). Figure 6 illustrates the relative loca­tion of the interleaved H.V. and L.V. pancake coils in a shell type transformer and the corresponding form of the two equivalent networks. Consequently, these networks are similar to the ones introduced in Figure 2 for surge calculations of the concentric core type coils, except that the shell type coils have a much closer inductive coupling. Therefore, leakage inductances can be used in the computation of the inductance net~vork and the coil resistances can be omitted. As compared ~vith the core type design, it becomes, also, easier to include several windings, like the H.V. and L.V. windings into the surge calculations.

- 6 -

. "~'- ':::'.

-'c····

---------------

Lecture 4

A comparison with lest results is shmvn in Figure 7 for the example of a network ,vith 10 nodes taken from Figures 9 and 10 of McWhirters Paper2) \vi~h the applied I·lave on node 1. The comparison with test results looks fair and duct voltages can be obtained by the same method.

3. Determination of the Impulse Voltage Distribution by Testing Models.

This method has the disadvantage that a model has to be created before the design of the particular unit is completed. The model itself may consist. either of an equivalent-circuit like the one used for calculations, or the model may represent a scaled down version of the transformer itself or a combination of both forms.

The equivalent circuit model has the same limitations as encountered i~ surge calculations, particularly for concentric core type ,vindings. These limitations are caused mostly by the difficulties to compute the inductance­resis tanc·e net,vork and not so much by the accuracy wi th ,vhich an analogous capaci tance net,vork can be calculated.

In the scaled down model, sometimes also referred to as "The geometrical model"S) & 9)_, all inductances L and capacitances C are reduced at about the same rate as the dimensions. This increases the natural frequencies F because of F = 1/ (2rrYLC) so that the response of the scaled dmvn model to :standard impulse- waves applied in the test is different from the response of the actual transformer coils.

For this reason Mr. P. A.- Abetti8 ) has suggested a combination-of the scaled down model and the equivalent circuit model ,vhich he names liThe Electro­magnetic Model". This is the method used by the General Electric Company for their high-voltage concentric coil designs. The scaled down model is used in this electromagnetic model essentially for obtaining the required inductances. For this purpose, the number of turns in the model is raised so that its in­ductances become equal to the one in the transformer. The capacitances, how­ever, are supplemented by an equivalent circuit connected in parallel with the model coils and dimensioned to raise the resultant capacitances to the ones in the actual transformer. Since the required resultant lumped capacitances can be calculated vlith a fair degree of accuracy, the electromagnetic model can be made to be a close analogy of the actual winding.

This is ,vell dem0ns trated in Figure 8 by the comparison of tested surge voltages to ground and across a coil duct, obtained \-lith an electromagnetic model, with the·results of measurements of the actual unit .. These curves are taken from Figures 6 and 7 of an AlEE-Paper of Abetti 8). According to these curves, the maximum stress across a duct can be determined by Abetti's method with an accuracy of about 10%.

- 7 -

-.-' : ¢!E ".5..44£ .. ' ' l .. _ •• -_ ""_ I ._'(OZ •• WS •• , .& ........... __ ~5 _

," "

-. ' c "-, >'·,e ,-, .. - -'.,

LecturE 4

.c. The Initial Surge Distribution in Core Type Windings.

1. General Consideratio'ls,

The general methods discussed previously for determining ,the surge distribution in a coil are particularly intended for use at longer times where the inductance-resistance network becomes indispensable, If, hmv­ever, the calculations are confined to relatively short time intervals after the start of the impulse, that is to the so called "initial surge distribu­tion," vhere only the capacitance net"lOrk has to be considered, the problem becomes easier accessible to calculations and a more detailed analysis can be made of the internal voltage stresses.

This discussion shall be confined to the concentric cylindrical and continuous core type windings, as sho,vu in Figure 9. A series capacitance cs and a ground capacitance Cg with corresponding voltage 1/2 e and E can be associated with each element in the corresponding capacitance network. The elements themselves represent either layers or pancakes. In either case the same equations apply in a surge analysis so that the vord element shall be reserved for both, layers and pancakes. The concentric pancake winding will serve as an example in all numerical cal~ulations.

Since the relative voltage distribution in the capacitance network does not change with time during the initial period under consideration, the surge calculation is reduced to an electrostatic problem. However, such a distribution can only be generated if charging current flows from the line into the winding and between its elements. Therefore, the metallic connec­tions to and between these elements remain significant.

This is explained in some detail in the closing remarks for the AlEE Paper #64-l96)with reference to its Figure 25 for the example of a two-ele­ment pancake winding with three turns per element, Since this literature has been enclosed in the original notes, it shall be afterwards shortly re­ferred to as the "Paper".6) From the discussion of its Figure 25, it can al­so, be concluded that the capacitances of each inside inter turn space of a pancake, like, for instance, between 1 - 2 and 2 - 3, is the same as if these turns would be disconnected from each other.

2. A Basic Analysis

On this basis the voltage riistribution of e and E in the capacitance net­tvork, Figure 9, can be derived, as \ViII be shmvn with reference to Figurl' 10. For this purpose introduce:

X'= Distance of an inside \.Jinding point P from the line end A.

I x = Axial spac~ occupied bv a single element.

L = Length of winding.

- 8 -

_ .. _.- - - -- ._-"'.:..--------_-:. -.-

",'

.4i, ...... ,. -,

.' , .... _-_.- -...... ----_ .. -_. __ .. _ .... --_._ .. ------_._-~-'--~~- .. ~-~-~-..,.......-~-~---"'. ,..;; ....... -' ..... ; ..... , ............ ,.::..,'..;,:.::.. .. ;,

,...-" )

Lecture 4

N Total number of pancakes in winding.

E Voltage to ground at point P.

~ E Voltage across the element at point P.

e = ~E = Maximum duct voltage at point P.

El ; el = Values of E and e at line end A.

I Current to ground at point P.

i Winding current at point P.

Lumped ground capaci tance bet~.,een any junc tion point be tween two elements and ground.

Cs = Lumped series capacitance across

Cg N cg Total ground capacitance

Cs = csiN = Total series capacitance

t = time

p = d dt A differential operator.

Because of Kirchhoff's first law:

~(currents) = 0 at junction point P,

each element.

of Hinding.

of winding.

obtain

I = i (x) - i (x + D. x)

filhere I and i can expressed by the vol tages

E and e = -2LE at P according to

I = CO' P E; o

i = 1/2 C s p e

'Because ofi.:lx = L/N, this furnishes

i (x) -

i = L N

i (x +.:. x)

c pilE s- ~ x

=

.. -s

, i l (' (1)

~\ ,

-- -- ------------------ ---- - ---.-------------~--~- -+".;. =.t" ~ ;-

/

. . ' ... • ~. '. ,-. .4%.

LectUrE 4

If the c~pacitance net,vork Figure 9, is divided fine enough so that it can be considered as continuous, the equations (1) may be written:

di dx

Because of

di = dx

(2)

the quantity p in equations (2) may be eliminated so that both equations may be combined into

E

or, by

E

L 2 d 2 E ( - ) -2

N dx

introducing the total winding values C g

Cs d2.=E:...-..~ Cg d(x/L)2

and C , s

(3 )

Solutions of this differential ~quation are known to be the exponential functions +u(x!L)1nd -a(x/I)for which the hyperbolic functions e e -

+a(x/L) -a(x/L) sinh a(xlL) = e 2 -e i

+a(x/L)+ -a(x/L) xl e e

cosh a( L) = --~2---

may be substituted. Consequently, the solution of the differential equation (3) may be written in the general form

E = A sinh a (x/L) + B cosh a (x/L)

where Ai B and a represent constants to be determined.

For obtaining (i, substitute equation (4) into (3) and find:

1 = Cs 2 u Cg

c­C 0; =\ '.3

~Cs

or

distl-ibution constant

which may also be writt~n

u = c g N

c sl N

= N '-;!; ~s

\!hcre

= ~ =(i!N distribution cons-tanL Cs /

--------10

_ . .S :: _._'

. .....

(4 )

(5)

(6)

-____ . __ "_"~~'_V . __ .• _. _. __ • __ ...

'.

Lecture 4

is another form for the constant characterising the hyperpolic functions forming the solution of the differential equation (3). The distribution constants a and : are important quantities since they will be found to be indicative for the accumulation and corresponding size of electric stresses in a winding and, therefore, are a measure for the quality of the design.

The other constants A and B in equation (4) are to be derived from the boundary conditions that a voltage E, is applied at the line end A in Figure 10 while the other end B is either grounded or left open, that is

E(x = 0) E l ; E(x = L) = 0 (B grounded)

E(x 0) = El;

i(x L) 0 by equation dE or, (2), dx (x = L) =

For the conditions (7) the equation (4) becomes

El = B; A sinh a + B cosh a = 0

which furnishes A = -El cosh a/sinh a

so that equation (4) assumes the form

sinha cosha(x/L) - cosha sinha(x/L) E = El ' or sinh a

E = El sinha(l - x/L) (liB" grounded) sinh a

For the condition (8), the equation (4) furnishes:

(7)

(8) 0

(9)

A cosh a + B sinh a = 0, or A = -El sinh alcosh a

so that the equation (4) becomes

cosha coshax/L - sinhalsinhax/L E = El ., and cosh a

E cosh a(l - x!L)

El cosh ex (B open) (10)

Corresponding expressions for the duct stress e may be derived from equa­tions (9) and (10) as shown in connection with equations (2) and (3) of the "paper". Consequently, the duct stress e is determined essentially by the slope dE/dx of the voltages E to ground. According to the properties of the hy­perbolic functions in equations (9) and (10) this slope has its maximum at the line end A of Figure 9~ This can also be explained by the current distribution

- ;.n the capaci tance net~.,ork since the ground currents I have to be supplied ./ hrough the series capacLtances Cs and, therefore, load these series. caracitances Cs much more on the line end than in the rest of tIle winding.

- 11 -

- ~' •• p • ... ,.=:>. < -,"

iA' ~ Hj ...... .......

) --- .. -

--',

i

(~'--'''' /

, ';'

Lecture 4

3. Insulation Grading.

As mentioned, the duct stresses e are about proportional to the slope of the curve of the voltages E to ground in Figure 9. The fact that this slope decreases from the line end towards the interior of the winding, would, there­fore, suggest to decrease the insulation between pancakes ~vhere the duct stresses are lower. This, however, becomes self-defeating since the change of the insulation in one part of the winding has a material influertce on the existing stresses in another part of the winding, as explained in detail in the "paper,,6) under "Graded Insulation" and illustrated in Figure 11. The distribution constants al and a2 in these curves are a measure for the insu­lation clearances provided for on the line end and in the interior since, ac­cording to equation (5), a large a corresponds to a small series capacitance Cs ' that is to large clearances. Consequently, for decreased inside c,learances, that is for eX2 <aI' the duct stresses at the line end are increased in Figure 11 and vice versa. This condition is much more critical for small values of 0,

like for 0 = 2, than for large oneS, like for a = 10.

4. Properties of the Impulse Vol tage Distribution in a Pancake Hinding.

For a'more general analysis, the capaci t9-nce net~"ork Figures 9 and 10 of the series capacitances Cs and ground capacitances Cg associated with each element shall be named the major net~?ork. AS illustrated in detail in Figure 12 by a picture of the individual elements and their turns, each series capacitance Cs represents the lumped value of another capacitance network assigned to a single element. This new net,vork is named minor network and is formed by inter­element and inter-turn capacitances ce and c t associated with each turn. The whole winding is represented by a series of such minor networks dove-tailed into one major ne~vork. This simplifies the calculations since each type of network can be treated separately. An analysis of the major network furnishes the ground and duct voltages E and e. The minor net\vorks supply the series capacitances Cs to be entered info-the--major network and furnish also the inter­element and inter-turn voltages V and v.

As an approximation, these calculations are reduced to two dimensions with coordinates x and z in the direction of the major and minor networks.

In an analysis the boundaries of the net\vorks are preferably chosen along equal potential lines. The ground in the major net~vorks represents such an equal potential boundary. In a minor net~vork, hmvever, this kind of line can only be established under certain conditions. For instance, if the corresponding major net~vork is uniform, that is, if its capacitances do not change ~vith their location, the center lines between adjacent elements are on equal potential for reasons of symmetry. In an ordinary coil, this uniformity is maintained only on its inside, but is lost towards the ends, like at· the left coil end B of the circuit in Figure 12. In a pancake coil, in particular, one side of such an end element is practically open since the ground is relatively far a\Vay.

- 12 -

" ", P{~ "";;"

'tnet---

• < .. H ' ?' .

Lecture 4

The end element can be converted into an inside element by the addition of an outside metal surface connected to the line end, like on the right coil end A of the circuit in Figure 12. Such a metal surface is commonly known as static plate in a pancake winding and as static layer in a layer winding and shall, in general, be called a shield. If such a shield is located where the next centerline bet,yeen elements ,.,ould be found in a uniform extension of the winding beyond its ends, the whole coil can be treated as uniformly in­sulated.

If the end element remains unshielded like on the left coil end B of Figure 12, the surface of the next inside element may serve as its approxi­mate equipotential boundary according to field plots shown in Figure l5C.

Under these conditions a number of voltage distributions E and e in a m~jor network and V and v in a minor network are plotted in Figure 12 below the network against their respective location x and z. The major network in these plots is shielded so that its distribution depends only on its num­ber of elements N and on its capaci tan~e ratio cgl Cs which are_ combined in the distribution constant a = NyC Ic Likewise, the distribution in the

g s. minor net,york changes with its number of turns n and its capacitance ratio CiCt which are combined in another distribution constant 0= nt'ce/ct.

'---'1 The duct and turn voltages e and v are given in those curves by the -' slopes of the corresponding ground and inter-element voltages E and V in the

major and minor networks. This leads to the following relationship between the two types of voltages in the major network if a surge is applied at one coil end A and the other end B is either grounded or open. Then the relative distribution of the ground voltage E for a grounded terminal B becomes identi­cal ,yith the distribution of the duct voltage e for an open terminal Band vice versa. The distribution of the t,yO voltages in a grounded major net­,york and the corresponding distribution of the two voltages of an unshielded end element become identical if their constants a and (( are the same, as shown in Figure 12 for 0: and 0= 3. The addition of a shield, however, changes this and makes the minor voltage distribution somewhat symmetrical to the element center.

According to Figure 12, all voltages E, e and v reach their peak value El em; Vm at the line end. These end stresses increase also with 0: and and are important since they largely determine the insulation of the ,yhole ,V'inding.

For a shielded winding the analytic end s tresses V m = ~m/2 and v across an element for x = a or turn for z = 0 are, therefore, plotted in Figure 13 against 0: and' in form of nonlinearity factors Rand r taken from Figures 5 and 13 of the "paper" in order to shmV' their close relationship. These factors Rand r represent the ratios of the peak stresses ~TI_and V to their respec­tLve lin~ar values ElfN and liln and go over into 0: a~d~for large values of

-.13 -

. ... ~;:: . .. ~ .•. -_.JS.-. _" .. J?- .

-:r%rt :"'rtZ-'-

. - .---.--.. ~. -" .. ---~. .. ....... "w

/

LecturE 4

'these constants. By applying these results to the line end of a shielded winding with a given number of elements N and turns n, th.e max. voltage V = Vm across the element becomes proportional to 0: while the maxi-mum turn to turn voltage v = vm in the whole winding increases with the pro­duct of both constants 0: and),''-.

These end stresses Vm and vm become more complicated functions if shielding is omitted. This is illustrated in Figure 13 by plotting the shielding effect upon the actual end turn stresses vm and the series capacitance cs in form of their ratios with and without shields against~: Consequently, the shielding causes a considerable increase in the series capacitance Cs and in the corres­ponding voltage V~ acro~ the line ele~nt, but only a moderate reduction of the turn to turn stress vm at a given Vm particularly for a larger number of element turns. This means that the effect of.a shield upon the maximum turn to turn stress Vm at the line end is rather indirect since a reduction of this turn stress is mostly due to a decrease in the voltageVm across the line ele­ment rather than due to a redistribution of voltages V within this element.

Further insight into the shielding effect is obtained in Figure 15, A to C by a comparison of the calculations with analogue field measurements. For this purpose, a cross-section of the winding has been simulated on resistance paper with small metal pieces representing the individual turns. In the example shown, voltage is applied bet~veen the terminals of a t,vo element coil vlithout considering any ground surface. This is done for the three conditions of a coil with two end shields, without any shields and with just one end shield. The numerals I to 6 distinguish the individual elements. The corresponding voltage distribution, that is the voltage between an inside point and the left coil terminal, is plotted below each field against the location in the coil and compared with calculations. The contrast between the two outside fields and the center field in Figure 15 demonstrates the great effect of shields upon the field distribution.

, If, instead of this, .those shields are interpreted as simulation of equi­potential centerlines between adjacent elements, the fields at the left in Figure 15 appears as a two element cutout from the inside of a multi-element winding. Likewise, the field of .the right two elements #5 and 6 becomes the symmetrical half in a coil ~vi thout end shields, but wi th four elements 115 to 8, two of ~vhich are not seen, except in the voltage distribution shown below. Con­sequently, the field distribution of an unshielded coil changes fundamentally if the number of its elements is increased from tvo to four. In a t~vo element coil, the equipotential boundary in the field of a line element becomes the centerline of the adjacent duct for reasons os symmetry. The potential of the four element field, however, varies little in each inside element #6 or 7. Therefore, the surface of either one of these inside elements may be used as an approximate equipotential boundary for the net~vork of the next line element, as illustrated by the calculated voltages.

- 14 -

,/'"" ,

-' , ........

Lecture 4

This property of an unshielded ~.;rinding is maintained if the number of elements becomes greater than four, as shown in Figure 19 of the "Paper,,6) for a six-element coil ,.;rithout ground. Again, 'the voltage in the first in­side element #2 or 5 is nearly constant. The addition of shields reduces, in this case, the voltage drop in the line elements from about 40% to the linear value of about 16% of the applied voltage.

If the picture of an actual transformer is completed by the presence of ground surfaces~ as shown in Figure 21 of the "Paper,,6), both distributions in the six-element model are distorted considerably. For instance, the effect of the ground raises the voltage drop in the line element from about 40 to 87% of the applied surge in the unshielded coil and from about 16 to 29% in the shielded winding. Furthermore, the potential in the element 2 of the unshielded winding and in the elements 3 and 5 of the shielded coil increase in the direction from line to ground in place of an expected decrease appearing in the a9alysis. As a rasult, the voltages at the back ends Dl, DZ' D3 of the elements cannot be found by the analytic methods developed while test and calculation agree quite well at the front ends A2 and A3. Likewise, the com­puted voltage distribution within the line element coincides fairly close ,.;rith measurements in both cases.

- 15 -

"-

, .~. ~':~ .• :.--: .. " A&r± .... -~a ... ;.-·

\ I ,

"

, " .- -' _ ... -; ~ I

;, • J;'J ~'" '." r --

,

DESIGN GF TH.AN'SFCHIvrErtS - EEW-27l

INSULATICN CF TRANSFORMERS AND INSUlATING MATERIALS

The proper application of insulation is one of the most important phases of transformer design~ and it presents some of the most difficult problems. It is important because the life of the transformer~ to a large extent~ depends on the insulation. More failures result from jnsulation troubles than from apy other cause. Insulation problems occur jndesign because of the difficulty in evaluating voltage stresses accurately; the inherent erratic nature of insuJating materials; and the variations in strength resulting f~om processing j foreign materials 1 aging or deterioration.

Insulation must often serve more than one purpose in a transformer. In addition to its function as an electrical insu1ator~ it may often have to act as a mechanical support and also as a thermal-conductoro Such re~uirements oft.en diet·ete the choice of the dielectric materials to be used.

The problem of insulation of transformers may be divided into two generEl, parts - voltage stresses and insulation characteristics, Before the proper insulatiuu can be determined for a transformer 1 tha voltage stresses in the various parts of the I'rinding must be known or assumed. Hence, voltage stresses in transformer's wiD,' first be considered o

I, VQL TAGE STRESSES IN TRANSFGHMEHS

10 Voltage Stresses in Service

The ultimGte criteria of a good design from an insulation viewpoint is that ':,he transformer must stand the voltage stresses that it gets in normal operc.tion urlder actual service conditions. These voltages may be divided into three types~ continuous voltages 1 switching surges 1 and lightning surges,

The-long time? or continuous voltages 1 to which the insulation is subje~t€d determines the insulation design from a thermal viewpoint, These ·:on"tinuous '101 tf: €:es are t1s1'ally ra ther definitely known, Iiiost continuo'us O'ier~ vol tages ar,e for reg1;lation requirements and are generally of a loV! value, in the ord'3r of 10 to 20 percent. Runaway overvoltages may also be considered as long­time f:itresses. They may reach tw::i ce the values given for regulation, RUI'1away' overvol'tages affect insulation design only indirectly~ in that tb.ey may fix the minimum rating of protective equipment that can be used, such as lightning arresters,

Switching operations due to sudden load changes that may set the system in cscillation and combine with reflected waves may result in surges of long

_( duration = up to several hundred microseconds. Tests that have been made cn / systems indicate that the magnitude of such waves seldom go above four times

normal voltage to grotmd. 11 few cases have been measured that showed five times normal i and it is thought that six times norm&l is the very highest that can be expected .from si1itchingl_or from arcing grounds.

, '

-.. ~ ... ,"";:~ --: ~-.: :-

Lightning voltages resulting from direct strokes near the transfornler or from traveling waves along the line have a relatively short duration~ usually less than 100 li1icroseconds~ but may be high in magnitudeo The-lightning voltages are often limited by the insulation strength of the line or by the protective equipmento These lightning voltages are by far the most dangerous to transformer insulation of any of the overstresses to uhich it is subjected 9 and usually set the insulation design levelo Lightning voltages may occur as a steeP uave choppsd on the front9 as in the case of a direct stroke; as a chopp·ed rrave 9 such as when a traveling wava flashes over a line insulator on the tail of the nave~ or as a full TIaV8 9 such as a traveling uave that does not flash overo In magnitude lightning voltage_s may go up toJO .tC)_.2Q, times normal operatillg voltage to groundo Uith unequal voltage distribution within the winding the overvoltages between parts of winding~such as co:Hs and tur~s7 may go exceedingly higho Overvoltages of 100 to 300 times normal in such places arc CO!!!1!lon o Predet9rmining these tra.nsient voltage stresses presents the greatest problems in the dcsi:;n of insulation in transformers o

2u Jl.ielectric Tests to Simulde Service Conditio"21

One of the greatest aids in recent years to the design of insulation fc~ transformers has been the ·standardization of insulation le76ls and the est~bli~h~ ment of standard dielectric tests for the various voltage classeso Both impulse and commercial frequency tests are specified to represent service conditions o

These tests set a definite level to use as a basis for the insulation designo Hence j from these levels the voltage stresses at the terminals of the various windings are definitely knowno

a o lmEulse Tests

A standard impulse voltage wave to simulate lightning in~rvice has been defined by the American Standards Association (A~) as one that rises to crests value in 105 microseconds and decays to half value in 40 microsecondso

FIGa

Steep Wave 9 Chopped on Front C:e~· .. _c,-

100% ---:-1-1 Standard Full Wava

o

For z.. 1=l/2 x 40

K ::.. _ i et K1"" 0 0 01.65_ I I K2~ 3j)8 ~ \7 t ~ T1J;;.:l in/{seCa

·!i:~:v~'J---. ~---..:.l.I1"!" .. --~:---'i"'---OOO;-~--:P4-o ! 10 20 30 40 ;0 . 60 70

\i" ! t" C:, I Time in Microseconds

1 IMPULSE VOLTAGE WAVES -2-

' . . $-.- ..... _ CP .. '_,~"5." - -.. (-"..4_-._,\ ._c ".- __ .!i' _ ... s._

... - _ .. _ ... -_ .. - .. ----~-.-------~ ........ -~~~-'-'-------......... -~.~""'-'-----~--

E::L~t}18:"' 0. PCSlt-:'-:3 C: ci. r~egative pcl&rit,y· ~~a."'II:'"e rna:r ba ·.lSeu'3 b.:.t negati't18 is :~2;:'C::1..::e:~j2:d fer cil-insu1a ted and pcsi ti ve for dTy=tYPE: -::qu~pm:;n t. --- .,-........ _ ......... _---------._-.-....-

The standard ASA impulse tests consists of o~e application of a redu:,ad vo::tage full wave} and biO applications' of a chopped wave.9 follmvsd t-y C!i.3 application of a full wave. The reduced full Have is So to 70 percent of tha final full vlave and is intended as a pattern wave for comparison purposes i.i~ fault detscticn. The chopped Haves are chopped en the tail in not less than l k: 3 rr.icrcse:,onds depending en the voltage class j and are int,ended part.i8u~ larly to test the line and pcrtionef the Idnding~. The final full=\·rave test penni ts time fc!' id.nding oscillations to develop so that the interior parts of the windir~g are also stressed. During impulse tests} the transi''Jrmer is ex:;i "':ed at nermal voltage and the impulse applied on the_cre1?t ~f_the_nc~a.J­voj.:tage of oppcpi te pola....~ ty. Excitation may be<";c.;rri t ted by clltual- a.greement. '"\

In additien to the ASA ~~pulse tests as outlined above, the National E1.s::':;ic }fan~facturers Association" NENA, has included Hfr?E:!-::_QL":'.r.:l'§.:y~_i..'Ilpuls_e tssts li fo!' tri3nsformers. In these tests the voltage i'Jave is chopped c;,-. 'ihe

-::-:y-:::t:- before it reaches the crest by a rod gap in air. Since the :r.agnit.ude of these voltage·s is set at a higher value than for the cho:::c;ed i"ave test::::, and tr!8 rate of change of voltage may be greater j the3e tests 3.re more severe on the li::e tcr:-.s and ceils than any of the other tests describe.::!. Usually the frcr.t~ ef=wa7e tests are made without excitation on the tranSfC:1iler to facilitate 7cltage measurement. /

j The ',{estinghcuse !!"Q-~ali ty Control Impulse Testsf! for pCiler trans= fcrmers consist of t"jO chopped I'Taves folloHed by two full waves t-nthout ex(:ita~ tic:t:.. Bot.h the chepped and the full wave tests are made at 9S to lOS percer.t of the ASA levels. These are streamline tests that can be made on a porduetion basis tc simulate service conditions and to verify quality in the transfo~ers.

Transformers are designed to meet standard ASA impulse and NEMA fro.:t=cf-wave tests unless otherl-.'ise specified.

b. Low=Frequency Tests

Long before impulse testing was developedj tr~isformers were given a lew-frequency test to verify their adequacy for service. These tests now cO!"~3i5t of an applied voltage test follcvled by an induced vcltage test. The applied test fcr each class above IS kv is at tw'ice normal line voltage plus ene k7 rCll:-rded off to the nearest S kv. For IS kiT class a:1d belor the tests i·;-:re set special and are semevlha.t higher than by the above rule o The indu.ced test fer fully insulated windings is at twice the normal Hi.nding voltage. O=iginally the induced test was intended primarily to verif,y the insulation between turns and coils but it is too low to have much value for this pU~pCS9 a3 :::cmpared to the impulse test. However, this is alt-lays the last dielectric test applied to a transformer~ and it does serve a useful purpose as an extra :::he·:;,k on detecting any trouble from previous tests and in testing across parts of "'i.ndings $ and even between ccils where theTe is considerable voltage such a3

in shell~fcrm transformers.

-3-- --- .. _-------------

, r

., .;. .,,: .. ,...: .. "%' . ,.,.;1', .... )

In graded insulation designs for grounded neutral scrvicc~ the principal lOTI frequency test is a special induced test at a hjgher level. When the insulation level corresponds to the line voltage the induced test is made at 3046 times normal voltage to ground. Sometimes the insulation and the lightning protection level of a system is set one voltage class lower than the line voltagco For instance, a 138 kv system will be insulated and protected for a 115 kv level. In such cases the induced test for graded insulation will correspond to that for the insulation class. (

Since the induced test overexcites the transformer, it is necessary to use a frequency high enough to avoid an excessive exciting currento ASL Standards recommend liMiting the exciting current to about 30 percent of rated load current. To meet this requirement usually a frequency of 120 cycles or more is rec;.uired. V1het: frequencies higher than 120 cycles are used the severity of the test is abnormally increased and the duration is reduced in proportion to the increase in frequency. For frequencies of 120 cycles or less the duration of the induced test is one minute; and for higher frequ-:mcies the tima is reduced to give a test of 7200 cycles.

Graded insulation windings are also given an applied test prcviou3 t.o the induced test corresponding to the voltage class of the winding at the neutral.

The impulse and low-frequency tests for the varjous voltage classes \ of both distribution and power transformers are summarized in Table I.

j

., ./

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,< ~:: ... q:r .~. ..;.' f:-.. .. ......... ~<

<+ .. "". . . it " ..w.,.' ,i,; ... z' "ob -·'eO·· .' i'

-STANDARD IMPUlSE AND LOTI-FP,EQUlmCY TE-ST VOl.TAGES FeR TRANSFOR1lERS

it NEUA Front=of~ BAS! St!lldal'd Tm. u159 Tests j :Lo";7~FreQu~n.cy Test Ins'i,.l.= i Wa.ve Impulse Tests LI Chopn~d Ilava I 1ation Crest I Time to I' ~!in.Time Full Wave Oil Dry-Class Vol tag~ i FO Kv to FO 10 5x40 L!S . Immersed Type

__ ~K~v ____ ~~!~Cv~ __ ~~~M_S __ ~i~C~r~e~st~~M~S ____ ~r~~v~Cr~e~s~t __ ~I-:K~v~R~j,~~ __ ~~K_v_ru~~~~~ •

Tr?!'lsfo:cmal'S 15 Xv or Less and 1)00 Eva or Below ~. Distribut.1.on

102 'Ir --- - :1 36 1 00 30 ., 10 I 4

205 : - I 54 1025 45 15 I 10 5" 0 I - - I 69 10 5 60 19 12

1~:~5 . ~i: J: ,1~~ i:~ ~~~1 I ~i . ~ rrarormers ~1_15 Kv or Less and Over 0500 Kvo. =1 p~~p.r I

I 102 L 75 0 0 , 54 105 45 I 4 . 20' P = - I ~ - = 15 10 l 5,,0 ~J. 121) Oat;, 88 L6 75 19 I 12 I 8 0 66 ~ii 165 I 0 0 ; 11 110 1.8 - 95 III . 26 19

1,5 0 ~iJ 1qr; ,o,,? d 130 2 0 0 110 34 '31

2; 3401 /.,,(.;

,

Transformers

I 580 0 0 58

I 710 0 0 71 825 08825

960 0.96 1070 1 0 07

. 12LO 1 U

I~oo 11:40

Over 15 Kv and All Kva Ratin~s ~ Power

175 230 20 0 400 520 6':10

750 86;

1035 1210 . 1500 1785

150 200 2S0 350 450 550

650 750 000

1050 1300 1550

11 50

i ~~ 140 185 230

275 I 325 '_ 3Q &;

460 575 600

.. ..

_ ... ~o._'_. _-__ -=-_-=*_0-0-"- ___ 0 ____ -'-:'. _ ._- ------------

..... ' .. " .. ' ,':'.";

,'00 :'{#0:~ .;::.:~~:-.;:.,t:~S;::,~:- 0 '.

. I" .' ~ ... .... • _ , ""'" ,~ -' .• 0 ;::.'_;:: ~:".o ... ~ c •• _ .... :_ ':.!~:.':F4o,;~:o-:',~~ ... ~~~-f;;;t~~:,,&:\~::,-~

-.- -""----"------ .... ~ " '.

From standardized dielectric tests~ tt.,e maximum voltr.:ge stresses at the line terminals of the various windings of a transformer are definitely knm7Ilo Ons of the chief problems in the insulation design is to determine ho'l"1 the stresses under the differcnt conditions of tests and service uill be distributed in the various parts of the windingso In general the lo,,-frequency voltage distribution presents no problem since it is usually a matter of Itvolts per turn"o Houever~ special attention oust be given to cases involving series windings, pre7entive autos, and special winding arrangements where the voltage division is determined by the imp~dan~es of the v£rious parts and may be further complicated by induced effectso In the case of graded insulation designs, it is essential to determine just how the induced test will be ma.de - which winding to excite from; what point in each winding to ground~ and the polarity of each winding -before the design can be medeo A voltage diagram based on the conditions of test will shol'l clearly the low-frec:uency voltage stress conditions in the various parts of the trr.nsformero These test conditions must then become a part of the design information~ since the insulation design may be determined by the con-di t:3..ons of teste In genere.l the IO\/~frequency voltage distribution problems arc simple cOli1pared to those for imp.l1se, or transient voltages o

40 a o IprouJ,.s'e Vol taQ:e Distribution = Ini tiel Distribution

The impulse or transient voltage distribution in a winding can best '. be studied by considering first the electrostatic or initial voltage distrib".ltiono Strictly speaking$ it is the distribution resulting from abrupt changes ·in voltage 0 In practice the initial distribution gives the voltage when steep waves strike a winding, or when a ~ave is ChOPPA~ either on the front or on the tail. The initial voltage distribution deDends UDon the relative caoacitance throu h

atween coil elements as comoared to the c."oacitance from the coil ground 0

A transformer winding may be represented as in Fig. 2. Since the inductance of the winding does not affect the initial~ or electrostatic distri~ bution·the circuit may be simplified"as shown in Fig. 3. If the series and shunt capacitances are all e~ual the relative current distrrDUtion during the charging time at the instant the surge strikes the winding will be given by the number~ , in Figo 30· The resulting voltage distribution to ground wjll then be represented by the numbers in Fig. 4. This initial voltage to ground is now plotted in Fig, 5~ Curve A. It can be seen that the current required to supply the shunt ~apacitance elements causes a large voltage c'!rop across the line series elew.ent o

It is the.ca~t~Qe to ~oun~ that pulls the curve downward and results in high voltage concentration at the line end of the winding. II there were no ground capacitanco 9 the voltage distributicn would be uniform as shown by the straight line)? B? in Figo 50 Hence) to get good initial voltage distribution, the ground capacitance should be made as small as ~ossible~ and the~~~acitanc~ relat~ii'ely Iarge o A shell=form trsnsformer wit."h wide coils and a shorrcoil s~-gooavoltage distribution as compared to a core-form transformer ~ith coils o~narrow radial build and long coil stack o

Another method to improve the impulse voltage distribution in a winding is to design with capacitance from the line to supply the current to

, -0-.

.. ---..,

)

)

ground required by the shunt cap8.citances. If these shieJdiI'!g capacitors could be accurately proportioI'!ed to supply the ground current as indicated in Fig. 6~ perfect or uniform voltaEe distribution would result. However, such a remedy is sometimes more haz&rdous than the fauJ.t it is intended to correct. The quest jon of shielding is in jts final analysis, o'!e of economics and ;::racticability in design.

From the above discussion, it is seen that the initial voltage dis­tribution depends on the capacitance relationships in the windinr. In practical design, a distribution constant: .

0< =V ~t Cst

is first determined

0<. = Distribution constant

Cgt = Total Coil capacitance to ground

Cst = Total series capacitance from one end of coil stack to the other

The capacitances can be calculated sufficiently accurately by applyi!1g the" basic plate condenser formula, C = KK' A , .. hich reduces in practical units tOg d

C = 0.224 KA d

C = Capacitance in micromicrofarads A = Area of plates, average, in sq. d = separation between plates in in. K = Dielectric constant

For oi19 K = 2013

in.

For oil impregnated pressboard or paper~ K = 4026

For a combination of oil and PoB. as in winding-to~ground, high-to-Iow and coil-to-coil spaces~ K = 3.0

With the voltage distribution "factor, 0(" , known.J the voltage to ground at any point in a winding made up of a singJe group of uniform coils, for either a core or shell-form transformer, may be calculated by the following relations 8

--- ---------------

!:-

... , .. ~." _.*-

- .-/

, )

For neutral~ or O!1e end, groundedg

e :::: e sinh x 0 sinh (~

For neutral~ or one end i freeg

ex = Voltage f~om point x to ground

eo = Voltage of applied surge

= Percent of duct space from the point of winding in question to grollild

~ Distribution factor ~~ V :~ Cct

For development of the above relations refer to notes by Paul Narbut~ October 2l~ 1949.

These formulas can be used for multi-group windings also by first calculating the voltage at the series connections from the group'cap~citances and then applying the formulas to the line groups of coilso In calculating capaci­tances judgrne~t may be used to simplify the procedure and yet to approximate actual circuit conditions. For instance, in shell-form coils the turn-to-turn capacitance may be neglected because it is soall compared to the coil~to-coil capacitance whereas in core-form strap conductor windings the turn-to-turn capacitance is usually appreciable and should be included. 110re details regarding these practical considerations are given in the Design Manual and the Insulation Data Book for various types of windings. All of the practical design data for obtaining the electrostatic voltage distribution as given in the Design Manual and Insulation Data Book are based on the above fundamental formulas.

o.

-9-

1\

'\ " . ./

,.,;,1;

bo D~.E""~1:i9J~~i-.91L..at !m,! 'l,jm8. ,;tn and Oscillations

t:axj_IftUil Vol taqe to Ground

The maximum voltage to ground at any point in a t~ansformer winding involves a consideration of any possible oscillations in the windingo If the initial distribution varies greatly from uniform, or final distribution, the winding is apt to go through a series of oscillations before reaching it~ final stateo The insulation to groQ~d at eve~ point in the winding must bs adeGuate to withstand the maximum crest of the oscillations occurring at thE! pointo In oreer to determine the maximum stre~s bGtween any tvo points in a winding resulting from o[JcilJations, it is necenssry to eotimnto the ma7.:ir.'nm volts per tu.-u for the section of TIinding baing considered, or elsQ to plot the voltage to ground against time for the t~o points and to take the difference in voltage at the time the voltage i;:; maximUIilo There" is no shortc'U'c, accurate, and simple method for determining the maximum transient volts per tUZ11 or the volts to ground at any point for a given timo,o The actual uind:l.eg must be considered, and from its arrangement and constants it must be represen'tca by some idealized circuit that is practical to solve matheoatic~llyo Then tho capacitance and inductance constants of the circuit Buot ba ovnluatca. ?h~ final solution can be no more exact than the accuracy ill reprosontin:; thG winding by en equivalent circuit and 1n evaluating the constant!]. Henco, good judgment is required in setting up the problem. At b30t, the co@plete solution of such a circuit is usually a long, tedicus, time-consu~ing, and to soms deg~eo an approximate process. The designer is continually faced with the ~conomic problem of spending extra time for a more complete and exact calculation of voltage stresses, er the use of greater insulation margins to cover ~der vari­ations resulting from ~uicker and more approximate methods.

Practical approximate m~thods have been developed for plottinz ~-...... voltage against tice at any point in a winding br graphical means from thG

initial voltage distribution curve and the distributed inductance and cap~oi­tance of the winding. Since the inductance of a winding fixes the axis about which the winding oscillate~, it is desirable to change the abscisoa of the initial distribution curve "from percent duct space to percent inductanco, or turn~ squared. The variation of the initial cistribution curve fron a straight line is first plotted and gives a composite oscillating ~ave. This coopoaite wave is broken up into a fundamental and even harmonic waves. The periodo of "~ the fundamental and various harmonics can be calculated. Then the voltage for any point in the winding can be plotted against time by recombining the harmonica which appear at the point and superimposing on the axis of oscillation for the" point. The voltage between any points in the winding can be obtained by plotti~z a voltage-time curve for these points.

Since time and space limits the discussion here, reference is given below to rather complete discussions and analyses of voltage di~tributiou in transformer windings:

Manual of Surge Stren...~h Analysis for ShI311-l?ol'n Transformers bY' R. t. Brorm, Eng. weco No. lS"2"o

Calculation of Surge Stresses in Cora-Foro T~n~£orGer~ -An Approximate Graphical llethod by B. V. ~ipteu, Eng. Memo No. 216.

-10-

""

",

'i'ransient Voltr,gc3 in ST..wetricaJ. tU..':1ped l!et:::ol"'!w by P. L. B311c.chi and A. J. Palemo, gng.-none no. 2270 (This is a mathematical (I.nIl11sis~ and applic3 to oithai' core or shell-form transforooro). .

Analytical Studiea of Surge Voltage O;:;ci11ationo in. Sholl-For-r:t TI~ndinglJ by Paul Uerbut, EnJ. l1c~Q 110. 3400

c. J1.nfln of 11.15J.~,r',l D'-nt.:Ij.bJ-'tiojLC".,,~l'l t.,;') i1')~0~m~t'l'L/\~·\.:."}A~r'\.1"J Oscillation Volt:CC;:1:1

fhs initinl or electrostatic volt~gc diotrib~tioll C~-VG in n GO~~ tool for uoe in estinating the voltage otrsGccc ill uindincoo It 10 roluti7~ly eo.01 to calculato and C~!1 be predet~:n.~,-,ln~c1 r.:'-thel" Qccur::i:.;:;l;-. C2'~::a it 10 ill that 1::; noedod to estitlat~ tho ilJpulDO volt.'l[£O stres:JcD in n \7inl11::;. ~;J? inDt~co, in Q ~1nple core-fo~ trcnofor=or if tho coil-to-coil c=i tho turu-~ tu!"~ iooulation nt the liI:~ end io provid~d to uith::lb .. r..d ./(,00 vol~'~~o .l".?c:J t~::> initial d1st~ibut1cn end the reotriction is inpoDcd in the desicn rcquiriu~ t~~t all t~a and all co11 Dect10ns oust have the a~o in~ulatio~ uo et tho li~J end, than the turn and the coil in!lulat1on C3n ro fixed fro:! t};o initial voj.t .... ..:::;J· distribution cur7O. Also, the m~i~ volt~g~ to ~Torzd ~u bo eo~o~~ic:~ ~~ tho illi tial diotribution curve.. Refer to Sketeh F:1S. 70

:, c:I ...,

r-I

~ .p. A CI) 0 k Q)

Pt

, "'0, I ,

I , , D-1;\

125 1:,.1 ,-~,

, , 100 -:' 1_ ~Drl.ow:1 VoltnD to Grouzl

.'

75

;0-\ ,

25

., .

\ , , ,

- .• ' •• ! .• .• ,. ~.. \ . -- " . ,\

FiC. 70 ,l::lT.1.r::::l C;:,~i1loM.c~ Fron Ini t:1o.1 Volto.;::;::> Dle- . tr1b'.lt1cnp:::~~.?:;J l:.pplicd t.~, COo !Jld ot Dinuma wi th G~c~ Elld Gi-ounded 0

~"-e..., ..... ,.h;'\ . o "i

100 75 50 ~; 0 ~ Percent Duct Spco .

- rrrrrnrrtrrrrD0-:L _ .. . <i'------ .'. ---, 11 ' . '7 - ..

-, ':'"'' ,4 J ... :, ........... , .. ': .. ",' - .' .-~ -,. ..'<!: • - . ~ ":': r"'

',~

.... -,.., J

/

· The initial voltage curve, Ii, ,'fill oscillate about the straight line. The maximum voltage to ground at any point will be represented by the envelope curve, B. Each ordinate on B is as far above the straight line as the corresponding ordinate on A is below the line. Curve A h£s a distribution factor, c!. , of 3. It is seen that it just oscillates up to 100 percent voltage to ground. Note that curve D which has a distribution constant, C>( , of 6 may oscillate up to .~25 percent of the applied surge. The winding could reach 125 percent only if the applied wave were rectangular, or had a very long tail, so that tho point, P, uould remain at 100 percent until the.uinding had time to oscilJate to its maximun valuo. In practice, dua to losses, windings will not quite sniug up to the theoretical value but experience indicates that the damping is not ve~y great.

Consider another application where the two ends of a 'l'?indir..:; arc impulse tested simul·~aneously. This l'lOuld repreccnt a delta .. :1r.1:1116' in servic~. tiith traveling uaves striking t-;;o bushings at the same instant. Ref;;r to Fig. 8.

:0 as ~ r-I

~ ~ s:l Q) tJ s.;. Q)

~

150

125

100 , ,.

#

75

I

50 1~~--25

E ..... ~. ~ " ....

t-f? !~:J.Ximum Pyssiblo 'VoH,:;.g;; to G::.'Ound

llaxinUlll Vol t:lca to G:;round at Timo ';jhcn P has Di'cpped to 5~ Vn1uoo

~ Fig, 8. Eaxic~ Oscillation -14. \..,. from Initial Vol~ga Distribu-

__ "tion Cu...-va 0 S'Jl"Go f.pplied ....... B to Eoth Ends ot winding Simu­

Itaneou:;lyo

o ~.~----~----~~-----?----~~ 100 75 50 25 . a

-==::::::J Percent Duct 5:pce . '.

(. .~otYr«~ I ·to'

-12-

...

-.... -.

-. '-~-.-,;~~<~:':~~'" ," -----_ .. ~~.~~:::::> .. ,~, ..

"

./

-.. ... .. ::.;.'. ,. '-.,. * .. ·W"'~~~':"··'';'5:\'js:'1':;<'WW*·% -··M"'·~.

Tho :ini tisl 'Voltage disti.'ibution can be obt2.incd by plotting t7.'O CUl"\"GG t::'..n1 B ll.S though the surge struck each end \7ith the other groun:1cd, and by adding curves 11 rr..d B to get curve C. If P \1ere held at 100 prCf.li1'c. -U'iltil the s..-ing of the ~indin6 roachad maximum value, the voltage uould approach 160 parccnt as shovn in curve p. HOllever, the point, P, 'I'1ill decrease with the to.il of the wave. tilth a Dtandard Y.'8ve P .. ould be at 50 percent i'! ~.O nicro~occnds. If the period of the uinding \1ere 80 microseconds so that it uould reach ~aA~mlli~ value in 40 microseconds, the wi~di~g would s~ing up to 110 percent of the applied uavo as sh07ln by the dotted curve Eo Hence, it is necessary to calcUlate ths period of the Ilinding ill ordor to e:>tir:ate the r:::a:ri1ru:n vol b.G':; to p·ound.

rho period can. be readily calccl.o.tod fro:) the c:lrcui:~ cO;:Jot::nt.o t.;,' o08bining tho distributod inductanco OLd capaci~nco .into l~ped conot8nico The pariod for a single group of co110 ac at tha middle of a cOTo-fo?~ c~l~ of COils, or at tho contor of D. sb.oll-foro gl"OUp of coilJ, G t';7o"r.JGcil not7.'oz-:': ~1th ·outu::.l 1::.duc;tl.lcO coupling ::lO inil:1cJt:::d in l"igo C) ~ou2d OJ t::.:Jt!."

Fig. 9. Period for ~~o~ Mesh Net~ork TI1th Inductive Couplingo

... ....

!G Period of uiriaing at X in rn1crosacondo

•

G Capacitance as shown in sketch in ~icrc~icrofD.rads

e S3lf-i~ducta!'lc3 of the groups in eonriCJ$ .

C g L12 -(Ll + 12) = 2

cutual induct~nca bctneen groups in henries

Lt2 = selr-i~duc~~~ce of the t~o groups toge~~ero

.I;.

If two groups of windings are separatec like tHO' col~'1s in a ty;O­leg core-forZl transfo~~r, or two grouos 'of coil;) in a ~hell-roril Ylinoing, tho outual inductance, U, may be neglGctedo The paric~ at the series connection bet~een the groupe F~Y be celculated by the folJo~ing formulas ~n1ch refer to the cireu1t in Fig. lao

·: .. ,'.-

, ..

___ _ ,._ •• _ •• P __ .·.·, .... .t:_:. ___ :...~::~ .•• ____ ..• ___ ~_".~--"' __ . ____ •

--

T ~ Period at series connection X in mlcrococon10

01, C2 and Cgl = Capacitances as shown in sketch in microoicro~econdso

L1 and L2 = Salf-inductance of groups in h3nrieso

'" This method of calculating the period cay b~ extended to ,thre3 or more mesh networks o With the initial voltage distribution and the calculated period the general suings of the winding can be predicted very clo06lyo ,r-O? instance, a transformer with a load tap changer by means of a series t~~n~formor presents a probe 1m in determining the voltage at Xp see Fig. 110

I I

Hl ...... -: :- - .. "'" X <-B , .. \ ~ 1\ « t, \ I "

Fig. 11. Initial and Maximum Voltage Between Series and Regulating Transformers at Xo

G) bO CIS ~ r-i

~ ~ I:l G) 0 ~ Q)

134

I

I " 125

/ / ,

1001 \

\ 7; \

50 \

\ A

\~ -

'\ '\ ,

\ ,

If tlla cou:Jtants are such 8.S to' gi va an initial distl'H.,-ution so that point X nill be nt 11, thon X tl.ay sning up to 130 or 140 pGrc""nt 8.t, Bo IIO\;,evel'~ if Cl Co.11 1;3

increased to bring X up to D 1 then the winding Vlill swing only up to 100 percent at E. This method of increesing the capacitance across the serie:.> tranoforI!ler by special winding arrangement to limit the Siiing at X ha~ been used in actunl design and the voltc.ge distribution date. obtained to verify the reaultoo

In eOf1e typ~s of problems th·:; 'Voltage stres:::'.3!:J c:.u pZ'otJ.bl] bee'Go bo appro~i8ated b.7 cou8id~rin3 the rnaxioil3 volts per turno An &uto t~ngZor~or vith a voltage r~tio that appTo~~~CS unity prosents u very d1fricul~ insulntiou problem. Refer to circuit in Pigo 120

Fig. 12. Series Uinding of Auto~Transformero

Y2

HOXO

Since the characteristic impedance of the tI'ans3i~.:J1on line at !:l is usually 10';7 CD 200 to 500 ohms ... as compared to the lwpedanca o~ the series winding~ the surge voltage from Hl concentrates across the ~eries uindin3~ causing an excessively high volts per turno The high volts'pe~ t·~ m~y c1:0 be transferred to the closely coupled parts of the other w-i!::UngJ 0 ~:.11.J arrangement presents a difficult protsction and design problo~ th~t hnc net yet bsen coopletely and satisfactorily sol.ado Syst~m prot~ction problc~c erG' involved 0 Each problem is special? hut adequate insulation to stand tho volta per turn must be provided. Estimating the volts per tu...-n 10 the c.:!st ap~ro~e~o

******* Another oimilarproblem is e~countared in the caoe of Q rocrolati~3

transforrier as shoun in Fig. 130

, .

..." .• .,..,.=-,."" .. "",.-""' ... r< .. .,.. • .,.,.,.=·_'-.,..,,.,-.""' ... ""'..; .. " ........... ---,..,;...-.. ~~ ... - ....... """:.-........... "'""' ........ - ... ~."~,.,~.::.,~ .. ',.?.: .... :-' .. .,.. .. ,-.. ""-_.:-'.7,.-...... ':"". ~~-::-••.. .,....""". _""'. ~ ...... , "" ..• -7C',.-C.""'. "".-,,~""'. , ...... -..,~.,~.."......,.."....~,....,.,..,..".-.~-~~-,.~ .' .", ~ .. ;"., ,'. - ~

-.• ".,--_ .. - ............... -:...:--.--...:...~ .. ~--...:........- .. -----....-- ·k C~·"' er£ ,;> '. >~ -·k· .. , ••• >--4 y. ih·- '.:';;:. ., r 17"

j

L ~-----P Turns lbtio

Fig o 13. Isolated Windings in Re..ot:"Ula ting Transforcar.

~---------------4~-----~ S

If a surge strikes the series winding from the L side and the S side is grounded . through the line impedance r.hich is equivalent to 200 to 500 ohms ~ a relati'~~ly large volts per turn may appear across the high-voltage side of the seri(;'J

.. transformer" Since the series transformer may have p ~ta';j=\1p ratio p in this case 1 to 51 the voltage would be stepped up; and in th~ tapp3d windin~i acting as an auto=transformer, it may be still further st~pp~d up. Du~ to damping, coupli~1 a?d oversuings the voltage would notnocesss·r~]y to stopped up in the ratio of t:.::e turns lI but it1>'O'Uld probably be hi~h enough to ruquiro protect~ve equfF~ent to limit the voltage a~d set a kno~ level for th~ primary of the series transformer and the tapped delta winding. At the present tin!), one corner of the del~~ would be grounded and deion arresters.applied as ind1· cated in the sketch. The voltage stresses in these windings will be determined mostly by the protection level. The best approach in determining the stresses is probably by estimating the volts per turn.

e.. Experimental Data on Vo1tage Distribution :in Typical i'lindJn'1~

Voltage distribution curves obtained with a cathods-ray oscil~ lograph on four different transformers will aid in visualizing the response of a winding in soae of the examples discussed aboveo

1'hefirst set, Figo 14~ Tlas obtained on a lO\1c»voltage uinding in a shell-form transformer. It was a t~o h1gh-lo~ design arranged as sho~ in the sketch.. In Ca) both ends of the winding were tested simultaneously and the oscillogram shous that the middle of the winding sT1ings up to 25 porccnt

/-\ overvoltageo In (b) one end of the u1nding lias tested u1th the other end )

_._--------------

....

grounded. 'Ine midpoint of the winding only oscillated up to 5Q percent of tha applied wave.

* * '* * * '* *" In Figo 1; a similar conditj.on~ except the 10';7 voltage of a core

form transformer is shown. Both ends of the r1inding were impulse tested together~ and the ta.ps 8.t the middle oscillated up to 85 percent above the applied volb.g·3o The reaSon it went to a higher value than the shell-forn is that the initi~l dist~ibution for the core=form transformer i3 much poorer th~ that for the sholl for~o

The surves in Fig. 16 are for a line group of ~holl=for.3 tranc= for~er coils as indicated o The applied nave and the volt~ge~ at tho Derion connections bet·;ie.:m coils ereshoi7no These cu:rVGS i:ihoi7 hO:1 tho ... ~vc::: p:'o8'l".:lG:J

through the winding 0

***~***

In Figo 17 the response of a core~form tra.nsformer winding io shoTIno The oscillations in the winding are clearly shown. The curves ~it~

·expanded time scale in (b) show how each pair of coils is subject~d to streeD as the surge prograsses through the windingo These curves shou ~hy tho coil-to~

. coil ins'iletion cannot be reduced appreciably in the bedy of the uinding o Th0J also verify the nesd fOl" full line clearances from line leads to t.:l.p;J lo~tcd 25 percent or more uith1n the windingo

=17=

'.

100_

o

100

50

o

o

b 8 1 /1

111111

H. V. Winding

.... -----_...l 10 ~1

/ Voltage at Lo 170 Series COlmoction'

i I 10

[5

I I I

20

Time in Microseco~ds

Applied Dave

iii j i

30

(a)o Both Leads 9 and 10 Uere Surged Simultaneous1yo

~ Applied Wava .

, Voltage' at LV Series Connection

10 20

Time. in Nf.icroseconds ..

·30

(b)o Lead 9 was Surged and 10 was grounded.

Fig. 14. Voltage at LoVo Series Connection in Shell Form Transformer, 10000 KVA;; 1Eh. ~ 60N ~ Ho Vo 50 0 8. KV for 88Y9 LV 1302 h..'V ~ Experimental Voltage Distribution on Impulse Tests. Os cillo grams CSHB = 3130

--"7~ .. -.....".~,.---....".,.----,.....,... .• """"~.""" .. ,_-..... -:;" .. ;.~: •. "".~.,-.,.:.;,""~:~._-... ..,.,.. .. ,... .. -.. "p. ·=·:.7~::··~,,,.~-"·,,~,{:··,,,,,';..,""";:,,~""' .. :~".,..: ..... : ..,.,~t·-~·;".~~·2,.""'3't~?'~""I:.-_ ..... --:. ...... t.;: .... ::.~:-.. ,:.!,,-.<: .• ~_-~ •. "'"':,' ~_,...,. .. -:-.. ," ..... :... .

-.

" .,

Ho Va

:3 _...l----"I

2 - __ -.or

Ho V. Winding

Dri1 11 , 1;\'4 :3n2

I 54.3 543 f ' < t#

f9fJ I~ Fr-171 " -1J 171

II ,~ ; LoV. Tap3 ,...

L. V q tIinding

185 _L ___ ' Voltage at LoVo taps

150

co tlO IU

..,;I 100_ .....

~ ..,;I s:: Q) CJ M Q)

p,. 50 -'

20

Time = nleroseeond~

Voltage at Lo V~ Tap Changer in 111ddle of Uindina of Cora PO?J Transformer. 6000 gwao ll :3 P"no p 6(j;Yf) novo 69-.%.05 !Ivo Uy:J~ LoVo 1302 avo Deltao ~~I:inontal Vol~~: Diotribu~ion ou !=pul09 '.rest. Oscillograms C~B - 4050

-----~.--- -----.. _------.:--

-19--~--~--...:...:....-

.,

,-----. )

---

~ _.::::=:.-:.-t _____ 3...:;/\ H:i. t 'Y il. .\ ~ filII n l,-l

& fI j : B C ~ : ~ G:~ T

I I. r r~ 1

II -Lo Va Ho v. ~:I,'I! · I /1 I ~r: l~

[I :.JI~ i Ii ~. II c:l.. .0: 10 (3 I -.J

~~-.. ~-!T.,--------=:::-.~:.::...:=----~-------!:=::------~~---Y-2T

-=- 4V'\'..L_·--=:::::J===-~ ____ 2_~_5V_T ___ ....Ip:,J,-·_11_1·~_2tVT H~_ .. S-I!" 'i/,

I, I '.

i .,

I Pf -' I !~

'. "':' .. -,'

100 ~

U:i:th .:30;~\3-6C< Timing S:;'.,ep<,

G) 50 1lO. CIS +l r-1

~ ~

0 i ld

, 0 20 30 .A '~e"· ~4:i "'" c.

1OC

(b). With 10 "'\SeOo ....,~~

T:i.rn.i:::; C:-.-::::::p"

<D 50 ~ CIS

+l r-1

~

* 0 ~

0 2 4 6 8 10 »..seco

JF~go 16. Voltage Distribution in Line Group of Shell Porm Auto - Tren~rormero 65000 KVAo 9 1pho 9 6QA1s HoVp 15807 for 27) KaV. Ip L.V. 7602 for 132 Ko VoY9 To Vc> 1302 A Os,:dllcgrel!:3 E "" 238

" . ," ,

"""

.~.-.

..... ;,

H ... l Ho Va />,'-14

~ 1278

LoVa~ 15

n

H=l

;----z3~~8 , ~~·a ij..-..-').

L-J

680 16U

Voltage Distribution in Hoi" Uinding of Core Form T1"an$forme:-~ Type SLo 250 !vao>, lPho 17 60IVHoVo 69 A'7o fo:rA!.oVo 702 [vo for 12047 K70 Yo

Wire Wound. Coils ... 0064 Wi:re 0 Mo To "" 5571

~ ~ 12 Oscillog~ams CSH=ZP613o See Pages 22 and 23 for Voltage Distribu~ion C~veso

X2-=-

~,,,, .,,- .

,-.... ", ... .'6,_" _ .• IIt .. --; .... _, .-:5",.: .... 'OW L .,_

.~ .. -'~ ... ".,.:.-., ......... ',. .,-~:~ ... --.~ ... ~" "~~" "-'-'" "'-" ~

j

1

1 !

,j

j 1

''.

I ~.J &i""'~"\. . '''f)~. I ~~

• . , I ! '! / I ,ec>~ I ..... 7

.. : , ' "<. ',,; '"

70j, /S ea.) , Vt>/fetse /J/.s1(i4·~~+li~~rJ !h t~JI, """

, 'WlncJ/n!/. L)(t?I.7:l 7)n1c?, Sc~/e,-lal) /.-1 sec. See P"!je 1.z I tr COirIflef£e T/f/e Ci'1c/ SI< etch Si~ow/n.:J W1n.c//p):] 11 r'(a.l1j eme.nf. t:?.!'c;IIOfr~ n1S cSI/- tTJ '.

/Jee! ~/C( ve i" )( .. ;, '1r

QJ I')D rtl"lr -.I \ 'l'. " : . ~I • "I '" I _ ~r tatn' " 't' 'I

...... ' I'D n" .,_~ .- /:) I ............ , I -.:~ ,.. _I _ H ~ ~D, ,

1--""'" \' t ~~ I ~1C '.\..o

8D T,'me in

--',"" (, '

;, I

( '-.,

I '. ',~, :,'L'

:I.

! r II

ii :11

II I! II

I

II

'I! .- !

I

; ,

'1 ,; "

~

r'

;

l}! .",1

'~ ~((l

1 "

~ \ c .... · " ,~

~1'l ~ ....

...... ......

"1

J r

'j

:1 1

I

r':: co, .. :.~ t-. I-~ W !:=:'

:"1 H z -. r·'~ 0 1<:; [ij ~

100 / ---.... r-·-J,-90

I

80

70

fl'

~:ji 1

#- ~-3 I

60 / I

. 5f)

::1,0

! ! ,,I ~;!. i' Ie, (-

/ tV ,.I II

l ;'~

~,I

/ IJ II

;30 I: .~~ .!' :1

/ I; I'

-, ~. \

Figa 15. (b) Voltage Distribution in Ho V. Winding. Expanded Time Scale - 36 Hicroseconds. See Page 21 for Complete Title and Winding Arrangement. Oscillograms CSH-A-6130

, .

~-~ =-t-l ~II"I~ I T r I ' __ I-I . '. I. fl-I,-I,-I' I i ...... '

' .... ' .. 1------,- -. 'I "..--.~

- ,I' == _ L.2::.: /

/ - J; lk-I~ ~ .[

I~- T - N-::--:.- ~-.,J .1 . 11-' 111>r~;':E7i:=-~' '~+:0~'I~F;; I :I::-"'I~t -I)~";'~I' 0 :r:'.!-~I:"~~C-:::'::

:J '~18~9~;~LJ -.~~'

.,

r7 -;~0

. I I It /'<-1[0-11 I . , . Dr-c--~r~·· f....l:-.-!Ii 1_ 71 L.·· /;r!2~13I--rJ( _0 I -, .i"'I>'""" •• ~-.I·..,.--o..]~_I-:-;::-I-:::I-=-- I ~I ' r7~'I'~--1J ~::::=:r(,~rl~

rLI~I' :,'--.v _/ ~ . --.-I, I ,

-17/-' 71 Il

----. - - [,. '---, ....-~----. -- j~ ""'" _ - 'M . 1 ... - . I 11~=15 ~.' -., ~~ ~-~ .- -'-=---.' _. _I~":"-:~J ,- .-ncc-,""""- r ....::.' ...... ~~.I:.-~~, ..... ~~~~.' - ... ~:.. .... ~,~.7o:tr..:lOCl;:n:;:(;: . ....;-t.t&dk-M..~ ... -~~_·""'r.\:O:-.;:-!j,.,..;~;-~ ____ . .:,::.....~'-.='.M .. ;:.;;-.::I':a.:;a';;:,.: •.• ~ ............. ~~

{.J 2 4 6 8 10 1:: 14 16 H!~'O~~"'-·'21. 26 28 .30 :32. 34 36

Tlmo in Mlcrostl.'lconds

(' \ ( '\ , .~,

o ('<) N o .

, . r.(

r·'.~~ ,p

: j r~

,:~ i~ "';'

)!

f ! : ! ! ',; I ; i,: i

,I

:·1

II .I

'.: I 1

~.11 ,: ~

,I

:i~ :,'

;1 ~

"::'{~

I I:·· ..

~.

t~ oil~insulated self-cooled shel1~form transformer. rated at lO~OOO leva., single pha.oe p 60' cYC).SS9 69=kv delta to 13 0 8 k"v delta is shO".'m in sketch belo-:f o

In this problem c=nsider the high=voltage winding onlyo

l r''':: .-

The high='701h.ge \"finding; cOr:i.sis·cs of' eight rectangula.r pnncake coils 3/S-inch thick. The limitin;; brec.o.th of e",:Jh con is 12'1 s.nd the r:',Quld. is 22:.1 :;0: ~6" ...-rith h:o inch radii. The separ<::tiG::l be7\:een ::;oi:'s is Ol1e inch llnd from line coils to stc.tic pl:::.tes ons-half ir.-cno

The h.igb=to=low space from SoPo to SoPo is two inches o

The iron diI:1,:msions are as follow~ g

Opcnir",,; =: 15 VJ

Haight inc2u.ding tongue wedges ::: 411:

Tong~9 inoluding gap ~ lSn 1~OIE8 lI.3Gleot tilG t~i.r:l'='''~c~turn capa:.itan:;so

In :::::::.lculz.:::'ng -:;:-.'3 gr:;vn:l cap9.citan':'J consider the perimeter of iron tongue e.s ociplate al':.d the coil n'.ou..!.u as t;;,e othsl"o .A;3sume the ground capa;)itance i'rc=. the outsida rim of" the coils to iron and t~~ equal to that of the inside coil rim to iron tongueo

. Jo Speoify tha ASA impulse and Im.-i'requency te~~o . .J "'. :"; 20: Calculate the '701tage distribution conste.nt , ""\,J and plot !L'1 initial voltage

distribution curve using percent duct space a~ abscissa and p~rccnt voltage as ordinate o

30 l1hat is the initial voltage stress in percent? aQ From static plate to inside of line ceil o

b o Across ooi1 duct from ceil 12 to 110 .

LtV. C~'ds I ~fo4-

'.

'."

. :;--

,."

'.

Wo Lo Teague

)

GENERAL REFERENCES ON I}WuLSE CALCULATIONS

1. "Das Eindringcn einer elektromagnetischen Welle in eine Spule mi t Windungskapazitaet" (The penetration of an electromagnetic wave into a coil ",ith ~vinding capacitance),K.H. Wagner, Elektroteclmik und Maschinenbau (E&?:-l). Vol. 33, 1915, pages 105-108, Vienna ,Aus tria Text in German.

2. "Determination of impulse stresses \vithin transformer ~vindings by computers", J.H. McWhirter, C.D. Fahrnkopf, J.H. Steele, AlEE Transactions, Part III (Po\ver Apparatus and Systems), Vo1.75" 1956, pages 1267-74.

3. "Surge analysis of continuous coils by computers", G.N.Stein TEM #965 of 12.18.1961.

4. "A new method of calculating the electric stresses in .s. winding subjected to a surge voltage", P. Waldvogel and R.Rouxel, Brown Boveri Revie\v, Vol.43, No.6, 1956, pages 206-13. Switz~rland.

5. "A study of the initial surge distribution in transformer coils" G.M. Stein, TEH #1032 of 8.7.1962 .

6. "A study of the initial surge distribution in concentric transformer windings", G.M.Stein, IEEE Transactions, Power Apparatus and Systems, Vol. 83, 1964, pages 877-93, copy attached.

7. "Abstract of a study of the initial surge distribution in concentric transformer windings", G.M. Stein, TEM #1125 of 3.20.1964

8'- "Transformer models for the determination of transient voltages" " P.A.Abetti, AlEE Transactions, Fower Apparatus and Systems, \01.72, Part 111,1953, pages 468-80.

9. "Electromagnetic models for transformers", T. Hurter and G. Ecklin, Brown Boveri Revie~." Vol. 45, No.9, 1958, pages 410-18, Switzerland. Abstract in the Engineers Digest, Vo1.20, No.2, 1959, England.

10. "Transformer Engineering", L.F. Blume and others, book, Chapter XVII, John Wiley & Sons, London - Ne~" York.

: ... . . - .~ . .-. -~~.-~~-~.~:..: . ."'_ 0-

~

\ /'

• .1._.

REFERENCES ON HITERLEAVED WINDINGS

11. "Design of po.wer Transformers to withstand surges due to lightning, with special reference to a new' type of windingll A. T. Chadwick, J.M. Ferguson, D.H. Ryder, G.F. Stearn, lEE Proceedings, Vol.97, 1950, paper # 987, pages 737-50, England .

. 12. "Interleaved transformer windings", J.B. Price, Electrical Review, 1959, pages 927-30, England.

13. "Transformer windings", J.F.Stearn, British Patent ft587,997 and United States Patent #2,453,552.

14.

15.

16.

17.

"Improved core form transformer winding", E.J. Grimmer and W.L. Teague, AlEE Proceedings, Vol.70, 1951, Paperjfo 178.

"Calculation of initial surge voltage distribution in Hi-Cap coils for core form transformers", E.J. Grimmer, TEM #653 of 9.18.1950

"Impulse stresses in transformer windings", R.A. Zambardino, Electrical Times, 1960, pages 3-8 and 81-83, England.

"Design and impulse calculations of single conductor interleaved concentric windings", Reference Westinghouse Design Manual pages # 1159.23 - 25, 29, 30, copy attached.

18. "Electrical inductive apparatus", G.M. Stein, U.S. Patent if 3,090,022.

-19. "Graded insulation in interleav~d windings", G.M. Stein, U.S. Patent 4ft 3",246,270.

20. "Oil insulated Hisercap strap ~.,ound pancake coils with single or multiple conductors", Westinghouse insulation specification # 783,071 .

.... :;. ~.

/

G. Jr. Stein, Ft'llow lEI,'/:,'

Summary: Certain proper( i~~ uf transfnrlllcr windings in their responsc to lightning surges are investigated by a systematic study of the initial surge distribution, that is, by excluding the time e/Tcct. The investigation is further confined to stresses between Iay('rs or pancakes and between turns of concentric

. "'illdillb'S and to the voltage di,trii>ution between such windings and groundc(l parts. Insulation grading is considered. The

./ i~fluen~'e of static shields at. the linc ends is given special con­Bldemtmn based on !l. new an:lly~is of the series capacitance. By comparing: the calculations with measurements of the electric field distribu tioll on resllitance paper, some limitations in re­placing the actual field problem by circuit problems are un­covered and Hllitable approximatiuns are developed for ubtaining a praetical Rolu tion.

The in~tda t iOIl of trall~iorlller winding..; ha.s to be dimensioned to with;;talHllightning ;5ulge~. Thi" is an important problem, ilceall,.;{' mo!'t of the winding; ~p:t('C is not copper, but insula­tion, ,.0 t.hat the answer larg;pl~· determines the size of the appar:lt II,..

LightniJl~ ,t riking a transmi~~i()llline ercates tr:welingwaves which lllay l'nH'r equipment slich as tran"formers a.nd gen­erate \'nltage ~t.re~~es in the windings. c\:; illustrated in Fig. 1, the,,<.' wa\"C';; appear at the t<.'rminai:; in form of full W:l.ves, or, if cut off b~' arrcstel"li, as chopped wa\'es which may ha\'e a very l't<.'eP front if the lightning strik<.'s close to the nnit.

TIl<' volta~e ~tresses are the result of l'l('.·tric and magnetic fields whiC'h apJl<.'ur in a winding under ~\lI"l!;e conditions and thus hecome functions of location and time. This fieldprob-

-lem hai' been conn-rted into a circuit pl"Oblem in which the response to the surge i~ replaced by that in a continuous network of indud:mee" and capacitance,;.' By using this

·methorl, lllll.lly attempts ha\"e been made with varying success to prerleterminc the \"oltage transient" by the help of computers or modeb.:-"

.\" a fir!'t ~(('P for a fundamental study, thi" paper will neglect

FUlL -IfA'!E

TIME ----

(FRONT I

E I

TlME­

CHOPPED WAvE WITH STEEP FRONT

rig. I. Surge 'voltage waves

Pal",r 64-19, rt'c·u"ulumoed h~' tht' IEEE Tran8forrners Committee and approved hy the I1::EE Tec·hni .. al Operation" Committee for preo;ent.ltion at tht' IEEE Winter I'o\\"t'r :\Iecting, ~ew York, N. Y., Fehruary 2-i. 1!11l4. :\lanus,'ril.t suhmitted July 29. 1963: made a,·ailahle for prilltillg Dt'Cemher 5. I!Jli3.

G. "I. f';n:ls i~ with the Wc:<tillghou,;c Ele .. tric rorllOtation, Sharon, I'a.

The allthur wishes to acknowled~ .. the eontrilmtion oC the field me:t­~U",!IIentH mad .. h~" L. E. Saller with results shown in Figs. 11l-21.

f';F:PTF.Ml •• CI. WI;'!

any tran~ipnt phCnOIll('li:L I,,'yond casp;;. where the till\(' frum the start of t ht' applied 1\":L\'e and the COnSN]Upnt. curreHt. flo,,' for charging the ('a[la('itanl'(~" are "hort eHough "0 that no "ub­staritial magnetizing rurwllts can d(~\"l'lop alollg thc ('oudu('­tors of thc winding. ,\ccording to K. W. \Vaguel· 1 the wind­ing voltages form, undt'l" this ('ondition, a ~o-called initial surge distribution for which only the elc<"lrir fidel with it:; equil'a.lent capacitanec nl'twork remains to be analned bl' reducing the windinf!: to all clectro"tatie model. 1:hen th~ highest stre:;"p" will appear insiuc (he eoil at the "amp time that the applied voltage reache,; its maximuill. EX[ll'ripnce shows that the above approximation is frequ('lltly ntlid only within about 0.1 miC'ro"econd. This is a much "horter time than normally encollntered in commercial te~t" ami actual field service a.t the peak of the applied I"oltage. Howe\'cr, the initial di::;trihution i" indicati\'e of the effect of thc roil size and shape on the I"olt:q:?;p ~Lresse" under stl'ep front wa\"cs and on the amplitude of the \"ollUge o~cilbtioll~ at lon~er times.6 The analy . .,i" Ill:Lcle will abo furnish the lnmpt'd capacitances to be u~ed in computer calculations where coil inducta.nces ure included.

The discussion will bE: further conTIned to the concentric layer and pancake windinr;s {llustrated in Fig. 2. 'Whcn the analysis of the two types of windings becomes different, special consideration will be giwn to pancake windings. Since the indiyidual layers and pancakes correspond to each other in surge calculation~, they "hall be both referred to :1" winding elements.

The problem i~ to find thc \"oltagc ~trp;:"e" bd\\w'n e!leh

LV LINE

DUCTS

LAYER

/

INSULATION

CORE

...J

PANCAKE . WINDING

P.1NCAKE

DUCT

Fig. 2. Concentric transformer windings

.. .,.-..

elemcnt and groulld as well as bl'twccn dements and between turns, particularly at the line cnd. These "tresses depend on jJle &,lribution of the continuous electric fidds out,side the

:lductors. In accordance with previous practice, and as an ·;J.jlproximation, which will tum out to have its limitat.ions, this field proulem is converted into a circuit problem by the intro­duction of IUlllperl capacitances. In general, the lumped ca­pacitance networks thus obtained are in turn assumed to be ~ubdidded finl'/lellough to be treated as continuous so that the stre~~e~ ('an be a~sociated with individual winding points and l'l'prcsented by analytic funl'tions.

This procedure requires that t he actual windings have to he rCl'i:tced fin::t by a ~ystem of l:tlpacitances which has the ~ame dielectric properties under the condition of an initial \'olta~e di~trihlltion. Since the arl Hal respon~e of the winding to t he applied impulse voltage i" a transient phenomenon from the beg;inning, for which the e1ectro~tatic treatment is only an approximation, the metallic connections between the ends of the individual elenwnt" rf'main an important part of :1ily e'luivaiPnt capacitance network. .\ccording to Fig. 2, lI'indings ollly will he con~idercd where adjacent ends of clements are alternately connected together.

T1", all:t!Fi~ oi these structurc~ is ~implifiet! by distingushing Ld ";cen the major \'oltage eli::: I I'ihntion, repre~entillg the volt­:lc;e levels at t he connections between adjacent elements, Fig. 2, :cnd the minor \'oltage distribution indicating the voltage changes over the ~Ul'face of a single element. These two problems require different capacitance networks. The first or major network consists of the lumped ground capacitances from e::\('h e]f'ment to ground and of the lumped series capaci-

,-,-q,llces lX'tween the ends of adjacent elements, us shown in );s, 3(.\) and 7(A). These series capacitances will b~ .ob­

t;ined from a solution of the second problem where the ground capacitances are omitted and each element is represented. by a minor capacitance network consisting of lumped capacitances

, between turns of adjacent elements and between consecutive turns, us shown in Fig. 10. .\ solution to problem 1 will furnish the voltages to ground at the junction points ootween elements and the element-to-element voltages between ad­jacent junction points. The turn-to-turn stresses will appear in an analysis of problem 2, but will actually depend on both voltage distributions. '

Windings with uniform insulation and with an 'insulation graded according to the voltage distribution are co.nsidered. This will include also the effect of shielding the first line ele­ment.

The Major Voltage Distribution

For computing the major voltage distribution, distinguish between the fields outside and inside the winding. As shown in Fig. 3(.-\), the outside field is represented by the voltages F1 and ground capacitances c, from individual elements to ground' while the inside field corresponds to the voltages e and series capacitances c, between adjacent junction points of elements. The ground surface appears in Fig. 3(A) as a. straight line and represents the cqu:l.l potential surf:u:es of the core, the tank wall, and other grouqded parts including neigh-

_ p.oring windings.

_~;;I~ORl[ INSULATION

All clements of 3. uniformly insulated.inajor network, Fig. 3(:\), have the same ground and series capacitance'S CII and Cr.

This includes the elements at the end points A and B. The condition proves true in a winding where all duets or-all alter­nate ducts between elements are alike and the coil ends have

.,.":.' 1'5

'--.--.---- -- L ----L_____ x .----- -'-6X-1 I I i

-- --I

E~~~ l~lu-~q~l lJE I A, _ I ~ -v 1 _11_ LINE I e, - - - - e -

I I - ,'WINDING'! I'll I (A) L1~ ELEMENTS~ ill' I : I , , I I I

l ii' : I :

I

(a)' E,: I, K I <. II'

I I

GROUND

liNE

E, I 1 1 "I: lC) 1,_ rKg Kgr GROUND

I liNE A Ks B

iGROUNO I (!~I

i 'Z _._ t.

8

Fig. 3. r,'ajor capacitance net';;or!( of a winding wiih uiliform insulation

A-lumped ground capacitances from each element to ground and lumped series capacitances between the ends of

adjacent elements 8-Single lumped capacitance C-Equivalent 1r, consisting of capacitances K •• K .. K.

static shields. Certain properties of the roltage distribution in such a network are knolVn. 1,s,7 Others ha\'e not been men­tioned yet, 50 that a detailed cliccussion shall be included in this analysis.

For this purpose, consider a winding of the length L and the tot:l.l number of elements N. Let a surge voltage El be ap­plied at the coil end A and distinguish between the two funda­mental cases that the other end B is either grounded (E=E·, e=eO) or open (E = EO, e =eO). The voltage E to ground at any distance x from the line enu A and for a coil length L is then given bys.7

E-=sinha(1-x/L), ~=cosha(l-x/L), a=Nv'cg/c. (1) El sinh a E, cosh a

Of particular importance is the element-to-element stress e between adjacent junction points since its value is also a measure for the turn-to-turn stres!', and sufficient insulation has to be provided between elements and between turns to withstand these stresses. At point x obtain either by the chord or difference of E(x) or, for sufficiently small values of the space Ax occupied by an element and its insulation, approxi­mately by the slope or gradient of E(;t):

e-E(:z:-,u)-E(x+Ax) by chord of E(:z:)

dE L dE e~-2,u dx = -2 N ;;; by slope of E(:z:) (2)

Ax=L/N

Repeatedly throughout this paper, se',ernl equn.tions will have common factors. This will be shown us one equa­tion, and the factors which are different will bQ distinguished by brnckcts I I. By using this symbolism, derive ",;th ~qua­tion 1,

e· ~osh o:(l-x/L) - = 2 ~~~-"--' E1 · sinh a X {Sinh il eO sinh a(l-x/L) . ~ -=2---'---'-.....; Et cosh a

by chord of E(;r;)} by sTope of E(x)

(3)

8i8 Stdn-Surge DistributiOn in C01ll:enlric TTan~jo"71ler Winding. SSPTnIln;:n 19M

'-

)

whe!'l' sillh (3 a~ well a:; f3 can be u. factur in the equation for e·,'I~"l orco/J~"l'

The <tuallt iLies {3 alid a shall be rl'ierrl'd to as major di:;tribu­tioll ('()n~l:l!:ts :lne! b(:comc

1-- ~-

a= V C,/C" .6= v' c~/c.= ("(lY (4)

if (Ju=.\" Cg and C s = c,/Y re]l("(.·"(,I1( the total ground and scri(~s ('apacitallc·(· uf the winding. Xote that {3 depends onlv on the size of the indi\·idual clements and their clearance to' ground while a = N {1 is determined by the dimensions of the whole coil. For ;;ufficiently small valucs of {3, the chord and slope forms of equation 3 become alike. For larger values of {1 they diller in both cases, that is, for g!'Ollll(IL'd and opcn coil end B, by the !"ame factor 1 ;:;;; i3!"inh {1;;;; 0.85 for 0 ~ (3 ~ 1 where {3 = 1 i~ a ~omewhn.t extreme nJ.luc.

The maximum value of c apl)(,!lr~ at the line pnd .1. Dis­tillgui~h b('tl'."e(·n the actual ntlue CI = c(x= LIN) which ap­pcar,; hl'tw('en the first two ekmcnt s and a fictitious value eo= e(x=O) which represents an extr:lpolatiun of e(x) to point A. By e(jllation 3 obtain then

CI' /E,·="2 cosh (a -P')/sinh a

clo/EI=2sillh(a-fj)/coslia X~'fJSillh{3 b}"chordOfE(X)} (5) eo /E, = 2 dllh a ~ by slope of E(x)

eoo/E I =21.nllha

WhCll ("oll1ilinrd with equatiun 3 and rOlilparcd with equation I, tlll':-'c qU!lntitips furnish fnr til!' ('hord and slope form of e the identities

and

e' EO el' EO(x=L/N)

cosh a(l-x/L) cosh (a-fj)

sinh a(l-x/L) sinh (a-p)

(6)

(7)

Consequently, the distribution of the initial stresses e between elements can be obtained by a test of the initial stresses E to ground which can be read with greater accuracy, In this tech­niquc, the distribution E(z;) and only one value of e, prefer­ably its maximum el =e(x = LIN) across the first duct, are mea~ured in per unit of E, and furni;;h for any other point x (see E'qtl:ltion 8):

10

o

~ 0.6

02 OJ

0.4 0.6 X/L ---

___ EiE • eO/e' ° L 0

------ElEL • e'/e~

0.8 1.0

•

Fig. 4. Major surge voltage dis­tribution in a wind· ing with uniform

Insulation

-----------------

7,:"

Sillce the distribution of R u!'d c in ('(Iuat inll () i< ;ndl'IH·rHlent. of fJ [ietording to equation I, it fIl:Ly 1)(' ,(tiriied by pInning the yoltage ratio,,· ag!lin,t x,"L for different \·:tIUl:~ of a, as shown ill Fig. 4. Bec:ltl~e of

EO E' sinh axiL --- =2 ---'--E. EI sinh 2a (9)

the stresses for an open and· groullded coil elld B practically coipcide in Fig. 4 for large values of a, for instancc for a = 5 or 10.

In order to examine tIl(' conditions near the line clld (xIL« 1), de\'elop equation 1 and the chord form of equation 3 into

E' /E'} _"I/L. f 0 I-I . EO/EI =f +2 t l=Ff''''J slIlhax/I.

eO/Ell . "/L i t-e O/E,(=2 smh {3[e- T -2tl=Fe2"'J lcoshax/L]

(10)

(11 )

where (he minus ~igll in the hracket ( 1 belongs to the calcula­tion of E" and c' and the plus sign is to be u~ed for EO and eO.

?\ear the line end, th:tt is, for x«l, and for ;;ufficiently large valuc? of a = N {3, that is, for a relatively long winding, the stresses obtained for an open and grounded end B arc reduced to the same \'alues.

e E. - =2

E-Slllhfj fora»landx/L«l

el I· . (12)

Let e(} '" represent the value of eo for a.n infinitely long coil and. find also

Consequently, these voltages become independent of the eon­nection at B and of the length L of the coil 01' its number of elements N, In particular, note

(14)

where ellEI becomes proportional to IX.

As a result, an increase of the winding 1€'llgt It makes the rela­tive stresses el El near the line end larger as compared with a linear distribution elEI = 2/N while the actual ~tn~:\S cremains approximately the same. This effect can be d .. :<r.ribed by a nonlinearity factor R=Xe/(2E1). Its YUIlle HI ;IL x=Q for a grounded (Ro = Ro 0) (mel opcn (Ro = Ro 0) ('nil end B is obtain('ri by the chord form of Nluation 5 as

Rt°} sinhfJ { \"'. Ro o· = -fJ- a ctnh a -N sinh fJ for a») (15)

where the pIns and minus signs in the exponent of the braeket { I are to be associMed with Ro' and Ro 0 rp,;pectiwiy. These values of Ro are plotted against IX in Fig. 5 wlH're tlll'Y increa!;e proportionally with N or IX for large values of a. The intro­duction of Ro also permits the calculation of the strei'ses e at any point x according to

e=2(Et/N)no(e/eo) (16)

where eleo and Ro are given by equations 1,6, and 15 or call he·

Siein-Surae Distribution in Concentric Tran8/ormer Windinas 879

.. ~-·o=:::-::-::~~--:· :'=~-.----=:'.,,-=.....:..:...:..--:-= =-_. __ _

6r-~----------~------~~

5

L

4

5

fig. 5. Non­linearity factor of a major surge voltage distribu­tion at the line end of a winding with uniform in-

sulation

taken from Fig~. -l: and 5. According to these figures, note eO>eo ;:0 thaL the initial stresses e for a grolmded coil end Bare ;;cnerall.\· more oevere than for an open end.

In the p:,r( ~cllIar c[tse of el/ F:t, equation 1 t can be <':011-

wrtpd into ,he nomographic form:8

'I( el/ EI \ fl j J-'--,( a) g(J3) = D lC(!3l

with

D g(/J)=--­

l+(alb)csch 2tJ

(17)

(18)

a~ ;;hown in Fig. 6. The values of u 0, so, and" Q, 8 Q correspond to a grounded and open coil end B respecth·ely. They repre­sent straight scales of the variables eJ E and ex with consta.nt .'pacing D and scale factors a and b, while w is a. curved scale of the mriable (3 with variable distances f and g from the 3

:lnd u scales. While this nomograph, Fig. 6, has been primarily designed

for computing the voltage el between the first two elements, it may be u~ed also for finding the voltage across any other num­ber J[ of elements next to the line end by substituting Jf{3" for 13. In this way, also, the voltage e between any two ad­jacent elements inside of the winding can be able to be obtained as the difference of two "oltages towards the line end.

The two fundamental cases of a grounded and open coil end B in Fig. 3(.\.) can be used for deriving the voltage distribution also for other conditions at B. As, an example, two separate voltages EI and E2 are applicd at .. 1 and B. Then any voltage E to ground inside the coil is the sum of E(x) resulting fl'om a :,ource EI at ..t with B grounded and of E(y=L-x) obtained in· a distance y from B for a source at B with A grounded. Consequl'ntly, write

(c; E"(.r) E2 E·(y=l.-x) , ,:. = -- + -

-.Cl EI EI Ez

:tnd find by equation 1

E sinh a(1-.rIL)+(EdEI ) sinh axiL

EI sinh ct (19)

By eqnation 2 find then between eleml'nts

.. ~Z' .

e eush a( l-:rl 1.) -(Ed R I ) cosh ("xl I. -=2 -- X EI Rinh ct

hy chord of E(x)' \ (20)

\'.\' slope of E(x)f

For E2=EI th('~e ('(FIn,tions go O\'el' into the ('a~c that thc "amI' surge voltage is applied ~ill1\llt:1npow.;ly to both ends of the winding.4

In other conditions encollntpred Jat!,1' ill this analysis, the coil end B is grounded through a l'apal'itance. In sitch prob­lem:; the "oltage al'ross the ('oil will he dctermin('d fir~t and the corresponding ';ultage::; HI and E2 at thc coil end:; .1 and B will be used for romputing the "ollage di,tril!1ltion inside the winding aCl'ordinc; to equations 1!J ;tnd 20. If the applied "oltage £1 i:i gin:n, E~ lIlay be found by n:p!a<.:in;;;! net',vork of elements, Fig. 3(.\), with a ~ingle Illmp(:d or ('ntran('c e:1paei­lance K, Fig. 3(13), normally obtained if the network is grounded or open, or in general with an equin,lent 7r consi,-;ting of the cap:lcitances K~, Ie, [(~; ~ee Fig. 3(C). T~lese lumped capacitance:; are 0.1:<0 u"eful in eire-nit !'ah:llbti!Jns im'oh'ing ~erics and regulating tr[\n~formers.

For finding these lumped capacitanl'es, con:-iiuel' Llw wind­ing as divir!cd into many ~mall element::; with CV«I's ~o that at the line end.t their \-oltage e l':ln be rOlllputed by the .',!;,'adient form eo/ E, of equation ,5, the current in Cg Illay be neglected, :!lld the cUITcnl in Cs becolllcs identieal with the line <:lllTPnt II. Since the ;;arne eurrent II flows into l'ith('r kind of network, Fig. 3(.\) or 3(8), obtain

(21)

where p =d:'dt is the operator fOl: the differentiation against the time t. Distinguish also l\. = K = for :nfinitely long coils and findT for a grounded (J(=KO) and open (K=KO) coil end B by equations 5 and 21:

K·=K"'ctnh a=C, _ct_>C. tanh ct

tanh ct KO=K'" tanh a=C, ---<Cv

a

::'! 0.50 0

~ 0.45 .... _____ 0 __ ._ ·----i ~ 0.40 0.5 I­<fl

FE 0.35

~ I-

zO.3O ... I ~

... 0.25 ,!l!

. -~ ~ 9< 0.20 .. - US

, , , , , , , , , , , , <) ,

0.6

0.55

0.5

~-C.4S , t.M

(22)

ti , <D

~ ... .J <5 <.> 0 ... 0 . 5 0 a: ~

Fig. 60 Norncgr .. ph for cO~!,:Jtil'lg surge volt&;l! stressos~in a winding

SSO Strin-S"r~ Distribution in Con~entric Trans/o'''''I'!r Winding. :';EP't'EMUEI< HIM

"

...... --.... ,

II hi,·1i for a»l ill both l'a~('~ redllce:' to

J{ = }\"= 'V'CgI,', = ~ for ,,=.\"13»1 (23)

('''lI-('qll('lItl~', in !'e1atin'I~' IOllg; coib with a bl'ge llUlllb('j of ,·I"lIll'lIt:'.\', tll(' CnlntlH'(' capacitance J-i. h"('Ollle:i indcpClldl'nt "I' t It" ('()i1I('II~tlll_likl' tIll' \'oltag,' di,-trillltlion of cqualioll 1:2 Ilt':ir tlt(' Jill(' ('lid.

FIJf obtainillg the equi\'a!t'nt ".. of F:,~. 3(C) rhange thi~ lIel­

\I (Irk illto Fig. am) :l('('ordingto

(24)

:!Jld find h~' t'quation 22

a 1 tanh a/2 1 K =J(~tallh-=-Cg--- < ('0

o :!:J a/2 2 (25)

K~ a J( =---=1',-- < (',

' ~illh ('( , sinh ClI

GRAIJEO h;;ULATIOX

.\c(·ordill,!! to Fig. 4, the stres:-;es E and c decrease rapidly il'Olll the lillt' pnd A, parti('ularly in ]l:lll('uke coils with a largc di"tl'ibutioll con:<taut a. This l'llgge"t,- all investigatioll of the p!fcet of r('dll(;ing the insulation ekaranc'es in a certain dis­tune!' from the line end. If the raJlacitall('C~ Cg and c, ha\'e to 1)(' ehung('d for thi,; purJlo~c to any l'xtent, the voltage dis­tribution llla\' be materially altrl'ed in the whole winding. This distl'iJmtion "hall, therefore, bc analyzed for the condi­tion:' that l' 9 and c, and the cOl're"ponding quantities of -Y, L, ('g, Co, K, K~, Kg, K., a, and p haw different \'alues di:;till­,!.(ui"hed by :;ub~cripts 1, 2, 3 in different parts 1, 2, 3 of the ;"inding, a,; indicated in Fig. 7,n.nd that ('gand C, are uniformly di,;tributed in each part. Likewj"c, \'oltage::: EIJ E2, Eo to ground "hall appear at the :;tart (A, P, Q) of each coiI part ~"hile N'=.Y,+.vZ+N3 and L=L,+L,+L3 remain the total \\"indin~ \':llues.

T,,'o COIL PARTS

In the case of two coil parts iIIuI"trated in Figs. 7(A) and (B) obtain with pquation 24

(26) - =---E, K,"+K,

whel'c 'K2 lIlay a,,;;umc the value~ K~" or K/', depending on whether the coil end B is open 01' g:rollnrted. Equtltion5 l!l. 22, and 2.'5 fllrni;;h th!'n

E." lEI} [ K:"' .. ' 1-'J-' . = ('!Ish a, +- Slllll "" I dnh "" -E,o/E, K.'"

(27)

With lhc voltage:; E. and E, thus determined at the ends A :luc! P of the two coil parts, the voltage distribution within (':Il'h part can be found hy ('on"ide\'in~ it to be a complete winding by ibdf "'ith volta~(':; EI and E, applied at the ends of I 'art 1 and with E2 applied on onc end of part 2 while its other "lId is grounded or open. 111C mllles of E/E. and e/E. in part I :lrc then found by equation:; 19, 20, and 27 if a, {3, ancl L :II'l' replaced by a" {J" and L(. In part 2 fin;t compute E/E2 and elE~ according to equation I by ;,ub,;tituting a2, {32, x- L, :tnell.! for cr, {3, x, and L. This gi\'es (EIEI ) = (E':E2)(7~·:/E.) :uIII e/E. = (e/E2) (E2/EI).

In a prnetical application, part 1, located next to thc linc 1'1111, mny reprcsent the fully insulated portion of a winding Wh08C insulation clcarances would ha"e to be u,,;ed uniformly in the whole coil if they were not reduced in part 2. For com­parison purpo"e", the stre~ses e in the winding with gmdcd

"

, -'---x-i L-1--,--' ,-, ,-, L-'

-PART 1- -' -' PART 2 GROUND I

(8) E~ t Kgl K

g+ iJ2 ~ ! I , I

A K~I P K2 GROlJ'IID

-' -PART 1 ,-PAR72 PART3'-!

E~ fKg, Kg{H2 Kg, lE3 ~

A K's, P, K~ K3

(c)

K92

Fig. 7. Major capacitance network of a wincHn::! with graded insulation

A-Sectionalized network B-Lumped capacitances of a 2·part network C-Lumped capacitances of a 3·part network'

insulatioIl . .;;hall, therefort', be ref('rrt'd to the maximum ~tre~:; eo at x=O in a ('ol'l'e,;ponriing; winding Il'itl! uniform in:,uiatioll (C9=;gl, c,=c", 13=13,). For n. pancake cOllstrul'tion, the winding is usually long cnou(.!;h (a = p,.\'» 1) to permit the approximation eo, 1:'. ~eo"'/ E" which is indcpendent of the winding length L Thus develop e/eo~= (e/E,) (E,/ea~),

and find for jln.rt 1 by equation" 13 and 20

~=-~ [eOSh a,O-x/L,)-l!.: cosh a,:C/L,] in part 1 eo~ sinh a, E,

(28)

where Ez/E. a"sumes the values E,"/EI and E2o/El given in equation 27 for a grounded and open coil end B. For part 2 obtained by equations 3 and 13

e" E'cosh(l-x/L)a,LIL:

eo"

, eO

EI sinh ClI, sinh {3, X -- inpal't2

E.o sinh (I-x/ L)""L/L, sinh.81 cush a.

(29)

As a numerical example, e/ea'" i" plotted in Fi~. 8 agn.inst x/L for X=50, .V1/,'i=L1/L=O.I, ('gl=Cg'!, anrl a !lumber of values of C'I/l'"= ({3t/{3.) 2= (K1 "",'K,"')2 and of {3, correspond­ing to a, = {3, = {3,.V = 201' 10 ill a uniformly ill~uln.lI,t1 winding, This "holl"!; that th!' st re"se bl'lwf'l'n ('Iemrut" i,dncl1':\s{'d in the already hi!;h-,.;tre~~ecl purt 1 and lo\\"prt·d ill thc low-stressed part 2 if a reduction of the clearanres in part 2 is aecompanied by an inerea"e of C,z. Larger ('Iearanrcs in part 2 havc the opposite efred. The~c eonditiolls arr al~o illustrated in Fig. 9 by plottin~ ('.·('o~ at the "tal·t of parts 1 and 2 a!,':linst. e.l/cl'!. As a result, in:-:ulation grac~ing; j" of limited mlue "inc{' it may increase the already exist ing rli1T('reJlcc~ ill the ,"oltagc >ltre;;;:e:; in different part:; of the wilHling.

Further e\·jdencc of this effl'ct is found in the di:-:continuity appearing in the function e(:r) n.t point P in Fig. 8. This dis­continuity i" the J'f'~llit. of an ahrupt change in thc valuc,; of Cg

and c. at point P in Fig. i and becomes for {3( n.udI3-1«1 by equationR 27 to 29

e(z=L,-O) K,""sinhi3, e(z= L,+O) = KI~ sinh i'3"

C.,! for 131 anel .8::« 1 C . ..: ...

(30) ,

00

Fig. 8. Major dis­tribution of the ele­ment-to-element volt­a!Zes in a winding with graded insulation of

two coil parts

xtL -

fIJr c'ilher :m opr:n or grounded coil end B. In [J.ddition to .::rl':!ting this uniavorable initial voltage distribution, this cL'cuntinuity may also trigger extra voltage oscillations later 011 in time.

THREE COIL PARTS

The "nalysis of the effect of a graded insulation with three ·-:i p.lrts becomes similar to the analysis. made for two coil

.Lrts, Fig. i (.\.), if the corresponding capacitance network is I~placed by the lumped capacitances shown in Fig. 7(C). Equation 24 furnishes then

'E, K.. E. K" E. (E.)(Ea) E, = K,"+K; EI = K1-+K,"-K,i.E./E.(E;,= EI & (31)

which becomes by equations 22 and 25 for K3 = K~" or K."

(32) E. [ K.'" sinh at _( Ea)]-l - = cosh al+--; -.-- cosh aa--EI KI smh aa . E.

By again referring the voltages : between elements to a common value eo'" at point .4. in part 1, their ratio e/ eo'" is given in part 1 by the same equation 28 as in the case of two coil parts. For part 2 find, according to equations -13 and 20,

~ = (E.) sinh {3! _1_X eo" E, sinh {31 sinh aa

{cosh a,(I-X-LI)_~ c~sh a: X-Lx} in p:11't 2 (33)

L~ Ea L:

:l.I1d for part 3, according to equations 3 and 13"

cosh (l-x/L)aaL/L, sinh a,

sinh (I-x/ L)aa£/La cosh aa·

in part 3 (34)

;llere E.IE" E3!Et, and EalE, may be COIl:lputcd by equations 31 and 32 by introducing Ea·IE,· or E 3°(E,O, depending on whether the coil end B is open or grounded.

. -\ graded insuL'\.tion with three coil p3.rts could be applied to 3. dcltaoConnectcd 3-phase winding in which both coil ends have to he heavily insulated:md any reduced insulation has to be ('onfincd to the center section of the. winding. In this ca..~,

". ;c

1.4

1.2

1.0 ~o 006 ..

0.6

0.4

0.2

0 0 2 4

C::;;l/ CS2

___ . __ _

Fig. 9. Effect of insulation gra::lng with tv;o coil parts upon the maximum '/oltage stress beto.'1een elements in each part

howewl', part 3 normally !i('." far :twav from the lill!' end .·1 ~o that only a ::mall fraction of the apI;lil'd -ur;;c w,itag;e EI will penetr[J.te to this part unless the distriotllion con,tant:-; al

and a,! are relatively 5mall. This i" _-omc\\·hat illu~tl'ated in Fig. S. If, therefore, the \o:dlle of a~ i~ rdati\Oely hrr,,'C, the distribution constant {33 may be repl:LC'e<i by i32 in ,~ ('alcubtion of the stl'e~:,cs in parts 1 and 2 ~o that the st raet lire is reduced to Figs. i('-\') and (B) for t\\"o coil p:J.rts.

The Minor Voltage Distr:bution

In order to make minor networks accessible to an analytic treatment, the calculation will_be confined to the conditions where a separate network can be ~soeiatcd with each ele­ment, as shown in Fig. 10. For this purpose an equipotential surface appearing as a straight line in Fig. 10, has to be estab­lished between adjacent elements, similar to the ground in a major network, Fig. 3(A). However, while the ground is always an equipotential surface of known physicul dimensions which usually can be approximated by a straight line in a 2-dimensional analysis, a corresponding surface in the duct be­tween the elements can only be °found under ~pecial condi­tions. Examples are cases of symmetry, as, for instance, a uniformly insulated winding where all ducts or all alternate ducts are alike. Equal alternate ducts appear, for instance, if the space on one side of each element is filled with insulation and becomes a cooling duct on t he other side, as shown in the inner coil of Fig. 2. Further examples of equnl potential boundaries are metallic ~nrfnce;; introduced a,: static i'hields or a condition where the sl\1'face of :tn element it~elf is approxi­mately at a constant potential.

These various cases can be co\wedby the analy~is of the model, Fig. 10, with equal alternate ducts so that, [OL' reasons of symmetry, the centerline::; a'a" and b'b' between adjacent elements are at a constant potential equal to that of the junc­tion between them. The capacitance network of olle clement extends then from a'au to b'bu with volt:1.ge (Ii~tribution::; of V and V-V which assume the ~ame inaximum value V at each end. Then the analysis of the minor \"oltage distribution in Fig. 10 becomes similar to t,hat of the major voltage distribu­tion in Fig. 3 by letting the inrlivirlU:1.1 "lements in the minor' network b~ ~rtlliv!!!ent to the ..... hole winding in the mf\jor network and :!l50 by lett.in~~ the individuai turn in the minor network correspond to the :-ingle element in the major network .

Similar to the fields outside :lnd insi(ie the wimlin~ repre­sented by the major network, Fig. 3, distinguish in the minor' net"'ork, Fig. 10, between the outside field in the space be-

tWl'en clements and the iu;;ide field between turns. These fields are described by the external voltages V and f"r-V at eapaeitall(,p" ka :.lond /';b per-unit element length and by v and kT

[)t't \\"een adjacent turns respectively. Only single conductor turns willlJl' considered. The di~cussion shall be further con­fincd to uniformly insulated minor networks. These are net­\\"o;'k~ of elements where all conductors and tlH~ir insulation arc the same and the fringing effect at the ends is neglected. For this rcason, the specific capacitances ka are equal as well as kb

and kr and can be able to be replaced by total capacitances Ca, Cb, and CT between elements and between turns re­spectively.

Under these conditions the voltages V and v at a distance z from the element end b' in Fig. 10 actually become functions of the two variables z and x. However, in each element, that is, in each minor net\york, consider x = constant so that V and !I

can be treated here as functions of z only. The introduction of a dependence on x may, therefore, be confined to the maxi­mum ir = V(z=O). The corresponding function ir(x) is then obtained from the calculation already made for the major network by substituting {3/2 for {3 and V for e in equations 3, 5, 10 to 18, and 20, and in the nomograph, Fig. 6.

As function of z in the minor network, Fig. 10, of elements with the height Hand n+ 1 turns each, the, distribution of V is shown in the Appendix to be

V l-cb/ca sinh (l-z/ H)y . -=--- T sinh "Y

Cb/C~ [ sinh (1-2Z/11h/2] -- 1+--'---'-"':"":"=-l+Cb/C" sinh ,",(/2

(35)

with a minor distribution constant 'Y and its normalized form 'Ya given by

'"'(= V2(ea+cb)/cT=2A'"'(/Z, "Ya= VCa/CTI A= V(l+cb/ca)j2 (36)

where ).. is introduced as a measure for the dissymmetry of c" and Cb. For reason of symmetry, only values 0 ~ Cb ~ Ca will have to be considered.

The tum-to-turn stress v is obtained either by the chord or difference of VCz) or, for sufficiently small values of the turn thickness x=H/n, by the slope or gradient of V(z) in the form '

V= V(z-~z/2)-V(z+az/2) by the chord of V(z)

HdV v~ -- - by the slope of V(z)

n dz

which become.~, by equation 34,

(37)

~ =[l-cb/ra cosh (l-z/H)-y + Cb/ea cosh (1-2z/11h /2]X V I +Cb/ra sinh'"'( 1 + Cb/ca sinh "y/2

{

2Mh 2. by chord of V(Z)}' 2n (~)

"Y /n by slope of V(z)

This result is similar to equation 3 for the stress e between ends of clements in a major network.

For Cb ~ c" the maximum value ii of v appears at z = H /2n and becomes, by the chord form of equation 38,

ii. [1-1:6/1:" cosh (,",(-,",(/211.) -=.=2 Sinh ,(211.) --- • h + V 1 +c,./c" Sin '"'(

C./ca cosh ('"'(-7/n )/2J (39) l+ct/ca sinh ,",(/2

Flo:;. 10. Wnor c::pa cit Ll nee

networks

The corresponding extrapolation Vo to z = 0 may be written

Vo. [l-cb/ca Cb/Ca ] -=.=2 9mh "Y/(2n) --- ctnh "Y+--- ctnh"Y /2 V l+Cb/Ca l+cb/ca

(40)

For 'Y»I and 'Y/n«l these values are reduced to

ii Vo -=~-::.="Y/n for "y»1 and "Y/n«l V V .

(41)

Because of the similarity of equation 3D and equation 5 for e·/Et, the value of ii/V can be computed by the nomograph, Fig. 6, for the grounded non line end B. For this purpose the quantity 'Y/2n is replaced in equation 39 by P in both terms, while ex is substituted for 'Y in the first term and for 'Y/2 in the second term.

In the extreme case c" = Cb, that is, when the element is sym­metrically insulated, the first term in equations 35 to 40 dis-appears so that the second term is reduced to -

~ = ~[1+ sinh "Ya(1-2z/H)]. :'.. = cosh "Ya(I-2z/H) 17 2 sinh '"'(aVo cosh "y~

V cosh "Ya{l-2z/H)

V sinh "Ya

ii cosh (-Ya--fa/n)

-V= sinh"Ya

(42)

{

. h "Ya Sill -

X 11.

"Ya/n

by chord of V(z)

by slope of V(z) Vo V=ctnh "Ya

For Cb=Ca

In the other extreme case Cb = 0, that is, when one of the two element surfaces is open, the second term vanishes from equa­tions 35 to 40 and the first term is reduced to

V sinh "y(I-z/11)

V= sinh '"'( :'..= cosh "y(l-z/H)

Vo cosh 7

v cosh '"'(I-z/H)

-v= sinh 7

ii cosh (,",(-,",(/(211.))

V= sinh '"'(

(43)

{

2 sinh 2. X 211.

,",(/11.

by chord of V(z)

by slope of Vez) Ua -y==ctnh '"'(

For 1:6=0 ---'"-""""'~---

SEPTEMBER 19,,-1 Stein-Surge DiBtn"bul:ion in Conuntric Tram/OrTner Windi>tU8

"

.", ..... : .. , ~ ~.,.. .

> "­>

~

"r'"

--c ~c b 0

1 0.2 ,.. ---- cesco

Fig. 11 (left). Minor distribution of ele­ment-to-element volt-

ages

Fig. 12_ Mir.or dis­tribution of turn-to­

turn voltages

For Cb=C. the values of V and I' of equation 42 and also the second term of {''luations 35 and 38 show a certain symmetry with re~pect to z=H/2. This abo heromes apparent if V/ii' n.nd vll'o are plutted against z/H, as ~hown in Fib'S. 11 and 12 for ~en'ral values of 'Y ...

For Cb=O the volt..'1.ges "", V, V, and t'o ill equations 43 for the minor n{'twol'k and also the functions in'the fir>it term of equa­tions 3.5 and 38 to 40 ean be made identical to equations 1, 3, and 5 for thl' (·ol'l'E';<Jlonding voltagl's EO, eO, e\ 0, and eo 0 in the major netwol'k. FOI' this Jlurpo;;e z/l/; 'Yand 'Y/(2n) are re­p\art'd by x/L. Ct. und B fE':~pectivl'ly, This shows that for Cb=O the minor nl'twork. Fig. 10, is reducl'd to the shape of thl' major network, Fig, 3, and the cun'(',. of v/f' and vivo in Fi~. 11 and 12 a:::'''111111' the same form as Eo/g\ and eO/eo in Fig. 4, Xot{' also that analogous to eleo, as giwn by equations 1 and 6, thl' chord .and slope fOlms of ['.'1'0 1X'('ol11e identical in r'llIut ions 42 and 43.

Fig. 12 shows al:;() that for C&=Ca the turn-to-turn stresses 11

at both endi" of thl' ('leml'nt arl' much gn'ater than in its c(,lltl'r, and that for ('b=O these "tre,:~s are highest at one end. '11 Ii,. {'ffpet can Ill' stlllli('{1 more in dt-tail by int.roducing a non­'''-:l'arity fucto!' r= n I'/f' wit.h r= ro for z=O which for the slope

;j"ill of ('(t'tatiolls 42 und 43lx>C'omes

r9= 11:;: = )"Ya dnh 1'" _ ror {"to =ral • (44)

Y /-y':!-." clnh Y2,.. for l"b = 0 f Whl'n plotted again:<t 'Ya in Fig. l:l, til(> (11I:mtity ro of the minol' network cxhihit.~ propertit's simii:u- tn 8 0 of the major lli'twork in eqlla.tion 15 and Fig. 5. Thwc, in both nctworJss

Fig,13(ri!lht). Non­linearity factor of the minor voltage distribution at the end of an element -' 'r'" , ,

3 ' -~ -".,.

:2 .

(he \'alue~ of ro am! Ro illCl"ea"e proJlort ionaIIy to f a and a for hr!!;e yalut's of fa and a re~pectin'ly.

The diffcrpnce betwccn the extreme condition" Co = ca, wlwn the element i" :;\'mmetric:llly insulated, and Cb=O, whpn olle l'lement ~urfa('e 'is open, can also be iIIustratl'd hy dl'l"i\'illg from equation" 42 and ·!3 thp mtio

1'/ r(r&=O) _'J siuh y':!",a/I! i' / l"( Cb = r,,) - - sinh "2",'; n

ctnh V:!",a - t'luil (-.a/llli \. '} ---'---:-'-''------- .. _-

dnh 'i<l-trlllil 'ialll

(45)

plotted against fa/n for diffcf"{'nt ndllP~ of'Ya in Fi~. 14. The actuul amount of the tum-to-tllrn "trc~" /" ma.\' he

computed for any n,lllc~ of ! and x aee'OJ'ding to

E\ (V)(t.) l.'=~ -; - Hurl) n;\ I 0 Z'o

(46)

The quantities ~,.. -r'o and Ro are found hy equation;; 1. ii. and 15 by slIh:;tituting: 13/2 for 13. The mlues of t'. '1'0 and ro are gin'n fOI' C"b=O and I'b=Ca by equations 42 to 44.

The maximum values vo". and ii", of u appt'ar at the line end (.r=0, z=O) \\'here equation 46 reducE'S to

V"I llom ay -::::> .. '::::> -'. for ,,»1: ;3«1; ,»1; "Y/n«1 E, E, n.\

(47)

Con;;equentlr. the maximum turn-to-tum "tl1''''' t' '" inerNlses apllroximately "'ith the product of the t\\"o di"trihution COll­:-;tants Ct and 'Y in eontrac':nction to the maximum elemt:>llt­to-element stre~s el whi('h, :.~" 8ho\\'n by equation 12, increa~es '"ith onh' the one distribution con"t.ant a,

n,· usin .... the ,·olta .... e di"trihution of Y and t' in equations 35 and '38 th; lumped ~~rie,.; papacitanec C, a!'~o("iated wit.h {'aeh element may he computed in terms of the slim of th(> total capal'itancl' C"~ hd\\'eCn tll"O adjacent dement~ and CT Ix·tween all turn" of an (·It'mellt. This lumped rapaeitanee C", i.~ a function of "Ya und Cb/ea and repiac(';< the minol' net-work, Fig. 10, in the major net,,'ork. Fi1!:. 3. Gncler the"'l' ('ouditiolls nh­tain, as "hown in the .\ppcndix,

("la+dnh -.~)

-y':! ('tnh y::?-." for fb=Cq ur h= 1

for rt =0 or ;\.= IIv':?

'48,

If ploited :1.l-1!-ill"t 'Y" for diff('rent vdu(>;; of 'Ya . ."n, :1.,- ~h(I\\'n in Fig. 15, the quantity C"b. '(I',,+CT) rcache~ a maximum of 1.:H2 at l'b = l'1I and 'Y~ = ::?AI-l.:L-~li;'1f''' its lowe;:t "alu('!' at ('~ = O,and ,':uiei" \\;thin a ratio

-.-.---',:..........--.~- ........ -.- ~-

,,,--..,.,.. i

/

.•. . ,r.,. 'G'O?'

C,ICb=Ca) i'a+ctnh 'Ya -.. ---c,(rb =0) v'2 ctnh y2'Ya

(49)

\\'hieh i;; in(·luded in Fig. 15.

T:le Enact of 5l',ielJing ~t t:.c Li.:o End

'fhe m!ljor network, Fi~, 3, h:l.S been analyzed under tIle condit ion that the insulation is uniform throughout the whole winding, that is, that all ducts 01' all altel'llate ducts between element,; [Ire alike, Then each centerline between two ad­jacent clements is at an equal potential and the series capaci­tance c. can be computed, as !'hown in the Appendix. How­ever, the clements at coil ends A and B have an open surface on one side so that here the uniformity of the insulation is discontinued. This nonuniformity of the coil ends penetrates to a certain degree into the ,,'inding and, exactly speaking, only the centerline between the two clements in the middle of the coil ill abo an equipotential line.

The uniformity of the coil insulation could be restored by extendino- the coil uniformly up to infinity beyond each line ('lelllcnt." This condition is frequently simulated by providing a metallic i<urface, commonly referrcd to as a static shield, or ju,;t a .. ; a shield, on the centerline between the yne eleme~t and the fictitious next consecuti\'c e/ement,as Illustrated III

Fig. 2. :\. winding shielded,in this way as;;umes in principle the samc properties as a uniformly insubted coil.

In an unshielded winding the outside surfaces of the end element,~ arc boundaries of an outside field to ground which could be represented by a certain capacitance network to O'round. In an unshielded layer wound coil, this end ground ~apaeit;ance is significant, as compared with the minor inside capacit~nce network, Fig. 10, and the shield has the double purpose of eliminating this end ground capacitance and to convert the rest of the winding into a uniform network. In an unshielded pancake winding, however, the end ground capacitance becomes very smail, as compared wit~ ~he capacitance fa between the end element and the next lllSlde element. For this reason approximate the other capacitance c towards the outside by Cb = 0 in an end element when cal­c~lating its minor voltage distribution. This dissymmetry will have a profound effect on the series capacitances and volt­age;; at the line end of an unshielded winding, particularly in its first two elements.

"'95'

If, therefOle, the analy~i~ prt'scntcd in the pr('\'iuu~ ,:cction is to be used for investi~util!f, the ~hicldill;':; effpc(, an approxi­mation has to be introciuc('d for the lllv;hieldcd 01' nonuniform condition. III order h tiwl thi,~ ~j)i)roxim~tif)n :1nd, [tt thl' same timc, to check also tb accuracy of ~he c:llculaLiollS for u shio;)!dcrl windin~, a lr.cdd of the minor voltage di~tribution was simulated 011 resist~nce p~per,9 as shown in Fig. 16. The paper itself took_cure of the field between clements. Resistance paint was added to simulate the turn-to-tum field. Metallic plates were used to represent the turns. .\ccording to the dimensions chosen, this model represented a coil with a distance S = 2.10 em (centimeter,,) between adjacent elements, a tum width W=1.90 cm, a turn thickness T,=0.31 em, an insulation thickness T 1=0.16 cm between adjacent turns, an element height !I = 14.1 em, and with n=29 insulation spaces between the turns of c!1.eh elemep..t. The r~tio chosen for the resisti\'ities in the spal;es bet\\'ccn the simulated turns and in the space between the two simulated elemcnt;; wa~ equiva­lent to a ratio CT/ fa = Ul of the dielectric con<;tants fT between turns and fa between elements.

The co!'re~pondillg voltage distrihutioll was SLl!died on :3"

2-element morlel with t\\-O shield~, Fig. 16(.-\.), without. shields, Fig. lG(B), and with only Olle ~hielJ, Fig. W(C). The meas­ured equipotellt.iallines are plotted in the~c models for differ­ent fraction~ E/ Ji}1 of the applied ';olta:;;\~ Fl.

Except for the fringing effect at the e)('ment end~ :=0 and z=H, the field of the shielded winding, Fig. 16(.-\.), is quite symmetrical, and the centerline between elemellts becomes the potential line E/El=0.05. Consequently, equation 42 for Cb=Ca with the cur .... es shown in Fig. 11, will apply to the voltao-e distribution at the turns.

In the unshielded winding, Fig. 16(B), the field still retains a certain symmetry since, within the limit" of the test ac­curacy, the potential line E/E1 =0.5 continues to coincide with the centerline between the two elements. Therefore, equa­tion 42 for the condition Cb = 0 with the corresponding curves shown in Fig. 11 will describe the voltage distribution at the turns.

If, however, only one end is shielded, as shown in Fig.

1.4 7 I I ! 1/

Cbl Co - I i./f Fig. 14 (left>. Comparison of the relati>'e maximum turn-to-turn voltages In a symmotrlcally In­sulated element and In an ele­ment with an open surface and comparison of these voltages in a shielded and unshielded end

1.2

1.0

O.B

...6

N

;I'

~

~ \\ \

VI i A' i ,

/ .-! 1 1 ,-t--0.8..L1 I !

I ,

1'---..' I 1--~o.6 ! I I " I . ",,"

~ :::t::-b ,1 Ii)''': f\ ['oJ 1/ '~il I I".. ,

~I " Kl/, i I

6

5 I 5' .0

" 4-:i' ;:, .0 ...

ID 0 0.2 0.4 0.6 1.2 'Yol. --

--FO'I EOUAL POTENTIAL 8CA.J'jO/lRV MIDWAY BETWEEN ELEhENTS IF 'l> • Co ANO cbo() .

----- rOR EOUAL POTENTIAL BCUOIRV MOHAY BETWEEN ELEMENTS IF co' Co AND AT ADJACENT ELEMENT IF Co • 0

(5HIELOING EFFECT I

element .j 0.6 + \ fo..

"02 ' ~"..' ~ , I

3 ~ ~

... 0

" ..... 0.4

0.2

o a

~

A'~ f''' V ".. "', , "..

2

f'-.. I 1 i , I

'~ i ; t--... 2

't--'O_i~

\

i 3 4 'Yo--

[-"1-! 1 , 5

o 6

.. ..

FOR EQUAL POTENTIAL BCllJNOt\RY { __ CsJ(Co tCT) Fig. 15 (right). Rolatlve lumped !/JfNIAY ·BETWEEN ELEMENTS IF Cs(Co • Cp)

~- Co AND Cb -0 --csCCo. -0) series C<l;,;:clfances of IndIvidual '0

elements and the effect 0 M!ONAY BETWEEN ELEMENTS IF Cs(Co

' Cb) • f FOR EOUAI.. POTENTIAL BOt..MW1Y {--_CS!(CotCT)

shielding upon this serIes ca- ~ - Co AND AT ADJACENT ELEMENT ---'S(~ -0) .

---.-----.-------- pacJtance . F cb • O_:"~_EL_O_ING_,_ E_FF_e::T.l ___ _ ---~ -- .~,.,.==...~~~-..,----

SEPTEXBEK 19(;4 SIn-Surge Diatribulion in Con«ntrie Traru/ormcr Windings

,... .' . ~- -~~".'

. ..... 'i'!~:"'." 4_£._£

0.3 0.4 0.5 0.6 0.1

1.0

(A) 0.2

= = 0.4 §5 §'§

= = = = HIELO ~ §§S-L Tc = =1 = =

~ ; lL ~ ~TTi = = 0.5~ §5 = =

03 ~+S+~ 08 (8)

IC(C), ~he "hare of the potential line E/EI=0.5 is fund3.-· menw.lIy changed. Then neither this line nor the center­line between the elements remains suitable as an equipotential ~::)Un(i::try of the fields associated with each element. As com­pared with a. voltllg,e drop of 0.5 EI in each element of a coil, Fig. 16(A), with both ends shielded, the voltage E in the ;;hieldcd element of Fig. 16(C) varies only between 0 and 0.12. Consequently, in the field of the unshielded element, Fig.

--', iCC), the surface of the shielded element practically replaces . ~le centerline between elements as a constant potential bound­~'lry. If ze,ro voltage is used for this potential, the voltage dis­tribution on the surface of the unshielded element continues to correspond to the condition c&=O in Fig. 11, but with the modification that ca/2 and "fa/ vi are substituted respectively for Ca and "fa in equations 43 to 45, 48, and 49, and that "f be­comes identical with "fa. Then the nonlinellrity factor ro in equation 44 goes over into

ro = nvo/V = 1'" ctnh 1'a for Cb =- 0 (SO)

This value of To derived from c&=O, when the equipotential boundary of the first element lies at' the next element, is identical with the result already obtained for C&=Ca and plotted in Fig. 13 for the condition that the centerline between elements is the boundary.

For the same cases c&=O and C&=Ca find in place of equation 45

iii V(c&=O) 1 ctnh 'Ya-tanh( 'Ya/2n) ii/V(Cb=ea) cosh'Ya/n ctnh'Ya-tanh'Ya/n

(51)

which is added to the curves in Fig. 14 and illustrates the shielding effect upon the relative maximum turn-to-tum volt­age. Note that in Fig. 14 both sets of curves reach a maxi­mum as a function of "fain which is the value where the shield has its greatest effect as far as the voltage distribution in the minor network is concerned.

/''' Shifting the equipotential boundary of the first element to I . /he surface of the second element for Cb = 0 also changes equa­

tions 48 and 4!J into

~=~ ctnh 'Ya forCb=O\ ca+cr 1+'Ya2

c,(c~=O) . nh l' .' ...;.;...~...;..= 'Y4 ta 'Ya- . c,{eo=ea)

386 J--::.:.

(52)

'.

-----. -~~- .. - -- -----_ .. _-----0.2 . 0.3 0.4 0.5 ::ig. 15. r.~easurcd flald dis-

o i1f'6 0.7

\ = 1.0

§'§ 0.4 =

0.3

02

(C)

trl!Jution In a 2-eloment panc .. ke winding

These values are included in the cun'cs oi Fig. 15 and iIIus­t.rated the shielding effect on the series capacitance.

In order to apply these curves to the conditions in Fig. 16, calculate from the giyen dimensions and

. Surface CapaCItance = Constant --. - (fa or ET)

Spacmg

the quantities

(53)

(Ca/cT)=(H/S)(T,n/W)(fa/Er)=8.63, 1'a= 2.94, 1'a/n = 0.101, and write

• C, (l+CT) C, ~ =- ;;: C,.+CT

(54)

ii(Cb=O) v/f"(Cb";'O) f"/El(C~=O)

ii(Cb=Ca ) =- iJ/f/(c~=C,.) V/El(C~=C,.) (55)

The relative values of the turn-ta-turn voltage v and seri~ capacitance c. in Figs. 16(A) to (C) are then computed as:

(I). For C&=Ca: In a winding, Fig. 16(A), with both ends shielded, identify C.=Cd so that Fig. 15 and equation 54 furnish c.d(C,.+CT)=1.202 and c,r/c .. =1.340. Note also VIE! (c~=c,,)=O.5.

(In. For c&=O in a winding, Fig. 16(B) with both ends un­shielded, identify C.=C,u so that Fig. 15 and equation 54 furnish c,u/(C,,+Cr) =0.422 and c.uica =0.471. Because of VIE! (Cb=O) =0.5, obtain by equation 55 and Fig. 14

ii[Fig. 16(B») = ii(Cb=O) = v/ V(c~=O) = 1.435 ii[Fig. 16(A)] ii(Cb=C .. ) v/ V(Cb=ea)

(Un. For c&=O in the unshielded end of the winding in Fig. 16(C) with the other end shielded, identify c.=c.1II so that Fig. 15 and equation 54 furnish c.m/(ca+cT) =0.310 and c,m/ca=0.346. Because of VIEl(c~=O)=O.88 in the un­shielded element and of v/V(cb=O)/iiIV(c&=c,,) =1.048 ob-tained from Fig. 14, find by equation 55 .

ii[Fig. 16(C)] =~Cb=O) = 1.8-1).. ii{Fig. 16(,\,)J ii(~=ea)

and herewith also

ii[Fig. 16(C)] 285 v[Fig. 16(B)1 = 1.

;:; _ h

.. ----

I i I . i i t r .-1--

1.0

0.9 . 1 I I -~t-- -~ e-W -~I 1 0.6

I I--+'tc.+--+---+==-i'

I • I I - ii' . , __ -0.8

: 0.7 - +-\!-.-+--+--+_r--~ w­.... w

0.7 . '\. ",.Etw.:::m -f----

w Q61-+-+--P'-<l:--t---l-+-+--H.-i C)

'" ~ o >o.s ... Z ::> a: Q4 1--+--+-7'f-::+--t--!-+-+--+-i--j w Cl.

0.3

V ~

w .... wo.s

,

.~

2 1-1--_

3 I I ~P'"

.~ -r<'" i I W' I

.• . 02 ! I/. 1 __ 'MEdsURED _

0.1 f+!:-t--t--r-

0.2 0.4 0.6 0.6 1.0 LOCATION UF EACH ELEMENT z /H ---

I /~. ·······CALCULATED

!I' I 11' I --

~ti t I I I I I i

I

02

0.1

0.2 0.4 0.6 o.S !.O LOCATION IN EACH ELEMENT Z/H~

Consequently, the maximum turn-to-turn stress in a coil end increases when proceeding from Fig. 16(A) to 16(B) and 16(C). This is confirmed in these figures by a corresponding increase in the crowding of the field lines and becomes also apparent by a change in the slope of the·voltage distribution EIE! plotted against zlH in Fig. 17 for the models, Figs. 16(A) and 16(B). E.,:cept for small test variations, this dis­tribution agrees quite closely with a. calculation of V IV for V = EIi2 by equations 42 and 43 and has the shape already shown in Fig. 11.

In a corresponding evaluation of the field in Fig. 16(C), the effect of the shield was replaced by an extension of the 2-ele­ment model into a 4-element unshielded winding. This is accomplished by adding the image of the 2-element field with respect to the shield surface. In the resultant distribution of EIE! plotted in Fig. 18, the voltage decreases and increases within an inside element and thus assumes a somewhat different character from V IV shown in Fig. 11 for a uniformly insulated winding.

Fig. 17 (above left). Voltage distribu-tion In a 2-elcment pancake winding

FIg. 18 (above center). Voltage distribution in a 4-element pancake winding without

shields

Fig. 19 (above right). Voltage dis-trlbution in a 6-element panca!<e

winding

Fig. 20 (right). Voltage distrib!.l-tion in a U-ele-ment pancake winding without

shields

AI,,-,---:-______ ~.., 1.0

09

- TESTED 1 WITHOUT --- TESTE:J I WITH ....... CALC:.Ji..A-:-ED I SM:E .... uS -~ CALCU:..ATi::O r SHlELDS

AI i.O

Q.9

A2 08

0.7

1 A4

0.6 ..,-.... w

A5 o.sw <:> <t ~ 0

0.4 > A6 >-

Z ::>

Q.3a: .., C1.

A8 0.2.

0.1

8 0 0.2 0.4 0.6 0.8 1.0

LOCATION IN EACH ELEMENT z/H .,....:.-

By leaving the dimensions of each element the same as in Fig. 16, the general character of the unshielded 4-element \vinding was found to be maintained when their number was increased in additional models. Examples are the case of six elements shown in Fig. 19 and of 12 elements shown in Fig. 20 derived from a 6-element field 1;\1.th only one end shielded. The potential in the serond clement from the line varies in all three cases (Figs. 18 to 20) by only 13 to 19% of the total voltage drop in the line element. The voltage distribution in the line element has, therefore, been computed by shifting the potential boundary to the surface of the next element, that is, by substituting "f = "fa in equation 43 of V IV, as in equations 50 to 52 for the turn-ta-turn voltages and series capacitances. The results in Figs. 18. to 20 conform. quite closely to the test values for an unshielded wiuding, re­gardless of the number of elements, if the calculated distribu­tion is referred to the total measured voltage drop in the

line element. A similar conformation of the calculation by . test results is obtained in Fig. 19 for a shielded 6-element coil. This voltage distribution can be computed by equation 4Z in the whole winding by assuming a linear major voltage distribution.

SEPTEMBER 1964

The comparison with test results can be extended to the calculation of the equivalent series capacitance Cr , as plQtted in Fig. 15, by using its v:l.lues for findi.ng the major voltr.:;c­distribution. This has been studied for the example of a 6-

Slei_Surqe DiBtnoution in Concentric Tram/onn" Winding. 881'

'. ... .. +. ,:p .. -.

--- .- ----- -- -cknwnt \\"indin~ with grounded surfa('(~" in a di"tance G from

. both ('nds of the ('Iem('llt~ ami with one winding end ;rrounded, :is illu"Lrated in Fig. 21 for G=3A9 cm. Dy making the size . : the indi\'idual clements the same as in Fig. 16, the total

,nding ll'ngth became L = 24 cm. TIll' dielectric ['onstant between elements and ground

\\'a~ dlO~ell to have the same value fa as between elements. The t['4 re~ults for the con'~ponding voltage distribution EO, '1~\ are fouad in Fig. 21 for the shielded and unshielded condition. The \'o!tage drop VI in these cun'es becomes about :20% of the applied voltage EI in a shielded line element, but ri~es to nearly 87% if the ~hie!tl is removed. On the other hand, the 10;ted voltage;; in the inside elements nos. 3 and 5 for the ~hielded condition and nos. 2 and 4 for the unshielded case :-how a rise rather than a drop when proceeding from line to grollnd. 3ince the analy~is macle furnishes instead a steady ,Imp irom line t6 growlfi in all elements according to Figs. 4 :ll1d 11, thi" [lnalpis appears inadequate to find the \'oltage drop r' in indi\'idual elements under the influence of a nearby ground or the voltage di"tribution V IV in any inside element, no matter whether a ~hicld is used or not.

However, the formulas derived for the minor voltage dis­tribution Vlf' are in fair agreement with the test results in fi~. ~l if the cal.cubtion is confined to the line element only "nd i'cicrred to the total te~tcd element voltage. The values of V If' were computed by equation 42 for the shielded con­I!iticil and by equation 43 for "'I = "'I a in the unshielded case.

Lkewise, a comparison between test and calculation of the major voltage distribution EO / EI had to be limited to those junction points between clements which face the line end side. This comparison has to be made by using the equations de-

ved for the series capacitance c, and will, therefore, be a. ,-l;eck for their validity.

In order to compute the major volt:J.ge distribution in Fig. 21, first find by equation 53 cglca=2 (S/H)(W +S)IG = 0.342 and introduce

Calc, =(calc.)(c~/c.) (56)

In the shielded case, that is, for C";CIl =0.746, then obtain

A I .. • '1.t.

!\ I\" \ ,

t-' •

l- I'.. • \

f-~

~-G'" eG ~= I .0

p;:-~ '~~-- .' -1..-aooT I" ° .:-.+.-

'}

-' --~

I".. _~3 . - .....

0.9

o.6~ ~

0.512

I _ I-r~ ... ~ O.4a A 2 t~

",

2/ .. f" ~

r- ,.-A

lL - - r-'.:3.

A 3 ....... '--

",' .. to( 'N 5

.~ ~ ~ t-. .-, !~ ~ ., ~

I

!.L

~

> ... 0.3~

<>:

o.2~

0.1

,Fig. 21 (left). . Voltage distribution In a 5-element pancaka winding with one end .

grounded

Fig. 23 ·(right). Equiv­alent circuit of a 12-Glament grounded pancake wind Ina

. without shields

A-Sectionali'lp.d np.t· *- .. P ! 1 9 o ~ M ~ M ~. ~~ LCCATIOI'I IN EACH ELEMENT ZlH -- B-Network of

- '.'EASUlED 1·.·.m.oJT --'.~'RED \WITH .~ •••• Ct.!.a.uTEO SHIELDS -Ul..W.ATED SHIElDS lumped capaCitances

, •..• 0,

-----_._-------- - -------_. __ ._-cg/clI=0.255, 8= VC Olcrl=0.504, a=68=3.02i. The dis­tribution of E" lEI was calculated for these values by equation 1 for a continuous network and marked on the ordinate of Fig . 21 in comparison with the test results.

In 3. corresponding calculation of the unshielded ~ase, the equivalent series c:lpacitances of the individual elements are too much diJIerent from each other to form a continuous net­work. By considering the second elements on both winding ends to be :lpproximately a.t equal potential, these elements will not contribute a.ny seri-"s capacitapce to the network so that it assumes the form shown in Fig. 22. In each end ele­ment (nos. 1 and 6) the capacitance C,=C,lII has a.lready been found under this condition with Cal C,m = 2.89. By equation' 56 then compute ca/c'l!I = 0.aS5. In euch c<!nter element (nos. 3 and 4), c, becomes a. q1lantity C,IV obtained from Fig. 15 for cb/ca=0.5 and "'1= 1.94 ill the form C,IV!(Ca+CT) =0.882. Equations .54 and 56 then furnish Cal c,(V = 1.018 and cg/c .. v = 0.348.

If these values are used first to obtain the voltage dis­tribution in the circuit, Fig. 21, without any grounded sur­faces, find

E, calc. III -= = ().370 EI 2[(Ca!C,llI)+(Ca/C,IV)1

and, for reasons of symmetry, El/ EI = 1- (E31 E1) = 0.630. These values are marked on the ordinate of Fig. 19 where they are in close agreement with test results. For a corre­sponding analysis of the network, Fig. 22, with ground sur­faces, apply a number of delta-Y transformations and ob­tain the distribution of E" lEI marked on the ordinate of Fig. 21 for 3. comparison with test values.

The system used in Fig. 22 for developing a capacitance n€'t­work for a. 6-element unshielded coil can be extended to a IaI'ger number of elements, as illustrated in Fig. 23(A) for the example of 3. 12-element coil. This is accomplished by approximating c, by c.m and C.rv in the first three and last three elements (nos. 1 to 3 and 10 to 12) while the symmetrical value Cd is used for each of the six center elements (nos. 4 to 9). Without any grounded surfaces, obtain the relath-e voltages

Rg. 22 (right). Equivalent circuit of a 6-element grounded pancake winding without

shields

, j

888 Steirt-Suratt Di.tn~ in C~ftWitric TramformfT Wt1ldiftq. .. -~ .. , -.-.. -~.: ...

SEP'l'EYBER IgM- I. -.'.~: - -~--""'---' .. "".-,.~'"" ... ~.' ....",.,-,,.... • .,.... ""'~. C'!"}! .. .:-~t::~ ........... ~'" ~ ._-f"~. __ ~;,i",,"'_':":,(~~"""'" ~~.~i.~

and.for rC[l."()ll~ of symmetl'~-, E5/ EI = 0,;), EJEI = 1-E6/EI =

0.622, EjE,=1-Es/EI=0.7fi5. Their compari30n with te~t results is made 011 the ortlinnte of Fig. 20 and becomes a measure for the accuracy of the approximations introduced fol' the serics capacitance c •.

If a ground is added in Fig. 23(A), the uniformly insulated section between the points .13 and A 7 with ground and series capacitances Cg and Csl ill each clement may be treated as a continuolls network which in turn is replaced by an equivalent ... of capacit.ancrs Kg! and lei according to equation 25. The distribution of c and E if thrn computed in a network consist­ing of this rqui\'alent ... nncl of C,IIr and Csl\', as shown in Fig. 23(Bl. Mtprward;;, the eontinuous network -is reintroduced het\\'('rn .13 and A7 in place of the equivalent ... in order to find the di~trihutioll of E and e in this center part of the wind-lng.

,\5 a study of the results obtained it! Figs. 17 to 21 for the \'oltage distribulion in a shielded unci un:;hiclclccl winding, the effect of the ~hield in obtaining a reduction of the line end ~tresses can be summarized as follows:

The maximum elr:mcnt \-oltage;; VI and CI ill a major net­work arc dccrt'ased because the addition of a shield raises the ~eries capac-itance of the line clement from the condition c~ = ° to the condition Cb =ca• The re/ati\-e nature of these two cases is shown in Fig. 15. The corresponding effect on the maximum turn-to-turn voltage iim is twofold, a reduction of f-I in the major network, and a decrease of ii/V in the minor network. Fig. 14 shows this second phenomenon for various parameters. These results are further illustrated in Table I by a summary of the line end voltages taken from the test values of Figs. 19 and 21 for a 6-element model. \Vhile the addition of a shield reduces the voltage VI across the first element next to the line to about one-half in the absence of any ground surface, and to one-third in the presence of a ground, the corresponding voltage iim across the first turn is decreased to apprm,:imately one-third and one-fifth respec­tively. This makes vm without a shield and without a ground about eight times as high and with a ground abOut 30 times as high 'as in a linear distribution.

Conclusions

The study made of the initial impulse voltages reveals that the method of com'erting the actual field problem into a cir­cuit problem has considerable limitations. A rigorous anal­ysis of a ~urge distribution in transformer windings appen.rs, therefore, to become a formidable ta..~k even without con­sidering coil inductance and a corresponding variation with time.

However, as far as the initial \'oltage distribution is con­cerned, the following general conclusions can be drawn from the cirt"uit analysis presented in this paper and from the type of approximations which had to be made.

1. For sufficiently long pancake coils, the actual length of the winding and its connection on the nonline end has little effect on the initial stresses at tha line end, where the surge is applied, and on the value of the entrance capacitance replacing the capacitance' network. If, however, the coil length becomes significant, the initial stresses in an open coil are smaller than

T3blo I. Tested Lina End Voltages in a 6-Element Coif

End Sl:ields

Oulside Ground

None

Voltage Across First Duct, Ct/E1

Voltage Across First

Clement. V,/E,

Voltage Across Fir~t

Turn, v",/EI

linear linear Volls Per Volts E!~mcnt rer Turn

lIN l/(nN)

Yes None Yes None

0.330 0.368 0.402 0.770 _

0.188 0.395 0.291 0.868

0.048 0.167 0.016}

0.0057 Yes 0.037

0.175

2. Insulation grading ha;; its limitations ~illce a reduetiol1 of the insulation clearance~ inside the coil raise;; it;; initial volt­age stre~ses at the line epd. Thi~ i~ experienced in addition to any po~sible voltage o~eillation~ ('all~ed b~· the insulation grading.

3. A.~ a function of the eapacitance ratio in ('on~ecl\tive

spaces between elemcnt5, the series capacitance ha.~ a maxi­mum which is 22% lar~er thun the sum of the cOI'l"c"ponding capacitances between clpments and between turn~.

4. The volta~e di'>tribution inside an E+ment is lIOt linear since its own di!'trihutioll constant enter" the ~trr~, calcula­tion. As a result, shielding of the lille element ha~ the clouble effect of improving the yoltage distrihution on the coil ~llrface by incren.;;ing the ;;erie'> capacitance of this ele!1lent, and of improving the di~tribution inside the element. Thus, the stre;;ses between turn~ benefit more than stresses belween elemenh.

5. The relath-e initial voltage distribution between elements of a uniformly insulated winding is identical with the distri­bution of the corresponding voltages to ground. Since these growld voltages can be read more accurately, their test may be substituted for measurements of the element voltages except for their vaiue at the line end.

Appendix. Analysis 01 the r.'Htior Capacitance Network

For computing the voltages V from the tum at z to the center­line a'a' in the minor capacitance network, Fig. 10, introduce the capacitance currents ia and i~ from this pl1rticular tum to the two adjacent element.<! on either sidc as well as the COlTe­sponding current iT between turns. Then find at point z for p=d/dt:

iT(Z+ 6z/2) -iT(z- 6z/2) = ib -ia,

i..=pVka6z, ib=p( V- V)k~6z

iT = -pvkT /6z

By eliminating ia , i~, iT, and p and by substituting v = t.V, obtain for sufficiently small values of t. V and 6z

Introduce the general solution in the form

V = al sinh oz+a2 cosh oz+a.

with unknown constant.<! at, a2, a3, find obtain

(57)

(58)

(59)

The constant 0 may be replaced by the minor distribution constant "(=v'2(Ca+Cb)/CT because of .

(60)

Consequently, the boundary conditions

in a I!rounded coil. _____ --_-_,~ _____ .J:(~_:=Qt== _V,

SF.PTt:MRER 1964

:;. "

SUi_Sur(Je DWribution in Concentric Tra,,4ormt:r WindingB

r" ._~;#.A.:;;'f~_ ....

--~-~-~-~----~~---'"-~-

Q, = --;-- -- cosh 1'+-- , at= V .--r ( ~ Q )~ ~ ~1I1h'Y Ca+Cb Ca+Cb Ca+Cb

~. th:lt the t'C[uaLion 58 can be bronght into the form

.;..= _~."_ sinh i'(l_-=z/H) +~ [1-sinh i'Z/H] V r,,+cb sinh l' C,,+Cb sinh l'

(61)

and, by the slope form of equntion 36, into

~ =:2' [~ C()~h 'Y(l-z/ H) +~ cosh 1'z/ II] V n Ca +Cb sinh l' C.+Cb sinh l'

(62)

\\'hich may be also transformed into 35 and 33 respectively. For finding the equivalent [cries capacitance c, of each element,

con:;irler its definition as a lumped capaeitance which is ~ub­sti:utrJ for the network between the lines a'a' and b'b" in Fig. 10. C"Iw'l[upntly, the power cou:;umed in c, has to be equal to I.:lt~ jl' ... scr (,uIl~lI111e,1 in this network if the applied voltage hus the sume value j7 ill either case. In each section ~z of this r:~t work finrl the power

1/:2(k"..lz)P between a'a' and the element

ll~(.r .. ?.:;z)( V-V)' between b'b" and the element

l/:2(kr/ <lz)v' between adjacent tUI'llS of the element

s·) that, for a per-unit applied voltage, for i.lz = H In, und by equa­j"n GO, the total power in the network becomes

Introduce equations 61 and 62 and

----" j~d obtain

2cac& c,=-­Ca-rQ

C, 1 Ca ~ Q Z J.I{ -= 1+-.-- [- cosh 21' (1--)+- cosh2'Y-+ Cr 0 _ smhl l' Q H Ca H

with a solution

c, 1 [(ca Cb) 2 ] - = 1+- -+- ctnh 1'+-.-C, l' ct. ea 9mh l'

which may be transformed into

c. (2 1') (CII Cb ) 1 ' -= 1+- ctnh;; + -+- -2 - etnh 'Y Cr l' - Cb CII 'Y

(63)

(64)

(65)

For a numerical evaluation of this equation substitute the nor­malized minor distribution constant 1'a = V ca/cr and the dis­symetry ~= V(l+Cb/ca)/2 of Ca and Cb according to equation 35 and find

(66)

Then equation 65 can be changed into equation 48 which fur­nishes c./( Ca+CT), as plotted in Fig. 15.

> Nl)menclature

j<ljor Network

\' = total number of winding elements . J[ = number of winding elements next to the line end A L = length of. winding . x = dist:mce from line end ... 1 -of winding, Fig. 3 'J = distance from nonline end B of winding, Fig. 3 AZ=L/N=spaee taken by one winding element G = dietnnee between ends of elements and ground

"f" ....

E = vollage to groullrl at point x E l, E:=voltag(-s to grounri at coil ends A(x=O) and B(x=L) in

a winding with uniform insulation E l, E., E. = voltages to grounu at the starts A, P, Q of each coil

part in a winding with graded inBlllation; Fig. 7 El 00 Ea=v(,ltagcs from ends of elementll (AI to AS) to coil end

B in a 6- or l:2-element winding, Fib'S. 22 and 23 e = voltage at I between ends of adiacent elements, Fig. 3 R= Nc/(2E l ) = nonlinearity 'factor of E(x) Co, Ro = values of e and R at line end 11 extrapolated to x=O el=e(x=L/N)=value of e between the first two elements next

to the line end A h = line current Cg = ground capacitance of carh clement c,=serres capacitance nf eaeh elcment C g=cgN, Cs =c,/N = tnhl ground and series capacitances of

winding a=VCg/c" ;3=Vcg/c.=a/.V=m!ljor distribution constants K = entrance capacitance of winding = [tpparent lumped capaci-

tanre to ground at line end A, Fig. 3 eo"', K'" = values of Co and K for an infinitely long winding E" eO R" K't EO: eO; RO; K O \ = values of E, e, R, K for a grounded (0)

or open (0) nonline end B, Fig. 3 Kg, K.=capaeit:Lnce3 of the equivalent ;r of a major network 1,2,3=subscripts distinguishing qu:wtities in different parts

(1,2,3) of a winding with graded insulation

Jfinor N etu'ork

H = height of each element n+ 1.= total number of turns in each element z=distance from element end b', Fig. 10 ::.z=H/n=space taken by one turn S=riistance between arij:lcent clements JV = width of turn T. = turn thickness T, = insuln.tion thickness bet ween adjacent turns V=outside voltage between point·z and element end a', Fig. 10 V= V(x) = value of Vat clement end b'(z=O), Fig. 10 ill = il(x=L/2NH V V.o= il(z=O) 5 =values of at line end A, Fig. 3, corre-

sponding to el and eo v=tum-to-tum voltage at point z' ii=v(z=H/(2n»=value of v between the first two turns at

clement end b' , Fig. 10 r =nv / V = nonline:uity factor of V( z} vo, rQ = values of v and r at element end b' extrapolated to z=o V"" 110m = values of ii and va u.t line end A ia, ib = capacitance currents between one tum at elements point

z and the two adjacent elements, Fig. 3 ir-capacitance turn-to-tum current at z Ca, Cb = total element-to-element capacitances on either side of

an element (0 ;'iCb ;'ica) cr=total turn-to-turn capacitance of an element ka, kb, kr=values of Ca, Cb, CT per-unit element height Cr =-2caC&/(Ca+Cb) = resultant element-to-element capacitance

between the centerlines a'a' and b'b' on either side of an element

A=VC1+cb/ca)/2=dissymetry of the capacitances Ca and Q

'Y=V2(Ca+Cb)/cT=minor distribution constant 'Ya=VCa/cr=normalized minor distribution constant

General Er=dielectric constant of the insulation between turns Ea==dieleetric constant of the insulation between elements and

from winding to ground t=time, p=d/dt E=2.718=basis of the IUtural logarithm te, I, w = ordinates of three nomographic scaiea I, g, D=abscissa vlllues loc:1.ting. three nomographicscaies a, b = nomographic scale constants . aI, a!, as, ci=constants appearing in th~ solution equation 58 of-

the dilferentilll equation 57· •

1. DAB EI=?.IXGE:1 Elx::a E:'EKTP.O!I.~GXETtSCI!EN' 'WELLE IN Enni: Sl'Ul.B HrT \V:~'D=OS!uP.l.Z:'!'":", 7.arl V-lilly Wagner. Elektr&-. technik und .U.uchinenba, .. V!enna. Austria, .1915 .. pp. 89-92.

":'-' ',"

---.-----~.------. - .------.-----------,.~~~ re .... ... ,4, •..•.

,!\1..¥4i.

2. D ETt:ID1[XATION OF l~IPl:L:-;E STHI':~5f-:A WITHI:i TR.\:-lSFOnMEp.

,,""InINOS nY CO~!I'I:'n:R~, J. H, McWhirter. C. D. Fahrnl~orf, J. H. Steele. AlEE _TralL.actioll., ut. III (Power Apparatus a7!d Syslems), YO!. 75. I ()51i, PlY- 12G7 -73.

3. PREDETER~n~.\Tlo:-,: ny C'AT.ct.;L.\TTO:-: OF TIlE FLECTIHe STREESI:9

IN .\ \\·I.'<nrNG SITllH:("'I"BP TO _~ DI;IHa: VOLT.\GE, P. Waldvogel, Pouxcl. Paper .\"0. 1:::5, CIGIlE, Pari:3, rr:l.!lte, pp. 1-1G (i,1 Fr"nch).

4 .• MB'rnoDEs poul! L'i:-rUllE DES T<:NSh,KS .<NomULEB DANS I.EB 1·K.~X'WOI!~!ATEVI!S, P. A. Abetti. i\lcmoire couronnc au Concourd de Fondation Georije :'Ifontefiore, Scosion 1955, Section scientifiquG et technique, vol. 70, 1957, pp. 851-904.

5. VORAUSBBSTIMMUNG DER ST08SBEANSPRUCHUNGEX IN TRANS­FORMATOREN MIT lIU.FE VON \\·ICKI.U:WS~fODELl.EN, Klaus Gadek. Reinhold Nitsche. Elektrotcchflischc Zeilschritt, Berlin, Ger­many, edition A, vol. 83, no. 21/22, 19G2, pp. 728-35.

6. DIE TRANsFon~IATonEN (book). Rudolf KUchler. Julius Springer Verlag, Berlin, Germany, 1956, pp. 12G-28.

7. STOSSERSCHEIXUXGEN IX EI.EKTRISCHEX ~IA5CHINEN, B. Heller, A. Veverka. V EI1 Verlall Trchn·il.:, Berlin, Germany, 1957, pp. 31-39.

8. NO~IOGRAPIIY AND E~IPlmCAI. EQUAl'IOXS, Dale S •. Davis. Reinhold Publishing Corporation, New York, N. Y., 1955, pp. 173-74.

9. USE AND THEORY OF TIlE ANALOG FIELD PLOTTER (book). Inalruction Jfanual I.V24, Sunshine Scientific Instruments, Phila­delphia. Pa.

J. H. McWhirter (Westinghouse Electric Corporation, Sharon, Pa.): Dr. Stein has presented very interesting as well as useful information. He has very wisely chosen a limited aspect of the subject of impulse voltage distribution and made a thorough study of it. As he has said, this is a fonnidable task without considering the complexities resulting from introducing the induetanc(!S and the tran:;ient variation of the voltages.

To emphasize one of the difficulties, let us consider the very basic one of defining initial distribution. We may define this in tenns of an experiment whieh we can perform in our mind, even though we may have some difficulty actually performing the ex­periment. Consider that we apply a voltage which rises to a crest value of unity in time DJ.. At this time, DJ., we measure the volt­ages within the winding. These measured voltages are defined as a function Vex, Y. z, DJ.), where x, y, and z are the space co­ordinates of the various points within the winding. The initial distribution is the limit of this function as DJ. approaches zero. This implies no charge flow through inductive erements. All charge on capacitive elements within the winding must then come from the voltage source through other capacitive elements.

It seems to me, the initial distribution function as defined in this manner is very near zero everywhere within the winding since there are series inducts.nces involved which are paralleled by ex­tremely small capacitances. To attain voltages which are an appreciable fraction of the applied voltage requires charge flow through these inductances. Examples of these inductances are the leads, the individual turns, and the static shields and the con­nections between coils which all have inductances even though they may be small.

This definition of initial distribution leads to confusion and to . trivial and not very useful answers. Let us try to arrive at an­other definition of initial distribution which may be more useful and will more nearly correspond to our usual ideas. In order to arrive at this, consider the voltage at a particular point in the winding at, time· DJ. where the applied voltage has a rise time 1lI..

The insert in Fig. 24 shows the applied voltage which rises to

INDUCTA~!CE

O'.sTRISUTION

I I

V(t::, t)

INITIAL DiSTRiBUTION "'l21= '" I ---

~ I a I > I t: I § I .

~ °l-A t--l t-oL-----~------------------------

w Cl ~ I-

~t =Microseconds(Log scole)

...J Cl.. ::E <!:

~~ o I Period _ 211 (Loq scole)

to

Fig. 24

broad plateau in the vicinity' of one microsecond. (There will be other plateaus but they are not of interest at the moment.)

Now consider a graph of the relative amplitudes of the responses to an applied step function. In order to afford a comparison with the top curve, this is plotted below as a functioR of the oscillation period of 211"/"'. The shape of this curve is not to be taken too seriously except that the plateau in the top curve around 1_ microsecond corresponds to a deficiency in the winding response of components with periods of around 1 microsecond. When the "valley" between the two parts of this curve is less deep and less broad and as its center deviates significantly from 1 microsecond, our usual concept of initial distribution is less meaningful and useful.

Evidently, the oscillations associated with Jeads. connections between coils, and static plates are usually to the left in the bot­tom curve and these elements can be considered as presenting no impedance to the flow of initial charge. Other elements with less rapid oscillations are to the right and the physical elements pro­ducing these oscillations can be considered as presenting infinite impedance to the flow of initial charge.

Through experience we have learned which winding elements can be assumed to be equipotential connections and which can be assumed to be open circuits for the various ty'Pes of windings. This experience is unsatisfactory for detennining the limitations of these assumptions and it does not tell us what assumptions to make in analyzing a new type of winding.

Does Dr. Stein have any comments on this discussion of a definition of initial distribution and how it applies to the work reported in his paper? -

In Fig. 14, it is difficult to readily see the effect of the shielding upon the maximum turn-ta-turn voltage. Perhaps if the infonna­tion were to be plotted in a different ma.nner, the results would be more useful.

unity in time 1lI.. We can plot a curve of the winding voltage at G. M. Stein: This is a reply to Mr. McWhirter's discussion. time Ill. versus 1lI.. We know several points on this curve. When Mr. McWhirter is concerned about the conditions under which Ill. is very large (say, greater than several hundred microseconds), the actual transient phenomena. in a winding can be appro:d-the distribution will be essentially according to the winding in- mated by an electrostatic voltage distribution and particularly ductances. According to the previous argument, the distribution at what times. A similar question has been raised in the review at. Ill. equals zero is fairly close to zero. What shape docs the of the paper with an objection to the met:ill.ic links .. ·hich ap-curve have at intermediate times? If the initial distribution, pear in the circuits between adjacent. clements and force their. as we use it, is something special, the curve s~?~d have_a fairl!~ __ ~e~ds_~_~eon the_same ~tenti~: __ _ __ . __ _

SEP'l'DrBEll 1964 Steln-Surllfl Diatribution. in. Concentric Tram/onne,- Winding. 89L

r·---

.c' 3d. .,.+:,.t __

.. ,. ·"c- d,.!e.l,'

"

rT!TTTT'r-:----r'ITi'B-_ ELEVATION

EQUIPOTENTIAL: LINES I ~/ Y

1 r-r--I-lf-Lr 5H4i1~r'rl+ 6~LToIHJ;IJJs

1 NET,,'JORK t DEVELOPMENT

';:;. 2;. G~r.cr(ll inside netwodt of !;in(Jle elements

,\n attem!1t shull be made to answer these questions by using the example, Fig, :25, of a 2-element pancake winding with three turns per element. The numera.ls 0 to 6 designate tum ends. The elements are also shown in a plan view side by side and are

.. - ..... ::1a11y replaced by a developed mashed network of capacitances /nd inductances.

- A voltage applied between 0 and 6 generates electric fields be­tween the turns and a voltage difference from turn to turn in any section of the ,nnding. Consequently, the voltage changes steadily along the conductor of each turn. Therefore, the space between consecutive turns contains closed equipotential surfaces which are distinguished by dotted lines and intersect the conduc­tors at the turn ends 1, 2, 4, and 5. As shown in the network de­velopment, these equipotential surfaces can be used to divide the total network into Bub-networks associated with each tum. In particular, the first and last turns in each element, for instance from 0 to 1 and from 2 to 3, become meshed inductance and capacitance networks which have the same shape as used in the surge analY8is of a single transmission line facing a ground surface. This delaYI3 the generation of an electrostatic voltl1ge distribution inside the winding, as ~Ir.l\1c"'nirter hn.S pointed out; because a charging current flowing from the line into the capacitance of the line element, as indicated by arrows, will have to p3.8S through such an inductive-capacitive network between 0 and 1 in form of a traveling wave of very high- frequencies. However, from 1 to :2, this current may find its way through the capacitances without using the path· through the conductor and its inductances. From 2 the currcnt may reach the end 4 in the other element by way of the two transmission lines from 2 to 3 and from 3· to 4 and of the normally very short and, therefore, relatively low inductive bterelement connection from 3 to 3-. It is true that this circuit from 2 to 4 may be bypassed through the interelem~nt rapacitances which are not shown. However, the presence of a low inductive link from 3 to 3- will confine the voltage drop dcroSS

the ,,;nding to itl! elements, and thus produce the.highest stresses. It "ill, therefore, be conservative to include the interelement con­nections into the capacitance networks until the relative re-

,Juctances of the two current paths from 2 to 4 are better known. ( ~Ir. Me Whirter further would like to see a more practical repre-

, ,ntation of the shic!ding effect upon the T\lll.'Cimum turn-to-turn ;-oltagc il th:m ghren in Fig. 14 of the papcr. This stress is shown in Fig, 14 as a function of two variahles wliicll are the normalized minor distribution constant Ii and the ratio of "'f,,/n if n + 1 repre­::ant3 the total number of tilrns in each element.· It becomes in­deed revealing if v is evaluated in terms of n in pla('c of plotting its change against "aln. ' This shall be carried through for the condi­tien that the equal potential boundary in the field of an unsiiieided line element, that is for ~-O, coincides with the,ne:d; element.

2.0 '~ ---p '~ , ,

1.9 \

1 \ 1.8

E c: 1.7 -0 c: 0

_.1.6 _ 0

0 (,)

" " .0 cf 1.5 u

,> I> ....... ..... I> I> 1.4

~

0~

1.3

1.2

1.1

1.0 0 3 4 5 6

"'(0-

Fig. 26. Shielding eHact on the relative'maximum turn-to-tum voltage for dlm~ront numbers of clement tums

For an analysis and numerical evaluation of a corresponding formula for ii, in which n is one of the variables, the equation 51 of the paper is changed into

O/V(Cb=O) 1 cosh "'fa(l-1/2n) p- (6~

ti/V(~=Ca) coshha/2n) coshl'a(1-1/n)

This may also be written:

2 1 +e-'Y4 %(I-I/fn)

P=1+/I-"./" 1+6-"1·2(1-1/") (68)

and becomes for sufficiently large values of 1' ..

2 P=1+6-"1';" for l'a»1 (69)

Consequently, the stress ratio p varies between 1 and 2, as illus­tmted by the plot of p against "'fa for different values of n in Fig.-26. The value of p = 1 appears for n = 1 and '" while p = 2 is reached for "'fa = '" and 1 <n< CD. If, instead of this, p would be plotted agllinst n for a constant I'a, this stress curve would assume a maximum Pm at some value n=n",. This maximum Pm corre­sponds to the crest valucsof p=ii/V(C/l=O)/ii/V(cb=ca)appearing in Fig. 14 of the paper as function of I'a/n and is detennined by applying ()p/<:l("'fa/n)=O to equation 67. Then obtain

O-cosh I'll (1 __ 1_) sinh "'fa (~-}-)-1/2 sinh 1''' (70) 2nm ~Il", n",

which may ab!o he writtfm

O-sinh 1',,2 (1-.!.)-2 sinh "fr. (71) n.. n".

Consequently, n;,. can be eomputed as function of 1'a by the parameter form

),

-....

1 - [- "'J llm=1+1/2--SlIlh- 1 2SlIlh - ; ,a/11m 11m ( 'n) ia=llm -

llrn (72)

with ),Jn m I>S parallleter so that P~I lIlay he f"und by equatiun GS or 6!1. As illustrateel in Fig. :!G, t he values of n", vary between 11 '" = 2 for "'I. = 0 and n", = 1.5 for ,a = 0:> while the amount5 of Pm lie slightly abuve the values uf P "LtaiIH'd for n = 2.

;;;ilH'e in most practical cases th!' number uf condudors n + 1

in ea(·/t winding element is fairly bq;e, for instance n> 10, and ,a becumes usually slllaller than G, the quantity P ill Fig_ 26, and thus

"-

the inilucllcc or ~hieldin:; upon the tlll'll-t,,-tllrn stress ii fur a ,'un­stant elelllont vnltage P, is fJuite rtlodl'rate in size. On the ot!:c;­hanel, the shieleliug clTpl'! Oil the series ('apa('itull('e Cs of the Jille elelllcllt anel thus un its voltage V= V, it~cif is very pl't,f .. unci, :IS shown in Fi;!;s. ].5 to :! I of the p~'p(>r. This means 1ft:!! the' infiuen('e of a shield U[J'>Il the lIl:txilllUrtl tum-to-turn stress f at tI,e line cud is 'ralher iuelircct. sill1'e 1L reduction "f t his ~(.fess is mostly clue to 1L decrease ill the voltage i', across the line element rather tlmn due to a redistribution of \-oltagcs wit hin this element_ -

~. p. -- ..