Alfred Still.

Principles of electrical design; d. c. and a. c. generators online

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for the apparent tooth density. As a check, it may be stated
that the tooth density in alternators is rarely higher than 18,000
gausses in 25-cycle machines, and 16,000 gausses in 60-cycle



252 PRINCIPLES OF ELECTRICAL DESIGN

machines. Higher densities are used in some steam-turbine-
driven machines, with a view to reducing the size of the rotor.
A good system of forced ventilation is then imperative.

77. Length of Air Gap. Inherent Regulation. In A.C. ma-
chines, just as in D.C. machines, the length of air gap should
depend upon the armature m.m.f and therefore on the pole
pitch, T, and the specific loading, q. In salient-pole machines,
the air gap will not be of constant length, but will increase from
the center outward, in order to produce the required distribution
of flux. A practical method of shaping the pole face will be
explained later. The clearance to be allowed between pole
face and armature surface at the center of the pole may be de-
termined approximately by making it of such a length that the
open-circuit field ampere-turns shall be not less than 1.75 times
to twice the full-load armature ampere-turns. In large turbo-
alternators this ratio may be as low as 1 to 1.5, in order to reduce
the weight of copper on the rotor, and keep the short-circuit
current within reasonable limits. The distribution of armature
m.m.f. will be discussed later; but, for the purpose of estimating

the air gap, the ampere-turns per pole may be taken as -*-

In no case should the air gap be less than one-third to one-half
the slot opening.

A large air gap has the effect of improving the regulation of
the machine; but otherwise it is objectionable, seeing that it
leads to increased magnetic leakage and higher cost, due mainly
to the greater weight of copper in the field coils.

The inherent regulation of a generator, at any given load, may
be defined as the percentage increase in terminal voltage when
the load is thrown off; the speed and field excitation remaining
constant. Owing to the low power factors resulting from the
connection of induction motors on alternating-current circuits,
it is practically impossible to design a generator of which the
inherent regulation is so good that auxiliary regulating devices
are unnecessary. It is, therefore, uneconomical to aim at very
good inherent regulation, especially as efficient automatic field
regulators are now available. The inherent regulation of com-
mercial machines usually lies between 5 and 9 per cent, at full
load on unity power factor, while it may easily be 20 per cent.,
or higher, on 85 per cent, power factor, with normal full-load
current taken from the machine. This very marked effect of



DESIGN OF ALTERNATORS 253

a low power factor will be explained later in detail; but it may
be stated here that the effect of a lagging armature current
is very similar to that of a change of brush position in a con-
tinuous-current dynamo, causing the armature ampere-turns
which on unity power factor have merely a distorting effect
to become partly demagnetizing.

Not only must the armature be weak relatively to the field,
but the inductance of the armature windings should be small
if the inherent regulation is to be good. Thus the regulating
qualities of an alternating-current generator depend on both
armature reaction and armature reactance; but since these cannot
be made so small as to dispense entirely with external regulating
devices, the designer rarely aims at getting very good inherent
regulation.

With steam-turbine-driven machines, in which the pole pitch
is always very large, the air gap frequently exceeds 1 in. in
length. The writer knows of a machine, designed for an output
of 5,500 k.v.a. at a speed of 1,000 revolutions per minute, and
a frequency of 33J, with the single air gap 3^ in- long. Whether
or not the designer was justified in trying to obtain satisfactory
regulation by this costly and somewhat crude expedient is at
least questionable. Machines of three times this output arc
now built with air gaps from 1 in. to lj^ in. long.

Good inherent regulation means that the current on short-
circuit may be very large, and this is sometimes objectionable.
With the exception of high-speed, steam-turbine-driven units,
the short-circuit current in modern A.C. generator (with full-
field excitation) is about three to five times the normal full-load
current; but in connection with the larger units, and on systems
dealing with large amounts of energy, power-limiting reactances,
external to the generator, are usually installed to prevent the
current attaining a dangerous value before the automatic circuit-
breakers have had time to operate. Many of the largest units,
driven at very high speeds by steam turbines, are now purposely
designed with large armature reaction and highly inductive
windings, in order that they may be able to withstand momen-
tary short-circuits without mechanical injury; but notwith-
standing these features of recent introduction, the momentary
short-circuit current in some of the 20,000 to 30,000 k.v.a. units,
may be of the order of 15 to 20 times the normal full-load current.

For certain electro-metallurgical work, or electric smelting,



254 PRINCIPLES OF ELECTRICAL DESIGN

as, for instance, the electric production of calcium carbide,
an alternator with poor regulation is desirable. In other words,
where a constant-power machine is needed, a powerful armature
reaction and magnetic leakage are useful; with a decrease in the
resistance of an electric furnace, the current will rise, but if this
increase of current causes a falling off in the pressure at the
generator terminals, the power consumed will not increase to any
appreciable extent.



CHAPTER XII

ARMATURE WINDINGS LOSSES, AND TEMPERATURE

RISE

78. Types of Windings. Fundamental winding diagrams for
single-, two-, and three-phase, machines were illustrated and ex-
plained in the preceding chapter (Art. 67). Beyond this it is
not proposed to say much regarding the actual arrangement of
armature windings in alternating-current generators. Much
excellent matter has been published on the practice of armature
winding; 1 but it has little to do with the principles of electric
design, and, in the end, is really a study of the most convenient
and economical way of connecting together the active conductors
in the slots. There is almost no limit to the number of styles
of winding that can be used on alternators, or to the names that
may be, and are, given to these different windings; but the funda-
mental principles underlying the generation of an alternating
e.m.f. can be studied without a detailed knowledge of the many
practical types of armature windings.

There is one broad distinction that can be made, and alternator
windings may be divided into :

(a) Double-layer windings.

(6) Single-layer windings.

(a) Double-layer Winding. This is practically identical with
the usual D.C. winding, the coils being generally of the same
shape; but instead of tappings being taken to a commutator,
the coils are connected together in the proper order, the phase
windings being kept separate until finally connected star or mesh
as may be decided. With this style of winding, the number of
conductors per slot must be a multiple of two. All coils are of
the same size and shape, which is an advantage; but on the other
hand, the end connections are rather close together, and there
must also be substantial insulation between the two coil-sides
in each slot. This type of winding is, therefore, not very suitable
for high pressures. One great advantage of the double-layer

1 MILES WALKER: "Specification and Design of Dynamo-electric Ma-
chines," LONGMANS & Co.

255



256



PRINCIPLES OF ELECTRICAL DESIGN



winding is that it lends itself readily to fractional pitch lap
windings, in which the two sides of a coil are not similarly placed
relatively to the center lines of the poles, with the result that tooth
harmonics in the e.m.f. wave may be almost eliminated.

(6) Single-layer Winding. With this winding there is only
one coil-side in a slot, and the number of conductors per slot
may, therefore, be either odd or even. Several shapes of coil are



FIG. 95. Three-phase, single-layer winding; three slots per pole per phase.

necessary in order that the end connections may clear each other,
and this involves a larger number of special tools or formers and
a larger number of spare coils than for a double-layer winding.
These disadvantages are, however, sometimes outweighed by the
fact that the total number of coils in the machine is smaller.
Good insulation is easily obtained because the end connections
may be separated by large air spaces, and the single-layer winding
is, therefore, suitable for high voltages.





FIG. 96. Three-phase, single layer winding; four slots per pole per phase

Considering each phase winding separately, the full number of
turns per pole may encircle one pole only as shown in Fig. 95, or
they may be divided between a pair of poles, in two equal parts,
as shown in Fig. 96. Both diagrams show one phase only of a
three-phase generator. In Fig. 95 there are three slots, while in
Fig. 96 there are four slots, per pole per phase. The coils of the
other phase windings would be similarly arranged in the re-
maining slots, the ends projecting beyond the slots being shaped



ARMATURE WINDINGS



257



or bent so as to clear the other coils, generally as shown in,
Fig. 97.

All the conductors of one phase are usually connected in
series, but sometimes parallel circuits are used. It then becomes
a matter of importance to see that there is no phase difference
between the e.m.fs. generated in the conductors of parallel
circuits. In other words, the conductors of parallel circuits
should be so disposed in the available slots that they cut the
same amount of flux at the same instant of time. Having
mentioned this point, it does not appear necessary to enlarge
upon it.




FIG. 97. End connections of single-layer armature winding.



79. Spread of Windings. In two-phase and three-phase
machines, all the slots on the armature are utilized. With
full-pitch windings, 1 the number of slots per pole is divisible by
2 for a two-phase generator, and by 3 for a three-phase generator.
Thus, with distributed windings (more than one slot per pole
per phase), the "spread," or space occupied by each phase wind-
ISO
ing, is -g- = 90 electrical degrees for a two-phase machine, and

180

-Q- = 60 degrees for a three-phase machine.

In single-phase machines, nothing is gained by winding all
the slots on the armature surface; after a certain width of wind-
ing has been reached, the filling of additional slots merely in-
creases the resistance and inductance of the winding, without any
appreciable gain in the matter of developed voltage. This is

1 Short-pitch windings are very common in two-pole machines, as they
tend to simplify the end connections. In this case the double-layer winding,
as in D.C. machines, would be used.

17



258 PRINCIPLES OF ELECTRICAL DESIGN

made clear in the vector diagram, Fig. 98. The winding is sup-
posed to be distributed in a very large number of slots, and the
diameter of the semicircle represents the resultant generated
e.m.f. if all the slots are filled with conductors (connected in
series). If, as is usual in practice, only 75 per cent, of the slots
are utilized, the spread of the single-phase winding will be about
135 electrical degrees; the resultant e.m.f. will be AB, which is
not much shorter than AC', but the length and weight of copper

arc AB

in the two cases are in the proportion - A Kr< - The fact that,

arc



in polyphase machines, the whole of the armature surface is
available for the windings, while only a portion of this surface
is utilized in the single-phase alternator, accounts for the fact
that the output of the latter is less than that of the polyphase
machine for the same size of frame. Given a three-phase machine,
it is merely necessary to omit one of the phase windings entirely




FIG. 98. Vector diagram illustrating "spread" of armature winding in
single-phase alternator.

'and connect the two remaining phases in series, to obtain a
single-phase generator. The modified machine will be capable
of giving something more than two-thirds of the output of the
polyphase generator, the limit being reached when the copper
losses become excessive.

80. Insulation of Armature Windings. With very high
voltages, such as are used on many power transmission schemes,
a special study has to be made of the problems of insulation.
These problems then become of extreme importance, and many
difficulties have to be overcome that do not trouble the designer
who is dealing with pressures of the order of 5,000 to 10,000
volts.

The reader is referred to Art. 28 of Chap. V, where slot insula-
tion was discussed, and since the same insulating materials
are used in alternators as in dynamos, there is little to be added
here. It is the practice of some manufacturers to have the



ARMATURE WINDINGS 259

question of insulation studied by experts who decide upon the
most suitable materials to withstand the particular conditions
under which the machine will have to operate, and then advise
the designer of the machine regarding the space to be allowed
to accommodate this insulation. If high-class insulating materials
are used, the slot lining, i.e., the total thickness of insulation
between the conductors and the side or bottom of the slot,
should have the following values:



Terminal voltage

500 0.045 in.

1,000 0.060 in.

2,000 0.080 in.

4,000 0.12 in.

8,000 0.19 in.

12,000 0.27 in.

81. Current Density in Armature Conductors. Although the
armature may be stationary, the permissible current density
in the conductors will depend to some extent upon the peripheral
speed of the rotating field magnets, because the fanning effect
will be greater at the higher velocities. The cooling effect of
the air thrown against the conductors by the rotation of the
field magnets is not so great as when the armature rotates, and
moreover, the air is warmed to some extent in passing over the
heated surface of the field coils. The current density in alter-
nator armatures usually lies between 1,500 and 3,000 amp. per
square inch of cross-section. The formula previously used in
the design of dynamo armatures requires some modification,
and the writer proposes the following empirical formula for
current density in the armature windings of alternators with
rotating field system, up to a peripheral speed of 8,000 ft. per
minute :

600,000 v
A = + g (96)

The symbols have the same meaning as in formula (51) on page
97; the peripheral velocity, v, being calculated by assuming
that the armature is rotating instead of the field.

82. Tooth and Slot Proportions. In deciding upon the
number of teeth on the armature, a compromise must be
made between a very small number of teeth which involves
the bunching of conductors, with consequent high internal



260 PRINCIPLES OF ELECTRICAL DESIGN

temperatures and high inductance and a large number of teeth,
involving more space taken up by insulation, and a higher cost
generally. Although larger slots are permissible in A.C. than
in D.C. machines, a slot pitch (X) greater than 2.5 in. is not
recommended. The upper limit might be 2.75 in. if the air
gap is large, while the lower limit is determined by considera-
tions of space available for conductors and insulation, bearing in
mind the higher cost of a large number of coils. In large turbo-
alternators, the slot pitch may be as large as 3 in. or even
3^, in. but in such cases a slot wedge built up of laminated
iron plates is generally used, thus virtually reducing the slot
opening and equalizing the flux distribution over the slot pitch.
In a three-phase machine, the number of slots per pole per phase
is usually from 1 to 4; but in turbo-alternators, with large pole
pitch, the number of slots may greatly exceed these figures.

The conductors must be so arranged that the width of slot
is not such as to reduce the tooth section beyond the limit
corresponding to a reasonable flux density in the iron of the
tooth (see Art. 76 of the preceding chapter); but, on the other
hand, a deep slot is sometimes objectionable because it leads
to a high value of slot leakage flux. The depth of the slot
should preferably not exceed three times the width, although
deeper slots can be used, and may, indeed, be desirable in cases
where poor inherent regulation is deliberately sought.

83. Length and Resistance of Armature Winding. Apart
from the pitch, T, and the gross length of armature core, l a , the
length per turn of the winding will depend upon the voltage and
also upon the slot dimensions. The voltage will determine the
amount by which the slot insulation should project beyond the
end of the armature core, and the cross-section of the coil will
be a factor in determining the length taken up in bends at the
corners of the coil. A rough sketch of the coil should be made,
and the length of a mean turn estimated as closely as possible
for the purpose of calculating the resistance and weight. With
the high pressures generated in some machines, it is necessary
to carry the slot insulation a considerable distance beyond the
end of the slot in order to guard against surface leakage, and
although no definite rules can be laid down to cover all styles
of winding, the straight projection of the coil-side (and insula-
tion) outside the slot would be at least % (k.v. + 1) in.; where
k.v. stands for the pressure between terminals in kilovolts. On



ARMATURE WINDINGS 261

the basis of an average size of slot, the actual overhang beyond
end of core would have a mean value of about J^ (k.v. + 3 + j),

where r is the pole pitch in inches. On this basis, and as a very
rough estimate, the mean length per turn in inches, would be

2/ a + 2.5r + 2 k.v. + 6 (97)

The cross-section having been previously decided upon, the
resistance per phase of the armature winding can readily be
calculated.

84. Ventilation. The gross length of the armature core (l a
in the last formula) will depend upon the space taken up by the
radial vent ducts and insulation between stampings. If radial
ducts are used, they are from % to % in. wide, spaced 2 to 4
in. apart, the closer spacing being used when the axial length
of the core is great and the peripheral velocity low.

In turbo-alternators, axial vent ducts are being used in place
of radial ducts. If there are no radial openings between the
armature plates, the length of the core can be reduced, and this
is always desirable in high-speed machines. The relation be-
tween net and gross lengths of armature core will then be
approximately l n = 0.92/ a . Even when axial ducts are used,
one or more radial openings at the center of the core are some-
times provided so that the cool air may be drawn in at both ends
of the armature and discharged at the center. The fan for forced
ventilation may be inside or outside the generator. In large
units the external fan is generally to be preferred. The reader
is referred to Art. 33, Chap. VI, where the ventilation of dynamos
was discussed.

85. Full-load Developed Voltage. The losses in the armature
core at full load will depend upon the developed e.m.f., which
is not quite so easily calculated as in the case of a D.C. dynamo.
The pressure that has to be generated in the armature windings
of an alternator for a given terminal voltage, will depend not
only upon the IR pressure drop, but also on the IX drop. In
other words, the inductance of the armature windings, and the
power factor of the load, must be taken into account when
calculating the developed voltage.

The vector diagram, Fig. 99, refers to a machine working on a
load of unity power factor. The current is in phase with the
terminal voltage OE t ; but the developed volts are OE g and not



262



PRINCIPLES OF ELECTRICAL DESIGN



OP as would be the case if the IR drop only had to be considered.
The vector PE represents the e.m.f. component necessary to
counteract the reactance drop in the armature windings. Al-
though the external power-factor angle is zero, there is an angle
\l/ between the current vector and the vector of the developed
e.m.f., which may be termed the internal power-factor angle.

Ea



(IX Drop)




""-Internal Power Factor

Angle

F IGL 99. Vector diagram for calculating developed e.m.f. non-inductive

load.

In Fig. 100, the external power-factor angle is 6 (power factor
of load = cos 6). The construction shows how the reactance
voltage (IX) becomes a factor of greater importance on the lower
power factors. The e.m.f. that must be developed to obtain
a constant terminal pressure must, therefore, be greater on low
power factor. This, however, is not the chief cause of poor
regulation on low power factors; it is the demagnetizing effect of



(IX)




FIG. 100. Vector diagram for calculating developed e.m.f. load partly

inductive.

the armature ampere-turns which is chiefly accountable for
poor regulation on all but unity power factor. From an in-
spection of Fig. 100 it will be seen that the greatest difference
between developed and terminal voltage occurs when the ex-
ternal power-factor angle is the same as the angle E g E t P, be-
cause the developed voltage is then simply the arithmetical sum
of the terminal voltage OE t and the impedance drop E E t .



ARMATURE WINDINGS 263

In connection with the predetermination of temperature rise,
the losses in the armature core may well be calculated on the
assumption that this condition is fulfilled.

The vector diagrams should always be drawn to show the
relation of the variable quantities in one phase of the winding; a
balanced load being assumed. It does not then matter whether
the phases are star- or delta-connected, except that, in the case
of a star-connected generator, the vector OE t would stand for
the voltage between one terminal and the neutral point, and its

numerical value would therefore be ~77* times the voltage

between terminals.

The length of the vector E t P in Figs. 99 and 100 is easily
calculated; but the numerical value of IX (the vector PE )
is not so easily estimated. Consider first what is to be under-
stood by the term armature reactance.

86. Inductance of A.C. Armature Windings. It is not always
easy to separate armature reactance (X) from armature reac-
tion (the demagnetizing effect of the armature ampere-turns).
Both cause a drop of pressure at the terminals under load, espe-
cially on low power factors. By departing from the conventional
methods of treating this part of the subject, and striving to
keep in mind the actual physical conditions, by picturing the
armature conductors cutting through the flux lines, it is hoped
that the difficulties of the subject may, to a great extent, be
removed.

The inductance of the windings, in so far as it affects regu-
lation, will be taken up again in Chap. XIV, and for our present
purpose which is mainly to design an armature that shall
not attain too high a temperature it is not proposed to add
much to what was said in Chap. VIII when treating of the flux
cut by the coil undergoing commutation. A distinction was
then made between the slot flux and the end flux. The same
conditions are met with in the alternator, where what is usually
referred to as the reactive voltage component (the vector E g P
in Figs. 99 and 100) is really due to the cutting of the end flux
by the conductors projecting beyond the ends of the slots: the
slot flux, being actually provided by the main poles, does not
enter the armature core below the teeth, and since it is not cut
by the armature inductors, it should not be thought of as pro-
ducing an e.m.f. of self-induction in the windings. The slot



264



PRINCIPLES OF ELECTRICAL DESIGN



flux may be considerable, especially on a heavy load of low power
factor, and it will have an appreciable effect on the inherent
regulation of the machine. The m.m.f. of the conductors
in the slot accounts for the fact that a certain percentage of the
flux in the air gap does not enter the armature core below the
teeth; but the point here made is that the slot leakage flux does
not induce a counter e.m.f. in the armature windings.

The core loss will depend upon the flux necessary to develop
the e.m.f. OE g of Figs. 99 and 100, where the component E g P is the
reactance voltage drop due to the flux linkages of the end con-
nections only; or, in other words, where E g P is the e.m.f. induced



Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 21 of 30)