ARTICLE 97. Current Transformation.-When the voltage (E. M. F.) of any current is raised or lowered, it is said to be transformed. As may be inferred from the origin and characteristics of continuous current, as briefly presented in Article 94, this type of current can be transformed only by means of moving apparatus. Continuous-current dynamos may be connected in series, in which case the voltage in the exterior circuit is the aggregate of the voltages of the D. C. dynamos thus connected; the only other process of transforming continuous current is by the agency of the motor generator mentioned in the previous article. Fig. 133 S Alternating-current voltage may be raised or lowered by the aid of static transformers, in accordance with the following theory. It has been noted in Article 93 that when a conductor carrying current is passed around a closed magnetizable core, magneto-electric force is set up in the core; when the current in the coil is of the alternating kind, the induced magnetic force retains the characteristics of alternations both in direction and flux density, and by virtue of this condition magnetic stress is set up which becomes the source of an electromotive force other than that of the current in the circuit which passes around the core. This induced electro-motive force acts in opposition to that of the magnetizing circuit and thus incites the latter to increased activity. If another conductor circuit is passed around the same core and is not connected with the magnetizing circuit, the increase of E. M. F. in the latter finds an outlet, or overflow so to speak, into this other conductor, and, under the constant pressure from its source, and the continued conflict between it and the back E. M. F. due to the magnetic stress set up in the core, it continues to pass into the second conductor. H.E.P. 210 H. v. S. This is the principle of alternating current transformation illustrated by Fig. 133, in which C is the core above mentioned, P is the magnetizing circuit called the primary, and S is the second circuit, being the secondary. It may be pointed out that this current phenomenon may be likened to what transpires in the operation of a generator, that the primary is like the field and the secondary the armature, while mechanical motion is represented by the alternations, that is the continuous coming and going of flux density and direction, which is practically of the same effect, as far as cutting of magnetic lines in a space of time is concerned, as when the armature revolves and passes through the field in that manner; and from this it will at once be clear that no such phenomenon can occur with continuous current that, though the core would be magnetized, there would be no current in the secondary. Static Transformer Analysis.-When the secondary is an open circuit, there is no transformation of E. M. F.; the magnetization of the core originates a back electro-motive force of practically the same value as that of the primary, being diminished only by the voltage required to overcome the resistance of the primary coil. When the secondary is closed, a current is set up in it opposing that in the primary, its first effort being to demagnetize the core, and, since it is the expressed purpose of the primary to magnetize the core, a conflict or stress is set up which calls forth greater efforts of the primary to overcome the opposition of the demagnetizing influences, with the result that a distinct current passes into the secondary, being of like frequency and other characteristics as the primary excepting as to the E. M. F., as it is the purpose of the process to alter or transform this by raising or lowering the voltage of the primary to any desired in the secondary. The E. M. F. in these two circuits is proportional to the number of turns in each which pass around the core, which is analogous to the principle of field excitation explained in Article 95. In Fig. 133 the primary is shown of one turn while the secondary has four turns around the core; the voltage of the secondary will therefore be four times that of the primary, while the current, ampères, in the secondary will be one-fourth of those of the primary. In this case the voltage is raised by a step-up transformer, the lowering of the voltage would be secured through a step-down transformer, both being of the same design and construction excepting as to the respective winding of the primary and secondary coils, which represents the ratio of transformation. In this connection it should be noted that with like current density per conductor section unit (square inch) the ratio of transformation must be accompanied by a corresponding adaptation of conductor cross-section; thus the conductor in the secondary of a step-down transformer must have an increased copper section over that of the primary which is inversely to the voltage drop. Static transformers consist of the core, the windings, and the shell. The cores are of many different shapes, being generally formed of laminated iron disks; the windings are of insulated copper wire. There is no particular limit to the transformation ratio, the principal consideration in this regard being the heat which is generated in the transformer and may rise to a degree at which the insulations would suffer destruction; high-voltage transformers are therefore especially designed to keep this feature well insured by employing different methods of cooling the transformer and its various parts. Transformer coils are often placed in oil, which receives the heat and transmits it to the shell where it is readily radiated; the oil is also separately cooled by passing water through pipe coils immersed in it; again cooling is effected by passing cold air through the transformers, either by a blower or fan system. The losses in static transformers may be kept very low by proper design and construction; they are due to the resistance of the secondary coils, to magnetic flux friction in the core, and to idle or eddy currents which are set up in the core; the aggregate need not exceed 2 per cent. ARTICLE 98. Current Transmission.-Theory.-Electric energy may be conducted to any distance, as its flow will always continue from a high to a lower potential, but, as in transmission of energy of any form, work is constantly being performed during its passage through the conductor, and, at some point or other, the energy thus expended may become so great a part of the impressed volume that its transmission, under such conditions, represents a waste rather than a gain. The work of the current during its transmission is that of overcoming the conductor's resistance to its free passage; just as the flow of water through a pipe is impeded by the roughness of the pipe's perimeter or its change of section, which is overcome by the expenditure of head, so the transmission of electric energy is made possible only by the overcoming of the conductor's resistance, which is accomplished by the expenditure of E. M. F. By Ohm's law C E ÷ R and E = CR and = REC, from which R, the resistance in any length of a certain conductor, may be ascertained from 1 X r÷ cm, where I is the length of the conductor in feet; = r is the resistance unit, being the resistance of one foot of copper wire of one mil section (one mil foot), which 10.8 ohms, but is taken as 11 ohms, whereby the irregularities of the wire's section and the faults of joints are compensated for; cm stands for the area of the conductor's section in circular mils; therefore R = 11 X 1 ÷ cm, and, inserting this in above equation for R, C is the current (ampères) which is to be delivered for service, Aluminum wire is well adapted for the purpose of transmission conductors; the ohmic resistance coefficient of aluminum is 17 per mil foot instead of 11, the coefficient for copper, and this value must be inserted in above formula when aluminum wire is being investigated instead of copper wire. Since, from above formula, the resistance may be found for any size of conductor, so may the size be determined from it to transmit a fixed current at a given line voltage over a known distance; that is, from above The weight of 1000 feet of 1000 cm copper wire is approximately 3 lbs. The weight of 1000 feet of 1000 cm aluminum wire is approximately 1.5 lbs. By symbolizing 1000 feet of the conductor's length as L, the weight of the conductor may be expressed from the foregoing formula by L2 X 33 X CE for copper conductors, and This refers to a single conductor. From these expressions and from formerly discussed current characteristics, it is apparent that E is the principal factor controlling the value of W, for instance when the ratio of percentage of line drop from the impressed electro-motive force is fixed, the doubling of the impressed voltage will halve C, double E, and reduce W to one-fourth; therefore, the weight of the transmission conductor for given length, current, and drop varies inversely as the square of the impressed voltage, and for given current and drop and impressed voltage in direct proportion to length of transmission, the weight remains constant; while for given current and drop the weight increases as the square of the length. For the purpose of hydro-electric practice all current transmission factors may be determined from these formulæ with sufficient accuracy to estimate the transmission conductors and their cost, but many refinements enter the problem when considered from a scientific stand-point. Diagram 16, appearing in connection with Article 28 in Part I. of this book, has been calculated for copper wire from above formula and is correct, within its scope, for the purpose of estimating the wire quantity. Transmission of continuous and of single and two-phase alternating currents is by two wires, all the current passing over every part, while three-phase alternating current may be transmitted by three conductors, each of which carries the current of its particular phase. In the above formulæ, for determining cm or W of transmission-line conductors, the length, when considering continuous and single and two-phase alternating currents, or in two-conductor circuits, is the developed length of the conductors or double the transmission distance, while for three-phase alternating current transmission the length is equal to the transmission distance. In finding the weight, therefore, L is multiplied by four for two-conductor lines and by three for three-conductor lines; for this reason a three-conductor transmission line (of three-phase current) requires only 75 per cent. of the weight of copper needed in a two-conductor line of the same energy. Of the current symptoms briefly outlined in Article 94 those specially applying to current transmission are: inductance, which is the absorption of electric energy while producing a magnetic field around the conductor, or the setting up of an electro-motive force opposite to that impressed in the alternate current conductor, resulting in voltage drop at the line terminal; capacity, being the reactance of the transformation of alter |