The above machine was directly connected to a 4-pole, 3-phase, 6000-volt, 25-cycle (hence 750 r.p.m) synchronous motor with a stationary armature. The efficiency was 734 per cent at 80 k.w. output, 81 at 120 k.w., 87 per cent at 160 k.w., and 91 per cent at 200 k.w. or full load. The power factor was practically 100 per cent at all these loads, showing the balancing of the lagging and leading currents as already pointed out. The wave forms of E.M.F. and current approximated closely to the simple sine curve. The efficiencies stated above signify the true watt output divided by the true watt imput, the latter including the true watts consumed by the motor.

It has just been

Transforming from Two- to Three-Phase. explained how the frequency changes may be employed to transform currents from two- to three-phase, or vice versa. This requires, however, two rather expensive machines demanding attention, so that when no change in frequency is desired, it is more economical to transform from two- to three-phase, or the converse, by means of simple static transformers. A method of this kind, devised by Mr. C. F. Scott,* is illustrated in Figs. 176-178. It

involves the use of two transformers, one wound for a ratio of transformation of say 1000: 100, and the other for a ratio of 1000 86.7. In Fig. 176, HI represents the primary and AB the secondary of the first transformer, KN and CJ being respectively the primary and secondary of the second transformer. The two primaries are fed from the two-phase circuit DE and FG, and one terminal of the secondary CJ is connected to the middle point of the secondary AB. The three-phrase circuit is connected to the points AB and C. In the diagram of potentials (Fig. 177) it is evident that AC and CB will each be equal to AB, so that ABC

*Electric World, March 17 and 24, 1894.

will be an equilateral triangle when CJ: AB:: √3:2::86.7: 100, hence the three secondary E.M.F's. represented by AB, BC and CA, are equal in value and differ by 120° in phase. This is the proper condition for supplying a three-phase circuit connected to the points A, B and C. In practice, especially in small transformers, it is a sufficiently close approximation if the E.M.F. of the secondary CJ is 90 instead of 86.7 per cent of AB.

This method is often employed when two-phase energy is produced by the generators (see Fig. 178) and it is desired to transmit some or all of it to a considerable distance. By transformation from two- to three-phase, a saving of twenty-five per cent in copper is secured in the transmitting conductors A, B, C. At the receiving station the energy may be distributed in three-phase form or may be transformed back again into two-phase current as indicated in Fig. 178. The large generators at Niagara are of the

two-phase type, and some of the energy produced by them is transformed in the above-described manner, so that it may be transmitted in three-phase form.

Transforming from Single to Polyphase. It is often very desirable to accomplish this result when it is required to operate motors from single-phase circuits, but the subject belongs to electric power more than to electric lighting. A method of this sort, invented by Mr. C. S. Bradley,* consists in causing, by means of a condenser, a lead of current in one branch of a circuit, and in combining this with lagging currents in another branch so as to produce a threephase current in the secondary circuit.

Size and Location of Transformers. Most systems of alternating current distribution employ transformers, and it is of great importance to exercise special care in deciding upon their sizes and locations. The constant core loss results in the course of a year

* Phasing Transformers Trans. Amer. Inst. Elec. Eng., September, 1895.

in a waste of a large amount of energy, and every effort should be made to reduce this to a minimum. When transformers were first introduced, it was customary to use a large number of them in small sizes; but it was soon found that the core loss consumed too great a fraction of the total output of the station, often amounting to 25 and sometimes to 50 per cent. This was partly owing to the fact that transformers at that time were not as well designed and constructed as at present, but it was due also to the custom of using too many small sizes. This is made evident by inspecting the table on page 184, which shows that a 600 watt, 125-cycle transformer has a core loss of 20 watts, while one of 50,000 watt

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capacity, or 83.3 times as great, has a core loss of 354 watts, which is only 17.7 times as much. In the first case the loss is 3.3 per cent, and in the second it is but .7 per cent, or about one-fifth as large. If the comparison be made between the 1 k.w. and the 10 k.w. transformers, it is found that the former has a core loss of 2.5 per cent (25 watts) and the latter of 1.08 per cent; these being the limits of sizes ordinarily used in electric lighting.

The actual case of a district in a small town is represented in Fig. 179. Originally there were installed 25 small transformers (indicated by dots and numbers) having a combined capacity of 340 lamps of 16 c.p. and a core loss of 1664 watts. These were after

wards replaced by two larger transformers (indicated by black rectangles), which had only 238 watts core loss, or about oneseventh as much, the saving being 1426 watts. If the first plant operated for 24 hours per day the core loss would have aggregated 40 k.w. hours for each day in the year, and probably this was greater than the useful energy consumed in the lamps. This may be a rather extreme case; but there were many others equally bad, and at one time the average practice was little better. Besides the advantage of lower percentage of losses in large transformers, a gain is made in the fact that the total required capacity is less. If, for example, a small transformer is installed for each house, it is necessary that its size should be sufficient to supply the maximum number of lights that will ever be used in that house at one time. Ordinarily, in fact for fully 99 per cent of the year, the number of lamps burning will be much less than this maximum, hence the transformer and its core loss are far out of proportion to the average useful current. On the other hand, a larger transformer, supplying ten houses for example, need not have ten times the capacity, because it is practically impossible that all of the houses will burn the maximum number of lights at the same time. In short, one 7.5 k.w. transformer will safely take the place of ten transformers of 1 k.w. each; and the former would have a core loss of only 85 watts compared with 10 x 25 = 250 watts for the latter.

A further saving may be effected by having sub-stations in which the transformers are concentrated or " banked," and connected in parallel. During the hours when the load is light, only one transformer need be operated, the primary circuits of all the others being open; but when the load increases transformers are added as required, thus the core loss is kept in reasonable proportion to the useful energy.

CHAPTER XI.

CALCULATION OF ALTERNATING CURRENT CIRCUITS.

THE properties of electrical conductors were given in Chapter I., which included a general discussion of economy in their design. The principles there laid down apply to alternating as well as to direct current conductors, but additional factors enter in connection with the former. In the long-distance transmission of power, these questions are of prime consequence; but in electric lighting the distances are ordinarily shorter, so that the problem is not so difficult or important. Hence it will not be necessary to consider the matter in detail or at great length in this work.

Choice of Frequency. One of the first points to be decided in designing an alternating current system is the best frequency to employ. Those generally used in the United States are 25, 40, 60, 125, and 133 cycles per second. It would be well if the Standardization Report of the American Institute of Electrical Engineers were followed and three standard frequencies of 30, 60, and 120 became generally adopted. These would cover almost all cases that arise, and being simple multiples of each other would facilitate the design and construction of apparatus in regard to number of poles, windings, etc. In other countries many different frequencies are employed, 100 cycles being a common value in England and on the Continent. Sixty cycles or less is considered to be "low frequency," and above that is called "high frequency," but anything between 60 and 120 is rarely used in America. frequency of 133 cycles was originally adopted when the alternating current was introduced for electric lighting, and is still used in many plants, especially those installed by the Westinghouse Company. A standard of 125 cycles is adopted for electric lighting apparatus by the General Electric Company. These high frequencies possess the advantage that the size and cost of transformers are less when they are selected. At the present time a 10 k.w. trans

A