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INFLUENCE OF WAVE FORM ON THE RATE OF INTEGRATING

INDUCTION METERS.

By E. B. Rosa, M. G. Lloyd, and C. E. REID.

We give in this paper the results obtained with five integrating induction wattmeters, on which we have made a large number of tests, although further work remains to be done. These results may therefore be regarded as preliminary, illustrating the methods employed and the results obtained when changes are made in the wave form by altering the magnitude or phase of the harmonics present.

Two of the meters employed were sent to the Bureau of Standards for test by the makers. The others were meters which we happened to have in the laboratory when the tests were undertaken. The following is a list of the meters:

No. 1, Stanley (magnetic suspension type), 50 amperes.
No. 2, Stanley (magnetic suspension type), 50 amperes.
No. 3, Fort Wayne, type “K,” 50 amperes.
No. 4, General Electric (1902 House type), 25

am peres. No. 5, Siemens & Halske, 25 amperes. All the meters are made for 60 cycles, single phase. The first four are American instruments; the last is of German make. Each meter was tested at full load and at 110 volts, and at approximately unity power factor.

In order to determine the effect on the rate of an induction meter due to varying the wave form, it is necessary to eliminate carefully any effects due to variation in the temperature of the meter or changes in the frequency of current, or other alterations in the conditions of the meter or circuit. In most cases the effect of a moderate distortion of the wave is small, and unless all measurements are made with great care the effects looked for may be masked by other effects or by errors of measurement. The meters were tested alternately with current of sine wave form and with a distorted wave, the distortion being produced by adding a harmonic of three times the frequency

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Fig. 1. --Showing the resultant of combining the fundamental and harmonic of three times the

frequency and 25 per cent of the magnitude of the fundamental, giving first a peaked wave and second (when the phase of the harmonic is reversed) a flat or dimpled wave. Both fundamental and harmonic are of sine-wave form.

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FIG. 2.-Showing the resultant of a fundamental and a harmonic, as in fig. 1, except that the phase

of the harmonic has been shisted 30° by changing the coupling 5o.

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FIG. 3. Showing the resultant of a fundamental and a harmonic as in fig. 1, except that the phase

of the harmonic has been shifted 60°.

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FIG. 4.-Showing the resultant of a fundamental and a harmonic as in fig. 1, except that the phase of

the harmonic has been shifted 90° by changing the coupling 150. The wave form for “peak” and "flat" are here alike, except that the steeper side is in advance in the “peak” and the more gradual slope is in advance on the "fat." “Peak" and "flat" are conventional terms, indicating the phase of the harmonic. If the coupling were shifted 15° more, the “flat” curve would become peaked.

of the fundamental, varying both the amplitude and phase of this harmonic. This was done by means of an alternating current generating set of three machines, two alternators and a direct connected driving motor, one alternator having four poles and the other twelve. The current from each machine is very nearly of sine wave form, and tests were made of the meters alternately with the fundamental only, and with the harmonic added. Three different relative values and four different phases of the harmonic have been employed. The three values of the harmonic are 10 per cent, 25 per cent, and 50 per cent, respectively, of the value of the fundamental. For example, since E=E,+E?,, in the first case the addition of 11 volts of the harmonic to 110 volts of the fundamental gives a resultant of about 110.5 volts, the wave being more or less peaked than a sine wave, according to the phase of the harmonic. In the second case 108 volts of the fundamental plus 27 volts of the harmonic gives a resultant of 111.3 volts. (The voltage in each case was reduced to exactly 110 by resistance in series. This resultant is shown in figs. 1 to 4, where the 25 per cent harmonic is in different phase in each of the four cases. This difference is produced by shifting the coupling of one of the generators to the driving motor, 5°, 10°, or 15° in the coupling corresponding to 10°, 20°, or 30° in the wave of the fundamental, and to 30°, 60°, or 90° in the phase of the harmonic. A shift of 30° in the coupling corresponds to 180° in the phase of the harmonic, and is the same as reversing the phase by reversing the connections at the terminals of the higher frequency generator. The latter is of course the more convenient, and was the usual method of changing from what we call a flat to a peaked wave. The curves shown in figs. 1 to 4 have been frequently verified by drawing the resultant waves by means of a curve tracer. This not only verifies the wave form, but serves to insure against errors in the connections.

The current, voltage, and power factor, as well as the temperature and frequency, were maintained as nearly constant as possible during a set of runs. A standard wattmeter which was calibrated by direct currents using two potentiometers to measure simultaneously the current and the voltage, was read by a telescope and scale. By means of a carbon rheostat the deflection of this instrument was maintained accurately constant while carrying alternating current during a set of runs on the meters. The wattmeter is of the dynamometer type and astatic. The fixed coils are stranded and wound on wooden spools, and very little metal is used in the region of the coils. The movable coils have very slight inductance, and every precaution is taken to avoid errors due to eddy currents or wave form. The instrument, being

, LLOYD

carefully calibrated with direct current, is then correct for alternating current.

Table 1.-DETERMINATION OF THE TIMES OF REVOLUTION OF THE DI8KS OF THREE

METERS.

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1

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2

1.31

3

1.55 1.55 1. 65 1.61

1.68
1.57

1.61

1.32 1.37 1. 30

5

1. 63

6

1.64 1.52

1.54

7

1.30
1. 37

1.63

8

1. 60
1. 67

9

1.33
1.30
1.40

m. 8.
0 45.70

47.00
48. 31
49. 63
51.00
52. 30
53. 60
54.97
56. 30
57.60

59.00 1 25.60 2

5. 48

45. 35
3 25. 30

26. 60
27.90

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1 5.30

6.85 8. 40 10.05 11. 66 13.30 14.82 16. 45 18.05 19. 72

21.30 2 9.90

42. 10 3 14.32

46. 65
48. 20
49.82
51.41
53.00
54.61
66.22
57.90

59. 48 4 1.03

2. 62

12

1.66 1.65 1.60 1.55 48.25 32. 10 32. 10 32. 20 1. 65

0 45.96

47.56 49. 24 50.81 52.42 54. 05 55.59 57.25

58.90 1 0.50

2. 05

50.30 2 22. 40

54.50 3 26.70

28. 35 29.95 31.54 33. 10 34. 78 36. 38 38.00 39.60 41.19 42.80

48. 60
32. 20
32. 22
32. 33
1.55

13 14

26. 60 39.88 39.87

15

39.95
1.30
1.30

16

161.35 161.35 161.42 161. 36

1. 62

1.60

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160.74 160.79 160. 71 160. 73 160. 68 160. 73 160.79 160. 75

1.59 1.56 1. 68 1.60

1. 30
1.35
1.40

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159. 60 159. 60 159.59 159.57 159.55 159.65 159. 70 159. 66 159.65 159.75 159.68

29. 20 30.55 31.95 33. 30 34. 63 35. 95

21

161.34
161.31
161.40
161. 45
161. 43
161. 31
161.32

1. 61 1.68 1.58 1.55

22

1.62
1.60
1.59

1. 35 1.33 1.32 1.40 1.33

23

24 25

160.70
160. 69
160.75

1.59

1.61

37.35
38. 68

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DETERMINATION OF THE RATE OF THE METERS AND THE FREQUENCY OF

THE CURRENT. The rate of the meters was determined by means of a chronograph and chronometer, record being made at the end of every revolution of the disk or drum for the first ten revolutions at the beginning of a

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