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GENERAL LECTURES
ON
ELECTRICAL ENGINEERING
BY
CHARLES PROTEUS STEINMETZ, A. M., Ph. D.
Consulting Engineer of the General Electric Company, Professor of Electrical Engineering in Union University,
Past President, A. I. E* E. Author of
"Alternating Current Phenomena," "Elements of Electrical Engineering/' "Transient Electric Phenomena and Oscillations/*
Second Edition.
Compiled and Edited by
JOSEPH Le ROY HAYDEN
Robson & Adee, Publishers
Schenectady, N. Y.

Copyright 1908 by

Contents

First Lecture General Review Second Lecture General Distribution Third Lecture Light and Power Distribution Fourth Lecture Load Factor and Cost of Power Fifth Lecture Long Distance Transmission Sixth Lecture Higher Harmonics of the Generator
Wave
Seventh Lecture High Frequency Oscillations and
Surges Eighth Lecture Generation Niruth Lecture Hunting of Synchronous Machines. . Tenth Lecture Regulation and Control Eleventh Lecture Lightning Protection Twelfth Lecture Electric Railway Thirteenth Lecture Electric Railway Motor Char-
acteristics
Fourteenth Lecture Alternating Current Railway Motors
Fifteenth Lecture Electrochemistry
Sixteenth Lecture The Incandescent Lamp
Seventeenth Lecture Arc Lighting Appendix I. Light and Illumination Appendix II. Lightning and Lightning Protection, ,

7 21 35 49 61
77
89 99 113 125 135 147
163
175 197 207 215 229 259

Preface

HE following lectures on Electrical Engineering are

T""" *

general in their nature, dealing with the problems of generation, control, transmission, distribution and

utilization of electric energy; that is, with the operation of

electric systems and apparatus under normal and abnormal

conditions, and with the design of such systems ; but the design

of apparatus is discussed only so far as it is necessary to under-

stand their operation, and so judge of their proper field of

application.
Due to the nature of the subject, and the limitations of
time and space, the treatment had to be essentially descriptive, and not mathematical. That is, it comprises a discussion of the different methods of application of electric energy, the means and apparatus available, the different methods of carrying out the purpose, and the relative advantages and disadvantages of the different methods and apparatus, which determine
their choice.

It must be realized, however, that such a discussion can be general only, and that there are, and always will be, cases in which, in meeting special conditions,, conclusions regarding
systems and apparatus may be reached, differing from those
which good judgment would dictate under general and average conditions. Thus, for instance, while certain transformer connections are unsafe and should in general be avoided, in special
cases it may be found that the danger incidental to their use is
so remote as to be overbalanced by some advantages which
they may offer in the special case, and their use would thus be

PREFACE

justified in this case. That is, in the application of general conclusions to special cases, judgment must be exerted to deter-
mine, whether, and how far, they may have to be modified. Some such considerations are indicated in the lectures, others

must be left to the judgment of the engineer.

The lectures have been collected and carefully edited by

my assistant, Mr. J. L. R. Hayden, and great thanks are due & to the publishers, Messrs. Robson Adee, for the very credit-

able and satisfactory form in which they have produced the

book.

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CHARLES P. STEINMETZ.

Schenectady, N. Y., Sept. 5, 1908.

FIRST LECTURE

GENERAL REVIEW

N ITS economical application, electric power passes

I

through the successive steps : generation, transmission,

conversion, distribution and utilization. The require-

ments regarding the character of the electric power imposed

by the successive steps, are generally different, frequently

contradictory, and the design of an electric system is therefore a

compromise. For instance, electric power can for most pur-

no poses be used only at low voltage,

to 600 volts, while

economical transmission requires the use of as high voltage
as possible. For many purposes, as electrolytic work, direct

current is necessary; for others, as railroading, preferable;

while for transmission, alternating current is preferable, due to the great difficulty of generating and converting high

voltage direct current. In the design of any of the steps

through which electric power passes, the requirements of all the other steps so must be taken into consideration. Of the

greatest importance in this respect is the use to which electric power is put, since it is the ultimate purpose for which it is generated and transmitted ; next in importance is the transmission, as the long distance transmission line usually is the most

expensive part of the system, and in the transmission the limitation is more severe than in any other step through which

the electric power passes.

The main uses of electric power are : General Distribution for Lighting and Power. The relative proportion between power use and lighting may vary from the distribution system of many small cities, in which

io

GENERAL LECTURES

practically all the current is used for lighting, to a power distribution for mills and factories, with only a moderate
lighting load in the evening.
The electric railway.
Electrochemistry,
For convenience, the subject will be discussed under the
subdivisions:
1. General distribution for lighting and power.
2. Long distance transmission.
3. Generation.
4. Control and protection.
5. Electric railway. 6. Electrochemistry.
7. Lighting.

CHARACTER OF ELECTRIC POWER.

Electric power is used as a. Alternating current and direct current. b. Constant potential and constant current. c. High voltage and low voltage. a. Alternating current is used for transmission, and for general distribution with the exception of the centers of
large cities; direct current is usually applied for railroading.
For power distribution, both forms of current are used; in electrochemistry, direct current must be used for electrolytic work, while for electric furnace work alternating current is
preferable.
The two standard frequencies of alternating current are 60 cycles and 25 cycles. The former is used for general distribution for lighting and power, the latter for conversion to
direct current, for alternating current railways, and for large
powers.

GENERAL REVIEW

u

In England and on the continent, 50 cycles is standard frequency. This frequency still survives in this country in Southern California, where it was introduced before 60 cycles was standard.
The frequencies of 125 to 140 cycles, which were standard
in the very early days, 20 years ago, have disappeared.
The frequency of 40 cycles, which once was introduced as compromise between 60 and 25 cycles is rapidly disappearing, as it is somewhat low for general distribution, and higher than desirable for conversion to direct current It was largely used also for power distribution in mills and factories as the lowest frequency at which arc and incandescent lighting is still feasible; for the reason that 40 cycle generators driven by slow speed reciprocating engines are more easily operated in parallel, due to the lower number of poles. With
the development of the steam turbine as high speed prime mover, the conditions in this respect have been reversed, and 60 cycles is more convenient, giving more poles at the same generator speed, and so less power per pole.
Sundry odd frequencies, as 30 cycles, 33 cycles, 66 cycles, which were attempted at some points, especially in the early days, have not spread; and frequencies below 25 cycles, as 15 cycles and 8 cycles, as proposed for railroading, have not proved of sufficient advantage at least not yet so that in general, in the design of an electric system, only the two standard frequencies, 25 and 60 cycles, come into considera-
tion.
b. Constant current, either alternating or direct, that is, a current of constant amperage, varying in voltage with the load, is mostly used for street lighting by arc lamps; for all other purposes, constant potential is employed.

12

GENERAL LECTURES

c. For long distance transmission, the highest permissible voltage is used; for primary distribution by alternating current, 2200 volts, that is, voltages between 2000 and 2600; for alternating current secondary distribution, and direct current distribution, 220 to 260 volts, and for direct current railroading, 550 to 600 volts.

i. GENERAL DISTRIBUTION FOR LIGHTING AND POWSR.

In general distribution for lighting and power, direct

current and 60 cycles alternating current are available. 25

cycles alternating current is not well suited, since it does not

permit arc lighting, and for incandescent lighting it is just at

the

limit ,

where

under

some

conditions

and

with

some

genera-

tor waves, flickering shows, while with others it does not show

appreciably.

iX

Fig. 1

The distribution voltage is determined by the limitation

of the incandescent lamp, as from 104 to 130 volts, or about

no no volts,

volts is too low to distribute with good regu-

lation, that is, with negligible voltage drop, any appreciable

amount of power, and so practically always twice that voltage

is employed in the distribution, by using a three-wire system,

no with

volts between outside and neutral, and 220 volts

between the outside conductors, as shown diagrammatically in Pig. i. By approximately balancing the load between the two

circuits, the current in die neutral conductor is very small, the

GENERAL REVIEW

13

drop of voltage so negligible, and the distribution, regarding

voltage drop and copper economy, so takes place at 220 volts,

no while the lamps operate at

volts. Even where a separate

transformer feeds a single house, usually a three-wire distribu-
tion is preferable, if the number of lamps is not very small.

When speaking of a distribution voltage of no, some

voltage anywhere in the range from 104 to 130 volts is

no employed. Exactly

volts is rarely used, but the voltages

of distribution systems in this country are distributed over

the whole range, so as to secure best economy of the incan-

descent lamp.

This condition was brought about by the close co-oper-

ation, in this country, between the illuminating companies and the manufacturers of incandescent lamps. The

constants of an incandescent lamp are the candle power for

instance 16; the economy for instance 3.1 watts for hori-
zontal candle power; and the voltage for instance no. By careful manufacture, a lamp can be made in which the filament

reaches 3.1 watts per candle power economy at 16 c. p. within

one-half candle-power; but the attempt to fulfill at the same

time ithe condition, that this economy and candle power be

no reached at

volts, within one-half volt, would lead to a

considerable percentage of lamps which would fall outside of

the narrow range permitted in the deviation from the three con-

stants; and so, if the same distribution voltage were used

throughout the country, either a much larger margin of varia-

tion would have to be allowed in the product, that is, the

lamps would be far less uniform in quality as is the case

abroad, or a large number of lamps would not fulfill the

requirements, could not be used, and so would increase the

cost of the rest

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GENERAL LECTURES

Therefore, all the efforts in manufacture are con-

centrated on producing the specified candle power at the

required economy, and the lamps are then sorted for voltage.

This arrangement scatters the lamps over a considerable voltage

range, and different voltages are then adopted by different

distribution systems, so as to utilize the entire product of
manufacture at its maximum economy. The result of this

co-operation between lamp manufacturers and users is, that
the incandescent lamps are very much closer to requirements, and more uniform, than would be possible otherwise. The

effect however is, that the distribution is rarely actually 1 10,

and in alternating current systems, the primary distribution voltage not 2200, but some voltage in the range between 2080 and 2600, as in step-down transformers a constant ratio of

transformation, of a multiple of 10 -f- I, is always used.

In the following, therefore, when speaking of no, 220 or 2200 volts in distribution systems, always one of the

voltages within the range of the lamp voltages is understood.

no In this country,

volt lamps are used almost exclu-

sively, while in England, for instance, 220 volt lamps are

generally used, in a three-wire distribution system with 440

volts between the outside conductors. The amount of copper

required in the distribution system, with the same loss of

power in the distributing conductors, is inversely proportional to the square of the voltage. That is, at twice the voltage,

twice the voltage drop can be allowed for the same distribution

efficiency; and as at double voltage the current is one-half, for the same load twice the voltage drop at half the current gives

four times the resistance, that is, one-quarter the conductor

material. By the change from the 220 volt distribution with
no volt lamps, to the 440 volt distribution with 220 volt

GENERAL REVIEW

15

lamps, the amount of copper in the distributing conductor,

and .thereby the cost of investment can be greatly reduced, and

current supplied over greater distances, so that from the point

of view of the economical supply of current at the customers'

terminals, the higher voltage is preferable. However,

in the usual sizes, from 50 to 60 watts power consump-

tion and so 16 candle power with the carbon filament,

and correspondingly higher candle power with the more

efficient metallized carbon and metal filaments, the 220 volt

lamp is from 10 to 15% less efficient, that is, requires from
i o to 15% more power than the no volt lamp, when producing

the same amount of light at the same useful life. This differ-

ence is inherent in the incandescent lamp, and is due to the far

greater length and smaller section of the 220 volt filament,

no compared with the

volt filament, and therefore no possibil-

ity

of

overcoming

it

exists ;

if

it

should

be

possible

to

build

a

220 volt 1 6 candle power lamp as efficient at the same useful

no life of 500 hours as the present

volt lamp, this would

simply mean, that by the same improvement the efficiency of

no the

volt lamp could also be increased from 10 to 15%, and

the difference would remain. For smaller units than 16 candle

power, the difference in efficiency is still greater.

This loss of efficiency of 10 to 15%, resulting from the

use of the 220 volt lamp, is far greater than (the saving in

power

and

in

cost

of

investment

in

the

supply

mains ;

and

the

no 220 volt system with

volt lamps is therefore more efficient,

in the amount of light produced in the customer's lamps, than

the /i /)n volt system with 220 volt lamps. In this country,

since the early days, the illuminating companies have accepted

the responsibility up to the output in light at the customer's

lamps, by supplying and renewing the lamps free of charge,

no and the system using

volt lamps is therefore universally

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GENERAL LECTURES

employed while the 220 volt lamp has no right to existence;

while abroad, where the supply company considers its responsi-

bility ended at the customer's meter, and the customer is left
to supply his own lamps, the supply company saves by the use

of 440 volt systems at the expense of a waste of power in the

customer's 220 volt lamps, far more than the saving effected

by the supply company.

In considering distribution systems, it therefore is

no unnecessary to consider any other lamp voltage than

volts

(that is, the range of voltage represented thereby) .

In direct current distribution systems, as used in

most large cities, the 220 volt network is fed from a direct
current generating station, or as now more frequently is

the case from a converter substation, which receives ks power

as three-phase alternating, usually 25 cycles, from the main

generating station, or long distance transmission line. In

alternating current distribution, the 220 volt distribution cir-

cuits are fed by step-down transformers from the 2200 volt

primary distribution system. In the latter case, where con-

siderable motor load has to be considered, some arrangement

of polyphase supply is desirable, as the single-phase motor is

inferior to the polyphase motor, and so the latter is preferable

for large and moderate sizes.

COMPARISON OF ALTERNATING CURRENT AND DIRECT CURRENT
A.t the low distribution voltage of 220, current can economically be supplied from a moderate distance only, rarely exceeding from I to 2 miles. In a direct current system, the current must be supplied from a generating station or a converter substation, that is, a station containing revolving machinery. As such a station requires continuous atten-

GENERAL REVIEW

17

tion, its operation would hardly be economical if not of a capacity of at least some hundred kilowatts. The direct current distribution system therefore can be used economically only if a sufficient demand exists, within a radius of i to 2 miles, to load a good sized generator or converter substation. The
use of direct current is therefore restricted to those places where a fairly concentrated load exists, as in large cities; while in the suburbs, and in small cities and villages, where
the load is too scattered to reach from one low tension
supply point, sufficient customers to load a substation, the alternating current must be used, as it requires merely a step-
down transformer which needs no attention.

In the interior of large cities, the alternating current

system is at a disadvantage, because in addition to the voltage

consumed by resistance, an additional drop of volitage occurs

by self-induction, or by reactance; and with the large conduc-

tors required for the distribution of a large low tension current,

the drop of voltage by self-induction is far greater than that by

resistance, and the regulation of the system therefore is serious-

ly impaired, or at least the voltage regulation becomes far more

A difficult than with direct current.

second disadvantage of

the alternating current for distribution in large cities is, that
a considerable part of the motor load is elevator motors, and the alternating current elevator motor is inferior to the direct

current motor. Elevator service essentially consists in starting at heavy torque, and rapid acceleration, and in both of these
features the direct current motor with compound field winding is superior, and easier to control.

Where therefore direct current can be used in low tension

distribution, it is preferable to use it, and ito relegate alternating current low tension distribution to those cases where direct

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GENERAL LECTURES

current cannot be used, that is, where the load is not sufficiently
concentrated to economically operate converter substations.
The loss of power in the low tension direct current system is merely the fr loss in the conductors, which is zero at no
load, and increases with the load; the only constant loss in a direct current distribution system is the loss of power in the potential coils of the integrating wattmeters on the customer's premises. In the direct current system therefore, (the efficiency of distribution is highest at light load, and decreases with
increasing load.
In an alternating current distribution system, with a 2200 volt primary distribution, feeding secondary low tension circuits by step-down transformers, the fr loss in the conductors usually is far smaller than in the direct current system, but a considerable constant, or "no load", loss exists; the coreloss in the transformers, and the efficiency of an alternating current distribution is usually lowest at light load, but increases with increase of load, since with increasing load the transformer core loss becomes a lesser and lesser percentage of the total power. The iV loss in alternating current systems must be far lower than in direct current systems:
1. Because it is not the only loss, and the existence of the "no load" or transformer core loss requires to reduce the load loss or iV loss, if an equally good efficiency is desired. With an alternating current system, each low tension main requires only a step-down transformer, which needs no atten-
tion ; therefore many more transformers can be used than rotary
converter substations in a direct current system, and the fr loss is then reduced by the greatly reduced distance of second-
ary distribution. 2. In the alternating current system, the drop of voltage
in the conductors is greater by the self-inductive drop than the

GENERAL REVIEW

19

ir drop ; the ir drop is therefore only a part of the total voltage drop ; and with the same voltage drop and therefore the same regulation as a direct current system, the fr loss in the alternating current system would be smaller .than in the direct current
system.
3. Due to the self-inductive drop, smaller and therefore more numerous low tension distribution circuits must be used
with alternating current than with direct current, and a separate and independent voltage regulation of each low tension circuit that is each transformer, therefore usually becomes impracticable. This means that the total voltage drop, resistance and inductance, in the alternating current low tension distribution circuits must be kept within a few percent, that is, within
the range permissible by the incandescent lamp. As a result
thereof, the voltage regulation of an alternating current low tension distribution is usually inferior to that of the direct cur-
rent distribution in many cases to such an extent as to require
the use of incandescent lamps of lower efficiency. While therefore in direct current distribution 3.1 watt lamps are always
used, in many alternating current systems 3.5 watt lamps have
to be used, as the voltage regulation is not sufficiently good to get a satisfactory life from the 3.1 watt lamps.

SECOND LECTURE

GENERAL DISTRIBUTION DIRECT CURRENT DISTRIBUTION HE TYPICAL direct current distribution is the system
T of feeders and mains, as devised by Edison, and since used in all direct current distributions. It is shown diagrammatically in Fig. 2. The conductors are usually under-
f ii
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/30
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GENERAL LECTURES

ground, as direct current systems are used only in large cities.
A system of three-wire conductors, called the "mains" is laid
in the streets of the city, shown diagrammatically by the

heavily drawn lines. Commonly, conductors of one million circular mil section (that is, a copper section which as solid

round conductor would have a diameter of i") are used for the

outside conductors, the "positive" and the "negative" con-

ductor; and a conductor of half this size for the middle or

"neutral" conductor. The latter is usually grounded, as pro-

tection against fire risk, etc. Conductors of more than one million circular mils are not used, but when the load exceeds

the capacity of such conductors, a second main is laid in

A the same street.

number of feeders, shown by dotted lines

in Fig. 2, radiate from the generating station or converter substations, and tap into the mains at numerous points ; potential wires run back from the mains to the stations, and so allow7 of

measuring, in the station, the voltage at the different points of

the distribution system. All the customers are connected to the

mains, but none to the feeders. The mains and feeders are

arranged so that no appreciable voltage drop takes place in the

mains,

but

all

drop

of

voltage

occurs

in

the

feeders ;

and

as

no

customers connect to the feeders, the only limit to the voltage

drop in the feeders is efficiency of distribution. The voltage at

the feeding points into the mains is kept constant by varying

the voltage supply to the feeders with the changes of the load on

the mains. This is done by having a number of outside

bus bars in the station, as shown diagrammaitically in Fig. 3,

differing from each other in voltage, and connecting feeders

over from bus bar to bus bar, with the change of load.

For instance, in a 2 x 120 voltage distribution, the station

may have, in addition to the neutral bus bar zero, three positive

GENERAL DISTRIBUTION
bus bars i, i', i", and three negative bus bars 2, 2', 2", differing respectively from the neutral bus by 120, 130 and 140 volts,
as shown in Fig. 3. At light load, when the drop of voltage
in the feeders is negligible, the feeders connect to the busses
i, o, 2 of 1 20 volts. When (the load increases, some of the
feeders are shifted over, by transfer bus bars, to the 130 volt busbars i' and 2'; with still further increase of load, more feeders are connected over to 130 volts; then some feeders are connected to the 140 volt bus bars, i" and 2", and so, by varying
2LJ
-2 -Z'
Fig. 3
the voltage supply to the feeders, the voltage at the mains can be maintained constant with an accuracy depending on the number of bus bars. It is obvious that a shift of a feeder from
one voltage to another does not mean a corresponding voltage change on the main supplied by it, but raither a shift of load
between the feeders, and so a readjustment of the total voltage in the territory near the supply point of the feeder. For instance, if by the potential wires a drop of voltage below 120 volts is registered in the main at the connection point of feeder
A in Fig. 2, and this feeder then shifted from the supply

26

GENERAL LECTURES

voltage 130 to 140, the current in the main near A, which
A before flowed towards as minimum voltage point, reverses A in direction, flows away from A, the load on feeder and thereA fore increases, and the drop of voltage in increases, while the
load on the adjacent feeders decreases, and thereby their drop of

voltage decreases, with the result of bringing up the voltage in
A the mains at the feeder and all adjacent feeders. This inter-

linkage of feeders therefore allows a regulation of voltage in the mains, far closer than the number of voltages available in

the station.

The different bus bars in the station are supplied with their

voltage by having different generators or converters in the sta-

tion operate at different voltages, and with increasing load on

the station, and consequent increasing demand of higher volt-

age by the feeders, shift machines from lower to higher voltage

bus

bars,

inversely

with

decreasing

load ;

or

the

different

bus

bars are operated through boosters, or by connection with the

storage battery reserve, etc.
In addition to feeders and mains, tie feeders usually con-

nect the generating station or substation with adjacent stations,

so that during periods of light load, or in case of breakdown,
a station may be shut down altogether and supplied from

adjacent stations by tie feeders. Such tie feeders also permit most stations to operate without storage battery reserve, that is, to concentrate the storage batteries in a few stations, from which in case of a breakdown of the system, the other stations
are supplied over the tie feeders.

ALTERNATING CURRENT DISTRIBUTION

The system of feeders and mains allows the most perfect voltage regulation in the distributing mains. It is however
applicable only to direct current distribution in a territory of

GENERAL DISTRIBUTION

27

very concentrated load, as in the interior of a large city, since

the independent voltage regulation of each one of numerous

feeders is economically permissible only where each feeder

represents a large amount of power; with alternating cur-

rent systems, the inductive drop forbids the concentration of

such large currents in a single conductor. That is, conductors of one million circular mils cannot be used economically in an alternating current system.
The resistance of a conductor is inversely proportional to

the size or section of the conductor, hence decreases rapidly with increasing current: a conductor of one million circular

mils is one-tenth the resistance of a conductor of 100,000

circular mils, and so can carry ten times the direct current

with the same voltage drop. The reactance of a conductor,

however, and so the voltage consumed by self-induction, de-

creases only very little with the increasing size of a conductor,

as seen from the table of resistances and reactances of

A conductors.

wire No. ooo B & S G is eight times the section

of a wire No. 7, and therefore one-eighth (the resistance;

but the wire No. ooo has a reactance of .109 ohms per 1000

feet, the wire No. 7 has a reactance of .133 oms, or only 1.22

times as large. Hence, while in the wire No. 7, the reactance,

at 60 cycles, is only .266 times the resistance and therefore not

of serious importance, in a wire No. ooo the reactance is 1.76

times the resistance, and the latter conductor is likely to give
a voltage drop far in excess of the ohmic resistance drop. The

ratio of reactance to resistance therefore rapidly increases

with increasing size of conductor, and for alternating currents, large conductors cannot therefore be used economically where

close voltage regulation is required.
With alternating currents it therefore is preferable to use several smaller conductors in multiple : two conductors of

28

GENERAL LECTURES

No. i in multiple have the same resistance as one conductor of No. ooo; but the reactance of one conductor No. ooo is .109 ohms, and so 1.88 times as great as the reactance of two conductors of No. i in multiple, which latter is half that of one conductor No. i, or .058 ohms, provided that the two conductors are used as separate circuits.
In alternating current low tension distribution, the size of the conductor and so the current per conductor, is limited by the self-inductive drop, and alternating current low tension networks are therefore of necessity of smaller size than those
of direct current distribution.

As regards economy of distribution, this is not a serious

objection, as the alternating current transformer and primary

distribution permits the use of numerous secondary circuits.

In alternating current systems, a primary distribution

system of 2200 volts is used, feeding step-down transformers.

The different arrangements are

A a.

separate transformer for each customer.

This is

necessary in those cases where the customers are so far apart

from each other that they cannot be reached by the same low

tension or secondary circuit; every alternating current system

therefore has at least a number of instances where individual

transformers are used.

This is the most uneconomical arrangement. It requires the use of small (transformers, which are necessarily less efficient and more expensive per kilowatt, than large trans-
formers. The transformer must be built to carry, within its overload capacity, all the lamps installed by the customer, since all the lamps may be used occasionally. Usually,
however, only a small part of the lamps are in use, and those only for a small part of the day ; so that the average load on the transformer is a very small part of its capacity.

GENERAL DISTRIBUTION

29

As the core loss in the transformer continues whether the
transformer is loaded or not, but is not paid for by the customer, the economy of the arrangement is very low; and so it can be understood that in the early days, where this arrangement was generally used, the financial results of most alternating current distributions were very discouraging.
Assuming as an instance a connected load of twenty 16 candle power lamps low efficiency lamps, of 60 watts per
lamp, since ithe voltage regulation cannot be very perfect allowing then in cases of all lamps being used, an overload of
1 00%, which is rather beyond safe limits, and permissible only on the assumption that this load will occur very rarely, and for a short time the transformer would have 600 watt rafting. Assuming a core loss of 4%, this gives a continuous power consumption of 24 watts. Usually probably only one or two lamps will be burning, and these only a few hours per day, so that he use of two lamps, at an average summer and winter of three hours per day, would probably be a fair
example of many such cases. Two lamps or 120 watts, for
three hours per day, give an average power of 15 watts, which is paid for by the customer, while the continuous loss in the transformer is 24 watts ; so that the all year efficiency, or the ratio of the power paid for by the customer, to the power consumed by the transformer, is only 15 , 24 or 38%.
By connecting several adjacent customers to the same
transformer, the conditions immediately become far more
favorable. It is extremely improbable that all the customers
will burn all their lamps at the same time, the more so, the greater the number of customers is, which are supplied from the same transformer. It therefore becomes unnecessary to

30

GENERAL LECTURES

allow a transformer capacity capable of operating all the con-

nected load. The larger transformer also has a higher

effiicency. Assuming therefore as an instance, four customers

of 20 lamps connected load each. The average load would be

about 8 lamps. Assuming even one customer burning all 20

lamps, it is not probable that the other customers together

would at this time burn more than 10 to 15 lamps, and a trans-

former carrying 30 to 35 lamps at overload would probably

A be sufficient.

1500 watt transformer would therefore be

3% larger than necessary. At

coreloss, this gives a constant

loss of 45 watts, while an average load of 8 lamps for 3 hours

per day gives a useful output of 60 watts, or an all year

efficiency of nearly 60%, while a 1000 watt transformer would

give an all year efficiency of 67%.

This also illustrates that in smaller transformers a low

coreloss is of utmost importance, while the i~r loss is of very

secondary importance, since it is appreciable only at heavy load, and therefore affects the all year efficiency very little.
When it becomes possible to connect a large number of
customers to a secondary main fed from one large transformer the connected load ceases to be of moment in the trans-

former capacity; the transformer capacity is determined by the average load, with a safe margin for overloads; in this case, good all year efficiencies can be reached.

Economical alternating current distribution therefore requires the use of secondary distribution mains of as large an
extent as possible, fed by large transformers. The distance,
however, to which a transformer can supply secondary current, is rather limited by the inductive drop of voltage ; therefore, for supplying secondary mains, transformers of larger size than 30 kw, are rarely used, but rather several transformers are employed, to feed in the same main at different points.

GENERAL DISTRIBUTION

31

Extending the secondary mains still further by the use of several transformers feeding into the same mains, or, as it
may be considered, inter-connecting the secondary mains of the different transformers, we arrive at a system somewhat similar
to the direct current system : a low tension distribution system of 220 volts three-wire mains, with a system of feeders tapping into it at a number of points, as shown in Fig. 4. These feeders

4. Alternating Current Distribution with Secondary Mains and Primary Feeders.
are primary feeders of 2200 volts, connecting to the mains through step-down transformers. In such a system, by varying the voltage impressed upon the primary feeders, a voltage regulation of the system similar to that of direct current distribution becomes feasible. Such an arrangement has these advantages over the direct current system: the drop in the
feeders is very much lower, due to their higher voltage ; and

32

GENERAL LECTURES

that the feeder voltage can be regulated by alternating current
feeder regulators or compensators, that is, stationary structures similar to the transformer. It has, however, the disadvantage ithat, due to the self-induction of the mains, each feeding point can supply current over a far shorter distance than with direct current, and the interchange of current between
feeders, by which the load can be shifted and apportioned between the feeders, is far less.
As a result, it is difficult to reach as good voltage regulation with the same attention to the system; and since
this arrangement has the disadvantage that any break-
down in the secondary system or in a transformer may
involve the entire system, this system of inter-connected secondary mains is rarely used for alternating current distribution, but the secondary mains are usually kept
separate. That is, as shown diagrammaftically in Fig. 5, a number of separate secondary mains are fed by large transformers from primary feeders, and usually each primary feeder connects to a number of transformers. Where the distances are considerable, and the voltage drop in the primary feeders appreciable, voltage regulation of the feeders becomes necessary; and in this case, to get good voltage regulation in the system, attention must be given to the arrangements of the feeders and mains. That is, all the transformers on the same feeder should be at about tthe same distance from the station, so that the voltage drop between the transformers on the same feeder is negligible; and the nature of the load on the secondary mains fed by the same feeder should be about as nearly the same as feasible, so that all the mains on the same feeder are about equally loaded. It would therefore be undesirable for voltage regulation, to connect, for instance, a main feeding a

GENERAL DISTRIBUTION

33

residential section to the same feeder as a main feeding a business district or an office building.

5. Typical Alternating Current Distribution.
In a well designed alternating current distribution system, that is, a system using secondary distribution mains as far as
feasible, the all year efficiency is about the same as with the direct current system. In such an alternating current system,

34

GENERAL LECTURES

the efficiency at heavy load is higher, and at light load lower, than in the direct current system ; in this respect the alternating current system has the advantage over the direct current system, since at the time of heavy load the power is more valuable than at light load.

THIRD LECTURE

LIGHT AND POWER DISTRIBUTION

A N DIRECT current distribution system, the motor

load is connected to the outside mains at 220 volts,

and only very small motors, as fan motors, between

outside

mains

and

neutral ;

since

the

latter

connection,

with

a

large motor, would locally unbalance a system. The effect of

a motor on the system depends upon its size and starting

current, and with the large mains and feeders, which are gener-

ally used, even the starting of large elevator motors has no

appreciable effect, and the supply of power to electric elevators

represents a very important use of direct current distribution.

In alternating current distribution systems, the effect on

the voltage regulation, when starting a motor, is far more

severe; since alternating current motors in starting usually

take a larger current than direct current motors starting with

the same torque on the same voltage; and the current of the

alternating current motor is lagging, the voltage drop caused

by it in the reactance is therefore far greater than would be

caused by the same current taken by a non-inductive load, as

lamps. Furthermore, alternating current supply mains usually

are of far smaller capacity, and therefore more affected in

voltage. Large motors are therefore rarely connected to the

lighting mains of an alternating current system, but separate

transformers and frequently separate feeders are used for the

motors, and very large motors commonly built for the primary

distribution voltage of 2200, are connected to these mains.

For use in an alternating current distribution system, the

synchronous motor hardly comes into consideration, since the

synchronous type is suitable mainly for large powers, where

it is operated on a separate circuit.

38

GENERAL LECTURES

The alternating current motor mostly used in small and moderate sizes such as come into consideration for power distribution from a general supply system is the induction motor. The single-phase induction motor, however, is so
inferior to the polyphase induction motor, -that single-phase
motors are used only in small sizes; for medium and larger sizes the three-phase or two-phase motor is preferred. This
however, introduces a complication in the distribution system, and the three-wire single-phase system therefore is less suited for motor supply, but additional conductors have to be added
to give a polyphase power supply to the motor. As the result
thereof, motors are not used in alternating current systems to the same extent as in direct current systems. In the alternating current system, however, the motor load is, if anything, more important than in the direct current system, to increase the load factor of the system ; since the efficiency of the alternating current system decreases with decrease of load, while that of a direct current system increases.
Compared with the direct current motor, the polyphase induction motor has the disadvantage of being less flexible:
its speed cannot be varied economically, as that of a direct current motor by varying the field excitation. Speed variation
of the induction motor produced by a rheostat in the armature
or secondary circuit, in the so-called form "M" motor is
accomplished by wasting power : the power input of an induction motor always corresponds to full speed; if the speed is reduced by running on the rheostat, the difference in power between that which the motor actually gives, and that which it would give, with the same torque, at full speed, is
consumed in the rheostat
Where therefore different motor speeds are required, provisions are made in the induction motor to change the number

LIGHT AND POWER DISTRIBUTION 39

of poles ; thereby a number of different definite speeds are available, at which the motor operates economically as "multi-
speed" motor.

The starting torque of the polyphase induction motor
with starting rheostat in the armature (Form L motor) is
the same as the running torque at the same current input, just as in the case of the direct current shunt motor with constant

field excitation. In the squirrel cage induction motor, how-
K ever, (Form motor) the starting torque is far less than the

running torque at the same current input; or inversely, to

produce the same starting torque, a greater starting current is

required. In starting torque or current, the squirrel cage

induction motor has the disadvantage against the direct

current motor. It has, however, an enormous advantage over

it in its greater simplicity and reliability, due to the absence

of commutator and brushes, and the use of a squirrel cage

armature.

> ; j

The advantage of simplicity and reliability of the squir-

rel cage induction motor sufficiently compensates for the disadvantage of the large starting current, to make the motor

most commonly used. In an alternating current distribution

system, however, great care has to be taken to avoid the use

of such larger motors at places where their heavy lagging

starting currents may affect the voltage regulation; in such

places, separate transformers and even separate primary

feeders are desirable.

The single-phase induction motor is not desirable in larger
sizes in a distribution system, since its starting current is still larger; in small sizes, however, it is extensively used, since it requires no special conductors, but can be operated from a single-phase lighting main.

40

GENERAL LECTURES

The alternating current commutator motor is a single-

phase motor which has all the advantages of the different

types

of

direct

current

motors ;

it

can

be

built

as

constant

speed motor of the shunt type, or as motor with the charac-

teristics of the direct current series motor : very high starting

torque with moderate starting current. It has, however, also

the disadvantages of the direct current motor: commu>tator

and

brushes ;

and

so

requires

more

attention

than

the

squirrel

cage induction motor.
Alternating current generators now are almost always

used as polyphase machines, three-phase or two-phase, and

transmission lines are always three-phase, though in transform-

ing down, the system can be changed to two-phase. The power

supply in an alternating current system therefore is practically

always polyphase ; and since a motor load, which is very desir-

able for economical operation, also requires polyphase currents,

alternating current distribution systems always start from poly-

phase power.
The problem of alternating current distribution -therefore is to supply, from a polyphase generating system, single-phase
current to the incandescent lamps, and polyphase current to the
induction motors.

PRIMARY DISTRIBUTION SYSTEMS

i. Two conductors of the three-phase generating or

transmission system are used to supply a 2200 single-phase

system for lighting by step-down transformers and three-wire

secondary

mains ;

the

third

conductor

is

carried

to

those

places

where motors are used and three-phase motors are operated

by separate step-down transformers. In the lighting feeders,

the voltage is then controlled by feeder regulators, or, in a

smaller system, the generator excitation is varied so as to main-

LIGHT AND POWER DISTRIBUTION 41
tain the proper voltage on the lighting phase. At load, the three-phase triangle then more or less unbalances, but induction
motors are very little sensitive to unbalancing of the voltage, and by their regulation by taking more current from the phase of higher, less from the phase of lower voltage tend to restore the balance. For smaller motors, frequently two transformers are used, arranged in "open delta" connection.
2. Two-phase generators are used, or in the step-down
transformers of a three-phase transmission line, the voltage is changed from three-phase to two-phase; the lighting feeders are distributed between the two phases and controlled by potential regulators so that the distribution for lighting is singlephase, by three-wire secondary mains. For motors, both phases
are brought together, and the voltage stepped down for use on
two-phase motors. This requires four, or at least three, primary wires to motor loads.
3. From three-phase generators or transmission lines,
three separate single-phase systems are operated for lighting; that is the lighting feeders are distributed between the three phases, and all three primary wires are brought to the step-
down transformers for motors. This arrangement, by dis-
tributing the lighting feeders between the three phases, would require more care in exactly balancing the load between all
three phases than two, but a much greater unbalancing can be
allowed without affecting the voltage. 4. Four-wire three-phase primary distribution with
grounded neutral, and 2200 volts between outside conductors
and neutral. The lighting feeders are distributed between
(the three circuits between outside conductors and neutral, and
motors supplied by three of such transformers. This system is becoming of increasing importance, since it allows economical distribution to distances beyond those which can be reached

42

GENERAL LECTURES

with 2200 volts : with 2600 volts on the transformers as the upper limit of primary distribution voltage the voltage between outside conductors is 4500, and the copper economy of the system therefore is that of a 4500 volt three-phase system.
5. Polyphase primary and polyphase secondary distribution, with the motor connected to ithe same secondary mains
as the lights.

SYSTEMS OF LOW TENSION DISTRIBUTION FOR LIGHTING AND POWER.

i. Two-WIRE DIRECT CURRENT OR SINGLE-PHASE no

Vows. Fig 6.

This can can be used only for very short distances, since

its copper economy is very low, that is, the amount of conduc-

tor material is very high for a given power.

Cu. i.

o
^
6

//Off
6. Two-Wire System.

LIGHT AND POWER DISTRIBUTION 43

2. THREE-WIRE DIRECT CURRENT OR SINGLE-PHASE no-

220 VOLTS. Fig. 7.

Neutral one-half size of the two outside conductors. The

two outside conductors require one-quarter the copper of the

no two wires of a

volt system; since at twice the voltage and

one-half the current, four times the resistance or one-quarter

O

f

Fi. 7. Three-Wire System.

the copper is sufficient for the same loss (the amount of con-

ductor material varying with the square of the voltage).

Adding then one-quarter for the neutral of half-size,

= i + r = X gives \

;

or altogether \

jg of the

no conductor material required by the two-wire

volt

system. That is, the copper economy is ^. This is the

most commonly used system, since it is very economical, and

requires only three conductors. It is, however, a single-phase

system, and therefore not suitable for operating polyphase in-

duction motors.

44

GENERAL LECTURES

3, FOUR-WIRE QUARTER-PHASE ( TWO-PHASE). Fig. 8.

Two separate two-wire single-phase circuits, therefore

no saving in copper over two-wire systems. That is, the cop-

per economy is :

Cu. i.

o

s^ //L

1. S

6

Fig. 8. Four-Wire Two-Phase System.

4. THREE-WIRE QUARTER-PHASE. Fig. 9.

Common return of both phases, therefore saves one wire

or one-quarter of the copper ; hence has the copper economy :

^Cu.

3 ^

In this case however, the middle or common return wire

carries A/2, or 1.41 times as much current as the other two

wires, and when making all three wires of the same size, the
A copper is not used most economically. small further saving is

therefore ma.de by increasing the middle wire and decreasing the

Fi. 9. Three-Wire Two-Phase System.

outside wires so tthat the middle wire has 1.41 times the section

of each outside wire. This improves the copper economy

to:

Cu. 0.73

LIGHT AND POWER DISTRIBUTION 45
5. THREE- WIRE: THREE-PHASE. Fig. 10.
A three-phase system is best considered as a combination of
three single-phase systems, of the voltage from line to neutral, and with zero return (because the three currents neutralize each other in the neutral).
Compared thereto the two-wire single-phase system can be considered as a combination of two single-phase circuits from wire to neutral with zero return.

10. Three-Wire Three-Phase System.

no In a

volt single-phase system the voltage from line to

neutral equals -y, in a three-phase system equals -T=J

VS The mi

-y no ratio

,.
of

Tj_
voltages

.
is

110 .
-r- -~r~, or

110 x
110

4*

3
and the square of the ratio of voltages equals j; and as the

copper economy varies with the square of the voltage, the

copper economy for the three-wire three-phase system is : Co.?

6. FIVE-WIRE QUARTER-PHASE. Fig. n.

Neglecting the neutral conductor, the five-wire quarter-

phase system can be considered as four single-phase circuits
without return, from line to neutral, of voltage no. Com-

pared with the two-wire circuit, which consists of two single-

y phase circuits without return, of

volts, No. 6 therefore

has twice the voltage of No.

i ;

therefore

one-quarter the

copper.

46

GENERAL LECTURES

Making the neutral half the size of the main conductor
= ^ adds one-half of the copper of one conductor, or g of j

+ so giving a total of j

$2, that is, a copper economy of :

t

r

,
1

\

Fi&. 1 1. Five-Wire Two-Phase System.

7. FOUR-WIRE THREE-PHASE. Fig. 12.

Lamps connected between line and neutral.

Neglecting the neutral, the system consists of three single-

no phase circuits without return, of

volts, and compared with

t

f

\

I
/wrg*

T

12. Four-Wire Three-Phase System.

the two-wire circuit of -y between wire and neutral without
return, it therefore requires one-quarter the copper.

Making the neutral one-half size adds g of the copper,

= or g of }

24, and so gives a total copper economy of

.

_7

5?]T 4

24'

LIGHT AND POWER DISTRIBUTION 47

8. THREE-WIRE SINGLE-PHASE LIGHTING WITH THREEPHASE POWER. Fig. 13.

Lighting: Half size neutral, same as No. 2, therefore

copper economy :

= Cu. ^ 16

Power: Three-wire three-phase 220 volts; that is, the

same as No. 5, but twice the voltage, thus one-quarter the

= copper of No. 5, or \ of |

:

-

3

Fig. 13. Single-Phase Ughtlng and Three-Phase Power.
The systems mostly used are:
No. 2. Three-wire direct current or alternating current
single-phase.
No. 8. Three-wire lighting, three-phase power. Less frequent
No. 6. Five-wire quarter-phase. No. 7. Four-wire three-phase.
As we have seen, the two-wire system is rather inefficient in copper. High efficiency requires the use of a third conduc-
tor, that is, the three-wire system, for direct current or singlephase alternating current.
Three-wire polyphase systems, however, are inefficient in
copper, as No. 4 and No. 5 ; and to reach approximately the same copper economy, as is reached by a three-wire system with direct current and single-phase alternating current, re-
quires at least four wires with a polyphase system.

48

GENERAL LECTURES

That is, for equal economy in conductor material, the polyphase system requires at least one more conductor than
the single-phase or the direct current distribution system.
While the field of direct current distribution is found
in the interior of large cities, alternating current is used in smaller towns and villages and in the suburbs of large cities. In the latter, therefore, alternating current does the pioneer work. That is, the district is developed by alternating current,
usually with overhead conductors, and when the load has become sufficiently large to warrant the establishment of con-
verter substations, direct current mains and feeders are laid under ground, the alternating current distribution is abandoned, and the few alternating current motors are replaced by direct current motors. In the last years, however, considerable motor load has been developed in the alternating current suburban distribution systems, fairly satisfactorily alternating current elevator motors have been developed and
introduced and the motor load has become so large as to make
it economically difficult to replace the alternating current
motors by direct current motors in changing the system to direct current; and it therefore appears that the distribution systems of large cities will be forced to maintain alternating current distribution even in districts of such character as would make direct current preferable.

FOURTH LECTURE

LOAD FACTOR AND COST OF POWER

The cost of the power supplied at the customer's meter

consists of three parts.

A A.

fixed cost, that is, cost which is independent of the

amount of power used, or the same whether the system is fully

loaded or carries practically no load. Of this character, for

instance, is the interest on the investment in the plant, the

salaries of its officers, etc.

A B.

cost which is proportional to the amount of power

used. Such a proportional cost, for instance, is that of fuel in a

steam plant.

A C.

cost depending on the reliability of service required,

as the cost of keeping a steam reserve in a water power trans-

mission, or a storage battery reserve in a direct current dis-

tribution.

Since of the three parts of the cost, only one, B, is propor-
tional to the power used, hence constant per kilowatt output, the other two parts being independent of the output, hence the higher per kilowatt, the smaller a part of the capacity of the plant the output is ; it follows that the cost of power delivered is a function of the ratio of the actual output of the plant, to

the available capacity.
Interest on the investment of developing the waiter power or building the steam plant, the transmission lines, cables and distribution circuits, and depreciation are items of the character A, or fixed cost, since they are practically independent of the power which is produced and utilized.
Fuel in a steam plant, oil, etc., are proportional costs, that is, essentially depending on the amount of power produced.

52

GENERAL LECTURES

A Salaries are fixed cost, ; labor, attendance and inspection
are partly fixed cost A, partly proportional cost B, economy
of operation requires therefore a shifting of as large a part
thereof over into class B, by shutting down smaller substations
during periods of light load, etc. Incandescent lamp renewals, arc lamp trimming, etc., are
essentially proportional costs, B.
The reserve capacity of a plant, the steam reserve main-
tained at the receiving end of a transmission line, the difference in cost between a duplicate pole line and a single pole line with two circuits, the storage battery reserve of the distribution system, the tie feeders between stations, etc., are items of the
character C ; that is, part of the cost insuring the reliability and
continuity of power supply.
A The greater the fixed cost is, compared with the propor-
tional cost B, the more rapidly the cost of power per kilowatt output increases with decreasing load. In steam plants very
A frequently is larger than B, that is, fuel, etc. not being the A largest items of cost; in water power plants practically al-
ways is far larger than B. As result thereof, while water power may appear very cheap when considering only the proportional cost B which is very low in most water powers the fixed
A cost usually is very high, due to the hydraulic development
required. The difference in the cost of water power from that of steam power therefore is far less than appears at first. As water power is usually transmitted over a long distance line, while steam power is generated near the place of consumption, water power usually is far less reliable than steam power. To insure equal reliability, a water power plant brings the item C,
the reliability cost, very high in comparison with the reliability cost of a steam power plant, since the possibility of a break-
down of a transmission line requires a steam reserve, and

LOAD FACTOR AND COST OF POWER 53
where absolute continuity of service is required, it requires also a storage battery, etc. ; so that on the basis of equal reliability of service, sometimes very little difference in cost exists between steam power and water power, unless the hydraulic development of the latter was very simple.
The cost of electric power of different systems therefore
is not directly comparable without taking into consideration the reliability of service and the character of the load.
As a very large, and frequently even the largest part of
the cost of power, is independent of the power utilized, and therefore rapidly increases with decreasing load on the system, the ratio of average power output to the available power capacity of the plant is of fundamental importance in the cost of power per kilowatt delivered. This ratio, of the average power consumption to the available power, or station capacity, has occasionally been called "load factor." This definition of the term "load factor" is, however, undesirable, since it does
not take into consideration the surplus capacity of the station,
which may have been provided for future extension; the
reserve for insuring reliability C, etc. ; and other such features which have no direct relation whatever to the character of the
load.
Therefore as load factor is understood, in accordance with the definition in the Standardization Rules of the A. I. E. E.,
the ratio of the average load to the maximum load; any excess of .the station capacity beyond the maximum load is
power which has not yet been sold, but which is still available for the market, or which is held in reserve for emergencies, is not charged against the load factor.
The cost of electric power essentially depends on the load factor. The higher the load factor, the less is the cost of the power, and a low load factor means an abnormally high cost

54

GENERAL LECTURES

per kilowatt. This is the case in steam power, and to a still greater extent in water power.
For the economical operation of a system, it therefore is

of greatest importance to secure as high a load factor as possible, and consequently, the cost and depending thereon the price of electric power for different uses must be different if the load factors are different, and the higher the cost, the lower the load factor.

Electrochemical work gives the highest load factor, frequently some 90%, while a lighting system shows the poorest load factor in an alternating current system without motor load occasionally it is as low as 10 to 20%.

Defining the load factor as the ratio of the average to

the maximum load, it is necessary to state over how long a

time

the

average

is

extended ;

that

is,

whether

daily,

monthly

or yearly load factor.

&. 14. Summer Li^htln^ Load Curve.
For instance, Fig. 14 shows an approximate load curve of a lighting circuit during a summer day : practically no load

LOAD FACTOR AND COST OF POWER 55
except for a short time during the evening, where a high peak
is reached. The ratio of the average load to the maximum
load during this day, or the daily load factor, is 22.8%. Fig. 15 shows an approximate lighting load curve for a
winter day : a small maximum in the morning, and a very high evening maximum, of far greater width than the summer day
curve, giving a daily load factor of 34.5%.
t
\\
7
Fi&. 15. Winter Lihtin& Load Curve. During the year, the daily load curve varies between the
extremes represented by Figs. 14 and 15, and the average annual load is therefore about midway between the average
load of a summer day and that of a winter day. The maximum yearly load, however, is the maximum load during the winter

GENERAL LECTURES
day; and the ratio of average yearly load to maximum yearly
load, or the yearly load factor of the lighting system, therefore
is far lower than the daily load factor : if we consider the aver-
age yearly load as the average between 14 and 15, the yearly load factor is only 23.6%.
One of the greatest disadvantages of lighting distri-
bution therefore is the low yearly load factor, resulting from the summer load being so very far below the winter load ; econ-
omy of operation therefore makes an increase of the summer
lighting load very desirable. This has lead to the development
of spectacular lighting during the summer months, as represented by the various Luna Parks, Dreamlands, etc.

BL^L/A

ACWX

vf*v

\

Jg

6

a /&
i

Fl^. 16. Factory Power Load Curve.

The load curve of a factory motor load is about the shape shown in Fig. 16: fairly constant from the opening

of the factories in fthe morning to their closing in the evening, with perhaps a drop of short duration during the noon hour, and a low extension in the evening, representing overtime work. It gives a daily load factor of 49.5%.

LOAD FACTOR AND COST OF POWER 57

This load curve, superimposed upon the summer lighting

curves, does not appreciably increase the maximum, but very

greatly increases the average load, as shown by the dotted

curve in Fig. 14; and so improves the load factor, to 65.4^

thereby greatly reducing the cost of the power to the station, in

this way showing the great importance of securing a large

motor load. During the winter months, however, the motor

load overlaps the lighting maximum, as shown by -the dotted

curve in Fig, 15. This increases the maximum, and thereby

increases the load factor less, only to 41.7%. This is not so

serious in the direct current system with storage battery

reserve, as the overlap extends only for a short time, the

overload being taken care of by storage batteries or by

the overload capacity of

generators

and

steam

boilers ;

but

where it is feasible, it is a great advantage if the users of motors can be induced to shut them down in winter with

beginning darkness. It follows herefrom, that additional load on the station
during the peak of the load curve is very expensive, since it
A increases the fixed cost and C, while additional load during
the periods of light station load, only increases the proportional
cost B; it therefore is desirable to discriminate against peak loads in favor of day loads and night loads. For this purpose, two-rate meters have been developed, that is, meters which charge a higher price for power consumed during the peak of the load curve, than for power consumed dur-
ing the light station loads. To even out load curves, and cut down the peak load, maximum demand meters have been
developed, that is, meters which charge for power somewhat in proportion to the load factor of the circuit controlled by the meter. Where the circuit is a lighting circuit, and the
maximum demand therefore coincides with the station peak,

GENERAL LECTURES
this is effective, but on other classes of load the maximum demand meters may discriminate against the station. For instance, a motor load giving a high maximum during some part
of the day, and no load during the station peak, would be preferable to the station to a uniform load throughout the day,
including the station peak, while the maximum demand meter
would discriminate against the former.
By a careful development of summer lighting loads and
motor day loads, the load factors of direct current distribution
systems have been raised to very high values, 50 to 60% ; but
in the average alternating current system, the failure of developing a motor load frequently results in very unsatisfactory yearly load factors.
\

-L

hoAp \Cvftvr\

I.

Fi&. 17. Railroad Load Curve.

The load curve of a railway circuit is about the shape of that shown in Fig. 17 : a fairly steady load during the day, with a morning peak and an evening peak, occasionally a smaller noon peak and a small second peak later in the evening, then tapering down to a low value during the night. The average

LOAD FACTOR AND COST OF POWER 59
load factor usually is far higher than in a lighting circuit, in Fig. 17:54.396.
In defining the load factor, it is necessary to state not only the time over which the load is to be averaged, as a day, or
a year, but also the length of time which the maximum load
must last, must be counted. For instance, a short circuit of a large motor during peak load, which is opened by the blowing
of the fuses, may momentarily carry the load far beyond the station peak without being objectional. The minimum duration of maximum load, which is chosen in determining the
load factor, is that which is permissible without being objectionable for the purpose for which the power is distributed. Thus in a lighting system, where voltage regulation is of fore-
most importance, minutes may be chosen, and maximum load may be defined as the average load during that minute during which the load is a maximum; while in a railway system, a half-hour may be used as a duration of maximum load, as a railway system is not so much affected by a drop of voltage due to overload, and an overload of less than half an hour may be
carried by the overload capacity of the generators and the heat storage of the steam boilers; so that a peak load requires serious consideration only when it exceeds half an hour.

FIFTH LECTURE

LONG DISTANCE TRANSMISSION

HREE-PHASE is used altogether for long distance

fF

transmission. Two-phase is not used any more, and direct current is being proposed, having been used

abroad in a few cases : but due to the difficulty of generation

and utilization, it is not probable that it will find any extended

use, so that it does not need to be considered.

FREQUENCY
The frequency depends to a great extent on the character of the load, that is, whether the power is used for alternating current distribution 60 cycles or for conversion to direct current 25 cycles. For die transmission line, 25 cycles has the
advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proportional to the frequency.
VOLTAGE
1 1,ocx) to 13,200 volts and more recently, even 22,000 volts is most common for shorter distances, as 10 to 20 miles, since this is about the highest voltage for which generators can
be built ; its use therefore saves the step-up transformers, that is, the generator feeds directly into the line and to the step-
down transformers for the regular load. The next step is 30,000 volts ; that is, 33,000 volts at the
generator, 30,000 at the receiving end of the line. No inter-
mediate voltages between this and the voltage for which
generators can be wound is used, as 30,000 volts does not
yet offer any insulator troubles ; but line insulators can be built at moderate cost for this vokage, and as step-up transformers

64

GENERAL LECTURES

have to be used, it is not worth while to consider any lower

voltage than 33,000 volts. This voltage transmits economically up to distances of 50 to 60 miles.

40,000 to 44,000 volts is the next step ; it is used for high power transmission lines of greater distance, where reliability of operation is of importance and the use of a conservative

voltage therefore preferable to the attempt at economizing by the use of extra high voltages.
A number of 60,000 volt systems are in more or less
successful operation, and systems of 80,000 to 110,000 volts
are in construction and a few in operation. Where the dis-
tances are very great, power valuable, and continuity of ser-

vice not of such foremost importance, such voltages are justified in the present state of the art

In such very high voltage systems, the transformers are
occasionally wound so that they can be connected for half

voltage, for operating the line at half voltage, until the load

has sufficiently increased to require full voltage; or the

Y transformers are built for star or

connection at full

voltage, and at first operated in ring or delta connection,

at

= 57% of full voltage.

rj-

The cost of a long distance transmission line depends on

the voltage used.

The cost of line conductors decreases with the square of
the voltage.

At twice the voltage, twice the line drop can be allowed with the same loss; at twice the voltage the current is only half for the same power, and twice the drop with half the
current gives four times the resistance, that is, one-quarter the conductor section and cost

LONG DISTANCE TRANSMISSION

65

The cost of line insulators increases with increase of voltage. The cost of pole line increases with increase of
voltage, since greater distance between the conductors is necessary and so longer poles, longer cross arms, and heavier
construction, and not so many circuits can be carried on the
same pole line. The lower the voltage, the greater in general is the reli-
ability of operation, since a larger margin of safety can be
allowed.
Since a part of the cost of the transmission line decreases, another part increases with the voltage, a certain voltage will be most economical.
Lower voltage increases the cost of the conductor, higher
voltage increases the cost of insulators and line construction, and decreases the reliability.
The most economical voltage of a transmission line varies
with the cost of copper. When copper is very high, higher
vokages are more economical than when copper is low. The same applies to aluminum, since the price of aluminum has
been varied with that of copper.
Aluminum generally is used as stranded conductor. In the early days single wire gave much trouble by flaws in the wire. Aluminum expands more than copper with temperature changes, and so when installing the line in summer, a greater sag must be allowed than with copper, otherwise it stretches so tight in winter that it may tear apart. Aluminum also is more difficult to join together, since it cannot be welded.
For the same conductivity an aluminum line has about
twice the size, but one-half of the weight of a copper conductor,
and costs 10% less ; but copper has a permanent value, while the price of aluminum may sometime drop altogether, as the metal has no intrinsic value, being one of (the most common

66

GENERAL LECTURES

constituents of the surface of the earth, and its cost is merely that of its separation or reduction.
LOSSES IN LINE DUE TO HIGH VOLTAGE
The loss in the line by brush discharge or corona effect is nothing up to a certain voltage, but at a certain voltage it
begins and very rapidly increases.
The voltage at which a loss by corona effect begins is where the air at the surface of the conductor breaks down, becomes conducting and thus luminous. This occurs at a
potential gradient of 100,000 to 120,000 volts per inch.
The potential gradient is highest at the surface of the
conductor.

JH

Ft&. 18.

In Fig. 18 let
R = radius of conductor.
= 2 d distance between conductor centres.

O At a point x from the centre the potential is ;

C
^ ~~ d x

C

2CX

_~_~_

d+x

d2 x1

= for:x d R

that is, at the conductor surface, it is :
Ql=e

LONG DISTANCE TRANSMISSION

67

Substituting this in the equation, gives :
_c
e If

hence :
c=eR

therefore the potential at point x is :

2 Rx

d2

x2 e

and the potential gradient:

= = + g ~~

<L1 dx

R 3

2
(d

2
(d

x2

x2

) 2

e

)

= hence for : x d

R = or the conductor surface : g

-j*

If this potential gradient becomes greater than the break-
down strength of air, or 100,000 volts per inch, corona effects
and energy losses take place:
= e
^- 100,000

gives:
= = e 100,000 R or E
the corona begins, and :
e
=- or j)

100,000 D, as die voltage where
E js the smallest radius

100,000

100,000

D which can be used, at voltage E, where is the conductor
= E diameter 2 R, and is the voltage between the conductors = 2e.

For instance, wire No. oooo

D = E = .46" ; corona effects begin at the voltage

100,000

= D 46,000.

For 100,000 volts (the smallest diameter for which no

-- corona effects occur is : _= E

_# i

100,000

68

GENERAL LECTURES

In high potential transformers in the coils no corona
effects may occur, because the diameter of the coil or the thick-
ness is large enough, but the leads connecting the coils with each other and with the outside, if not chosen very large in
diameter, may give corona effects and so break down.
In a line or transformer, if one side is grounded, the other
side has full voltage against ground, and so may give corona
effects and break down; while if not grounded, both sides have half voltage against ground and so give no corona effect. In
the first case, the line or transformer so may break down,
although the potential differences between the terminals are
no greater than in the second case.
For instance, in a 100,000 volt transformer or line, from
each terminal to ground are 50,000 volts, and if the conductor
diameter is \ ", no corona effects occur. If now one terminal
is grounded, the other terminal has 100,000 volts to ground and so at | " diameter gives corona effects, that is, glow and
streamers which may destroy the insulating material or

produce high frequency oscillations.
At very high voltages it is therefore necessary to have the system statically balanced or symmetrical, that is, have the same potential differences from all the conductors to the

ground.

Any electric circuit, and so also the transmission line,
contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the current, and as electrostatic energy, or electrostatic charge, due to
the voltage.

LONG DISTANCE TRANSMISSION

69

If:

= = C e voltage,

capacity.

= L = i current,

inductance.

the electrostatic energy is :
e2 C

2,

and the electromagnetic energy : i*L 2

In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see-
saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuits in which one of the forms of stored energy is small compared with the other.
In distribution systems up to 2200 volts and even somewhat higher, the electrostatic energy is still negligible and only the electromagnetic energy appreciable.
In static machines the electrostatic energy is appreciable, but the electromagnetic energy negligible.

LINES AND TRANSFORMERS
At voltages above 25,000 step-up and step-down trans^
formers are always used, which are therefore a part of the high
potential circuit
Three-phase is always used in the transmission line.
Some of the available transformer connections are given
in Figs. 19 and 20. Grounding the neutral of the system has the advantage of
maintaining static balance and so avoiding oscillations and disturbances in case of an accidental sitatic unbalancing, as for

GENERAL LECTURES
A) r-r
. 19. Transformer Connections.
instance, the grounding of one line. It has the disadvantage that a ground on one circuit is a short circuit and so shuts
down the circuit.

LONG DISTANCE TRANSMISSION

71

In connections I, 4 and 6 no neutral is available for grounding and so three separate transformers have to be
Y installed in connection for getting the neutral.
In connections 2 and 3 the neutral can be brought out from the transformer neutral.

<$/*

R&. 20. Six-Phase Transformer Connections.
T In the connection 5 and 7, the neutral is brought out
from a point at one-third of the teaser transformer winding. Assuming the line properly installed and insulated, break-
downs may occur, either from mechanical accidents or by high
voltages appearing in the line.

7*

GENERAL LECTURES

HIGH VOLTAGE DISTURBANCES IN TRANSMISSION LINES

These may be : A. Of fundamental frequency, that is, the same frequency
as the alternating current machine circuit.
B. Some higher harmonic of the generator wave, that is, some odd multiple of the generator frequency.
C. Of frequencies entirely independent of the generator,
or of a frequency which originates in the circuit, that is, high frequency oscillations as arcing grounds, etc.

If a capacity is in series with an inductance, as the line capacity and the line inductance, the capacity reactance and the inductive reactance are opposed to each other ; if they happened to be equal they would neutralize each other, the current would depend on the resistance only and therefore be very large, and with this very large current passing through the inductance and capacity, the voltage at the inductance and at the capacity would be very high.

For instance, if we have 20,000 volts supplied to a circuit

having a resistance of 10 ohms and a capacity reactance of

1000 ohms, then the total impedance of the circuit is

+ = Vio*

iooo2

1000 and the current in the circuit

= 20,000
iooo

20 ampreres.

If now in addition to the 10 ohms resistance and iooo

ohms capacity reactance, the circuit contains iooo ohms

inductive reactance, the total reactance of the circuit is

iooo

= iooo o ohms, and the impedance is the same as

= = the resistance, or 10 ohms. The current therefore z

r

LONG DISTANCE TRANSMISSION

73

2000 amperes, and the voltage at the capacity therefore is:

= capacity reactance times amperes

2,000,000 volts, and the

same voltage exists at the inductive reactance.

These voltages are far beyond destruction. That is, if in a circuit of low resistance and high capacity reactance, a high inductive reactance is put in series with the capacity
reactance, excessive voltages are produced.
In a transmission line the capacity of the line consumes
for instance 10% of full load current; that is, full load voltage sends only 10% of full load current through the capacity. To
send full load current through the capacity so would require 10
times full load voltage.
With a line reactance of 20%, 20% or j of full load
voltage sends full load current through the inductive reactance, while 10 times full load voltage is required by the capacity reactance; the capacity reactance therefore is about 50 times and therefore cannot build up with it to excessive voltages; but to get resonance with the fundamental frequency requires an inductive reactance about 50 times greater than the line
reactance.

The only reactance in the system which is large enough to build up with the capacity reactance is the open circuit reactance of the transformers. This is of about the same size

as the capacity reactance, smce a transformer at open circuit
and full voltage takes about 10% of full load current, and the capacity reactance also takes about 10% of full load current.

If therefore a high potential coil of a transformer at open secondary circuit is connected in series with a transmission
line, destructive voltages may be produced, by the reactance
of the transformer building up with the line capacity. In those transformer connections in which several high

GENERAL LECTURES
potential coils of different transformers are connected between
the transmission wires, this may occur if the low tension coil
of one of the transformers accidentally opens and the high potential coil of this transformer then acts as inductive reactance in series with the line capacity in the circuit of the other
transformer. 1

I

-

;

.

Fife. 21.
This may occur for instance in transformer connection 2,
Fig. 19, if as shown in Fig. 21, the low tension coil c opens.
Then the high tension coil C is an inductive reactance in series

Fi&. 22.
with the line capacity from 3 to i, energized by transformer
A; and C is a high inductive reactance in series with the line
capacity from 3 to 2 in a circuit of voltage B. That is, from 3 to i and from 3 to 2 excessive voltages are produced. So
T also in connection, Fig. 22, if for instance the low tension
A coil a opens, the corresponding high tension coil is a high
inductive reactance in series with the line capacities in a circuit

LONG DISTANCE TRANSMISSION

75

B of the voltages of the two halves, and C, of the other
former, and excessive voltages therefore appear from I to 2 and from i to 3.
This danger of excessive voltages by the accidental opening of a transformer low tension coil does not exist in delta connection, since in this always only one transformer connects from line to line. It is greatly reduced since the use of triple pole switches became general; and is very much less where several sets of transformers are used in multiple, since even if in one set a low tension coil opens, the other sets maintain the
voltage triangle.
L Especially dangerous in this respect therefore is the
connection No. 6; since in this case, when using two transformers in open delta, for smaller systems only one set is installed and an accident to one of the transformers causes
excessive voltages between its line and the two other lines. The open circuit reactance of the transformer is the only
reactance high enough to give destructive voltages at generator frequency, and in high potential disturbances, the transformer connections should first be carefully investigated to see whether this has occurred.

SIXTH LECTURE

HIGHER HARMONICS OF THE
GENERATOR WAVE
HE open circuit reactance of the transformer is the only
|
reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for (this.
Since, however, the inductive reactance increases and the
capacity reactance decreases proportionally to the frequency,
the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave
resonance rise of voltage so may occur between the line
capacity and the circuit inductance.
The origin and existence of higher harmonics therefore
bears investigation in transformers, transmission lines and
cable systems.
ORIGIN OF HIGHER HARMONICS
Higher harmonics may originate in synchronous machines,
as generators, synchronous motors and converters, and in
transformers.
These two classes of higher harmonics are very different. The former have constant potential character; the latter, constant current character; their cure and prevention therefore must be different, and the method of elimination of one
may be very harmful with the other type of harmonics. For
instance, die voltage produced by a constant current harmonic as coming from a transformer is eliminated by short circuit Short circuiting a generator harmonic, however, gives large

8o

GENERAL LECTURES

short circuit currents, due to the constant potential character, and is therefore dangerous.
HIGHER HARMONICS OF SYNCHRONOUS MACHINES
In synchronous machines, as alternating current generators, the higher harmonics are :
AT No LOAD
i st. The distribution of magnetism in the air gap depends on the shape of the field poles; it is not a sine wave; neither is the e. m. f. induced by it in an armature a sine wave.
Since there are a number of conductors in series on the armature, ithe voltage wave is more evened out than that of a
single conductor; but still it is not a sine wave, that is, contains harmonics of which the third is the lowest.
2nd. The change of magnetic flux by the passage of open
armature slots over the field pole produces harmonics of
e. m. f. ; that is, when a large open armature slot stands in front of the field pole, the magnetic reluctance is high ; the magnetism is lower than when no slot is in front of the field pole; that is, by the passage of the armature slots the field magnetism pulsates, the more so -the larger the slots and the fewer they are.
If there are n slots per pole, this produces the two har-
+ monics 2n i and 2n i.
AT LOAD
3rd. The armature reaction of a single-phase machine pulsates between zero at zero current and a maximum at maxi-
mum current.
The resultant armature reaction of a polyphase machine is constant, but locally there is a pulsation making as many
cydes per pole as there are phases.

HARMONICS OF GENERATOR WAVE 81

Since the field magnetism under load is due to the com-

bination of field excitation and armature reaction, the pulsa-

tion of armature reaction therefore causes a pulsation of field

magnetism, and thereby higher harmonics of the e. m. L wave.

m = If

number of phases, the higher harmonics : 2m

I

+ and 2m i are produced.

4th. The terminal voltage under load is the resultant of

the induced e. m. f. and the e. m. f. consumed by the reactance

of the armature circuit ; that is, the reactance produced by the

magnetic flux produced by the armature current in the arma-

ture iron. This armature reactance is not constant, but peri-

odically varies, more or less, with double frequency; that is,

when the armature coil is in front of the field pole its magnetic

circuit is different than when it is between the field poles, and

the reactance therefore is different.

This pulsation of armature reactance produces the third harmonic, since it is of double frequency.
The most common and prominent harmonic so is the third
harmonic in a synchronous machine. These harmonics of synchronous machines are induced
e. m. f*s, that is, constant potential or approximately so.

HIGHER HARMONICS OF TRANSFORMERS

In a transformer the wave of e. m. f. depends on that of the magnetism and vice versa. That is, with a sine wave of e. m. f., the magnetism must also be a sine wave, and if the magnetism is not a sine wave, but contains higher harmonics, the e. m. f. is not a sine wave, but contains the harmonics induced by the harmonics of magnetism.
The exciting current of the transformer depends on the
magnetism by the hysteresis cycle; if the magnetism is a sine wave, the exciting current therefore cannot be a sine wave, but

82

GENERAL LECTURES

must contain higher harmonics mainly the third harmonic,
which reaches 20 to 30% of the fundamental, or even more at
saturation.

Fi&. 23.
In a transformer, e. m. f. and exciting current therefore cannot both be sine waves, but a sine wave of e. m. f. requires an exciting current containing a third harmonic; and a sine wave of exciting current in a transformer or reactive coil thus produces a third harmonic of e. m. f.
If therefore in a transformer the third harmonic is sup-
pressed, and if this third harmonic should have been 20% of
the fundamental, then its suppression produces a third har-
monic of magnetism of 20% in the opposite direction.
A third harmonic of magnetism, however, of 20%, induces a
= third harmonic of e, m. f. of 3 x 20 60% ; the e. m. f. being
proportional to magnetism and frequency.

HARMONICvS OF GENERATOR WAVE 83
The -third harmonic of exciting current is positive at the maximum of magnetism, and the third harmonic of magnetism is negative at the maximum, hence is zero and rising at the zero of the magnetism ; and at this moment the e. m. f. induced by the third harmonic and by the fundamental therefore are both maxima and in the same direction, that is, add. The suppres-
sion of the third harmonic of exciting current thus produces a very high third harmonic of e. m. f., which greatly increases
the maximum e. m. f. ; that is, the e. m. f. wave is very low for
a large part of the cycle and then rises to a very high peak, as
shown by Fig. 23 ; and the maximum e. m. f. may exceed that of a sine wave by 50% and more, thus giving high insulation
stress and <the possibility of resonance voltages.

EFFECTS OF HIGHER HARMONICS

In a three-phase system the three phases are 120 apart,

= and their third harmonics are 3 x 120

360 apart, that is, ir

phase with each, and for the third harmonic the three-phase

system therefore is a single-phase system.

In a balanced three-phase system, the third harmonics can not exist in the voltages between the lines and in the line
currents, if there is no return over the netutral. The three voltages between lines, from i to 2, 2 to 3, and 3 to i, must add up to zero; but since the third harmonics would be in phase with each other, they would not add up to zero, therefore they cannot exist. The three currents, if there is no return over the neutral or the ground, must add up to zero; and since their third harmonics must be in phase with each other, they must
be absent. In a balanced three-phase system, third harmonics
Y can exist only in the voltage from line to neutral or voltage,
in the current from line to line or delta current, and in the

84

GENERAL LECTURES

line current only if there is a neutral return or ground return to the generator neutral or transformer neutral.

In a three-phase generator, if the e. m. f. of one phase contains a third harmonic, as is usually the case, then by connecting the three phases in delta connection, the third harmonics of the generator e. m. f.'s are short circuited and so produce a

triple frequency current circulating in the generator delta.
This triple frequency circulating current can be measured by connecting an ammeter in one corner of the generator delta, and the sum of voltages of the three third harmonics can be measured by putting a voltmeter in a corner of the generator delta. This local current in the generator winding is the triple

frequency voltage divided by the generator impedance (the stationary impedance, at triple frequency, but not the synchronous impedance, since the latter includes armature reaction). In generators of low impedance or close regulation,
as turbine alternators, this local current may be far more than
full load current ; delta connection of generator windings there-
fore is unsafe. As a result, generator windings are almost always connected in Y. Even with delta connection of generator windings no triple frequency appears at the terminals, since its voltage disappears by short circuit.

If the generator winding is connected in Y, the triple

frequency voltages from terminal to neutral are in phase with
Y each other; that is, in a three-phase connected generator, a

single-phase voltage of triple frequency exists between the

neutral and all three terminals, and the neutral therefore is not

a true neutral. Between the lines no triple frequency voltage

exists, since from terminal to neutral and from neutral to the

other terminal the two third harmonics are in opposition and

so neutralize.

'

i

I

HARMONICS OF GENERATOR WAVE 85
This third harmonic between generator neutral and line
must be kept in mind, since when large it may produce danger-
ous voltages by resonance with the line capacity.
When the generator neutral is grounded, the potential
difference from line to ground is not line voltage divided by
Y V3, that is, the true voltage of the system; but superimposed
upon it is this single-phase triple frequency voltage; and -the
voltage from line to ground, especially its maximum, may be
greatly increased, thus increasing the insulation strain. For
this single-phase voltage all three lines go together, and so may
A cause static induction on other circuits, as telephone lines.
circuit of this single-phase triple frequency voltage then exists
from the generator neutral over the inductance of all three
generator circuits in multiple, and over the capacity of all three
lines to ground, back to the generator neutral ; that is, we have
capacity and inductance in series in a circuit of the triple har-
monic, and if capacity and inductance are high enough, we may get a dangerous voltage rise.
In this case of grounded generator neutral, if the neutral
Y of the connected step-down transformers is grounded also,
and the low tension side of these transformers connected in Y,
the third harmonic of the generator has no path; the current produced by it would have to return over the open circuit reactance of the step-down transformer, and is limited thereby to a negligible value.
If, however, the secondaries of the step-down transformers are connected in delta, so that the third harmonic can circulate in the secondary delta, the third harmonic can flow through the transformer primary by inducing an opposite current in the secondary; in this case the step-down transformer short circuits the third harmonic of the generator. Grounding the primary neutral of step-down transformers

86

GENERAL LECTURES

with grounded generator neutral therefore is permissible only
if the transformer secondaries are also connected in Y. With

delta connected transformer secondaries, however, it is not

safe

to

ground

the

generator

neutral

and

transformer

neutral ;

since this produces a triple frequency current in generator, line

and

transformer ;

and

even

if

the

generator

reactance

is

so

high

that the generator is not harmed by this current, it may burn

out at -the transformer, and probably will do so if the trans-

former is small compared with the generator.

This therefore is a case where delta connection of the

transformer secondaries does not eliminate the trouble from

the third harmonic, but makes it worse. The itriple frequency voltage from line to ground would
Y be eliminated by short circuiting it in this manner, by delta
connection of step-down transformer with grounded generator and transformer neutral, and static induction on other circuits
so would disappear; but we get magnetic induction from the three triple frequency single-phase currents which now flow
over the lines to the ground. If the generator neutral is not grounded, it is safe to
ground transformer neutrals. With ungrounded generator neutral, a triple frequency voltage can be measured by voltmeter, which then appears between generator neutral and
ground; this voltage under unfavorable conditions, may give
insulation strains in the generator by resonance rise; in the circuit from generator neutral over triple frequency voltage, generator inductance, capacity from line to ground and capacity from ground to generator winding in series.
In this case the capacity is much lower and the power therefore much less, that is, less danger exists.
When running two or more three-phase generators in
parallel, with grounded neutrals :

HARMONICS OF GENERATOR WAVE 87
a, If the generators have different third harmonics, these harmonics are short circuited from neutral over generator to the other generator and back to neutral; a triple frequency current thus flows between the generators, that is, the current
between the generators can never be made to disappear. That is, for the third harmonic, the two generators are
two single-phase machines of different voltage, having the neutral as one terminal and the three three-phase terminals as
the other single-phase terminal.
b. With two identical generators running in multiple, if the excitation is identically the same, no current flows between the grounded neutrals. If the excitation of the two generators
is different, one is over-excited the other is under-excited (that is, one carries leading, the other lagging current) then a triple frequency current flows between the neutrals of identical generators. Since in parallel operation the terminal voltages are in phase, if by difference of excitation the two terminal voltages have a different lag behind the induced e. m. f/s, the
third harmonics, which lag three times as much as the fundamentals, cannot be in phase in the two machines; and thus
triple frequency current flows between the machines. In machines of very low reactance as turbo-alternators,
even small differences in excitation of identical machines with
grounded neutral may thus cause very large neutral currents.
In parallel operation of three-phase machines with
grounded neutral, machines of different wave shapes frequently
cannot be run together at all without excessive neutral currents, and the ground has to be taken off of one of the machine types.
Even with identical machines, such care has to be taken in keeping the same excitation that it is frequently undesirable to ground all the neutrals, but only the neutral of one machine is grounded and the other machine neutrals are left isolated. In

88

GENERAL LECTURES

this case, provisions must be made to ground the neutral of some other machine, if the first one is out of service. The best way is, when grounding generator neutrals, to ground
through a separate resistance for every generator and to choose this resistance so high as to limit the neutral current, but still low enough so that in case of a ground on one phase, enough current flows over the neutral to open the circuit breaker of the grounded phase.
The use of a resistance in the generator neutral is very
desirable also, since it eliminates the danger of a high frequency oscillation between line and ground through the generator reactance in the path of the third harmonic, by damping the oscillation in the resistance. For this reason,
the resistance should be non-inductive. To ground the gener-
ator neutral through a reactance is very dangerous since it intensifies the danger of a resonance voltage rise.
In grounding the generator neutral, special care is necessary to get perfect contact, since an arc or loose contact would generate a high frequency in the circuit of the third harmonic
and so may lead to a higher frequency oscillation between line
and ground.

SEVENTH LECTURE

HIGH FREQUENCY OSCILLATIONS AND SURGES

N an electric circuit, in addition to the power consump-

tion by the resistance of the lines, an energy storage

occurs as electrostatic energy, or electrostatic charg-e

due to the voltage on the line (capacity) ; and as electromag-

netic energy, or magnetic field of the current in the line

(inductance). In the long distance transmission line, both

amounts of stored energy are very considerable, and of about

equal magnitude; the former varying with the voltage, the

latter with the current in the line. Any change of the voltage on

the line, or the current in the line, or the relation between volt-

age and current, therefore requires a corresponding change of

the stored energy; that is, a readjustment of the stored energy

e2C

in the system, the electrostatic energy

and the electro-

L2
i

magnetic energy

, from the previous to the changed cir-

cuit conditions. This readjustment occurs by an oscillation, that is, a series of waves of volitage and of current, which
gradually decreases in intensity, that is, dies out.
These oscillating voltages and currents are the result of the readjustment of the stored energy of the circuit ito a sudden change of conditions, and are dependant upon the stored energy of the circuit, but not upon the generator frequency or wave shape; therefore they occur in the same manner, and are of the same frequency, in a 25 cycle system as in a 60 cycle system, or a high potential direct current transmission; and occur with sine waves of generator voltage equally as with distorted

92

GENERAL LECTURES

generator waves. While the power of these oscillations ulti-

mately comes from the generators, it is not the generator

wave nor one of its harmonics which builds up, as discussed in

the previous lectures; but the generator merely supplies the

energy, which is stored as electrostatic charge of the capacity

and as magnetic field of the inductance, and the readjustment

of this stored energy to the change of circuit conditions then

gives the oscillation.

These oscillating voltages and currents, adding to the

generator voltage and current, thus increase the voltage and

ithe current the more, the greater the intensity of the oscilla-

tion, and so may lead to destructive voltages.

Obviously, the intensity of the oscillation, that is, its

voltage and current, are the greater, the greater or more abrupt

the change was in the circuit, which caused the oscillation by

requiring a readjustment of the energy storage. The greatest

change in a circuit, however, is the change from short circuit

to open circuit, and the instantaneous opening of a short circuit

on a transmission line as it occasionally occurs by the sudden

rupture of a short circuiting arc therefore gives rise to the

most powerful, and thereby most destructive oscillation.
The wave length of oscillation thus depends on the length

of the circuit in which the stored energy readjusts itself. For

instance, in the short circuit oscillation of the system, the wave

extends over the entire circuit, including generators and trans-

formers ;

and

the

entire

circuit

so

represents

one

wave,

or

one-

half wave, that is, the wave length is very considerable. If

the readjustment of stored energy (takes place only over a

section of the circuit, the wave length is shorter. For instance,

if by a thunder cloud a static charge is induced on the trans-

mission line, and by a lightning flash in the cloud, the cloud

discharges, the electrostatic charge induced by it on the line