  The facility with which alternating current can be transformed from one voltage to another, thus permitting high pressure transmission of electric energy to long distances through small wires, and low pressure distribution for the operation of lighting systems and motors, gives a far greater variety of systems of transmission and distribution than is possible with direct current. Furthermore, when the fact that two phase current can be readily transformed into three phase current, and these converted into direct current, and vice versa, by means of rotary converters and rectifiers, is added to the advantages derived by the use of high tension systems, it is apparent that the opportunity for elaboration becomes almost unlimited. These conditions have naturally tended toward the development of a great variety of systems, employing more or less complicated circuits and apparatus, and although alternating current practice is still much less definite than direct current work, certain polyphase systems are now being generally accepted as representing the highest standards of power generation, transmission and distribution. A classification of the various alternating current systems, to be comprehensive, should be made according to several points of view, as follows: 1. With respect to the arrangement of the circuit, as
2. With respect to transformation, as
3. With respect to the mode of transmitting the energy, as
4. With respect to the kind of current, as
5. With respect to transmission and distribution, as
In order to comprehend the relative advantages of the various alternating current systems, it is first necessary to understand the principle of vector summation. Vector Summation.—This is a simple geometrical process for ascertaining the pressure at the free terminals of alternating current circuits. The following laws should be carefully noted: 1. If two alternating pressures which agree in phase are connected together in series, the voltage at the free terminals of the circuit will be equal to their arithmetical sum, as in the case of direct currents. Fig. 2,123.—Vectors. A vector is defined as: a line, conceived to have both a fixed length and a fixed direction in space, but no fixed position. Thus A and B are lines, each having a fixed length, but no fixed direction. By adding an arrow head the direction is fixed and the line becomes a vector, as for example vector C. The fixed length is usually taken to represent a definite force, thus the fixed length of vector C is 4.7 which may be used to represent 4.7 lbs., 4.7 tons, etc., as may be arbitrarily assumed. When there is phase difference between the two alternating pressures, connected in series, the following relation holds: 2. The value of the terminal voltage will differ from their arithmetical sum, depending on the amount of their phase difference. When there is phase difference, the value of the resultant is conveniently obtained as explained below. Ques. How are vector diagrams constructed for obtaining resultant electric pressure? Ans. On the principle of the parallelogram of forces. Ques. What is understood by the parallelogram of forces? Ans. It is a graphical method of finding the resultant of two forces, according to the following law: If two forces acting on a point be represented in direction and intensity by adjacent sides of a parallelogram, their resultant will be represented by the diagonal of the parallelogram which passes through the point. Fig. 2,124.—Parallelogram of forces. OC is the resultant of the two forces OA and OB. The length and direction of the lines represent the intensity and direction of the respective forces, the construction being explained in the accompanying text. Thus in fig. 2,124, let OA and OB represent the intensity and direction of two forces acting at the point O, Draw AC and BC, respectively parallel to OB and OA, completing the parallelogram, then will OC, the diagonal from the point at which the forces act, represent the intensity and direction of the resultant, that is, of a force equivalent to the combined action of the forces OA and OB, these forces being called the components of the force OC. Ques. Upon what does the magnitude of the resultant of two forces depend? Ans. Upon the difference in directions in which they act, as shown in figs 2,125 to 2,128. Ques. Is the parallelogram of forces applied when the difference in direction or "phase difference" of two forces is 90 degrees? Ans. It is sometimes more conveniently done by calculation according to the law of the right angle triangle. Figs. 2,125 to 2,128.—Parallelograms of forces showing increase in magnitude of the resultant of two forces, as their difference of direction, or electrically speaking, their phase difference is diminished. The diagrams show the growth of the resultant of the two equal forces OA and OB as the phase difference is reduced from 165° successively to 120, 60, and 15 degrees. According to this principle, if two alternating pressures have a phase difference of 90 degrees they may be represented in magnitude and direction by the two sides of a right angle triangle as OA and OB in fig. 2,129; then will the hypotenuse AB represent the magnitude and direction of the resultant pressure. That is to say, the resultant pressure AB=v((OA)2+(OB)2) (1) EXAMPLE.—A two phase alternator is wound for 300 volts on one phase and 200 volts on the other phase, the phase difference being 90°. If one end of each winding were joined so as to form a single winding around the armature, what would be the resultant pressure? By calculation, substituting the given values in equation (1), Resultant pressure=v(3002+2002)=v(130,000)=360.6 volts. This is easily done graphically as in fig. 2,129 by taking a scale, say, 1"=100 volts and laying off OA=3"=300 volts, and at right angles OB=2"=200 volts, then by measurement AB=3.606"=360.6 volts. Fig. 2,129.—Method of obtaining the resultant of two component pressures acting at right angles by solution of right angle triangle. The equation of the right angle triangle is explained at length in Guide No. 5, page 1,070. Ques. When the two pressures are equal and the phase difference is 90°, is it necessary to use equation (1) to obtain the resultant? Ans. No. The resultant is obtained by simply multiplying one of the pressures by 1.41. This is evident from fig. 2,130. Here the two pressures OA and OB are equal as indicated by the dotted arc. Since they act at right angles, OB is drawn at 90° to OA. According to the equation of the right angle triangle, the resultant AB=v(12+12)=v2=1.4142 which ordinarily is taken as 1.41. This value will always represent the ratio between the magnitude of the resultant and the two component forces, when the latter are equal, and have a phase difference of 90 degrees. Forms of Circuit.—Alternating current systems of distribution may be classed, with respect to the kind of circuit used, in a manner similar to direct current systems, that is, they may be called series, parallel, series parallel, or parallel series systems, as shown in figs. 2,131 to 2,134. Fig. 2,130.—Diagram for obtaining the resultant of two equal component pressures acting at right angles. Series Circuits.—These are used in arc lighting, and series incandescent lighting, a constant current being maintained; also for Figs. 2,131 to 2,134.—Various forms of circuit. These well known forms of circuit are used in both alternating and direct current systems. The simple series circuit, fig. 2,131, is suitable for constant current arc lighting. Fig. 2,132, shows the parallel constant pressure circuit; this form of circuit is largely used but is seldom connected direct to the alternator terminals, but to a step down transformer, on account of the low pressure generally required. Fig. 2,133 illustrates a parallel series circuit, and 2,134, a series parallel circuit. Several forms of constant current alternator, analogous to the Thompson-Houston and Brush series arc dynamos, have Fig. 2,135.—Typical American overhead 6,600 volt single phase interurban trolley line, Baltimore and Annapolis short line, Annapolis, Md. An objectionable feature is that the voltage of a constant current alternator will rise very high if the circuit be opened, because it is then relieved of inductance drop and armature reaction. To guard against a dangerous rise of voltage, a film cut out or equivalent device is connected to the terminal of each machine so that it will short circuit the latter if the voltage rise too high. Ques. What advantage have constant current alternators over constant current dynamos? Ans. The high pressure current is delivered to the external circuit without a commutator, hence there is no sparking difficulty. The above relates to the revolving field type of alternator. There are, however, alternators in which the armature revolves, the current being delivered to the external circuit through collector rings and brushes. This type of alternator, it should be noted, is for moderate pressures, and moreover there is no interruption to the flow of the current such as would be occasioned by a tangential brush on a dynamo in passing from one commutator segment to the next. In the revolving field machine, though the armature current be of very high pressure, the field current which passes through the brushes and slip rings is of low pressure and accordingly presents no transmission difficulties. Fig. 2,136.—Diagram of parallel circuit. It is a constant pressure circuit and is very widely used for lighting and power. If each lamp takes say ½ ampere, the current flowing in the circuit will vary with the number of lamps in operation; in the above circuit with all lamps on, the current is ½×5=2½ amperes. Ques. State a disadvantage. Ans. Some source of direct current for field excitation is required. Ques. In a constant current series system, upon what does the voltage at the alternator depend? Ans. The number of devices connected in the circuit, the volts required for each, and the line drop. Parallel Circuits.—These are used for constant pressure operation. Such arrangement provides a separate circuit for each unit making them independent so that they may vary in size and each one can be started or stopped without interfering with the others. Parallel circuits are largely used for incandescent lighting, and since low pressure current is commonly used on such circuits they are usually connected to step down transformers, instead of direct to the alternators. Fig. 2,137.—Diagram of parallel series circuit, showing fall of pressure between units. This system is very rarely used; it has the disadvantage that if a lamp filament breaks, the resistance of the circuit is altered and the strength of the current changed. The voltmeter shows the fall of pressure along the line. It should be noted that, although the meter across AB is shown as registering zero pressure, there is, strictly speaking, a slight pressure across AB, in amount, being that required to overcome the resistance of the conductor between A and B. Parallel Series Circuits.—Fig. 2,137 shows the arrangement of a parallel series circuit and the pressure conditions in same. Such a circuit consists of groups of two or more lamps or other devices connected in parallel and these groups connected in series. Such a circuit, when used for lighting, obviously has the disadvantage that if a lamp filament breaks, the resistance of the group is increased, thus reducing the current and decreasing the brilliancy of the lamps. This arrangement accordingly does not admit of turning off any of the lights. Series Parallel Circuits.—The arrangement of circuits of this kind is shown in fig. 2,134; they are used to economize in copper since by joining groups of low pressure lamps in series they may be supplied by current at correspondingly higher pressure. Thus, if in fig. 2,134, 110 volt, ½ ampere lamps be used, the pressure on the mains, that is, between any two points as A and B would be 110×3=330 volts. Each group would require ½ ampere and the five groups ½×5=2½ amperes. Fig. 2,138.—44,000 volt lines entering the Gastonia sub-station of the Southern Power Co. The poles used are of the twin circuit two arm type, built of structural steel, their height varying from 45 to 80 feet, the latter weighing 9,000 pounds each. These poles have their bases weighted with concrete. Transformer Systems.—Nearly all alternating current systems are transformer systems, since the chief feature of alternating current is the ease with which it may be transformed from one pressure to another. Accordingly, considerable economy in copper may be effected by transmitting the current at high pressure, especially if the distance be great, and, by means of step down transformers, reducing the voltage at points where the current is used or distributed. Ordinarily and for lines of moderate length, current is sent out direct from the alternator to the line and transformed by step down transformers at the points of application. With respect to the step down transformers, there are two arrangements:
Fig. 2,139.—Diagram of transformer system with individual transformers. The efficiency is low, but such method of distribution is necessary in sparsely settled or rural districts. Individual transformers, that is, a separate transformer for each customer is necessary in rural districts where the intervening distances are great as shown in fig. 2,139. Ques. What are the objections to this method of distribution? Ans. It requires the use of small transformers which are necessarily less efficient and more expensive per kilowatt than large transformers. The transformer must be built to carry, within its overload capacity, all the lamps installed by the customer since all may be used occasionally. Usually, however, only a small part of the lamps are in use, and those only for a small part of the day, so that the average load on the transformer is a very small part of its capacity. Since the core loss continues whether the transformer be loaded or not, but is not paid for by the customer, the economy of the arrangement is very low. In the second case, where one large transformer may be placed at a distribution center, to supply several customers, as in fig. 2,140, the efficiency of the system is improved. Ques. Why is this arrangement more efficient than when individual transformers are used? Fig. 2,140.—Diagram of transformer system with one transformer located at a distribution center and supplying several customers as A, B, and C. Such arrangement is considerably more efficient than that shown in fig. 2,139, as explained in the accompanying text. Ans. Less transformer capacity is required than with individual transformers. Ques. Why is this? Ans. With several customers supplied from one transformer it is extremely improbable that all the customers will burn all their lamps at the same time. It is therefore unnecessary to install a transformer capable of operating the full load, as is necessary with individual transformers. Ques. Does the difference in transformer capacity represent all the saving? Ans. No; one large transformer is more efficient than a number of small transformers. Ques. Why? Ans. The core loss is less. For instance, if four customers having 20 lamps each were supplied from a single transformer, the average load would be about 8 lamps, and at most not over 10 or 15 lamps, and a transformer carrying 30 to 35 lamps at over load would probably be sufficient. A 1,500 watt transformer would therefore be larger than necessary. At 3 per cent. core loss, this gives a constant loss of 45 watts, while the average load of 8 lamps for 3 hours per day gives a useful output of 60 watts, or an all year efficiency of nearly 60 per cent., while a 1,000 watt transformer would give an all year efficiency of 67 per cent. For long distance transmission lines, the voltage at the alternator is increased by passing the current through a step up transformer, thus transmitting it at very high pressure, and reducing the voltage at the points of distribution by step down transformers as in fig. 2,141. Fig. 2,141.—Diagram illustrating the use of step up and step down transformers on long distance transmission lines. The saving in copper is considerable by employing extra high voltages on lines of moderate or great length as indicated by the relative sizes of wire. Ques. In practice, would such a system as shown in fig. 2,141 be used? Ans. If the greatest economy in copper were aimed at, a three phase system would be used. The purpose of fig. 2,141 is to show the importance of the transformer in giving a flexibility of voltage, by which the cost of the line is reduced to a minimum. Ques. Does the saving indicated in fig. 2,141 represent a net gain? Ans. No. The reduction in cost of the transmission is partly offset by the cost of the transformers as well as by transformer losses and the higher insulation requirements. Fig. 2,142.—Single and twin circuit poles (Southern Power Co.). The twin circuit pole at the right is used for 11,000 volt circuits, while the single circuit poles at the left carry 44,000 volt conductors, being used on another division for 100,000 volt line. Every case of electric transmission presents its own problem, and needs thorough engineering study to intelligently choose the system best adapted for the particular case. Single Phase Systems.—There are various arrangements for transmission and distribution classed as single phase systems. Thus, single phase current may be conveyed to the various Again single phase current may be transmitted by two wires and distributed by three wires. This is done in several ways, the simplest being shown in fig. 2,143. Fig. 2,143.—Diagram illustrating single phase two wire transmission and three wire distribution. The simplified three wire arrangement at A, is not permissible except in cases of very little unbalancing. Where the difference between loads on each side of the neutral may be great some form of balancing as an auto-transformer or equivalent should be used, as at B. Ques. Under what conditions is the arrangement shown in fig. 2,143 desirable? Ans. This method of treating the neutral wire is only permissible where there is very little unbalancing, that is, where the load is kept practically the same on both sides of the neutral. Ques. What advantage is obtained by three wire distribution? Ans. The pressure at the alternator can be doubled, which means, for a given number of lamps, that the current is reduced Fig. 2,144.—100,000 volt "Milliken" towers with one circuit strung (Southern Power Co.). These towers are mounted on metal stubs sunk 6 feet in the ground. Where the angle of the line is over 15 degrees, however, these stubs are weighted with rock and concrete, and where an angle of over 30 degrees occurs, two and sometimes three towers are used for making the turn. The weight of the standard "Milliken" tower is 3,080 lbs., and its height from the ground to peak is 51 feet. The towers are spaced to average eight to a mile and a strain tower weighing 4,250 lbs. is used every mile. For particularly long spans a special heavy tower weighing 6,000 lbs. is used. The circuits are transposed every 30 miles. Multiple disc insulators are used, four discs being used to suspend each conductor from standard towers and ten discs to each conductor on strain towers. The standard span is 600 feet, sag 11 ft at 50° Fahr. Ques. What modification of circuit A (fig. 2,143), should be made to allow for unbalancing in the three wire circuit? Ans. An auto-transformer or "balance coil" as it is sometimes called should be used as at B. This is a very desirable method of balancing when the ratio of transformation is not too large. Ques. For what service would the system shown in fig. 2,143 be suitable? Ans. For short distance transmission, as for instance, in The standard voltages of low pressure alternators are 400, 480, and 600 volts. Fig. 2,145.—View of a typical isolated plant. The illustration represents an electric lighting plant on a farm showing the lighting of the dwelling, barn, tool house and pump house. The installation consists of a low voltage dynamo with gas engine drive and storage battery together with the necessary auxiliary apparatus. Ques. In practice are single phase alternators used as indicated in fig. 2,143? Ans. Alternators are wound for one, two or three phases. Three phase machines are more commonly supplied and in many cases it will pay to install them in preference to single phase, even if they be operated single phase temporarily. For a given output, three phase machines are smaller than single phase and the single phase load can usually be approximately balanced between the three phases. Moreover, if a three phase machine be installed, polyphase current will be available in case it may be necessary to operate polyphase motors at some future time. Standard three phase alternators will carry about 70 per cent. of their rated kilowatt output when operated single phase, with the same temperature rise. Ques. How are three phase alternators used for single phase circuits? Ans. The single phase circuit is connected to any two of the three phase terminal leads. Fig. 2,146.—Diagram showing arrangement of single phase system for two wire transmission and three wire distribution, where the transmission distance is considerable. In order to reduce the cost of the transmission line, the current must be transmitted at high pressure; this necessitates the use of a step down transformer at the distributing center as shown in the illustration. Ques. What form of single phase system should be used where the transmission distance is considerable? Ans. The current should be transmitted at high pressure, a step down transformer being placed at each distribution center to reduce the pressure to the proper voltage to suit the service requirements as shown in fig. 2,146. Thus, if 110 volt lamps be used on the three wire circuit, the pressure between the two outer wires would be 220 volts. A transformation ratio of say 10:1 would give 2,220 volts for the primary circuit. The current required for the primary with this ratio being only .1 that used in the secondary, a considerable saving is effected in the cost of the transmission line as must be evident. With the high pressure alternator only one transformation of the current is needed, as shown at the distribution end. In place of the high pressure alternator, a low pressure alternator could be used in connection with a step up transformer as shown in fig. 2,147, but there would be an extra loss due to the additional transformer, rendering the system less efficient than the one shown in fig. 2,146. Such an arrangement as shown in the fig. 2,147 might be justified Ques. How could the system shown in fig. 2,147 be made more efficient than that of fig. 2,146? Ans. By using a high pressure alternator in order to considerably increase the transmission voltage. Thus, a 2,200 volt alternator and 1:10 step up transformer would give a line pressure of 22,000 volts, which at the distribution end could be reduced, to 220 volts for the three wire circuit, using a 100:1 step down transformation. Fig. 2,147.—Diagram illustrating how electricity can be economically transmitted a considerable distance with low pressure alternator already in use. Ques. Would this be the best arrangement? Ans. No. Ques. What system would be used in practice for maximum economy? Ans. Three phase four wire. Fig. 2,148.—Angle tower showing General Electric strain insulators. The tower being subject to great torsional strains is erected on a massive concrete foundation. The construction is similar to the standard tower but of heavier material, and having the same vertical dimensions but with bases 20 ft. square. Ques. What are the objections to single phase generation and transmission? Ans. It does not permit of the use of synchronous converters, self-starting synchronous motors, or induction motor starting under load. It is poorly adapted to general power Ques. For what service is it desirable? Ans. For alternating current railway operation. There are advantages of simplicity in the entire generating, primary, and secondary distribution systems for single phase roads. These advantages are so great that they justify considerable expense, looked at from the railway point of view only, the single phase system throughout may be considered as offering the most advantage. Ques. What are the objectionable features of single phase alternators? Ans. This type of alternator has an unbalanced armature reaction which is the cause of considerable flux variation in the In order to minimize eddy currents, such alternators must accordingly be built with thinner laminations and frequently poorer mechanical construction, resulting in increased cost of the machine. The large armature reaction results in a much poorer regulation than that obtained with three phase alternators, and an increased amount of field copper is required, also larger exciting units. These items augment the cost so that the single phase machine is considerably more expensive than the three phase, of the same output and heating. Fig. 2,149.—Elementary alternator developing one volt at frequencies of 60 and 25, showing the effect of reducing the frequency. Since for the same number of pole, the R.P.M. have to be decreased to decrease the frequency, increased flux is required to develop the same voltage. Hence in construction, low frequency machines require larger magnets, increased number of turns in series on the armature coils, larger exciting units as compared with machines built for higher frequency. Ques. What factor increases the difficulties of single phase alternator construction? Ans. The difficulties appear to increase with a decrease in frequency. The adoption of any lower frequency than 25 cycles may result in serious difficulties in construction for a complete line of machine, especially those of the two or four pole turbine driven type where the field flux is very large per pole. Monocyclic System.—In this system, which is due to Steinmetz, the alternator is of a special type. In construction, there is a main single phase winding an auxiliary or teaser winding connected to the central point of the main winding in quadrature therewith. The teaser coil generates a voltage equal to about 25 per cent. of that of the main coil so that the pressure between the terminals of the main coil and the free end of the teaser is the resultant of the pressure of the two coils. Fig. 2,150.—Diagram of monocyclic system, showing lighting and power circuits. By various transformer connections it is possible to obtain a practically correct three phase relationship so that polyphase motors may be employed. In this system, two wires leading from the ends of the single phase winding in the alternator supply single phase current to the lighting load, a third wire connected to the end of the teaser being run to points where the polyphase motors are installed as shown in fig. 2,150. The monocyclic system is described at length in the chapter on alternators, Guide No. 5, pages, 1,156 to 1,159. Two Phase Systems.—A two phase circuit is equivalent to two single phase circuits. Either four or three wire may be employed in transmitting two phase current, and even in the latter instance the conditions are practically the same as for single phase transmission, excepting the unequal current distribution in the three wires. Fig. 2,151 shows a two phase four wire system. Fig. 2,151.—Diagram of two phase four wire system. It is desirable for supplying current for lighting and power. The arrangement here shown should be used only for lines of short or moderate length, because of the low voltage. Motors should be connected to a circuit separate from the lighting circuit to avoid drop on the latter while starting a motor. Ques. For what service is the system shown in fig. 2,151 desirable? Ans. It is adapted to supplying current for lighting and power at moderate or short distances. Either 110 or 220 volts are ordinarily used which is suitable for incandescent lighting and for constant pressure arc lamps, the lamps being connected singly or two in pairs. Ques. Where current for both power and light are obtained from the same source how should the circuits be arranged? Ans. A separate circuit should be employed for each, in order to avoid the objectionable drop and consequent dimming of the lights due to the sudden rush of current during the starting of a motor. Fig. 2,152.—Diagram of two phase three wire system. A wire is connected to one end of each phase winding as at A and B, and a third wire C, to the other end of both phases as shown. Disagreeable fluctuation of the lights are always met with when motors are connected to a lighting circuit and the effect is more marked with alternating current than with direct current, because most types of alternating current motor require a heavy current usually lagging considerably when starting. This not only causes a large drop on the line, but also reacts injuriously upon the regulation of transformers and alternators, their voltage falling much more than with an equal non-inductive load. Ques. What voltages are ordinarily used on two phase lines of more than moderate length? Ans. For transmission distances of more than two or three Ques. For long distance transmission at 30,000 to 40,000 volts, what additional apparatus is necessary? Ans. Step up and step down transformers. Fig. 2,153.—Diagram illustrating two phase three wire transmission. The third wire C is attached to the connector between one end of phase A, and phase B windings. Ques. Explain the method of transmitting two phase current with three wires. Ans. The connections at the alternator are very simple as shown in fig. 2,152. One end of each phase winding is connected by the brushes a and b', to one of the circuit wires, that is to A and B respectively. The other end of each phase winding is connected by a lead across brushes a' and b, to which the third wire C is joined. The current and pressure conditions of this system are represented diagrammatically in fig. 2,153. The letters correspond to those in fig. 2,152, with which it should be compared. As shown in the figure each coil is carrying 100 amperes at 1,000 volts pressure. Since the phase difference between the two coils is 90°, the voltage between A and B is v2=1.414 times that between either A or B and the common return wire C. The current in C is v2=1.414 times that in either outside wire A or B, as indicated. Ques. How should the load on the two phase three wire system be distributed? Ans. The load on the two phases must be carefully balanced. Fig. 2,154.—Diagram of two phase three wire system and connections for motors and lighting circuits. Ques. Why should the power factor be kept high? Ans. A high power factor should be maintained in order to keep the voltage on the phases nearly the same at the receiving ends. Ques. How should single phase motors be connected and what precaution should be taken? Ans. Single phase motors may be connected to either or Fig. 2,154 shows a two phase three wire system, with two wire and three wire distribution circuits, illustrating the connection for lighting and for one and two phase motors. Fig. 2,155.—Diagram of two phase system with four wire transmission and three wire distribution. In the three wire circuits the relative pressures between conductors are as indicated; that is, the pressure between the two outer wires A and B is 141 volts, when the pressure between each outer wire and the central is 100 volts. Ques. Describe another method of transmission and distribution with two phase current. Ans. The current may be transmitted on a four wire circuit and distributed on three wire circuit as in fig. 2,155. The four wire transmission circuit is evidently equivalent to two independent single phase circuits. In changing from four to three wires, it is just as well to connect the two outside wires A and B together (fig. 2,152), as it is to connect a´ and b. It makes no difference which two secondary wires are joined together, so long as the other wires of each transformer are connected to the outside wires of the secondary system. Ques. For what service is the two phase three wire system adapted? Ans. It is desirable for supplying current of minimum pressure to apparatus in the vicinity of transformers. It is more frequently used in connection with motors operating from the secondaries of the transformers. Ques. How should the third or common return wire be proportioned? Ans. Since the current in the common return wire is 41.4 per cent. higher than that in either of the other wires it must be of correspondingly larger cross section, to keep the loss equal. Figs. 2,156 and 2,157.—Conventional diagrams illustrating star and delta connected three phase alternator armatures. Ques. What is the effect of an inductive load on the two phase three wire system and why? Ans. It causes an unbalancing of both sides of the system even though the energy load be equally divided. The self-induction pressure in one side of the system is in phase with the virtual pressure in the other side, thus distorting the current distribution in both circuits. Ques. Describe the two phase five wire system. Ans. A two phase circuit may be changed from four to five wires by arranging the transformer connections as in fig. 2,158. As shown, the secondaries of the transformers are joined in series and leads brought out from the middle point of each secondary winding and at the connection of the two windings, giving five wires. With 1,000 volts in the primary windings and a step down ratio of 10:1, the pressure between A and C and C and E will be 100 volts and between the points and the connections B or D at the middle of the secondary coils, 50 volts. The pressure across the two outer wires A and E is, as in the three wire system, v2 or 1.41 times that from either outer wire to the middle wire C, that is 141 volts. The pressure across the two wires connected to the middle of the coils, that is, across B and D, is 50×v2=70.5 volts. Fig. 2,158.—Two phase four wire transmission and five wire distribution system. The relative pressures between the various conductors are indicated in the diagram. Three Phase Systems.—There are various ways of arranging the circuit for three phase current giving numerous three phase systems. 1. With respect to the number of wires used they may be classified as
Fig. 2,159.—Line connections of three phase three wire long distance transmission, and distribution system. The three phase alternator A, is driven by the water wheel B, and furnishes current at say 2,200 volts plus sufficient pressure to compensate for line drop. With 1:10 step up transformers C, this would give a transmission pressure of 22,000 volts plus line drop. It is this transformation that secures the copper economy of the system. At the distribution end are the step down transformers; one set reducing the voltage down to 2,200 volts, and supplying current direct to the synchronous motor, and through another set of other step down transformers, as L and K, to lighting and power circuits at 220 volts. Another set of step down transformers M reduce the pressure directly to 120 volts for power and lighting, the pressure being regulated by the regulators G. Arc lamps with individual transformers further reducing the pressure to 50 volts are connected to this circuit as shown. 2. With respect to the connections, as
The six wire system is shown in fig. 2,160. It is equivalent to three independent single phase circuits. Such arrangement would only be used in very rare instances. Fig. 2,160.—Three phase six wire system. It is equivalent to three independent single phase circuits and would be used only in very rare cases. Ques. How can three phase current be transmitted by three conductors? Ans. The arrangement shown in fig. 2,160 may be resolved into three single circuits with a common or grounded return. When the circuits are balanced the sum of the current being zero no current will flow in the return conductor, and it may be dispensed with, thus giving the ordinary star or Y connected three wire circuit, as shown in fig. 2,163. The transformation from six to three wires being shown in figs. 2,161 to 2,163. Figs. 2,161 to 2,163.—Evolution of the three phase three wire system. Fig. 2,161 is a conventional diagram of the three phase six wire system shown in fig. 2,160. A wire is connected to both ends of each phase winding, giving six conductors, or three independent two wire circuits. In place of the wires running from A, B, and C, they may be removed and each circuit provided with a ground return as shown in fig. 2,162. The sum of the three currents being zero, or nearly zero, according to the degree of unbalancing, the ground return may be eliminated and the ends A, B, and C of the three phase winding connected, as in fig. 2,163, giving the so called star point. Fig. 2,166 is a view of an elementary three phase three wire star connected alternator. Ques. What are the pressure and current relations of the star connected three wire system? Figs. 2,164 and 2,165.—Three phase four wire star connected alternator and conventional diagram showing pressure and current relations. Figs. 2,166 and 2,167.—Three phase star connected alternator, and conventional diagram showing pressure relations. Ans. These are shown in the diagram, fig. 2,166 and 2,167. Assuming 100 amperes and 1,000 volts in each phase winding, the pressure between any two conductors is equal to the pressure in one winding multiplied by v3, that is 1,000×1.732=1,732 volts. The current in each conductor is equal to the current in the winding, or 100 amperes. Ques. Describe the delta connection. Ans. In the delta connection, the three phase coils are connected together forming an endless winding, leads being brought out from these points. Fig. 2,168 shows a delta connected three phase alternator, the pressure and current relation being given in fig. 2,169. Figs. 2,168 and 2,169.—Three phase delta connected alternator and conventional diagram showing pressure and current relations. Ques. What are the pressure and current relations of the delta connected three wire system? Ans. They are as shown in fig. 2,169. Assuming 100 amperes and 1,000 volts in each phase winding, the pressure between any two conductors is the same as the pressure in the winding, and the current in any conductor is equal to the current in the winding multiplied by v3, that is 100×1.732=173.2 amperes, that is, disregarding the fraction, 173 amperes. Ques. What are the relative merits of the star and delta connections? Ans. The power output of each is the same, but the star connection gives a higher line voltage, hence smaller conductors may be used. Fig. 2,170.—T connection of transformers in which three phase current is transformed with two transformers. The connections are clearly shown in the illustration. The voltage across one transformer is only 86.6% of that across the other, so that if each transformer be designed especially for its work one will have a rating of .866 EI and the other EI. The combined rates will then be 1.866 as compared with 1.732 EI for three single phase transformers connected either star or delta. When it is remembered that the cost of copper conductors is inversely as the square of the voltage, the advantage of the Y connected system can be seen at once. Assuming that three transformers are used for a three phase system of given voltage, each transformer, star connected, would be wound for 1÷v3=58% of the given voltage, and for full current. For delta connection, the winding of each transformer is for 58% of the current. Accordingly the turns required for star connection are only 58% of those required for delta connection. Ques. What is the objection to the star connection for three phase work? Ans. It requires the use of three transformers, and if anything happen to one, the entire set is disabled. Ques. Does this defect exist with the delta connection? Ans. No. One transformer may be cut out and the other two operated at full capacity, that is at ? the capacity of the three. Ques. Describe the T connection. Ans. In this method two transformers are used for transforming three phase current. It consists in connecting one end of both windings of one transformer to the middle point of like windings of the other transformer as in fig. 2,170. Fig. 2,171.—Open delta connection or method of connecting two transformers in delta for three phase transformation. It is used when one of the three single phase delta connected transformers becomes disabled. Ques. What is the open delta connection? Ans. It is a method of arranging the connections of a bank of three delta connected transformers when one becomes disabled as in fig. 2,171. Change of Frequency.—There are numerous instances where it is desirable to change from one frequency to another, as for instance to join two systems of different frequency which Synchronous motors are generally used for such service as the frequency is not disturbed by load changes; it also makes it possible to use the set in the reverse order, that is, taking power from the high frequency mains and delivering energy at low frequency. Fig. 2,172.—Course of the Schaghticoke-Schenectady transmission line of the Schenectady Power Co. This transmission line carries practically the entire output of the Schaghticoke power house to Schenectady, N. Y., a distance of approximately 21 miles. The line consists of two separate three phase, 40 cycle, 32,000 volt circuits, each of 6,000 kw. normal capacity. These circuits start from opposite ends of the power house, and, after crossing the Hoosic River, are transferred by means of two terminal towers, fig. 2,173, to a single line of transmission towers. The two circuits are carried on these on opposite ends of the cross arms, the three phases being superimposed. The power house ends of the line are held by six short quadrangular steel lattice work anchor poles with their bases firmly embedded in concrete, the cables being dead ended by General Electric disc strain insulators. This equipment, together with the lightning arrester horn gaps and the heavy line outlet insulators mounted on the roof of the power house, is shown in fig. 2,174. While each circuit carries only 6,000 kw. under normal conditions, either is capable of carrying the entire output of the station; in this case, however, the line losses are necessarily augmented. This feature prevents any interruption of the service from the failure of one of the circuits. There are altogether 197 transmission towers, comprising several distinct types. Ques. In the parallel operations of frequency changing sets what is necessary to secure equal division of the load? Ans. The relative angular position of the rotating elements of motor and generator must be the same respectively in each set. Fig. 2,173.—Beginning of Schaghticoke-Schenectady transmission line; view showing transfer towers with power house in background. Ques. How is this obtained? Ans. Because of the mechanical difficulty of accurately Transformation of Phases.—In alternating current circuits it is frequently desirable to change from one number of phases to another. For instance, in the case of a converter, it is less expensive and more efficient to use one built for six phases than for either two or three phases. Fig. 2,174.—View from roof of power house of the Schaghticoke-Schenectady transmission line, showing anchor poles, strain insulators, lightning arrester horn gap and line entrance bushings. The numerous conditions met with necessitate various phase transformations, as
These transformations are accomplished by the numerous arrangements and combinations of the transformers. Fig. 2,175.—Three phase to one phase transformation with two transformers. The diagram shows the necessary connections and the relative pressures obtained. Three Phase to One Phase.—This transformation may be accomplished by the use of two transformers connected as in fig. 2,175 in which one end of one primary winding is connected to the middle of the other primary winding and the second end of the first primary winding at a point giving 86.6 per cent. of that winding as shown. The two secondary windings are joined in series. Three Phase to Two Phase.—The three phase system is universally used for long distance transmission, because it requires less copper than either the single or two phase systems. Ques. Describe the Scott connection. Fig. 2,176.—The Scott connection for transforming from three phase to two phase. In this method one of the primary wires B of the .866 ratio transformer is connected to the middle of the other primary as at C, the ends of which are connected to two of the three phase wires. The other phase wire is connected at D, the point giving the .866 ratio. The secondary wires are connected as shown. Ans. Two transformers are used, one having a 10:1 ratio, and the other, a ½v3:1, that is, an 8.66:1 ratio. The connections are arranged as in fig. 2,176. It is customary to employ standard transformers having the ratios 10:1, and 9:1. Ques. What names are given to the two transformers? Ans. The one having the 10:1 ratio is called the main transformer, and the other with the 8.66:1 ratio, the teaser transformer. In construction, the transformers may be made exactly alike so that either may be used as main or teaser. In order that the connections may be properly and conveniently made, the primary windings should be provided with 50% and 86.6% taps. Fig. 2,177.—Three phase to two phase transformation with three star connected transformers. Two of the secondary windings are tapped at points corresponding to 57.7% of full voltage; these two windings are connected in series to form one secondary phase of voltage equal to that obtained by the other full secondary winding. Ques. Describe another way of transforming from three to two phases. Ans. The transformation may be made by three star connected transformers, proportioning the windings as in fig. 2,177, from which it will be seen that two of the secondary windings are tapped at points corresponding to 57.7 per cent. of full voltage. Three Phase to Six Phase.—This transformation is usually made for use with rotary converters and may be accomplished in several ways. As these methods have been illustrated in the chapter on Converters (page 1,462), it is unnecessary to again discuss them here. Fig. 2,178, below shows the diametrical connection for transforming three phase to six phase. Fig. 2,178.—Diagram of diametrical connection, three phase to six phase. It is obtained by bringing both ends of each secondary winding to opposite points on the rotary converter winding, utilizing the converter winding to give the six phases. This transformation of phases may also be obtained with transformers having two secondary windings. Alternating Current Systems.—The saving in the cost of transmission obtained by using alternating instead of direct current is not due to any difference in the characteristics of the currents themselves, but to the fact that in the case of alternating current very high pressures may be employed, thus permitting a given amount of energy to be transmitted with a relatively small current. In the case of direct current systems, commutator troubles limit the transmission pressure to about 1,000 volts, whereas with alternating current it may be commercially generated at pressures up to about 13,000 and by means of step up transformers, transmitted at 110,000 volts or more. Fig. 2,179.—End of Schaghticoke-Schenectady transmission line at Schenectady; view showing entrance bushings and lightning arrester horn gaps. Relative Weights of Copper Required by Polyphase Systems.—A comparison between the weights of copper required by the different alternating current systems is rendered quite difficult by the fact that the voltage ordinarily measured is not the maximum voltage, and as the insulation has to withstand the strain of the maximum voltage, the relative value of copper obtained by calculation depends upon the basis of comparison adopted. As a general rule, the highest voltage practicable is used for long distance transmission, and a lower voltage for local distribution. Furthermore, some polyphase systems give a multiplicity of voltages, and the question arises as to which of these voltages shall be considered the transmission voltage. If the transmission voltage be taken to represent that of the distribution circuit, and the polyphase system has as many independent circuits as there are phases, the system would represent a group of several single phase systems, and there would be no saving of copper. Under these conditions, if the voltage at the distant end be taken as the transmission voltage, and the copper required by a single phase two wire system as shown in fig. 2,180, be taken as the basis of comparison, the relative weights of copper required by the various polyphase systems is given in figs. 2,181 to 2,188. Fig. 2,180.—Single phase line, used as basis of comparison in obtaining the relative weights of copper required by polyphase systems, as indicated in figs. 2,181 to 2,188. In the case represented in fig. 2,180, if the total drop on the line be 100 volts, the generated voltage must be 1,100 volts, and the resistance of each line must be 50÷1,000=.05 ohms. Calculated on this basis, a two phase four wire system is equivalent to two single phase systems and gives no economy of copper in power transmission over the ordinary single phase two wire Figs. 2,181 to 2,188.—Circuit diagrams showing relative copper economy of various alternating current systems. In this system two of the four wires of the four wire two phase system are replaced by one of full cross section. The amount of copper required, when compared with the single phase system, will differ considerably according as the comparison is based on the highest voltage permissible for any given distribution, or on the minimum voltage for low pressure service. If E be the greatest voltage that can be used on account of the insulation strain, or for any other reason, the pressure between the other conductors of the two phase three wire system must be reduced to E÷v2. The weight of copper required under this condition is 145.7% that of the single phase copper. On the basis of minimum voltage, the relative amount of copper required is 72.9% that of the single phase system. Fig. 2,189.—Twin circuit "aermotor" towers carrying 44,000 volt conductors (Southern Power Co.). These towers vary in height from 35 to 50 feet, and the circuits are transposed every 10 miles. The towers are assembled on the ground and erected by means of gin poles. They are normally spaced 500 feet apart with a sag of 5 feet 8 inches. The minimum distance between towers is 300 feet and the maximum 700 feet. Figs. 2,187 and 2,188 are two examples of three phase four wire systems. The relative amount of copper required as compared with the single phase system depends on the cross section of the fourth wire. The arrangement shown in fig. 2,188, where the fourth wire is only half size, is used only for secondary distribution systems. Fig. 2,190.—General Electric standard tower for high tension three phase transmission line. Fig. 2,191.—General Electric transposition tower for high tension three phase transmission line. Choice of Voltage.—In order to properly determine the voltage for a transmission system there are a number of The nature of the diversely various factors which affect the problem makes a mathematical expression difficult and unsatisfactory. Ques. What is the relation between the cross sectional area of the conductors and the voltage? Ans. For a given circuit, the cross sectional area of the conductors, or weight varies inversely as the voltage. Fig. 2,192.—General Electric standard tower under construction. Ques. Would the highest possible voltage then be used for a transmission line? Ans. The most economical voltage depends on the length of the line and the cost of apparatus. For instance, alternators, transformers, insulation and circuit control and lightning protection devices become expensive when manufactured for very high pressures. Hence if a very high pressure were used, it would involve that the transmission distance be great enough so that the extra cost of the high pressure apparatus would be offset by the saving in copper effected by using the high pressure. In the case of the longest lines, from about 100 miles up, the saving in copper with the highest practicable voltage is so great that the increase in other expenses is rendered comparatively small. In the shorter lines as those ranging in length from about one mile to 50 or 75 miles, the most suitable voltage must be determined in each individual case by a careful consideration of all the conditions involved. No fixed rule can be established for proper voltage based on the length, but the following table will serve as a guide: Fig. 2,193.—Line of the Schenectady Power Company crossing the tracks of the Boston and Maine Railroad near Schaghticoke.
Ques. What are the standard voltages for alternating current transmission circuits? Ans. 6,600, 11,000, 22,000, 33,000, 44,000, 66,000, 88,000. The amount of power to be transmitted determines, in a measure, the limit of line voltage. If the most economical voltage considered from the point of view of the line alone, be somewhere in excess of 13,200, step up transformers must be employed, since the highest voltage for which standard alternators are manufactured is 13,200. In a given case, the saving in conductor by using the higher voltage may be more than offset by the increased cost of transformers, and the question must be determined for each case. Fig. 2,194.—View of a three phase, 2,300 volt, 60 cycle line at Chazy, N. Y. The current is transmitted at the alternator voltage 2¾ miles over the single circuit pole line. The poles are of cedar with fir cross arms, and are fitted with pin insulators. They are from 35 to 40 feet high and are spaced at an average of about 120 feet. The conductors are bare copper wire No. 00 B. & S. The alternators consist of one 50 kw., and one 100 kw. General Electric machines. Ques. What are the standard transformer ratios? Ans. Multiples of 5 or 10. Figs. 2,195 to 2,197.—Diagram showing electric railway system. Three phase current is generated at the main station where it passes to step up transformers to increase the pressure a suitable amount for economical transmission. At various points along the railway line are sub-stations, where the three phase current is reduced in pressure to 500 or 600 volts by step down transformers, and converted into direct current by rotary converters. The relatively low pressure direct current is then conveyed by "feeders" to the rails, this resulting in a considerable saving in copper. Mixed Current Systems.—It is often desirable to transmit electrical energy in the form of alternating current, and distribute it as direct current or vice versa. Such systems may be classed as mixed current systems. The usual conversion is from alternating current to direct current because of the saving in copper secured by the use of alternating current in transmission, especially in the case of long distance lines. Such conversion involves the use of a rotary converter, motor generator set, or rectifier, according to the conditions of service. Fig. 2,198.—Example of converter sub-station, showing the Brooklyn Edison Co. Madison sub-station. The transformers are seen on the left, the converter shown at the right is a Westinghouse synchronous booster rotary converter, consisting of a standard rotary converter in combination with a revolving armature alternator mounted on the same shaft with the converter and having the same number of poles. The function of the machine is to convert and regulate the pressure. By varying the field excitation of the alternator, the A. C. voltage impressed on the rotary converter proper can be increased or decreased as desired. Thus, the D. C. voltage delivered by the converter is varied accordingly. This type of converter is well adapted for any application for which a relatively wide variation, either automatic or non-automatic, in direct current voltage is necessary. Also especially for serving incandescent lighting systems where considerable voltage variation is required for the compensation of drop in long feeders, for operation in parallel with storage batteries and for electrolytic work where extreme variations in voltage are required by changes in the resistance of the electrolytic cells. The suburban trolley forms a good example of a mixed system, in which alternating current is generated at the central station and transmitted to sub-stations, where it is transformed to low pressure, and converted into direct current for use on the line. Fig. 2,195 shows the interior of a sub-station of this kind. Ques. What direct current pressure is usually employed on traction lines? Ans. 500 volts. Ques. Mention another important service performed by a mixed system. Ans. If the generator furnish alternating current it must be converted into direct current in order to charge storage batteries. |
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