TheJ&P
Transformer Book
J & P Books
The J&P Transformer Book and The J&P Switchgear Book were published originally by Johnson
& Phillips Ltd, and have for many years been accepted as standard works of reference by
electrical engineers concerned with transformers and switchgear. They now appear under the
Newnes imprint.
TheJ&P
Transformer Book
Twelfth edition
A PRACTICAL TECHNOLOGY OF THE
POWER TRANSFORMER
Martin J. Heathcote, CEng, FIEE
Newnes
OXFORD BOSTON JOHANNESBURG MELBOURNE NEW DELHI SINGAPORE
Newnes
An imprint of Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
A member of the Reed Elsevier plc group
First published 1925 by Johnson & Phillips Ltd
Ninth edition 1961
Reprinted by Iliffe Books Ltd 1965
Tenth edition 1973
Reprinted 1967 (twice), 1981
Eleventh edition 1983
Reprinted 1985, 1988, 1990, 1993, 1995
Twelfth edition 1998
© Reed Educational and Professional Publishing Ltd 1998
All rights reserved. No part of this publication may be reproduced in any material form (including

2.3 Volts per turn and flux density 22
2.4 Tappings 23
2.5 Impedance 24
2.6 Multi-winding transformers including tertiary windings 27
2.7 Zero-sequence impedance 32
2.8 Double secondary transformers 33
2.9 General case of three-winding transformers 35
3 Basic Materials 40
3.1 Dielectrics 40
3.2 Core steel 41
3.3 Winding conductors 53
3.4 Insulation 59
3.5 Transformer oil 74
4 Transformer construction 103
4.1 Core construction 104
4.2 Transformer windings 118
4.3 Disposition of windings 143
4.4 Impulse strength 148
4.5 Thermal considerations 156
4.6 Tappings and tapchangers 167
4.7 Winding forces and performance under short-circuit 226
4.8 Tanks and ancillary equipment 245
4.9 Processing and drying out 280
vi Contents
5 Testing of transformers 313
5.1 Testing and quality assurance during manufacture 313
5.2 Final testing 315
5.3 Possible additional testing for important transformers 377
5.4 Transport, installation and commissioning 384
6 Operation and maintenance 398

APPENDICES
1 Transformer equivalent circuit 803
2 Geometry of the transformer phasor diagram 814
3 The transformer circle diagram 820
Contents vii
4 Transformer regulation 825
5 Symmetrical components in unbalanced three-phase systems 829
6 A symmetrical component study of earth faults in
transformers in parallel 851
7 The use of finite element analysis in the calculation of
leakage flux and dielectric stress distributions 904
8 List of National and International Standards relating to
power transformers 931
9 List of principal CIGRE reports and papers relating
to transformers 934
10 List of reports issued by ERA Technology Limited relating to
transformers and surge phenomena therein 937
Index 941
Foreword
The J & P Transformer Book has been in print for 75 years and during that
time it has been a rewarding work of reference for students, young engineers,
older engineers who have changed the direction of their careers to become
involed with transformers, practising designers and for generations of applica-
tions engineers. In the previous eleven editions the publishers endeavoured to
revise the work, extend it and to bring it up to date. The fact that The J & P
Transformer Book is still in demand is a tribute to the publishers and to the
authors who have carried the torch to light our way for 75 years. The first
edition was prepared by Mr H. Morgan Lacey in 1925, based on a series of
pamphlets entitled Transformer Abstracts that were first printed in 1922. The
book was welcomed as a key reference, giving a guide to British experience at

engineers and will be of as much use to new generations of engineers as the
previous editions have been to their predecessors.
Professor Dennis J. Allan FEng
Stafford, 16 March 1998
Preface to the twelfth edition
A brief history of the J & P Transformer Book and of its many distinguished
previous authors appears elsewhere in this volume. From this it will be seen
that most were chief transformer engineers or chief designers for major manu-
facturers. The effect of this has been twofold. One, all have tended to write
from a manufacturer’s point of view, and two, all have held very demanding
‘day jobs’ whilst attempting to bring the benefit of their particular knowl-
edge and experience to the task of revising and updating the efforts of their
predecessors. This is a task of great magnitude, and as a result of the many
conflicting demands for their time, even the many ‘complete revisions’ of the
J & P Transformer Book have not greatly changed the unique character that
can be traced back to 1925.
The production of the twelfth edition has been taken as an opportunity to
carry out an almost total rewrite, and, as well as making significant changes
to the structure, to change the viewpoint significantly towards that of the
transformer user.
It is hoped that the book will, nevertheless, still be of value to the young
graduate engineer embarking upon a design carreer, as well as to the student
and those involved in transformer manufacture in other than a design capacity.
To provide more specialist design information than this would require a very
much larger volume and would probably have had the effect of discouraging
a significant proportion of the prospective readership. For the more advanced
designer, there are other sources, the work of CIGRE, many learned society
papers, and some textbooks.
Primarily the objective has been to provide a description of the principles
of transformer design and construction, testing operation and maintenance, as

which enabled the chapters to be so generously illustrated.
These include:
ABB Power T & D Limited
Accurate Controls Limited
Allenwest-Brentford Limited
Associated Tapchangers Limited
Bowthorpe EMP Limited
British Standards
Br
¨
uel & Kjær Division of Spectris (UK) Limited
Brush Transformers Limited
Carless Refining & Marketing Limited
CIGR
´
E
Copper Development Association
Emform Limited
ERA Technology Limited
GEA Spiro-Gills Limited
GEC Alsthom Engineering Research Centre
GEC Alsthom T & D Transformers Limited
GEC Alsthom T & D Protection and Control Limited
Hawker Siddeley Transformers Limited
Merlin Gerin Lindley Thompson Transformers
Merlin Gerin Switchgear
Peebles Transformers
South Wales Transformers Limited
xiv Acknowledgements
Strategy and Solutions

output of up to 19 000 A at 23.5 kV, of a large generating unit in the UK, to
400 kV, thereby reducing the current to a more manageable 1200A or so, to
the thousands of small distribution units which operate almost continuously
day in day out, with little or no attention, to provide supplies to industrial and
domestic consumers.
The main purpose of this book is to examine the current state of transformer
technology, primarily from a UK viewpoint, but in the rapidly shrinking and
ever more competitive world of technology it is not possible to retain one’s
1
2 Transformer theory
place in it without a knowledge of all that is going on on the other side of the
globe, so the viewpoint will, hopefully, not be an entirely parochial one.
For a reasonable understanding of the subject it is necessary to make a
brief review of transformer theory together with the basic formulae and simple
phasor diagrams.
1.2 THE IDEAL TRANSFORMER VOLTAGE RATIO
A power transformer normally consists of a pair of windings, primary and
secondary, linked by a magnetic circuit or core. When an alternating voltage
is applied to one of these windings, generally by definition the primary, a
current will flow which sets up an alternating m.m.f. and hence an alternating
flux in the core. This alternating flux in linking both windings induces an
e.m.f. in each of them. In the primary winding this is the ‘back-e.m.f.’ and, if
the transformer were perfect, it would oppose the primary applied voltage to
the extent that no current would flow. In reality, the current which flows is the
transformer magnetising current. In the secondary winding the induced e.m.f.
is the secondary open-circuit voltage. If a load is connected to the secondary
winding which permits the flow of secondary current, then this current creates
a demagnetising m.m.f. thus destroying the balance between primary applied
voltage and back-e.m.f. To restore the balance an increased primary current
must be drawn from the supply to provide an exactly equivalent m.m.f. so

The relationship between the induced voltage and the flux is given by refer-
ence to Faraday’s law which states that its magnitude is proportional to the
rate of change of flux linkage, and Lenz’s law which states that its polarity
is such as to oppose that flux linkage change if current were allowed to flow.
This is normally expressed in the form
e DNd/dt
Transformer theory 3
but, for the practical transformer, it can be shown that the voltage induced per
turn is
E/N D K8
m
f1.3
where K is a constant, 8
m
is the maximum value of total flux in Webers
linking that turn and f is the supply frequency in hertz.
The above expression holds good for the voltage induced in either primary
or secondary windings, and it is only a matter of inserting the correct value of
N for the winding under consideration. Figure 1.1 shows the simple phasor
diagram corresponding to a transformer on no-load (neglecting for the moment
the fact that the transformer has reactance) and the symbols have the signifi-
cance shown on the diagram. Usually in the practical design of a transformer,
the small drop in voltage due to the flow of the no-load current in the primary
winding is neglected.
Figure 1.1 Phasor diagram for a single-phase transformer on open
circuit. Assumed turns ratio 1:1
If the voltage is sinusoidal, which, of course, is always assumed, K is 4.44
and equation (1.3) becomes
E D 4.44f8N
4 Transformer theory

great an extent as possible subject to the normal economic constraints. With
the growth in size and complexity of power stations and transmission and
distribution systems, leakage reactance
or, in practical terms, impedance,
since transformer windings also have resistance
gradually came to be recog-
nised as a valuable aid in the limitation of fault currents. The normal method
of expressing transformer impedance is as a percentage voltage drop in the
transformer at full-load current and this reflects the way in which it is seen by
system designers. For example, an impedance of 10% means that the voltage
drop at full-load current is 10% of the open-circuit voltage, or, alternatively,
neglecting any other impedance in the system, at 10 times full-load current, the
voltage drop in the transformer is equal to the total system voltage. Expressed
in symbols this is:
V
z
D %Z D
I
FL
Z
E
ð 100
where Z is

R
2
C X
2
, R and X being the transformer resistance and leakage
reactance respectively and I

of the load current.
Reactive and resistive voltage drops and phasor diagrams
The total current in the primary circuit is the phasor sum of the primary
load current and the no-load current. Ignoring for the moment the question
of resistance and leakage reactance voltage drops, the condition for a trans-
former supplying a non-inductive load is shown in phasor form in Figure 1.2.
Considering now the voltage drops due to resistance and leakage reactance
of the transformer windings it should first be pointed out that, however the
individual voltage drops are allocated, the sum total effect is apparent at the
secondary terminals. The resistance drops in the primary and secondary wind-
ings are easily separated and determinable for the respective windings. The
Figure 1.3 Phasor diagram for a single-phase transformer
supplying an inductive load of lagging power factor cos 
2
.
Assumed turns ratio 1:1. Voltage drops divided between primary
and secondary sides
Transformer theory 7
reactive voltage drop, which is due to the total flux leakage between the two
windings, is strictly not separable into two components, as the line of demar-
cation between the primary and secondary leakage fluxes cannot be defined.
It has therefore become a convention to allocate half the leakage flux to each
winding, and similarly to dispose of the reactive voltage drops. Figure 1.3
shows the phasor relationship in a single-phase transformer supplying an
inductive load having a lagging power factor of cos
2
, the resistance and
leakage reactance drops being allocated to their respective windings. In fact
the sum total effect is a reduction in the secondary terminal voltage. The resis-
tance and reactance voltage drops allocated to the primary winding appear on

including leakage and load characteristics
Z
0
s
D equivalent value of Z
s
when referred to
the primary winding
Then I
0
2
D
N
2
N
1
I
2
D
N
2
N
1
E
2
Z
s
and E
2
D

where E
1
D I
0
2
Z
0
s
Therefore I
0
2
D E
1
/Z
0
s
1.6
Comparing equations (1.5) and (1.6) it will be seen that Z
0
s
D Z
s
N
1
/N
2

2
.
Figure 1.5 Phasor diagram for a single-phase transformer

and c subscripts to indicate secondary phase phasors
10 Transformer theory
all the phases are shown. For instance Figure 1.6 shows the complete phasor
diagram for a three-phase star/star-connected transformer, and it will be seen
that this diagram is only a threefold repetition of Figure 1.4, in which primary
and secondary phasors correspond exactly to those in Figure 1.4, but the three
sets representing the three different phases are spaced 120
°
apart.
1.5 RATED QUANTITIES
The output of a power transformer is generally expressed in megavolt-
amperes (MVA), although for distribution transformers kilovolt-amperes (kVA)
is generally more appropriate, and the fundamental expressions for determining
these, assuming sine wave functions, are as follows:
Single-phase transformers
Output D 4.44f8
m
NI with the multiplier 10
3
for kVA
and 10
6
for MVA
Three-phase transformers
Output D 4.44f8
m
NI ð
p
3 with the multiplier 10
3

3
for kVA
and 10
6
for MVA
Transformer theory 11
Three-phase transformers
Output D E
2
I
2
ð
p
3 with the multiplier 10
3
for kVA
and 10
6
for MVA
The relationships between phase and line currents and voltages for star- and
for delta-connected three-phase windings are as follows:
Three-phase star connection
phase current D line current I D VA /E ð
p
3
phase voltage D E/
p
3
Three-phase delta connection
phase current D I/

C V
X
sin 
2

C
a
2
200
V
X
cos 
2
 V
R
sin 
2

2
1.7
where V
R
D percentage resistance voltage at full load
D
copper loss ð100
rated kVA
12 Transformer theory
V
X
D percentage reactance voltage D


C
a
2
2 ð 10
2
V
X
cos 
2
 V
R
sin 
2
2

C
a
4
8 ð 10
6
V
X
cos 
2
 V
R
sin 
2


2 Design fundamentals
2.1 TYPES OF TRANSFORMERS
There are two basic types of transformers categorised by their winding/core
configuration: (a) shell type and (b) core type. The difference is best under-
stood by reference to Figure 2.1.
Figure 2.1 Transformer types
In a shell-type transformer the flux-return paths of the core are external to
and enclose the windings. Figure 2.1(a) shows an example of a three-phase
shell-type transformer.
While one large power transformer manufacturer in North America was
noted for his use of shell-type designs, core-type designs predominate in the
UK and throughout most of the world, so that this book will be restricted to
the description of core-type transformers except where specifically identified
otherwise.
13