Figs. 2,876 to 2,879.—How to connect instruments for power measurement. There are several ways of connecting an ammeter, voltmeter and wattmeter in the circuit for the measurement of power. A few of the methods are discussed below. With some of the connections it is necessary to correct the readings of the wattmeter for the losses in the coil, or coils, of the wattmeter, or for losses in ammeter or voltmeter. This is necessary since the instruments may be so connected that the wattmeter not only measures the load but includes in its indications some of the instrument losses. If the load measured be small, or considerable accuracy is required, these instrument losses may be calculated as follows: Loss in pressure coils is E2 ÷ R, in which E is the voltage at the terminals of the pressure coil and R is the resistance. Loss in current coil is I2 R in which I is the current flowing and R the resistance of the current coil. In general let Ev = voltage across terminals of the voltmeter; Ew = voltage across the terminals of the pressure coil of the wattmeter; Iw = current through current coil of wattmeter; Ia = current through current coil of ammeter; Rv = resistance of pressure coil of voltmeter; Rw = resistance of pressure coil of wattmeter; R1w = resistance of current coil of wattmeter; Ra = resistance of current coil of ammeter. Then the losses in the various coils will be as follows: E2v ÷ Rv = loss in pressure coil of voltmeter. E2w ÷ Rw = loss in pressure coil of wattmeter. I2w ÷ Rv = loss in current coil of wattmeter. I2aRa = loss in current coil of ammeter. If connection be made as in fig. 2,876, the correct power of the circuit will be the wattmeter reading W-(E2v ÷ Rv + E2w ÷ Rw) in which Ev = Ew. In fig. 2,877, the power is W-E2w ÷ Rw. In fig. 2,878, the power is W-I2wR1w, or the correct power is the wattmeter reading minus the loss in the current coil of the wattmeter. In fig. 2,879, the power is W-(E2w ÷ Rw + I2aRa)· The usual method of connection is either as in fig. 2,876 or fig. 2,877. In either case the current reading is that of the load plus the currents in the pressure coils of the voltmeter and wattmeter. Unless the current being measured, however, is very small, or extreme accuracy is desired, it is unnecessary to correct ammeter readings. In fig. 2,877 a small error is introduced due to the fact that the actual voltage applied to the load is that given by the voltmeter minus the small drop in voltage through the current coil of the wattmeter. If an accurate measure of the current in connection with the power consumed by the load be required, the connections shown in fig. 2,879 are used, and if extreme accuracy is required, the wattmeter reading is reduced by the losses in the ammeter and in the pressure coil of the wattmeter. The loss in the pressure coil of a wattmeter or voltmeter may be as high as 12 or 15 watts at 220 volts. The loss in the current coil of a wattmeter with 10 amperes flowing may be 6 or 8 watts. It can be easily seen that if the core or copper losses of small transformers are being measured, it is quite necessary to correct the wattmeter readings, for the instrument losses. In measuring the losses of a 25 or 50 H.P. induction motor, the instrument losses may be neglected. A careful study of the above will show when it becomes necessary to correct for instrument losses and the method of making these corrections. Connections are seldom used which make it necessary to correct for the losses in the current coils of either ammeter or wattmeter, as the losses vary with the change in the current. On the other hand, the voltages generally used are fairly constant at 110 or 220, and when the losses of the pressure coils at these voltages have once been calculated, the necessary instrument correction can be readily made.

On a three phase system the transformers should be joined in delta connection, as a considerable advantage is thereby gained over the star connection, in that should one of the transformers become defective, the remaining two will carry the load without change except more or less additional heating. Between the transformers and rotary converter the circuits should be as short and simple as possible, switches, fuses, and other instruments being entirely excluded. The direct current from the converter is led to the direct current switchboard, and from there distributed to the feeder circuits.

Power factor True watts Error Error of indication
in per cent
of true value
1. 1,000 .3 0.03
.99007.6 0.85
.880010.5 1.31
.770012.5 1.78
.660013.9 2.32
.550015.1 3.02
.440015.9 3.98
.330016.6 5.54
.220017.1 8.55
.110017.3 17.30

NOTE.—In the iron vane type instrument when used as a wattmeter, the current of the series coil always remains in perfect phase with the current of the circuit, provided series transformers are not introduced. The error, then, is entirely due to the lag of the current in the pressure coil, and this error in high power factor is exceedingly small, increasing as the power factor decreases. In the above table it should be noted that the value of the error as distinguished from the per cent. of error, instead of indefinitely increasing as the power factor diminishes, rapidly attains a maximum value which is less than 2 per cent. of the power delivered under the same current and without inductance. It should also be noted that the above tabulation is on the assumption of a lag of 1 degree in the pressure coil. The actual lag in Wagner instruments for instance, is approximately .085 of a degree, and the error due to the lag of the pressure coil in Wagner instruments is, therefore, proportionally reduced from the figures shown in the above tabulation.

Ques. In large sub-stations containing several rotary converters how are they operated?

Ans. Frequently they are installed to receive their respective currents from the same set of bus bars; that is, they may be operated as alternating current motors in parallel. They are also frequently operated independently from single bus bars, but very seldom in series with each other.