Alfred Still.

Overhead electric power transmission; principles and calculations online

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OVERHEAD ELECTRIC
POWER TRANSMISSION

PRINCIPLES AND CALCULATIONS



BY



ALFRED STILL



ASSISTANT PROFESSOR OF ELECTRICAL ENGINEERING, PURDUE UNIVERSITY; MEMBER OF

THE INSTITUTION OF ELECTRICAL ENGINEERS; MEMBER OF THE AMERICAN

INSTITUTE OF ELECTRICAL ENGINEERS; ASSOCIATE MEMBER OF THE

INSTITUTION OF CIVIL ENGINEERS. AUTHOR OF "ALTER-

NATING CURRENTS AND THE THEORY OF

TRANSFORMERS" AND "POLY-

PHASE CURRENTS, ' '



McGRAW-HILL BOOK COMPANY, INC.

239 WEST 39TH STREET, NEW YORK

6 BOUVERIE STREET, LONDON, E. C.

1913









COPYRIGHT, 1913, BY THE
MCGRAW-HILL BOOK COMPANY, INC.



;^v::. 2 A ***

"**" Si.*; !.



THE. MAPLE PRESS' YORK PA



PREFACE

Although this book treats mainly of the fundamental principles
and scientific laws which determine the correct design of over-
head electric transmission lines, it has been written primarily
to satisfy the needs of the practical engineer. An attempt has
been made to give the reasons of things to explain the deriva-
tion of practical methods and formulas in the simplest possible
terms: the use of higher mathematics has been avoided; but
vector diagrams, supplemented where necessary with trigono-
metrical formulas, have been freely used for the solution of alter-
nating current problems. It is therefore hoped that the book
may prove useful, not only to the practical designer of trans-
mission lines, but also to those engineering students who may
wish to specialize in the direction of Power Generation and
Transmission, for these will find herein a practical application
of the main theoretical principles underlying all Electrical
Engineering.

The subject is treated less from the standpoint of the construc-
tion engineer in charge of the erection work, as of the office
engineer whose duty it is to make the necessary calculations
and draw up the specifications. The considerations and practi-
cal details of special interest to the engineer in charge of the
work in the field have already been presented in admirable form
by Mr. R. A. Lundquist in his book on Transmission Line
Construction.

Much of what appears in these pages is reprinted with but
little alteration from articles recently contributed by the writer
to technical journals; but in the selection and co-ordination of
this material, the scheme and purpose of the book have steadily
been kept in mind.

Systems of distribution, whether in town or country, are not
touched upon: the subjects dealt with cover only straight long-
distance overhead transmission. It is true that, when treating
of lightning protection, it is the machinery in the station buildings
rather than the line itself that the various devices referred to are
intended to protect; and, when considering the most economical
system of transmission under given circumstances, a thorough

v



267496



vi PREFACE

knowledge of the requirements and possibilities in the arrange-
ment of generating and transforming stations is assumed; but
these engineering aspects of a complete scheme of power develop-
ment are not included in the scope of this book.

In the Appendix will be found reprints of some articles dealing
with theoretic aspects of long-distance transmission which,
although believed to be of interest to anyone engaged on the
design of transmission lines, are not essential to the scheme of
the book. In the Appendix will also be found complete specifi-
cations for a wood pole and steel tower line respectively: these
should be helpful, not so much as models for other specifications
every engineer is at liberty to draw these up in his own way
but rather as containing suggestions and reminders that may be
of service when specifying and ordering materials for an actual
overhead transmission.

The writer desires to thank the editors of the following techni-
cal journals for permission to reprint articles or portions of
articles which they have published from time to time: Electrical
World, New York; Electrical Times, London; Canadian Engineer,
Toronto; Western Engineering, San Francisco; Journal of Elec-
tricity, Power, and Gas, San Francisco.

PURDUE UNIVERSITY, LAFAYETTE, INDIANA,
August, 1913.



CONTENTS

PAGE
PREFACE v

CHAPTER I

INTRODUCTORY AND GENERAL 1

CHAPTER II

PRINCIPLES AND THEORY ELEMENTARY 10

Losses in transmission Transmission by continuous currents
Transmission by single-phase alternating currents Transmission
by two-phase currents Transmission by three-phase currents
Relative cost of conductors required on the various systems-
Grounding the neutral on high-tension overhead transmissions
Effect of line Inductance on transmission of alternating currents
Fundamental vector diagram for line calculations; Capacity
neglected Effect of Capacity on regulation and line losses Use
of fundamental diagram for three-phase calculations.

CHAPTER III.

ECONOMIC PRINCIPLES AND CALCULATIONS 34

Choice of system Type of transmission line Length of span
Effect of span variations on cost of steel towers Duplicate lines
Costs of typical transmission lines Cost of conductors Economic
section of conductors: Kelvin's law Practical method of apply-
ing Kelvin's law Economical resistance voltage drop Econom-
ical voltage and calculation of conductor sizes Example illus-
trating quick method of determining economic size of conductors
Estimation of amount and cost of energy wasted in conduc-
tors Estimation of percentage to cover annual interest and
depreciation on conductors Economic voltage Costs other
than transmission line, liable to be influenced by voltage varia-
tions Annual charges depending on voltage Example: method
of determining most economical voltage Closer estimate of
economical voltage.

CHAPTER IV

ELECTRICAL PRINCIPLES AND CALCULATIONS 62

Material s C o p p e r Aluminum Steel Copper-clad Steel
Stranded cables with steel wire core Skin effect Inductance of
transmission lines Impedence drop: Regulation diagrams
Capacity of transmission lines Capacity of three-phase lines
Value of charging current Pressure variation on transmission

vii



viii CONTENTS

PAGE

lines Effect of "boosting" voltage at intervals along a trans-
mission line Fault localizing Surges: standing and travelling
waves The quantity LxC Relation between charging current
and inductive pressure drop Relation L/C: Surges Natural
frequency of circuit: Wave length.

CHAPTER V

INSULATION AND LIGHTNING PROTECTION 95

Insulator materials Design of insulators Pin type insulators-
Suspension type insulators -Weight of insulators Entering
bushings Formation of corona and accompanying losses of power
Corona considered as "safety valve" for relief of high-fre-
quency surges and over-voltage due to any cause Factors of
safety, and tests Distance between wires Distance between
conductors and pole or tower Practical limitations of overhead
transmission line voltages Lightning protection Protection
of overhead systems against direct lightning strokes and sudden
accumulations of high potential static charges Methods of
grounding Methods of relieving conductors of high potentials
before damage is done to insulation or to machines and apparatus
connected to the line: Water-jet arresters Spark gaps Horn
gaps Multiple-gap low-equivalent arrester Spark-gap arresters
with circuit-breakers or re-setting fuses Aluminum cell arrester
Condensers Spacing of lightning arresters Choke coils
Arcing ground suppressor General remarks on lightning pro-
tection.

CHAPTER VI

THE TRANSMISSION OF ENERGY BY CONTINUOUS CURRENTS 136

General description of the Thury System Straight long-distance
transmission by Continuous Currents Insulation of line when
carrying Continuous Currents Relative cost of conductors: Con-
tinuous Current and Three-phase transmissions Concluding
remarks on Direct Current transmission.

CHAPTER VII

MECHANICAL PRINCIPLES AND CALCULATIONS 150

Introductory The parabolic curve Effect of temperature
variations on overhead wires Abnormal stresses in wires due
to wind and ice Graphical method for determining sags and
tensions in overhead conductors Analytical method for deter-
mining sags and tensions in overhead conductors Tensions in
conductors when spans are of different lengths Tensions in
different sized wires on the same span Supports at different levels
Further examples of temperature-sag calculations Length of
spans: Copper and Aluminum Factors of safety Ties.



CONTENTS ix

CHAPTER VIII

PAGE

TRANSMISSION LINE SUPPORTS 195

WOODEN POLE LINES.

Kinds of wood used for poles Weight of wood poles Life of
wood poles Preservative treatment of poles Reinforcing pole
butts Typical wood pole lines Insulating qualities of wooden
poles Strength and elasticity of wood poles Calculation of pole
strengths Deflection of wood poles Calculation of pole deflec-
tions Yielding of foundations Spacing of poles at corners: Guy
wires Load to be carried by corner poles- Props or struts: Wood
poles in compression.

CONCRETE POLES

General remarks: Weights and costs Strength and stiffness of
concrete poles.

STEEL TOWERS

General remarks: Types of towers Flexible towers Loads to be
resisted by towers Steel and wood supports compared Design
of steel towers Stresses in compression members Outline of
usual method for calculating stresses in tower members Founda-
tions Stiffness of steel towers: Deflection under load Conclud-
ing remarks regarding steel tower design Determining position
of supports on uneven ground.

APPENDIX A

INDUCTANCE OF ELECTRIC TRANSMISSION LINES WITH UNSYMMETRIC-

ALLY DISPOSED CONDUCTORS ~r 239

Flux surrounding a straight conductor Effect of taking into
account the return conductor Calculation of the total flux
when there are several return conductors Practical application

Polyphase transmission.



APPENDIX B

INDUCTANCE OF ELECTRIC TRANSMISSION LINES AS AFFECTED BY SUB-
DIVISION OF THE CIRCUIT AND THE ARRANGEMENT OF THE CONDUC-
TORS . . 250

Single-phase systems Polyphase systems.

APPENDIX C

TWO-PHASE TRANSMISSION WITH THREE CONDUCTORS 256

Load non-inductive: Resistance of common conductor assumed
negligible Load non-inductive: Resistance of common conductor
taken into account Load non-inductive: Self-induction and
resistance of lines taken into account Load balanced, but in-
ductive.



x CONTENTS

APPENDIX D

PAGB

APPROXIMATE METHOD OP DETERMINING DEFLECTIONS AND
STRESSES IN FLEXIBLE TOWER LINES 262

APPENDIX E

GRAPHICAL STATICS APPLIED TO TRANSMISSION LINE CALCULATIONS

WITH SPECIAL REFERENCE TO STEEP GRADES 272

General problem Stretched wire: Supports on same level Cal-
culation of sag Position of lowest point of span: Supports at
different elevations Calculation of sag with supports on an incline
Example illustrating use of formulae Conclusions: Overhead
lines on steep grade.

APPENDIX F

SAMPLE SPECIFICATION FOR WOOD POLE TRANSMISSION LINE. . . .281
General description of transmission line Clearing Poles Cross-
Arms Grading Pole setting Grounding Spans Angles and
Curves Guying Insulators Stringing wires Locating and
numbering poles.

APPENDIX G

SAMPLE SPECIFICATION FOR STEEL TOWER TRANSMISSION LINE . . . 293
General description of line Duties of engineer in charge of con-
struction Clearing Towers Number of towers required
Working the test loads for towers Strain tower test loads
Flexible tower test loads Galvanizing test Foundations for
towers Grounding Guying Angles Erection of towers In-
sulators Number of insulators required Climatic conditions
Working voltage Design of Insulators Glaze Cement
Mechanical tests Electrical tests Packing of insulators Wire
clamps Conductors Joints in cables Spans a,nd wire stringing.



OVERHEAD
ELECTRIC POWER TRANSMISSION

PRINCIPLES AND CALCULATIONS

CHAPTER I
INTRODUCTORY AND GENERAL

An overhead electric power transmission line, consisting as it
does of wires stretched between insulators on poles or structures
the main purpose of which is to maintain the conductors at a
proper distance above the ground level, may appear at first sight
to be a very simple piece of engineering work. It is indeed true
that the erection of an overhead line of moderate length, capable
of giving good service on a comparatively low-pressure system,
does not present any insurmountable difficulties to a man of
ordinary engineering ability; but whether or not such a line will
be the best possible line for the particular duty required of it,
depends very much upon the knowledge, skill, and experience of
the designer. By the best line should be understood a line which
is not only substantially and lastingly constructed, but in con-
nection with which economic considerations have not been over-
looked.

It is an easy matter to design a bridge of ample strength for the
load it has to carry, or a transmission line with conductors of so
large a size, and supports so closely spaced and strong, that the
electrical losses will be small and the risk of mechanical failure
almost nil; but neither the bridge nor the transmission line will
reflect credit on the designing engineer unless he has had before
him constantly the commercial aspect of the work entrusted to
him, and has so chosen or designed the various parts, and com-
bined these in the completed whole, that all economic require-
ments are as nearly as possible fulfilled.

In the construction of electrical plant and machinery, such as
generators, transformers, and switching apparatus, the economic

1



2 OVERHEAD ELECTRIC POWER TRANSMISSION

conditions are, as it were, automatically fulfilled, owing to the
competition between manufacturers, each one of which is a spe-
cialist in his own particular line of business. This competition,
it should be observed, is not merely in the matter of works cost or
selling price, but in works cost plus efficiency and durability.
It is not necessarily the cheapest nor the most costly manufac-
tured articles that wins in the long run, but the one which is
commercially best suited to the needs of the user.

In the lay-out of power plants; in the development of natural
power resources and the transmission of electric energy from water
falls or coal fields to the industrial centers, the engineer who
may or may not be influenced by possibly conflicting financial
interests has much scope for the reckless and unwise expendi-
ture of other people's money. He must resist the temptation
if temptation it be and devote himself to the careful study of all
engineering problems from the economic standpoint.

The cost per mile of a finished transmission is not all-important.
It may frequently be said to be of importance only in so far as it
influences the annual cost of the line, which annual cost is under-
stood to include interest on the capital sum expended on the line.
If a heavy section of copper is used for the conductors, the loss
of energy in overcoming resistance will be less than with a lighter
section, but the initial cost will be greater: there is only one par-
ticular size of conductor which is economically the right size
for any given line operating under definite conditions, and this
is by no means easy to determine notwithstanding the apparent
simplicity of what is usually referred to as Kelvin's Law.

Efficiency of service, which includes reasonably good voltage
regulation and freedom from interruptions, must necessarily be
merged into the all-important question of cost. By duplicating
the transmission line and providing two separate pole lines, pref-
erably on different and widely separated rights of way, insurance
is provided against interruption of service over an extended
period of time; but whether or not such duplicate lines shall be
provided must be decided on purely economic grounds.

Again, lightning arresters may be provided in abundance at
both ends of the line and at intermediate points, and assuming
what is not necessarily the case that such profusion of protec-
tive devices will prevent interruptions which are otherwise
liable to occur through lightning disturbances, it does not follow
that they should be installed. Examples of this kind can be



INTRODUCTORY AND GENERAL 3

cited to an almost unlimited extent, and, in the chapter dealing
especially with economics, an attempt will be made to indicate a
mode of procedure in designing a transmission line from this, the
only standpoint of importance to the engineer; but the question
is a large one which cannot adequately be dealt with by set rules
or formulas. In such cases as the design of supporting structures,
when the calculations for strength have been made, it is the de-
signer of the transmission line and not the manufacturer of the
steel tower who shall decide upon the factor of safety to be used,
for this is the prerogative of the man who is going to be held
responsible for the commercial success of the undertaking. If
he is incompetent or timid, he will allow too high a factor of
safety, or follow blindly in the footsteps of others who may have
been equally incompetent or timid. If he is sure of himself, and
has carefully checked his calculations and deductions, he may
depart from precedent and construct a line which is cheaper
not only in appearance, but in fact than any line previously
constructed under similar conditions and within the same limi-
tations. The usual spacing of wood poles for lines working at
medium or low pressures is under 200 ft., yet the Madison River
Power Company have, for nearly three years, had in operation a
50,000 volt three-phase line supported on ordinary 8-in. top
45-ft. and 50-ft. poles of Idaho cedar spaced 300 ft. apart, with
many spans of 500 ft. and even more. Insulators of the suspen-
sion type are used. The designers of this line deserve commenda-
tion if the test of time proves their judgment to have been well
founded.

Of course the climate and probable weather conditions have an
important bearing on the safe span limit and mechanical design
of the line generally. The effects of wind and ice will be referred
to in Chapter VII.

A knowledge of the country through which a transmission line
is to be carried is essential to the proper design of the line and
supporting structures. Without a knowledge of the natural
obstacles to be reckoned with, including the direction and prob-
able force of wind storms, and whether or not these may occur at
times when the wires are coated with ice, the nature of the sup-
ports and the economical length of span cannot properly be deter-
mined. On the Pacific coast, where there is rarely, if ever, an
appreciable deposit of sleet on overhead conductors, it is possible
that the spacing of supports may generally be greater than in



4 OVERHEAD ELECTRIC POWER TRANSMISSION

countries where the climatic conditions are less favorable. At
the same time, it had been observed, in districts where the winters
are severe and sleet formation on conductors of frequent occur-
rence, that the effects of storms in winter on wires heavily
weighted with ice, and offering a largely increased surface to the
wind, are less severe than in summer when much higher wind
velocities are sometimes attained. These examples are here
mentioned to emphasize the necessity for a thorough investiga-
tion of local conditions before starting upon the detailed design
of a proposed transmission line.

There are obviously many preliminary matters to be considered
and dealt with before the actual details of design can be proceeded
with; but, although many of these are partly, if not wholly,
engineering problems, they cannot adequately be dealt with in
the limits of this book, or indeed within the limits of any book,
since the differences in local conditions, in the scope and commer-
cial aim or end of a transmission system, makes it next to im-
possible to formulate rules or devise methods of procedure which
can be of general utility.

Assuming that it is proposed to transmit energy electrically
from a point where the power can be cheaply generated to an
industrial or populous center where there is a demand for it, a
straight line drawn on the map between these two points will
indicate the route which, with possibly slight deviations to avoid
great differences in ground level, would require the smallest
amount of conductor material and the fewest poles or supporting
structures. There may be natural obstacles to the construction
of so straight a line, as for instance, lakes that cannot be spanned,
or mountains that cannot be climbed; but even the shortest
route which natural conditions would render possible is by no
means necessarily the best one to adopt. The right of way for
the whole or part of the proposed line may have to be purchased,
and the cost will often depend upon the route selected. By
making a detour which will add to the length of the line, it may
be possible to avoid crossing privately owned lands where a high
annual payment may be demanded for the right to erect and main-
tain poles or towers. Again, by paralleling railroads or highways,
the advantage of ease of access for construction and maintenance
may outweigh the disadvantage of increased length. A slightly
circuitous route may take the transmission line near to towns or
districts where a demand for power may be expected in the near



INTRODUCTORY AND GENERAL 5

future; and it may be wise to take such possibilities into account.
The engineer in charge of the preliminary survey work (a section
of transmission-line engineering which is not dealt with in this
book) should bear all such points in mind and compare the
possibilities of alternative routes. On a long and necessarily
costly transmission line, it is rarely possible to spend too much
time and thought on the preliminary work. Money so spent is
usually well spent, and will result in ultimate economies.

Coming now to the problems of a more strictly engineering
nature, one of the first things to be decided upon is the system
of electric transmission, whether it shall be by continuous cur-
rents with its simple two-wire circuit and ideal power factor, or
by single- two- or three-phase alternating currents with manifold
advantages in respect to pressure transformations and adapta-
bility for use with commutatorless motors, but handicapped by
low power factors and other complications due to the inductance
and electrostatic capacity of the circuit.

Although nearly all long distance transmissions especially
on the continent of America are by three-phase currents, the
other systems will be referred to briefly in the following chapter;
and since, with the latest improvements in continuous current
machinery, the series system of power transmission by continuous
currents may, under favorable conditions, hold its own in this
country as it does in Europe, an entire chapter will be devoted
to a discussion of the points for and against the use of continuous
currents on long-distance power transmission lines.

The choice of system and determination of the most economical
transmission voltage involve a knowledge of the cost and effi-
ciency of generating and transforming machinery and controlling
gear. It is obvious that a system of transmission that appears
good owing to the low cost and high efficiency of the line itself,
may yet be unsuitable and uneconomical because of the high cost
or unsatisfactory nature of the machinery in the generating and
receiving stations.

Apart from capital investment and power efficiency, a factor
of the greatest importance, almost without exception, is efficiency
and continuity of service. At the present time, the weakest
link in a power system with long-distance transmission is prob-
ably the line itself. Electrical troubles may be due to faulty
insulation, or they may have their origin in lightning or switching
operations causing high frequency oscillations and abnormally



6 OVERHEAD ELECTRIC POWER TRANSMISSION

high voltages, leading to fracture of insulators or breakdown of
machinery. Troubles are more likely to be due to mechanical
defects, or mechanical injuries sometimes difficult to foresee and
guard against. Trees may fall across the line, landslides may
occur and overturn supports, or severe floods may wash away
pole foundations; and against such possibilities the engineer
must, by the exercise of judgment and foresight, endeavor to
protect himself. The width of the right of way should depend
upon the height of trees, and be so wide that the tallest trees



Online LibraryAlfred StillOverhead electric power transmission; principles and calculations → online text (page 1 of 25)