The Alternate Current Transformer Vol. 1: The Induction of Electric Currents (1896) — part 33 of 35

In Figs. 196 and 197 are shown the efficiency curves of various transformers. It will be seen that the chief difference is that the more modern transformer has a higher efficiency at the low loads. A good transformer of any moderate size should have at least 80 per cent, efficiency at one-tenth load. And larger transformers of 15 and 20-kilowatt size and upwards will reach to 90 per cent, efficiency or more at one- tenth of full load.

Another method of delineating the efficiency is to plot the difference Px - P2 in terms of P2 ; in other words, to plot a curve the abscissae of which represent the secondary output P2, and the. ordinates of which represent the total loss of

THE INDUCTION COIL AND TRANSFORMER. 557

•1 -2 -3 -4 '5 '6 -7 -8 '9 I'D

Fractions <tf Full Secondary Load. FIG. 196. — Efficiency Curves of Transformers.

•2 -3 -4 '5 '6 '7 '8 '9 I'D

Fractions of Full Secondary Load. FIG. 197. — Efficiency Curves of Transformers.

In the above diagrams, horizontal distances represent the decimal fractions of full secondary load, and vertical ordinates the percentage efficiency corresponding thereto. The numbers against the curves refer to the following transformers : — No. 9. 5 horse-power Ferrauti Transformer „ 12. 5

20. 15

21. 15

22. 20

23. 6    kilowatt 
    

4-5 4 3 6-5

Mordey Transformer

Thomson-Houston Transformer Kapp Transformer

1885 type. 1885 type rewound. 1892 type. 1892 type rewound. 1892 type. 1892 type. 1892 type. 1892 type.

" Hedgehog" (Swinburne) Transformer 1892 type. Westinghouse Transformer ... 1892 type.

.558

THE INDUCTION COIL AND TRANSFORMER.

power in the transformer, viz., P, - P.2. In Fig. 198 is shown such a curve drawn for a 6,500 - watt Westinghouse transformer. The ordinates of the upper curve give the value of P!— P2 corresponding to the secondary output P2.

One important question which arises in this connec- tion is whether the true iron core loss by hysteresis remains constant at all loads of the transformer. This was at one time denied. It has, how- ever, been shown by careful experiments that the hys- teresis loss in the iron core is sensibly constant at all loads.*

The proof of this was obtained by careful measure- ments made of the total energy loss P - P2 for various transformers. This value was plotted down, as in Fig. 198, in terms of the secondary out- put P2. On the same diagram was drawn a curve represent- ing the total copper loss or C2 R loss for the primary

• The reader may be referred to a Paper by the author in the Pro- ceedings of the Institution of Elec- trical Engineers, Vol. XXI., 1892, entitled " Experimental Researches on Alternate - Current Transfor- mers," for full information on the experimental methods by which this question has been settled. See also The Electrician, Vol. XXX., pp.97, 120,162,446.

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THE INDUCTION COIL AND TRANSFOEMEB. 559

and secondary circuits taken together. These two curves are found to be sensibly parallel to each other through- •oui; their whole range, and hence the true iron core loss or hysteresis loss is a constant quantity at all loads. This is a necessary consequence of the fact that in constant potential transformers as designed for ordinary electric lighting work the induction in the core is constant at all loads, and this in turn is a consequence of the fact that the resultant mag- netising force in the core is constant for all loads. Generally speaking, we may state that for all fairly well designed closed iron circuit constant-potential transformers the iron core loss is constant for all loads. This enables us to determine the efficiency curve for any transformer of this description by three measurements. If we measure the total power loss in the transformer at no load we have the quantity which is constant ac all loads. Call this loss in watts w. If, then, we measure the resistances of the primary and secondary circuits and correct these values so as to obtain the true resistances Rx and R2 of the copper circuits at the final temperature reached by the transformer when working, we can calculate the copper losses (V R! and C22 R2 ior various values of the output of the transformer. We can determine the value of the primary current Cj corresponding to any value of the secondary current O2 to a sufficient approximation for this purpose by taking it as

equal to C2 2?, where Nz and N2 are the number of turns of

Nj

the primary and secondary circuits respectively. Hence, the total copper loss in the transformer is very approximately equal to

and the total power Px given to the primary circuit conse- quently corresponding to any secondary output C2 V2, where V2is the secondary terminal potential difference, is given by the equation

and P2=C2V2.

Hence the ratio of Pa to Plf or the efficiency at various

560 THE INDUCTION COIL AND TRANSFORMER.

CTJrHcd-OvOCOCMr-IOLOlO

vOOiCCOCOKJiOOtOCDiO

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THE INDUCTION COIL AND TRANSFORMER. 561

loads, can be calculated. This is a convenient and fairly accurate method to adopt in the case where we are testing large transformers. It is sometimes very difficult or impos- sible then to obtain the necessary non-inductive load in the form of incandescence lamps for very large loads such as 40 or 50 kilowatts, and in that case the above procedure may be followed. The table on page 560 gives the results of a large number of transformer efficiency measurements made by the author in 1892, employing many forms of transformers then, in use.

The table shows particularly what a great advance was- made in transformer manufacture in the course of the seven years between 1885 and 1892.

In the case of larger transformers the efficiency curves can be made still more square-shouldered, and efficiencies of over 90 per cent, obtained at one-tenth load.

Since the core loss at no load is an important factor in determining the efficiency of the transformer, it is obvious that no transformer can have a high efficiency at light loads unless the core loss is small. The iron core loss or no-load loss in the case of transformers of 30 kilowatt size and upwards can now be made to be less than 1 per cent, of the full secondary output. That is to say, it is possible to make the iron core loss of a 50-kilowatt transformer not more than 400 watts. In the case of smaller transformers, from 1 to 15 kilowatts, the core loss will in general be from 3 to 1-3 per cent, of the full secondary output. Thus, a 1-kilo- watt transformer, or one capable of giving out 1,000 watts in its external secondary circuit, is a fairly good one if it has a core loss of not more than 30 watts, or 3 per cent, of its full load ; a 6-kilowatt transformer if it has a core loss of not more than 120 watts, or 2 per cent. ; and a 15-kilowatt transformer is good if its core loss does not exceed 225 watts, or 1-5 per cent. These figures will be a guide to the reader to know what the core loss may be expected to be found in various cases.

We shall consider presently the causes which affect the magnitude of the core losses.

§ 6. Current Diagram of a Transformer. — Let a horizontal line be taken on which are set off distances proportional to

§

1

THE INDUCTION COIL AND TEANSFOEMEE. 563

the power output on the external secondary circuit, that is, to the secondary load of a transformer, and let ordinates at these points be drawn to any scale representing the magnitudes of the primary and secondary currents, the scale of the primary -current ordinates being taken so that if one unit of length represents one ampere of primary current, and the scale of the

secondary current so that one unit of length represents —

times the corresponding secondary current, then we shall delineate the lines called the current curves. For any closed circuit transformer of constant potential type these current .are nearly two lines running nearly parallel to each other as shown in Fig. 199. If C: stands for the mean-square value of the primary current, and C2 for that of the secondary current, and if NI. and N2 are the numbers of the primary and secondary turns respectively, then experiment shows that a good type of closed magnetic circuit constant potential trans-

former G! - ~ C2 is a nearly constant quantity, and that this

«i

•difference is practically the same as the mean-square value of the primary current when the transformer is not loaded. Let this last be called q. Then

•or <?! Wj = GI N! - C2 Na.

In other words, the difference of the primary and secondary ampere-turns at all loads is a constant quantity, and is equal to the ampere-turns at no load. This is merely the expression •of the fact that the magnetomotive force acting on this magnetic circuit is a constant quantity, and that therefore the induction is constant as well. This is, however, not the case lor open-circuit transformers. In Fig. 200 is shown the •current curves for a Swinburne "Hedgehog" transformer, and it will be seen that the difference of the primary and secondary ampere-turns is not constant, but increases as the load dimi- nishes. This is a consequence of the fact that in the open circuit transformer the difference of phase between the primary and secondary currents is considerable at light loads, but ibecom.es less as the transformer is loaded up, and that there-

oo 2

664 THE INDUCTION COIL AND TRANSFORMER.

Table A. — Test of a Westinghouse Transformer.

Power, 6,500 watts. Secondary volts, 100. Frequency used, 82'5 periods per second. Average final temperature of transformer, 96°F. Volts on primary circuit (Vx) = 2,400 (kept constant). Primary circuit resistance = 5'95 ohms at 96°F. Secondary circuit resistance = 0'0108 ohm at 96°F.

Secondary Circuit.

Primary Circuit.

II.,

-*^ o >.

S? =

Power

Power

53^5'" z § '

!*tS

Volts.

Amperes.

;akenout in watts,

Volts.

Amperes.

given in watts

&2£ a a ||

5 II a H .=

W2.

= Wi.

-S*^ S&

101-0

0

0

2,400

0-050

95

95

0

100-9

1-00

101

0100

205

104

49-3

100-8

1-98

2CO

"(

0-140

306

106

65-4

100-8

2-94

296

'(

0-180

401

105

73-7

100-7

3-87

390

| "

0-218

493

103

79-1

100-7

4-79

482

0-250

597

115

80-7

100-7

8-00

806

w

0-382

920

114

87-6

100-4

10-15

1,019

"t

0-472

1,139

120

89-5

100-3

13-07

1,311

0-580

1,440

129

911

100-1

18-00

1,802

"

0-800

1,930

128

93-4

100-1

19-90

1,992

0-880

2,118

126

94-1

100-0

21-93

2,193

0-960

2,330

127

94-1

100-0

24-74

2,474

1-080

2,609

135

94-8

100-0

29-66

2,966

1-285

3,096

130

95-8

99-8

37-20

3,713

1-610

3,870

157

96-0

99-5

42-00

4,179

1-810

4,324

145

96-7

99-3

46-65

4,633

2-002

4,792

150

96-9

99-2

50-40

5,000

2-160

5,174

174

96-7

99-0

52-16

5,164

2-240

5,422

258

95-3

98-9

55-60

5,499

Jj

2-383

5,702

203

96-1

98-8

57-68

5,700

2-478

5,885

185

96-9

98-9

59-32

5,867

2-550

6,041

174

97-3

98-7

61-32

6,053

"

2-633

6,271

218

96-7

98-8

6216

6,142

||

2-672

6,344

202

£6-8

£8-7

63-00

6,218

M

"

2-700

6,426

208

96-8

987

64-CO

6,317

2-750

6,522

205

96-9

S8-6

64-74

6,384

"

2-775

6,598

214

96-9

fore there must be an increase in mean-square or maximum value of the primary current, so that its greater value at light loads is a compensation for the greater difference of phase between the primary and the secondary current. This is on the assumption that the secondary circuit is a practically non- inductive circuit. If the carefully-drawn current diagram ot

THE INDUCTION COIL AND TRANSFORMER. 565

Table B. — Test of a Sicinburne "Hedgehog " Transformer. Power, 3,000 watts. Secondary volts, 100. Frequency used, 81'1 periods per second. Average final temperature of transformer, 145°F. Volts on primary circuit (7^ = 2,400 (kept constant). Primary circuit resistance = 24 '00 ohms at 145°F. Secondary circuit resistance = 0'051 ohm at 145°F.

Secondary Circuit.

Primary Circuit.

11

•Sis*

w

Power

Power

lift?!

Volts.

Amperes.

taken <>ut

Volts.

Amperes

given in

*£<£f

1 " 1

in watts, W2.

watts Wj.

f £•"

W C

101-8

0

0

2,400

0-756

121

121

0

101-7

100

102

0-761

213

111

47-9

101-5

2-97

301

0-786

414

113

727

101-3

484

490

0-811

608

118

80-6

101-3

6-00

f07

0-829

730

123

83-1

101-2

8-00

810

0-862

943

133

85-9

101-0

10-20

I,0i0

0-915

1,161

131

886

100-9

12-00

1,211

0960

1,361

150

890

100-6

14-00

1,408

1-013

1,551

143

90-8

100-3

15-87

1,5-2

1-066

1,750

158

91-1

100-0

17-89

1,789

1-133

1,951

162

91-7

100-0

19-80

1,980

1-197

2,129

149

93-0

99-9

21-62

2,180

1,260

2.344

164

93-0

99-7

23-66

2,359

1-321

2,525

166

93-3

99-5

25-46

2,534

1-397

2,732

198

92-8

99-3

26-46

2,628

1-430

2,823

195

93-2

99-1

27-42

2,718

1-465

2.914

196

93-4

99-0

28-28

2,8CO

w

1-500

2,988

188

93-7

98-9

29-26

2,896

w

1-532

3,103

207

93-3

99-0

30-20

2,9,0

"

1-566

3,185

195

94-0

any closed-circuit transformer of constant-potential type are examined, it will be seen that the difference between the ordi- nates of the primary and secondary current curves or lines increases slightly very near the origin, and as we shall see pre- sently this is an indication of the fact that the primary current is for all loads, except very small ones, practically in exact opposition, as regards phase, to the secondary current. As an example of the measurements of a complete test of a closed circuit and open circuit transformer, we give on page 564 and above, in Tables A and B, the figures obtained for a Westinghouse and Swinburne transformer respectively.

566 THE INDUCTION COIL AND TEANSFORMEE.

§ 7. The Power Factor of Transformers. — If under any conditions of load on the secondary circuit we measure the true power Pa being taken up by the primary circuit, and also the mean-square (v'mean2) value A of the primary current and the mean-square value V of the primary terminal potential difference, the ratio of P! to the product A V is called the power factor of the transformer at that load. The product A V is often called the apparent power or apparent watts given to the transformer, and the value of Pj is the true power or true watts given to the transformer. Hence the power factor (F) is defined thus :—

Power fac-\ _ True power in watts given to the transformer tor (F) / Apparent power in watts given to the transformer

The above relation may be symbolically expressed by writing

F = A or P1 = (FA)V. &. v

This last mode of writing it exposes the appropriateness of the term "power factor" ; since we see that it is a factor by which the value of the total mean-square value of the current must be multiplied to obtain that current which, when multi- plied by the mean-square value of the potential difference V, will give the true mean power being taken up in the circuit. Thus, if the power factor is denoted by F, this signifies that the portion F A of the current A is effective in conveying power, and the remainder (1 - F) A is ineffective, or, as it is sometimes called, is the wattless component of the current. Hence, we may, in imagination, divide the apparent power A V into two portions: a part F AV, which is a measure of the true power given to the circuit ; and a part (1 - F) AV, which is the wattless or powerless portion.

The true power Pt is obtained from the correct wattmeter reading, and the apparent power A V is the value of the product of the readings of an electrostatic voltmeter used to measure the mean-square value of the potential difference and that of an alternating-current ammeter used to measure the mean- square value of the current. A very important constant with respect to any transformer is its power factor at no load or on open secondary circuit, and the Table on page 567 gives the

INDUCTION COIL AND TRANSFORMER. 567

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668 THE INDUCTION COIL AND TRANSFORMER.

values of the no-load power factor for various types of trans- formers taken on certain alternators.

Generally speaking, it is found that the power factor of most closed iron circuit transformers has a value lying between 0-5 and 0-8, but that for induction coils on open-circuit transformers, such as the "Hedgehog" transformer, the power factor is about one-tenth of the value for closed iron circuit transformers.

It must not be supposed, however, that the power factor of an induction coil or transformer has a constant and fixed value for any particular transformer. The value of the power factor is affected to a very considerable degree by the form of the curve of primary terminal potential difference, and may vary within wide limits according as the curve is varied in form.

Power Factors of Trcmsformen taken off different Alternators at the same Primary Voltage.

Transformer.

Size in Kilow'tts

Power Factor.

Magnetising Currents in Amperes.

On

Thomson- Houston Alternator

On Mordey Alternator

On

Thomson- Houston Alternator

On

Mordey Alternator

Mordey -Brush . . . Thomson- Hou ston Mordey-Brush . . .

50 30 18

0-609 0-490 0685

0-704 0-536 0-751

0-668 0-562 0-326

0-623 0-569 0-332

In the Table above are given the power factors at no load of three transformers taken off a Mordey alternator having an E.M.F. curve similar to that shown in Fig. 175, and a Thomson-Houston alternator having an E.M.F. curve of the kind shown in Fig. 174, and it will be seen that the power factors and magnetising currents of the transformers are quite different in the two cases.

We must not, therefore, regard the power factor as an absolute constant for the transformer, but as a function to some degree of the form of the primary E.M.F. curve, although at the same time dependent essentially upon the nature of the magnetic circuit of the transformer.

TEE INDUCTION COIL AND TRANSFORMER. 669

If the primary E.M.F. curve and current curve were both -simple periodic or sine curves, then the power factor would be simply the cosine of the angle of lag of the current behind the electromotive force. If the transformer has its secondary circuit loaded up, the power factor approximates to unity as this loading takes place.

In the case of most closed-circuit transformers a very little loading-up of the secondary circuit causes the power factor to become unity, but in the case of an open-circuit transformer, whilst the loading-up of the transformer increases the power factor, it never actually reaches unity.

Table C. — Test of a Westingliouse Transformer.

Primary volts, 2,400 (kept constant). Secondary volts at no load = 101'G.

1 i

r i

Secondary Current, I2.

Copper Losses in Watts.

Total Secondary Drop in volts

Primary Watts.

Power-Factor,

F=w;

Primary,

Ij2x5-95.

Secondary, I2*x 0-0108.

1

True Power = W.

Apparent Power =Wj.

0-050

0

0

0

0

0

0

95

120

0-79

o-ioo

1-00

0-042

0

0

0

01

205

240

0-85

0-140

1-98

0-083

O'l

0

0

0-2

306

336

0-91

0-180

2-94

0-122

0-2

01

0

0-2

401

432

0-93

0-218

3-87

0-161

0-3

0-2

0

0-3

493

523

0-94

0-250

4-79

0-199

0-4

0-2

1

0-3

597

600

0-99

0-382

8-00

0-333

0-9

0-7

2

0-3

920

917

1-00

• 0-472

10-15

0-423

1-3

1-1

2

0-6

1,139

1,133

1-00

0-580

13-07

0-545

2-0

1-8

4

0-7

1,440

1,392

1-03

0-800

18-00

0-750

3-8

3-5

7

0-9

1,930

1.920

1-00

0-880

19-90

0-830

4-6

4-3

9

0-9

2,118

2,112

1-00

0-960

21-93

0-914

5-5

5-2

11

1-0

2,330

2,304

1-01

1-080

24-74

1-031

6-9

6-6

14

1-0

2,609

2,592

1-01

1-285

29-66

1-238

98

9-5

19

1-0

3,096

3,085

1-00

1-610

37-20

1-550

15-4

14-9

30

1-2

3,870

3,864

1-00

1-810

42-00

1-750

19-5

19-0

39

1-5

4,324

4,344

0-99

2-002

46-65

1-945

23-5

23-5

47

1-7

4,792

4,805

1-00

2-160

50-40

2-100

23-7

27-5

55

1-8

5,174

5,184

1-00

2-240

52-16

2-171

29-8

29-5

59

2-0

5,422

5,376

1-01

2-383

55-60

2-320

33-9

33-5

67

2-1

5,702

5,719

1-00

2-478

57-68

2-404

36-5

36-0

73

2-2

5,885

5,947

0-99

.2-550 2-633

59-32 61-32

2-474 2-560

38-7 41-2

38-1 40-6

77 82

2-1 2-3

6,041 6,271

6,120 6,319

0-99 099

2-672

62-16 ! 2-594

42-5

41-8

84

2-2

6,344

6,413

0-99

2-700 2-750 2-775

63-00 64-00

64-74

2-623 2-665 2-700

43-3 45-0 45-8

42-9 44-2 45-3

86 89 91

2-3 2-3 2-4

6,426 6,522 6,598

6,480 6,600 6,660

0'99 0-99 1-00

570 THE INDUCTION COIL AND TRANSFORMER..

This may best be illustrated by giving the figures of test of two transformers, one of the closed-circuit type (Westinghouse) and one of the open-circuit type (Swinburne) (see Tables C and D). It will be seen that a very small loading of the closed-circuit type suffices to bring the power factor up to unity.

Hence it follows that for closed- circuit transformers the apparent power given to the transformer is equal to the real power at and beyond about one-tenth of full load. In Fig. 201 are shown three curves illustrating the gradual rise of the power factor towards unity in the case of three types of transformer. In the case of an open-circuit transformer at no stage of the load is the true power taken up by the transformer identical in value with the apparent power given to the transformer.

Table D. — Test of a Swinburne " Hedgehog " Transformer. Primary volts, 2,400 (kept constant). Secondary volts at no load = 102 '00.

1

Copper Losses in Watts. ^ Primary Watts.

.

L

I|

m

•?'»

r£

23

I!

4

rr^ lc

CO""

i-

If

?*,K

i

«>O

|x

| X

J>

3s

§ u

Ii

i *

1

£pn

£^

HQ

H

«l

£

0-756

0

0

13-7

0

14

0

121

1,816

0-07

0-761

1-02

0-042

14-0

o-i

14

o-i

228

1,829 0-13

0-786

2-98

0-124

14-9

0-5

15

0-2

420

1,886

0-22

0-811

4-84

0-202

15-8

1-2

17

0-4

621 1,948

0-32

0-829

6-00

0-250

16-5

18

18

0-6

730 : 1,988

0-37

0-862

8-00

0-333

17-8

33

21

0-8

943 i 2,067

0-46

0-911

10-00

0-417

19-9

5-1

25

1-0

1,152 i 2,188

0-53

0-960

12-00

0-500

22-6

73

30

1-2

1,353 2,301

0-59

1-013

14-00

0-584

24-7

10 -C

35

1-3

1,538 2,432

0-53

1-066

15-88

0-663

27-2

12-9

40

1.5

1,746 2,559

0-68

1-133

17-89

0-746

30-9

163

47

1-7

1,932 ; 2,720

0-71

1-197

19-80

0-825

34-5

20-0

55

1-9

2,129 • 2,873

0-74

1-260

21-63

0-902

38-2

24-0

62

2-1

2,320 3,022

0-77

1-321

23-58

0-983

42-0

28-3

70

2-4

2,510

3,172

0-79

1-395

25-46

1-C60

46-6

33-1

80

2-7

2,706

3,350

0-81

1-426

26-38

1-098

48-9

35-4

84

2-9

2,829

3,422

0-83

1-460

27-28

1-136

51-2

380

89

3-0

2,890

3,501

0-83

1-498

28-21

1-175

54-0

40-8

95

3-0

2,993 i 3,596

0-83.

1-529

29-19

1-215

56-1

43-5

100

3-2

3,042 3,666

0-83

1-567 | 30-33

1-262

59-0

46-9

106

3-3

3,163

3,761

0-84

THE INDUCTION COIL AND TRANSFORMER- 571

In Fig. 201 the three curves show the progress of increase of the power-factor as the load on the secondary circuit is progressively increased. The upper curve represents the; growth of power factor (F) for a 6,500-watt Westinghouse transformer. Beginning at 0-8, it rises up to unity at about one-tenth of full load. Hence at and after this load the apparent watts are the same as the true watts, and the real power taken up in the transformer is quite accurately given by the product of the primary terminal pressure and the primary current, mean-square ( ^/mean'2) values being under-

FIG. 201.— Relation of Power Factor to Secondary Output.

stood. For an open magnetic circuit transformer like the "Hedgehog" the case is quite different. The power factor begins at a value of 0-08 or 0-06, and it never rises up above 0-8. Hence at no stage of the load is the real power taken up by the transformer equal to the " apparent watts." A transformer like the 4,000-watt Kapp appears to occupy an intermediate position, and although it has a medium power factor to start with, its power factor rises up to unity at about half-load. The importance of this fact in alternate- current station working is very great. It shows us, if we have a station wholly supplied with transformers of the type of Mordey, Westinghouse, Thomson-Houston, Ferranti, &c., that the apparent power supplied to the transformers is equal to the real power at any hour when all the transformers are more than one- tenth loaded.

572 THE INDUCTION COIL AND TRANSFORMER.

The reciprocal of the power factor of a transformer on open secondary circuit is a measure of the reluctance of the mag- netic circuit of the transformer. In the case of a transformer with an air-iron magnetic circuit (open-circuit type) the reluc- tance of the iron circuit is large and the reciprocal of the power factor large also, and may be a number approximating to 16 or 17. In the case of a closed iron circuit transformer like the Mordey transformer, with very short magnetic circuit and very small reluctance, the reciprocal of the power factor is very small, and will be a number approximating to 1-2 to 1-4. The introduction of any bad magnetic joint into the iron circuit, or the employment of iron of small permeability, im- mediately decreases the magnitude of the power factor of that transformer. Any joint or break in the magnetic circuit accordingly increases the value of the reciprocal of the power factor, and although this alone will not affect the total core loss in the transformer, it is an indication of the increased reluctance of the magnetic circuit. The advantage of a large power factor is that it involves a small value of the magnetising current of the transformer. In the case of an alternating current station large magnetising current involves additional waste of power in the passage of this current through the distributing mains. This point will be discussed at greater length in connection with the subject of alternating current distribution.

§ 8. Magnetic Leakage and Secondary Drop. — If a trans- former has the mean-square value of the potential difference of its primary terminals kept perfectly constant, whilst at the same time secondary currents of various magnitudes are taken from its secondary coil by altering the resistance of the external secondary circuit, we find that the mean-square value of the potential difference between the secondary terminals of the transformer changes with every change in the secondary load.

The secondary terminal potential difference (S.P.D.) becomes less as the secondary current and load increases. The diffe- rence between the secondary terminal potential difference at no load and at any load is called the secondary drop of the transformer due to that load.

THE INDUCTION COIL AND TRANSFORMER. 573

We may represent the variation of secondary drop with secondary load hy a diagram as follows : Let a horizontal line be taken on which are set off distances representing the fractions of the full secondary load, and let vertical ordinates set up at these points represent the value of the secondary potential differences at these loads. For convenience sake we may make these ordinates represent the magnitude of the secondary terminal potential difference diminished by a certain constant amount which is less than the least difference found with full load. For instance, suppose the secondary terminal potential difference at no load is 100 volts and at full load is 97 volts, we may make the vertical ordinates represent the terminal potential difference minus 90 volts. The curve

fir

94O 650 1300 1950 2600 3250 3900 4550 5200 5850 650Q-

Output in Secondary Watts.

a b is the horizontal line throngh a; Carve ac is the Curve of Drop due to secondary res'stance ; Curve a d, that due to primary resistance ; and Curve ae w the Curve of total Drop.

FIG. 202.— Secondary Drop Curves of 6,500- watt "Westinghouse Transformer.

defined, as in Fig. 202, by the extremities of these ordinates is called the secondary terminal volt curve, and it shows in a graphical manner the gradually diminishing secondary terminal potential difference as the transformer is loaded up. This " secondary drop " arises from two causes. The first is the loss of potential due to resistance, and the second is the loss of secondary potential due to magnetic leakage. Let the resistance of the secondary coil of the transformer be represented by E2, and the secondary current (mean-square value) be represented by (I2). Then E2(^) is the loss of voltage due to secondary resistance. If the primary terminal potential difference is kept constant, then,

574 THE INDUCTION COIL AND TBANSFOBMEB.

•over and above the loss of secondary voltage due to the resistance of the internal secondary circuit, there is a portion of the secondary drop which is due to loss of voltage by the resistance of the primary circuit, and, in addition to this, the loss above mentioned, which is due to magnetic leakage. Furthermore, the secondary drop is to a considerable extent dependent, as will be explained presently, upon the form of the curve of primary terminal potential difference. Hence the difference between the potential difference of the secondary terminals of the transformer at no load and full load, primary potential difference being constant, is dependent on four things, viz., upon —

(1) The resistance of the primary circuit ;

(2) The resistance of the secondary circuit ;

(3) The magnetic leakage of the transformer as affected by,

(a) Its construction.

(6) The form of the curve of primary terminal poten- tial difference.

The effect called the magnetic leakage in a transformer may be generally described as follows : The primary current creates in the iron core a certain total induction, or in usual language creates a certain number of lines of induction in the core which are linked with the primary circuit. The mag- netising effect of the secondary current is at any instant opposed to that of the primary, and hence creates an induction in the core in an opposite direction. The resultant, or actual induction in the core at any place is due to the difference of the opposed magnetising forces acting on the core. When the transformer has its secondary circuit open the magnetic induction in the core is that due to the primary current only, which is then generally called the magnetising current. When the secondary circuit is closed and a secondary current produced, the rise of induction in that part of the core enveloped by the secondary circuit is delayed, and its maximum value is reduced. The simplest way in which the effect of increasing the secondary current of the transformer can be regarded is as follows : Let us denote by the letter Z: the maximum value of the total magnetic induction in the core which would be produced by the primary current if it acted alone, and by Z2 the same due to the secondary current, these values being the inductions just within that part of the core enveloped by

THE INDUCTION COIL AND TEANSFOEMEE. 575

the primary and secondary coils respectively. The whole of the induction Z1 which is linked with the primary coil turns is not, however, linked with the secondary. Let a fraction, say ft Z1} of this primary induction escape linkage with the secon- dary coil, and a similar fraction, say ft Z2, of the secondary induction will escape linkage with the primary coil. Then the total induction linked with the primary coil is Zx - Z2 (1 - ft), because the induction caused by the primary current is opposed in direction to the induction caused by the secondary current, and the inductions, like the two currents, are opposite in phase and reach their maxima nearly coincidently. Also, for the same reasons, the total induction linked with the secondary circuit is

ft is called the coefficient of leakage.

The value of the total induction linked with the primary circuit is therefore the product of the number of primary turns Nj. and the resultant induction Z1-Z.,(l-ft), and, similarly, the value of ths total induction linked with the secondary circuit is given by the product of the number of secondary turns N2 and the resultant induction Zx (I- ft)- Z2. Hence we have the relation,

The total linkage of primary circuits

and induction traversing it I _ N: {Zl -Z.2(l -ft)} _ rp The total linkage of secondary | N2{Za (1 - ft) - Z2f circuit and induction traversing it J

It will be shown presently that this fraction T represents the ratio of the mean-square value of the primary terminal potential difference to that of the secondary terminal potential difference.

This ratio, which is denoted by T, is called the transforma- tion ratio of the transformer. Since the difference between Z2 and Z2 remains nearly constant as Z1 and Z2 increase, it is easily seen that the transformation ratio increases as Zl and Z2 increase, subject to the condition that Za— Z2is nearly constant at all loads.

Hence, if the mean-square value of the primary electro- motive force is kept constant, that of the secondary potential

576 THE INDUCTION COIL AND TRANSFORMER.

difference decreases as the currents, and therefore the inductions, in the core increase, and this effect is called the "secondary drop."