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when the angle ft was originally estimated; but, by using the
vector construction on the assumption of sine-waves throughout,
a very close estimate of these quantities can be made. The im-
portant point in connection with this method of analysis is that
the external power-factor angle 6 and the terminal voltage E t can
be calculated for any value of the armature current 7 C when the
phase displacement of the latter relatively to the open-circuit
voltage is assumed.

316 PRINCIPLES OF ELECTRICAL DESIGN

The field ampere turns necessary to produce the terminal
voltage OE t of the vector diagram Fig. 133 are made up of the
ampere turns for air gap and armature teeth, represented by the
maximum ordinate of the curve F of Fig. 131, together with the
ampere turns required to overcome the reluctance of the pole-
core, yoke ring, and armature core. These additional ampere
turns are readily calculated because the total useful flux per
pole is known, being represented by the area of the curve C of
Fig. 132.

Having determined the total ampere turns per pole which are
necessary to give OE t volts (of Fig. 133) at the terminals, it is
easy to read the corresponding open-circuit voltage from the
no-load saturation curve of the machine. In this manner the
regulation corresponding to a known external power factor, cos
6, can be calculated with greater accuracy than will usually be
obtained by the method outlined in Art. 108, and illustrated
by Figs. 129 and 130.

The meaning of the other quantities in Fig. 133 may be summed
up as follows:

The angle E OE' g , or a, is the phase difference between equiva-
lent sine-waves representing open-circuit voltage and " apparent"
developed voltage under load conditions. It is the result of
flux distortion due to the armature cross-magnetizing ampere-
turns. The vector OE g gives the r.m.s. value of the voltage per
phase actually developed in the armature winding by the cutting
of the flux linking with the " active" conductors.

The angle E g OI c or \f/ is the internal power-factor angle. The
difference in length between OE and OE' g is the voltage drop
due to armature demagnetization and distortion. The point
E is shown in Fig. 133 on PE' g produced, but it does not neces-
sarily fall on this straight line, and so indicates one important
difference between the construction of Fig. 133 and that of
Fig. 130, in which the assumptions made are not universally
applicable.

The use of vectors and vector constructions, such as were first
described, will usually give sufficiently accurate results without
the expenditure of time and labor involved in the plotting of
flux curves and e.m.f. waves. It is in the case of abnormal
designs, or when the conditions are unusual, that the problem
of regulation may be studied most conveniently and correctly
by a method such as that here described, which is subject

REGULATION OF ALTERNATORS

317

to modification in matters of detail and may be elaborated if
desired.

In the writer's opinion, a further advantage of the method of
flux distribution and wave-form analysis lies in the fact that the
designer obtains thereby a clearer conception of the factors enter-
ing into the problem of regulation than he is ever likely to obtain
if he confines himself to the use of formulas and vector diagrams,
which are always liable to be abused when familiarity with their
purpose and construction leads to forgetfulness of their meaning
and limitations.

111. Efficiency. In estimating the efficiency of an alternating-
current generator before it is built, the same difficulties occur as
in the case of the dynamo. There are always some losses such
as windage, bearing friction, and eddy currents, which cannot
easily be predetermined, and it is therefore necessary to include
approximate values for these in arriving at a figure for the total
losses. Very little need be added to what has already been said
in Art. 60 of Chap. IX, to which the reader is referred. He should
also consult the working out of the numerical example under
items (148) and (149) in Art. 63; and make a list of all the losses
occurring in the machine at the required output and power factor.

In the ratio efficiency =

output

' li ls the actual output of

the generator at a given power factor with which we are con-
cerned, and not the rated k.v.a. output.

Windage and bearing friction losses are never easily estimated ;
but the following figures may be used in the absence of more
reliable data.

APPROXIMATE WINDAGE AND FRICTION LOSSES EXPRESSED AS PERCENTAGE

K.v.a. output

f 50

Self -ventilated A.-C. generators \ 200

500 and
larger

Turbo-alternators: forced ventilation
(exclusive of power to drive fan) ....

2,000

5,000

10,000

15,000

20,000

Windage and
bearing friction

1.5 per cent.
1.0 per cent.

0.5 per cent.

1 . 8 per cent.
1 . 5 per cent.
1 . 2 per cent.
1.0 per cent.
. 9 per cent.

318 PRINCIPLES OF ELECTRICAL DESIGN

The power required to drive the ventilating fan for turbo-
alternators will generally be from 0.3 to 0.5 per cent, of the rated
full-load output of the generator.

The brush-friction loss is usually small. If A is the total area
of contact, in square inches, between brushes and slip rings, and
v is the peripheral velocity of the slip rings in feet per minute,

vA
the brush-friction loss will be approximately TT watts.

The hysteresis and eddy-current losses in the iron can be cal-
culated for any given load because the required developed voltage,
and therefore the total flux per pole, are known. The losses in
the teeth can now be calculated with greater accuracy than
before the full-load flux curves were drawn, because the maximum
value of the tooth density will depend upon the maximum value
of the air-gap flux density as obtained from the flux distribution
curve for the loaded machine, as explained in Art. 60 (page
196). Unless the density in the teeth is high, it is usually un-
necessary to calculate the actual tooth density because the
"apparent" tooth density may be used in estimating tooth losses;
but with low frequency machines the density in the teeth may
be carried well above the "knee" of the B-H curve, and it would
then be necessary to determine the actual tooth density as ex-
plained in Art. 37 of Chap. VII under dynamo design.

Eddy Currents in Armature Conductors. The PR loss in the
armature copper may be calculated when the cross-section and
length of the winding are known ; but in the case of large machines
with heavy conductors, the eddy-current loss in the "active"
conductors may be considerable, and an allowance should then
be made to cover this. The eddy currents in the buried portions
of the winding are due to two causes:

1. The flux entering the sides of the teeth through the top of
the slot.

2. The slot leakage flux which the armature conductors them-
selves produce when the machine is delivering current to the
circuit.

The loss due to (1) is independent of the load, and would be of
importance in the case of solid conductors of large cross-section
in wide open slots. With narrow, or partially closed, slots, it is
negligible; but occasion arises when it is advisable to laminate
the conductors in the upper part of the slot to avoid appreciable
loss due to this cause.

REGULATION OF ALTERNATORS 319

Item (2) may lead to very great additional copper losses if
solid conductors of large cross-section are used in narrow slots
of considerable depth. The calculation of the losses due to the
reversals of the slot leakage flux could be made without difficulty
if it were not for the fact that the dampening effect of the unequal
distribution of the current density through the section of the
solid conductor actually decreases the amount of the slot flux
and so reduces the loss. The best and most thorough treatment
of this subject known to the writer is that of PROF. A. B. FIELD
in the Trans., A. I. E. E., vol. 24, p. 761 (1905). The remedy in
the case of heavy losses due to slot leakage flux through the cop-
per is to laminate the conductors in a direction parallel to the
flux; thus, if copper strip is used, it must not be placed on edge
in the slot, but should be laid flat with the thin edge presented
to the flux lines crossing the slot, exactly as in the case of the
armature stampings, which are so placed relatively to the flux
from the poles. Owing to the fact that the leakage flux is con-
siderably greater in amount near the top than the bottom of the
slot, the losses due to both causes of flux reversal in the space
occupied by the "active" copper are of more importance in the
upper layers of conductors than in those near the bottom of the
slot. For this reason, the upper conductors will sometimes be
laminated, while the lower conductors are left solid. When the
method of lamination has been decided upon, the probable in-
crease in loss can be obtained from figures and curves published
by PROF. FIELD in the paper previously referred to; but it is
suggested that, for the purpose of estimating the probable effi-
ciency, the calculated PR loss in the armature windings be in-
creased 15 per cent, in the case of slow-speed machines of moder-
ate size, and 30 per cent, in the case of steam-turbine-driven
units of large output. This addition is intended to cover not
only the losses due to eddy currents in the armature windings,
but all indeterminate losses in end plates, supporting rings, etc.,
which increase with the load.

CHAPTER XV
EXAMPLE OF ALTERNATOR DESIGN

112. Introductory. The principles and features of alternator
design, as given in the foregoing chapters, will now be applied
and illustrated in the working out of a numerical example. A
steam-turbine-driven three-phase generator will be selected, be-
cause this design involves greater departures from the previously
illustrated D.C. design than would occur if the slow-speed type
of alternator with salient poles were selected. It is true that the
difficulties encountered in the design of turbo-alternators espe-
cially of the larger sizes, running at exceptionally high speeds
are of a mechanical rather than an electrical nature; but this
merely emphasizes the importance to the electrical engineer of a
thorough training in the principles and practice of mechanical
engineering.

It is not possible for a man who is not in the first place an ex-
perienced mechanical engineer to design successfully a modern
high-speed turbo-alternator. These machines are now made up
to 30,000 k.v.a. output at 1,500 revolutions per minute (25 cycles)
and 35,000 k.v.a. at 1,200 revolutions per minute (60 cycles).
Larger units can be provided as the demand arises; it is probable
that single units for outputs up to 50,000 k.v.a. at 750 revolutions
per minute will be built in the near future. With the great
weight of the slotted rotors, carrying insulated exciting coils, and
travelling at very high peripheral velocities, new problems have
arisen, and these problems should be seriously studied by anyone
proposing to take up the design of modern electrical machinery.
Engineering textbooks may constitute a basis of necessary
knowledge; but, with the rapid advance in this field of electrical
engineering, the information of greatest value (apart from what
the manufacturing firms deliberately withhold) is to be found in
current periodical publications, including the papers and discus-
sions appearing in the journals of the engineering societies.

Since it will not be possible to discuss the mechanical details
of turbo-alternator designs in these pages, a machine of medium
size (8,000 k.v.a.) will be chosen, and the peripheral speed of
the rotor will not be permitted to exceed 18,000 ft. per minute.
The mechanical difficulties will therefore not be so great as in

320

EXAMPLE OF ALTERNATOR DESIGN 321

some of the larger machines running at higher peripheral veloci-
ties, and the electrical features of the design will be considered
alone, reference being made to mechanical details only as occa-
sion may arise.

It is proposed to work through the consecutive items of a design
sheet, as was done for the D.C. dynamo; but the sheets will include
fewer detailed items, more latitude being allowed in the exercise
of judgment and the application of knowledge derived from the
work done on previous designs. An attempt will be made to
render the example of use in the design of slow-speed salient-pole
machines, and, with this end in view, references will be made to
the text when taking up in detail the items of the design sheet.
For the same reason namely, to make the numerical example of
broad application the writer may take the liberty of digressing
sometimes from the immediate subject, if matters of interest
suggest themselves as the work proceeds.

113. Single-phase Alternators. Since the selected design is
that of a polyphase machine, it seems advisable to state here one
or two matters of special interest in the design of the less common
single-phase generator. It is easier to design a polyphase than
a single-phase alternator, although this fact is not always recog-
nized, even by designers. Many of the single-phase machines
in actual service are less efficient than they might be; but the
problems which are peculiar to single-phase generators receive
comparatively little attention because these machines are rarely
used at the present time, the development during recent years
having been mainly in the direction of power transmission and
distribution by polyphase currents.

It is the pulsating nature of the armature m.m.f., as explained
in Art. 94, Chap. XIII that leads to eddy-current losses that
are practically inappreciable in the case of two- or three-phase
machines working on a balanced load, that is to say, with the
same current and the same voltage in each of the phase windings,
and with the same angular displacement between current and
e.m.f. in the respective armature circuits. Sometimes the poly-
phase load is not balanced, and in that case pulsations of the
armature field occur as in the single-phase machines, the amount
of the pulsating field being dependent upon the degree of un-
balancing of the load. The effect is then as if an alternating
field were superposed on the steady armature m.m.f. due to
the balanced components of the total armature current.

Without going into detailed calculations, it may be stated that
21

322

PRINCIPLES OF ELECTRICAL DESIGN

the remedy consists in providing ammortisseur or damper-
windings on the pole faces, as mentioned in Art. 94, Chap. XIII.
A simple form of damper is illustrated in Fig. 134, where a num-
ber of copper rods through the pole face and on each side of

FIG. 134. Short-circuited damping bars in pole face of single-phase alternator.

the pole shoe are short-circuited at both ends by heavy bands
of copper. Any tendency to sudden or periodic changes of flux
through any portion of the pole face is checked to a very great
extent by the heavy currents that a small change of flux will
establish in the short-circuited rods.

114. Design Sheets for Alternating-current Generator.

SPECIFICATION

Output, k.v.a

Number of phases. . .
Terminal voltage . . .
Power factor of load .

Frequency

Type of drive

Speed, r.p.m

Inherent regulation .

8,000

3

6,600

0.8
60

Steam turbine
1,800
Within 25 per cent, rise when full

load is thrown off.
130

Exciting voltage

Permissible temperature rise after 6 hr. full-load run

(by thermometer) 45C.

Ventilating fan independently driven (not part

of generator).

GENERAL OUTLINE OP PROCEDURE
(a) Design armature.
(6) Design field magnets.

(c) Draw flux distribution curves. Obtain wave shapes and form factors.

(d) Complete field system. Open-circuit saturation curve. Regulation, and short-circuit
current.

(e) Efficiency.

EXAMPLE OF ALTERNATOR DESIGN

323

CALCULATIONS

Sym-
bols

Assumed or
approximate
values

Final
values

1 Number of poles

P

r

/

Q
la

18.000
38.2

4

38.25
700
Y
800
700
11,340
H
40
31.416
inding
48
4
2.62
3
62.2X10*
5,910
51
46.8
49H
layer
2,000

4X9*X0.14

1
4M

14,300
8,500
14
28,000
4,900
120 kw.
210
0.01135
8.4
21
116
190
3,875
65.2X10*
drical)
8
3.76
1.625
0.3059
1.25

122.3

2. Peripheral speed (feet per minute) . . .
3. Diameter of rotor (inches)
4 Line current

5. Phase connection (star or delta)

Y

812

8. Armature ampere-turns per pole...
9. Length of air gap at center (inches).. .
10. Diameter of stator (armature) (inches)
11. Pole pitch (inches)
12. Pole arc (inches)
13. Number of inductors per phase
14. Number of armature slots per pole per phase. .
15. Slot pitch

(S/)

a

D

r
]

z

n
\
T.
*
Bg
I.

In

12,7.50

%
40

distributed w
48.7
4
2.62
3

6.000
51

16. Number of inductors per slot

17. Flux per pole (no load)

18. Average flux density over pole pitch (open circuit)...

19. Axial length of armature core ( "?. (in . ch " >) ' '
\ net (inches) . . .

20 Axial length of pole face (inches)

21. Determine style of winding
22. Current density in armature conductors
23. Size of conductor. How made up. Slot insulation

A

Single
2,000

24. Tooth and slot proportions.
25. Width of armature slot (inches)
26. Depth of armature slot (inches)

d

27. Apparent tooth density (no load) at center of tooth
28. Flux density in armature core

29. Radial depth of armature core below teeth (inches) .
30. Weight of core (iron) (pounds)

Rd

31 Weight of teeth (iron) (pounds)

32. Total core loss, including teeth (open circuit)
33 Length mean turn of armature coils (inches)

34 Resistance per phase (ohms)

35 IR drop per phase (full-load current)

volts

E g P
E' E

36. Total armature copper loss (full-load current) kw . . .
37. IX drop (ends) volts per phase winding
38. IX drop (slots) volts per phase winding
39. Full-load developed voltage (per phase winding) . . .
40. Full-load flux per pole
41. Shaping of pole face

3,875
65.2X10"
(Cylin
8
3.76
1.625

42. Number of slots per pole (rotor)
43 Slot pitch (rotor)

44. Slot width (rotor)

45. Permeance per square centimeter of air gap (center)

47. "Actual" tooth density in terms of air-gap density
48. Saturation curves for air gap, teeth, and slots
49. Permeance curve (if salient-pole design).
50. Open-circuit flux curve A
51. M.m.f. curve for flux curve A
52. Required area of full-load flux curve C

Fig. 137
Fig. 139

Fig. 141
Fig. 142

324

PRINCIPLES OF ELECTRICAL DESIGN

CALCULATIONS. Continued

Sym-
bols

Assumed or
approximate
values

Final
values

53. Resultant m.m.f . for flux curve C
54. Full-load flux curve C
55. E.m.f. wave shapes at no load and full load
56. Form factor, no load.

Fig. 1
Fig. 1
Figs.

42
41
L43, 144

1 10

58. Complete field-magnet design.

If

1 15

60. Cross-section of pole cores.
61. Cross-section of yoke ring.
62. Open-circuit saturation curve for complete magnetic
circuit

Fig. 1

46

27,000

37,000

1HXO 12

375

514

68 I^R loss (field) ; full load

66 kw.

69. Total cross-section of air ducts (forced ventilation) . .

., ., f Unity power factor. . .
70. Inherent regulation (full- g d factor

load current) . { Zero power factor ....
71. Short-circuit current (per phase winding) with full-
72. Efficiency at full load and specified power factor. . . .
73. Efficiency at fractional loads.
74. Approximate volume of air required (forced ventila-
tion) cubic feet per minute

v

6 . 6 sq. ft.
22 per cent.

1,950
0.955

29,000

75. Average velocity of air in ventilating ducts feet per

4,400

115. Numerical Example. Calculations. Items (I) to (11).
With a frequency of 60 cycles per second and a speed of 1,800
revolutions per minute, the number of poles is

2 X 60 X 60

At a peripheral velocity of 18,000 ft. per minute, the diameter

. .' , , , 18,000 X 12 00 .

of the rotor would be . gnn ^ = 38.2 in.

J-,oUU /x 7T

Since the air gap is not likely to be less than 1 in., let us decide
upon an internal diameter of the armature D = 40 in. (item (10)),
and determine the exact dimensions of the rotor after the air
gap has been decided upon.

The line current (item (4)) is

800,000

\/3 X 6,600

700 amp.,

' EXAMPLE OF ALTERNATOR DESIGN 325

and if we select the star connection of phases, this is also the
current per phase winding (item (7)).

Referring to Art. 75 for values of the specific loading (page 250)
we find that the average value there suggested is q = 650; but
the peripheral loading is greater in turbo-alternators than in
slow-speed salient-pole machines, because it is desired to keep
the axial length as short as possible, and the greater losses per
unit area of cooling surface can be dealt with by a suitable system
of forced ventilation. We may therefore select a value for q
equal to, or even greater than, the proposed maximum for self-
cooled machines. Let us try q = 650 X 1.25 = 812.

The pole pitch (item (11)) is

TT X40
T = - v = 31.416 in.

and the approximate armature ampere-turns per pole (item (8))
will be

31.42X812
(SI) a = 2 - = 12,750

Referring to Arts. 76 and 77, Chap. XI, we can get a prelimi-
nary idea of the required length of air gap as explained in Art. 77.
We shall, in this design, deliberately select a high value for the
air-gap flux density, and if necessary saturate the teeth of the
rotor while keeping the density in the armature teeth within rea-
sonable limits to prevent excessive hysteresis and eddy-current
loss. Let us try B g = 6,000 gausses, which is higher than the
upper limit of the range suggested in Art. 76. The principal
advantage of using high flux densities is that the axial length of
the rotor can thus be reduced; but if it is found later that the
selected value of B g leads to unduly high flux density in the stator
teeth, it will have to be modified.

The probable maximum value of the air-gap density on open

circuit is o X 6,000 = 9,450 gausses; and, assuming the ratio of
m.m.fs. to be 1.25, we have

9,450 X 5 X 2.54 = 1.25 X 0.4^ X 12,750

whence d = 0.835 or (say) % in-

In the case of medium-speed salient-pole designs, the periph-
eral velocity would not be decided upon by merely selecting
the upper limit of 8,000 ft. per minute as given in Art. 66 (page

326 PRINCIPLES OF ELECTRICAL DESIGN

238) . This has to be considered in connection with the pole pitch
(see Art. 74), a preliminary diameter of rotor being selected in
keeping with what seems to be a reasonable pole pitch. A few
rough calculations will very soon show whether or not the tenta-
tive .value of T will lead to a suitable axial length of armature
core.

Items (13) to (16). On the basis of q = 812, the number of
conductors per phase would be

Z = l(^} = 48.7

With four slots per pole per phase, and three conductors in
each slot, we have Z = 3X4X4=48.

For item (15) we have X = ^ - = 2.62 in., giving a cor-

\.t

700 X 3

rected value for peripheral loading of q = ^TT~ = 800 approx.

z.oz

Items (17) to (20). For the purpose of calculating the flux
required on open circuit, we may use formula (94) of Art. 70,

/> i
where E per pha se = ' /-, and k = 0.958.

The required flux per pole is therefore

6,600 X 10 8

V3 X 2.22 X 0.958 X 60 X 48
= 62.2 X 10 6 maxwells.

With the assumed value of 6,000 gausses for B g , the axial
length of armature core will be

62.2 X 10 6
a ~ 6,000X6.45X31.42 "

This is a short armature for a machine with a rotor 38.25 in.
in diameter; but it is what we are aiming at, and if the field
winding can be accommodated in the space available, the design
should be satisfactory.

We shall attempt to ventilate this generator by means of axial
air ducts only. If, then, there are no radial air spaces, the net
length of iron in the armature core will be approximately
l n = 0.92Z a = 46.8 in. (Art. 84); but these dimensions cannot
be finally decided upon until the slot proportions and tooth
densities have been settled.

Whirling Speed of Rotor. A matter of considerable impor-

EXAMPLE OF ALTERNATOR DESIGN 327

tance in the design of high-speed machinery is the particular
speed at which vibration becomes excessive. Without attempt-
ing to go into the mechanical design of shaft and bearings, it
should be pointed out that the size of shaft in turbo-alternators

Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 26 of 30)