Now let A1 A2 A3 and a, a, a, be the mean square values of the currents flowing in the mains and branches respectively for Fig. 95 (b and c), also V1 V2 V ̧ and v1 V2 V the same values of voltages across the mains and branches respectively for Fig. 95 (b and c); then if the mains are equally loaded we have--

1

2

=3

2 3

2

A1 = A, A,, and .. a1 = a, a, and V1 = V2 = V ̧,

1

whence A1 = 2α, sin. 60° = √√3a,, and ... A = √√3a, since the mains are equally loaded and the load non-inductive.

3

1

=

For Fig. 95 (a and c) we have, if A1 = A, A, and E1 = E2 = E3, that A1 =α1, A=ɑ, and A ̧=ɑg, and since V will now lag 30° in phase behind v, in each main and the corresponding branch circuit, we have V=2v sin. 60° = √3v, providing the load is noninductive.

CIRCUITS EQUALLY LOADED AND NON-INDUCTIVE.-Here if each main carries the same current A, and if the pressure between each pair of mains V, then the True Power absorbed in a noninductive load, Fig. (b)

True Power absorbed in a non-inductive load, Fig. (a)

W=3ar=3A

W=

100 × current of A + (w1 + w2−λ).

If, however, the load is inductive, then if 6= angle of phase difference between voltage and current, we have, as in the case of single-phase work, that for equal load the True Power absorbed in the inductive load, Figs. (a) or (b)

W= √3AV cos. Watts.

This latter can best be obtained by means of the non-inductive

Wattmeter for each of the two following conditions met with in practice.

3

CIRCUITS EQUALLY LOADED AND INDUCTIVE-ONE WATTMETER ONLY needed to obtain the true power. Assuming this to be W1, Fig. 95 (ca) or (cb), then with the thick coil in any main (A ̧ say, as shown) note the Wattmeter reading (w1) with its fine coil on to main A1, and the reading (w) with it on to main A, immediately after, then the True Power absorbed in the equally loaded inductive circuit W=w] + W2•

7

CIRCUITS UNEQUALLY LOADED AND INDUCTIVE-Two WATTMETERS ONLY needed to obtain the true power. Assuming the Wattmeters to have their thick coils in any two mains, as shown in Fig. 95 c (a or b), then True Power absorbed W=W1+ W2

Hence, when merely the true power in Watts only is required in a three-phase circuit, whether of the star or mesh type, one or two Wattmeters are required according to whether the circuits are equally or unequally loaded respectively. Also when such a three-phase circuit is both equally loaded and non-inductive the true power in Watts is given by the product 3 x amps. in one main × volts. across any pair of mains.

Apparatus. Source of three-phase alternating current (E) and circuit of variable nature to experiment upon (a and b, Fig. 95). Two Wattmeters W1 and W2; three Siemens dynamometers or Parr direct reading dynamometer ammeters A12 A; three electrostatic or hot-wire voltmeters V1 V2 V3.

1

1

2

Note. It must be remembered that for any specific measurement, the foregoing rules, and the instruments they entail, can be at once used without reference to the following test, which is devised solely in order to prove these rules.

Observations.--(1) Connect up as in Fig. 95 (a and c), and adjust the instruments to zero, levelling them if necessary.

(2) With the load non-inductive and the circuits equally loaded, take the readings of all the instruments for five or six different loads, noting the Wattmeter reading when placing the fine coil of, say, W1 successively on to A, and A, mains at each load.

1

1

2

(3) With an inductive load and circuits equally loaded, take the readings of all the instruments for five or six loads, placing the fine coil of, say, W1 successively on to 4, and A, mains at each load and noting its reading at each. Tabulate your results as follows

1

Inferences. State very clearly all that can be inferred from your experimental results.

(115) Measurement of Power in Two-Phase Alternating Current Circuits.

Introduction.-Two distinct forms of circuits are met with in the distribution of electrical energy by means of two-phase alternating currents of electricity.

The first entails the use of four wires, forming two circuits completely independent of one another, one to each phase. Since this requires four wires it is usually employed in short distance transmissions.

The second entails the use of only three main wires, and is therefore more economical in first outlay of copper than the above. It will therefore be at once obvious that the measurement of power in two-phase alternating current circuits will be made in more than one way, depending on the form and nature of the circuit in question. We will now deal with such measurements in the case of each possible condition.

Two-PHASE CIRCUITS OF THE 4-WIRE FORM.

Here two cases are possible according to whether the circuits are carrying non-inductive loads, such as incandescent lamps, or inductive loads, such as two-phase motors or transformers, etc.

Non-inductive load. The product of the amperes and volts in each circuit, obtained in the usual way, when added together gives the true power delivered from the generator; and if the two circuits are equally loaded, twice the PRODUCT for one circuit gives the Total True Power.

Inductive load.-Owing to the lag in phase between the current and voltage in each circuit, two non-inductive Wattmeters are necessary, one in each circuit, connected up in the ordinary way

as in single-phase circuits. Then the Total True Power delivered sum of the two

by the generator Wattmeter readings.

If the two circuits are equally loaded, as would be the case when supplying such as two-phase motors, then twice the reading of one Wattmeter gives the Total True Power, and only one such instrument is then necessary.

Two-PHASE CIRCUITS OF THE 3-WIRE FORM.

Here also there are two or three cases depending on whether the circuits are inductive or otherwise.

Equally loaded non-inductive sections.—Total True Power absorbed twice the product of the current in one outer main and the voltage across the section.

=

=

Equally loaded inductive sections.-Total True Power absorbed twice the reading of a Wattmeter connected with its thick coil in series with either outer main, and its thin coil connected to the centre or larger main which is common to both outers. Unequally loaded inductive sections. -Total True Power absorbed sum of the two readings of the Wattmeters connected with their thick coils in the outers respectively, and their thin coils connected to the common centre wire AB as shown in Fig. 96. This last case would be the one met with when the circuit was partly a lighting and partly a power one, running two-phase

motors.

=

Where the reader may not be quite conversant with the preceding methods of measuring power in two-phase alternating current circuits, a most useful experiment will be to prove the above statements in much the same manner as was set forth in the preceding test on three-phase measurements of power, only three or four ammeters and voltmeters with the two Wattmeters W and W2 and the variable two-phase rheostat being required.

2

(116) Efficiency of Ordinary Single - Phase Alternating Current Transformers.

General Remarks.-Before considering actual methods of testing that most important electrical appliance, the single-phase static transformer, which has become of such vast importance in alternating current systems of distribution of electrical energy, some introductory remarks are considered desirable.

There are a great many different forms and ways of building the kind of transformer in question, but they all come under one or other of two main heads, namely

(a) Those with closed magnetic circuits in which the magnetic induction or lines of force are contained solely, or nearly so, in iron.

(b) Those with open magnetic circuits in which the lines of force run partly in the iron core of the transformer, and partly in the air through which they complete their path. This type, however, has now become practically obsolete. In either case (a and b) the iron core is surrounded by or wound with two distinct and separate coils of insulated copper wire termed the primary and secondary. In all cases the former is the coil connected to the source of supply, while the latter has induced in it an E.M.F. which supplies current to some separate circuit, usually at quite a different E.M.F. to that acting on the primary.

The primary may be either the high tension (pressure) coil or the low, according as to whether the transformer is used as a step-down or step-up appliance respectively. Hence to avoid confusion, the primary will always be that coil which is connected to the source of supply, whether this be high or low tension.

The measurements of current, voltage, and power in tests connected, not only with transformers, but also with alternating currents generally, must be made with instruments possessing practically no self-induction and containing no iron. The best results will be obtained when employing electrostatic, hot-wire, and dynamometer instruments, for such measure the mean sq. values of pressure and current and are independent of the variations of frequency. If a circuit supplied with alternating current