inasmuch as there is as yet no entirely successful method of automatic
voltage regulation on very large units; and the less hand regulation
the better. Moreover, the design which secures this result also
tends to secure stability of wave form in the electromotive force, a
matter of even greater importance. There has been much discussion
as to the best wave form for use on alternating circuits, it having
been conclusively shown that for a given fundamental frequency
the sinusoidal wave does not give the most economical use of iron
in the transformers. For transmission work, however, particularly
over long lines, this is a matter of inconceivably small importance
compared with the stability and the freedom from troubles from
higher harmonics that result from the use of a wave as nearly sinusoidal
as can possibly be obtained. In every alternating circuit
the odd harmonics are considerably in evidence in the electromotive
force, either produced by the structure of the generator or introduced
by the transformers and other apparatus. These are of no particular
moment in work upon a small scale, but in transmission on a large
scale to long distances, or especially through underground cables,
they are, as will be seen in the consideration of the transmission line
itself, a serious menace. Inasmuch as the periodicity of an alternating
circuit must be maintained sensibly constant for successful
operation, great care is usually exercised to secure such governing
of the prime movers as will give constant speed at the generators.
This can now be obtained, in all ordinary circumstances, by several
forms of sensitive hydraulic governors which are now in use. The matter
Of absolute periodicity has not yet settled itself into any final form.
American practice is based largely upon 60 cycles per second, which
is probably as high a frequency as can be advantageously employed.
Indeed, even this leads to some embarrassment in securing good
motors of moderate rotative speed, and the tendency of the frequency
is rather downward than upward. An inferior limit is set by the
general desirability of o erating incandescent lamps off the transmission
circuits. For this purpose the frequency should be held
above 30 cycles per second; below this point, flickering of the lamps
becomes progressively more serious, especially with lamps having
the very slender metallic filaments now commonly employed—so
serious, indeed, as practically to prohibit their successful use—and
plants installed for such low frequencies are generally confined
to motor practice, or to the use of synchronous converters, which are
somewhat easier to build in large units at low than at high periodicities.
Occasional plants for railway and heavy motor service operate
at as low as 15 ~, and more at 25 ~. Nearly all the general work
of power transmission, however, is carried on between 30 and 60 ~.
The inferior limit at which it is possible successfully to operate
alternating arc lamps is about 40 ~; and if these are to be an important
feature in transmission systems the indications are that practice
will tend towards a periodicity above 40 ~, at which all the accessory
apparatus can be successfully operated. European practice is
based generally upon a frequency of 50 ~, which admirably meets
average conditions of distribution.
Transmission Lines.—Power transmission lines differ from those used for general electric distribution principally in the use of higher voltage and in the precautions entailed thereby. The economic principles of design are precisely the same here as elsewhere, save that the conductors vary less in diameter and far more in length. Inasmuch as transmission systems are frequently installed prior to the existence of a well-developed distribution system the conditions of load and the market for the power transmitted can seldom be predicted accurately; consequently, the cases are very rare in which Kelvin's law can be applied with any advantage; and as it is at best confined to determining the most economical conditions at a particular epoch this law is probably of less use in power transmission than in any other branch of electric distribution. A superior limit is set to the permissible loss of energy in the line by the difficulty attending regulation for constant potential in case the line loss is considerable. The inferior limit is usually set by the undesirability of too large an investment in copper, and lines are usually laid out from the standpoint of regulation rather than from any other. In ordinary practice it seldom proves advantageous to allow more than 15% loss in the line even under extreme conditions, and the cases are few in which less than 5% loss is advisable. These few cases comprise those in which the demand for power notably overruns the supply as limited by the maximum power available at the generating station, and also the few cases in which a loss rea ter than 5% would indicate the use of a line wire too small iom a mechanical standpoint. It is not advisable to attempt to construct long lines of wire smaller than No. 2 American wire-gauge (-257 in. diameter), although occasionally wire as small as No. 4 (°204 in. diameter) may safely be employed. Smaller diameter than this involves considerable added difficulty of insulation in lines operated at voltages in excess of about 50,000. The vast majority of transmission lines are composed of overhead conductors. In rare instances underground cables are used. In single-phase work these are preferably of concentric form, which, however, gets too complicated in the three-phase lines generally employed to secure economy in copper; for the latter, triplicate cables, lead sheathed, laid in glazed earthenware ducts, seem to give the best results. On account of the cost and the difficulty of repair of such lines they are not extensively used, and cables have not yet been produced for the extremely high voltages desirable in some very long circuits, although they are readily obtainable for voltages up to 30,000 or 40,000. As to the material of the conductors, copper is almost universally used. For very long spans, however, bronze wire of high tensile strength is occasionally employed as a substitute for copper wire, and more rarely steel wire; aluminium, too, is beginning to come into use for general line work. Bronze of high tensile strength (say 80,000 to 100,000 lb per square inch) has unfortunately less than half the conductivity of copper; and unless spans of many hundred feet are to be attempted it is better to use hard-drawn copper, which gives a tensile strength of from 60,000 to 65,000 lb to the square inch, with a reduction in conductivity of only 3 to 4%. As to aluminium, this metal has a tensile strength slightly less than that of annealed copper, a conductivity about 60% that of copper, and for equal conductivity is almost exactly one-half the weight. Mechanically, aluminium is somewhat inferior to copper, as its coefficient of expansion with temperature is 50% greater; and its elastic limit is very low, the metal tending to take a permanent set under comparatively light tension, and being seriously affected at less than half its ultimate tensile strength. Joints in aluminium wire are difficult to make, since the present methods of soldering are little better than cementing the metal with the flux; in practice the joints are purely mechanical, being usually made by means of tight-fitting sleeves forced into Contact with the wire. With suitable caution in stringing, aluminium lines can be successfully used, and are likely to serve as a useful defence against increase in the price of copper. Whatever the material, most important lines are now built of stranded cable, sometimes with a hemp core to give added flexibility.
With respect to line construction the introduction of high voltages, say 40,000 and upwards, has made a radical change in the situation. The earlier transmission lines were for rather low voltages, seldom above 10,000. Insulation was extremely easy, and the transmission of any considerable amount of power implied heavy or numerous conductors. The line construction therefore followed rather closely the precedents set in telegraph and telephone construction and in low tension electric light service. In American practice the lines were usually of simple wooden poles set 40 to 50 to the mile, and carrying wooden cross-arms furnished with wooden ins carrying insulators of glass or porcelain. The poles were little larger than those used in telegraph lines, a favourite size being a 40-ft. pole about 8 in. in diameter at the top and 15 in. at the butt, set 6 to 7 ft. in the earth. Such poles commonly bore two cross arms, the lower and longer carrying 4 pins, and the shorter upper arm 2 pins, so disposed that the upper pin on each side of the pole would form with the nearer .pins below an equilateral triangle 18 to 24 in. on the side. The poles therefore carried two three phase circuits one on either side, one or both circuits being spiralled. In European practice iron poles have been more frequently used, again following rather closely the model of telegraph practice, with similar spacing of poles, and with insulators, usually of porcelain, somewhat enlarged and improved over telegraph and electric light insulators, and spaced somewhat more widely. As between wooden and steel poles, the latter are of course the more durable and much the more costly. The difference in cost depends largely on the locality, and ultimately on the life of the wooden poles. This ranges from two or three up to ten or fifteen years, the latter figures only in favourable soils and when the lower ends of the poles have been thoroughly treated with some preservative. Under such conditions wood is often ultimately the cheaper material.
The use of very high voltages results in, for all moderate powers, the use of small and consequently light wires and in the necessity for heavy, large and costly insulators. For security against leakage and failure it becomes desirable to reduce the numer of insulation points, and with the resulting lengthening of span to design the line as a mechanical structure. A transmission line is subject to three sets of stresses. The most considerable are those due to the longitudinal pull of the catenary depending on the weight and tension of the wires. Under ordinary conditions these strains are balanced and come into play only when there is breakage of one or more wires and consequent unbalancing. It has been the common practice to give the poles sufficient strength to withstand this pull without failing. The maximum amount of the pull may be safely taken at the sum of the elastic limits of the wires, since it is unsafe so to design the spans as to be subject to larger stresses. There is also lateral stress on a line due to wind acting upon the poles and wires, the latter amounting to little 'unless their diameter is increased by a coating of sleet, a condition which gives maximum stresses on the line. Wind then tends to push the line over, and it also increases the longitudinal stresses, being added geometrically to the catenary stress. The actual possibility of wind pressure is very generally over-estimated, and has resulted in much needlessly costly construction. In the first place, save for actual tornadoes, for which no estimates can be given, even the highest winds at the level of any ordinary transmission line are of modest actual velocity. It is probable that no transmission line save on mountain peaks at a very high elevation is ever exposed to an actual wind velocity of 75 m. per hour, and only at intervals of years is a velocity of even 60 m. reached near the ground level. Further, the maximum wind velocities are practically never reached at very low temperatures when the line is under its maximum catenary stress, and sleet
