GENERAL LECTURES ON ELECTRICAL ENGINEERING BY CHARLES PROTEUS STEINMETZ, A. M., Ph. D. Consulting Engineer of the General Electric Company, Professor of Electrical Engineering in Union University, Past President, A. I. E* E. Author of "Alternating Current Phenomena," "Elements of Electrical Engineering/' "Transient Electric Phenomena and Oscillations/* Second Edition. Compiled and Edited by JOSEPH Le ROY HAYDEN Robson & Adee, Publishers Schenectady, N. Y. Copyright 1908 by Contents First Lecture General Review Second Lecture General Distribution Third Lecture Light and Power Distribution Fourth Lecture Load Factor and Cost of Power Fifth Lecture Long Distance Transmission Sixth Lecture Higher Harmonics of the Generator Wave Seventh Lecture High Frequency Oscillations and Surges Eighth Lecture Generation Niruth Lecture Hunting of Synchronous Machines. . Tenth Lecture Regulation and Control Eleventh Lecture Lightning Protection Twelfth Lecture Electric Railway Thirteenth Lecture Electric Railway Motor Char- acteristics Fourteenth Lecture Alternating Current Railway Motors Fifteenth Lecture Electrochemistry Sixteenth Lecture The Incandescent Lamp Seventeenth Lecture Arc Lighting Appendix I. Light and Illumination Appendix II. Lightning and Lightning Protection, , 7 21 35 49 61 77 89 99 113 125 135 147 163 175 197 207 215 229 259 Preface HE following lectures on Electrical Engineering are T""" * general in their nature, dealing with the problems of generation, control, transmission, distribution and utilization of electric energy; that is, with the operation of electric systems and apparatus under normal and abnormal conditions, and with the design of such systems ; but the design of apparatus is discussed only so far as it is necessary to under- stand their operation, and so judge of their proper field of application. Due to the nature of the subject, and the limitations of time and space, the treatment had to be essentially descriptive, and not mathematical. That is, it comprises a discussion of the different methods of application of electric energy, the means and apparatus available, the different methods of carrying out the purpose, and the relative advantages and disadvantages of the different methods and apparatus, which determine their choice. It must be realized, however, that such a discussion can be general only, and that there are, and always will be, cases in which, in meeting special conditions,, conclusions regarding systems and apparatus may be reached, differing from those which good judgment would dictate under general and average conditions. Thus, for instance, while certain transformer connections are unsafe and should in general be avoided, in special cases it may be found that the danger incidental to their use is so remote as to be overbalanced by some advantages which they may offer in the special case, and their use would thus be PREFACE justified in this case. That is, in the application of general conclusions to special cases, judgment must be exerted to deter- mine, whether, and how far, they may have to be modified. Some such considerations are indicated in the lectures, others must be left to the judgment of the engineer. The lectures have been collected and carefully edited by my assistant, Mr. J. L. R. Hayden, and great thanks are due & to the publishers, Messrs. Robson Adee, for the very credit- able and satisfactory form in which they have produced the book. ' 1 i i I , | CHARLES P. STEINMETZ. Schenectady, N. Y., Sept. 5, 1908. FIRST LECTURE GENERAL REVIEW N ITS economical application, electric power passes I through the successive steps : generation, transmission, conversion, distribution and utilization. The require- ments regarding the character of the electric power imposed by the successive steps, are generally different, frequently contradictory, and the design of an electric system is therefore a compromise. For instance, electric power can for most pur- no poses be used only at low voltage, to 600 volts, while economical transmission requires the use of as high voltage as possible. For many purposes, as electrolytic work, direct current is necessary; for others, as railroading, preferable; while for transmission, alternating current is preferable, due to the great difficulty of generating and converting high voltage direct current. In the design of any of the steps through which electric power passes, the requirements of all the other steps so must be taken into consideration. Of the greatest importance in this respect is the use to which electric power is put, since it is the ultimate purpose for which it is generated and transmitted ; next in importance is the transmission, as the long distance transmission line usually is the most expensive part of the system, and in the transmission the limitation is more severe than in any other step through which the electric power passes. The main uses of electric power are : General Distribution for Lighting and Power. The relative proportion between power use and lighting may vary from the distribution system of many small cities, in which io GENERAL LECTURES practically all the current is used for lighting, to a power distribution for mills and factories, with only a moderate lighting load in the evening. The electric railway. Electrochemistry, For convenience, the subject will be discussed under the subdivisions: 1. General distribution for lighting and power. 2. Long distance transmission. 3. Generation. 4. Control and protection. 5. Electric railway. 6. Electrochemistry. 7. Lighting. CHARACTER OF ELECTRIC POWER. Electric power is used as a. Alternating current and direct current. b. Constant potential and constant current. c. High voltage and low voltage. a. Alternating current is used for transmission, and for general distribution with the exception of the centers of large cities; direct current is usually applied for railroading. For power distribution, both forms of current are used; in electrochemistry, direct current must be used for electrolytic work, while for electric furnace work alternating current is preferable. The two standard frequencies of alternating current are 60 cycles and 25 cycles. The former is used for general distribution for lighting and power, the latter for conversion to direct current, for alternating current railways, and for large powers. GENERAL REVIEW u In England and on the continent, 50 cycles is standard frequency. This frequency still survives in this country in Southern California, where it was introduced before 60 cycles was standard. The frequencies of 125 to 140 cycles, which were standard in the very early days, 20 years ago, have disappeared. The frequency of 40 cycles, which once was introduced as compromise between 60 and 25 cycles is rapidly disappearing, as it is somewhat low for general distribution, and higher than desirable for conversion to direct current It was largely used also for power distribution in mills and factories as the lowest frequency at which arc and incandescent lighting is still feasible; for the reason that 40 cycle generators driven by slow speed reciprocating engines are more easily operated in parallel, due to the lower number of poles. With the development of the steam turbine as high speed prime mover, the conditions in this respect have been reversed, and 60 cycles is more convenient, giving more poles at the same generator speed, and so less power per pole. Sundry odd frequencies, as 30 cycles, 33 cycles, 66 cycles, which were attempted at some points, especially in the early days, have not spread; and frequencies below 25 cycles, as 15 cycles and 8 cycles, as proposed for railroading, have not proved of sufficient advantage at least not yet so that in general, in the design of an electric system, only the two standard frequencies, 25 and 60 cycles, come into considera- tion. b. Constant current, either alternating or direct, that is, a current of constant amperage, varying in voltage with the load, is mostly used for street lighting by arc lamps; for all other purposes, constant potential is employed. 12 GENERAL LECTURES c. For long distance transmission, the highest permissible voltage is used; for primary distribution by alternating current, 2200 volts, that is, voltages between 2000 and 2600; for alternating current secondary distribution, and direct current distribution, 220 to 260 volts, and for direct current railroading, 550 to 600 volts. i. GENERAL DISTRIBUTION FOR LIGHTING AND POWSR. In general distribution for lighting and power, direct current and 60 cycles alternating current are available. 25 cycles alternating current is not well suited, since it does not permit arc lighting, and for incandescent lighting it is just at the limit , where under some conditions and with some genera- tor waves, flickering shows, while with others it does not show appreciably. iX Fig. 1 The distribution voltage is determined by the limitation of the incandescent lamp, as from 104 to 130 volts, or about no no volts, volts is too low to distribute with good regu- lation, that is, with negligible voltage drop, any appreciable amount of power, and so practically always twice that voltage is employed in the distribution, by using a three-wire system, no with volts between outside and neutral, and 220 volts between the outside conductors, as shown diagrammatically in Pig. i. By approximately balancing the load between the two circuits, the current in die neutral conductor is very small, the GENERAL REVIEW 13 drop of voltage so negligible, and the distribution, regarding voltage drop and copper economy, so takes place at 220 volts, no while the lamps operate at volts. Even where a separate transformer feeds a single house, usually a three-wire distribu- tion is preferable, if the number of lamps is not very small. When speaking of a distribution voltage of no, some voltage anywhere in the range from 104 to 130 volts is no employed. Exactly volts is rarely used, but the voltages of distribution systems in this country are distributed over the whole range, so as to secure best economy of the incan- descent lamp. This condition was brought about by the close co-oper- ation, in this country, between the illuminating companies and the manufacturers of incandescent lamps. The constants of an incandescent lamp are the candle power for instance 16; the economy for instance 3.1 watts for hori- zontal candle power; and the voltage for instance no. By careful manufacture, a lamp can be made in which the filament reaches 3.1 watts per candle power economy at 16 c. p. within one-half candle-power; but the attempt to fulfill at the same time ithe condition, that this economy and candle power be no reached at volts, within one-half volt, would lead to a considerable percentage of lamps which would fall outside of the narrow range permitted in the deviation from the three con- stants; and so, if the same distribution voltage were used throughout the country, either a much larger margin of varia- tion would have to be allowed in the product, that is, the lamps would be far less uniform in quality as is the case abroad, or a large number of lamps would not fulfill the requirements, could not be used, and so would increase the cost of the rest ' 14 GENERAL LECTURES Therefore, all the efforts in manufacture are con- centrated on producing the specified candle power at the required economy, and the lamps are then sorted for voltage. This arrangement scatters the lamps over a considerable voltage range, and different voltages are then adopted by different distribution systems, so as to utilize the entire product of manufacture at its maximum economy. The result of this co-operation between lamp manufacturers and users is, that the incandescent lamps are very much closer to requirements, and more uniform, than would be possible otherwise. The effect however is, that the distribution is rarely actually 1 10, and in alternating current systems, the primary distribution voltage not 2200, but some voltage in the range between 2080 and 2600, as in step-down transformers a constant ratio of transformation, of a multiple of 10 -f- I, is always used. In the following, therefore, when speaking of no, 220 or 2200 volts in distribution systems, always one of the voltages within the range of the lamp voltages is understood. no In this country, volt lamps are used almost exclu- sively, while in England, for instance, 220 volt lamps are generally used, in a three-wire distribution system with 440 volts between the outside conductors. The amount of copper required in the distribution system, with the same loss of power in the distributing conductors, is inversely proportional to the square of the voltage. That is, at twice the voltage, twice the voltage drop can be allowed for the same distribution efficiency; and as at double voltage the current is one-half, for the same load twice the voltage drop at half the current gives four times the resistance, that is, one-quarter the conductor material. By the change from the 220 volt distribution with no volt lamps, to the 440 volt distribution with 220 volt GENERAL REVIEW 15 lamps, the amount of copper in the distributing conductor, and .thereby the cost of investment can be greatly reduced, and current supplied over greater distances, so that from the point of view of the economical supply of current at the customers' terminals, the higher voltage is preferable. However, in the usual sizes, from 50 to 60 watts power consump- tion and so 16 candle power with the carbon filament, and correspondingly higher candle power with the more efficient metallized carbon and metal filaments, the 220 volt lamp is from 10 to 15% less efficient, that is, requires from i o to 15% more power than the no volt lamp, when producing the same amount of light at the same useful life. This differ- ence is inherent in the incandescent lamp, and is due to the far greater length and smaller section of the 220 volt filament, no compared with the volt filament, and therefore no possibil- ity of overcoming it exists ; if it should be possible to build a 220 volt 1 6 candle power lamp as efficient at the same useful no life of 500 hours as the present volt lamp, this would simply mean, that by the same improvement the efficiency of no the volt lamp could also be increased from 10 to 15%, and the difference would remain. For smaller units than 16 candle power, the difference in efficiency is still greater. This loss of efficiency of 10 to 15%, resulting from the use of the 220 volt lamp, is far greater than (the saving in power and in cost of investment in the supply mains ; and the no 220 volt system with volt lamps is therefore more efficient, in the amount of light produced in the customer's lamps, than the /i /)n volt system with 220 volt lamps. In this country, since the early days, the illuminating companies have accepted the responsibility up to the output in light at the customer's lamps, by supplying and renewing the lamps free of charge, no and the system using volt lamps is therefore universally 16 GENERAL LECTURES employed while the 220 volt lamp has no right to existence; while abroad, where the supply company considers its responsi- bility ended at the customer's meter, and the customer is left to supply his own lamps, the supply company saves by the use of 440 volt systems at the expense of a waste of power in the customer's 220 volt lamps, far more than the saving effected by the supply company. In considering distribution systems, it therefore is no unnecessary to consider any other lamp voltage than volts (that is, the range of voltage represented thereby) . In direct current distribution systems, as used in most large cities, the 220 volt network is fed from a direct current generating station, or as now more frequently is the case from a converter substation, which receives ks power as three-phase alternating, usually 25 cycles, from the main generating station, or long distance transmission line. In alternating current distribution, the 220 volt distribution cir- cuits are fed by step-down transformers from the 2200 volt primary distribution system. In the latter case, where con- siderable motor load has to be considered, some arrangement of polyphase supply is desirable, as the single-phase motor is inferior to the polyphase motor, and so the latter is preferable for large and moderate sizes. COMPARISON OF ALTERNATING CURRENT AND DIRECT CURRENT A.t the low distribution voltage of 220, current can economically be supplied from a moderate distance only, rarely exceeding from I to 2 miles. In a direct current system, the current must be supplied from a generating station or a converter substation, that is, a station containing revolving machinery. As such a station requires continuous atten- GENERAL REVIEW 17 tion, its operation would hardly be economical if not of a capacity of at least some hundred kilowatts. The direct current distribution system therefore can be used economically only if a sufficient demand exists, within a radius of i to 2 miles, to load a good sized generator or converter substation. The use of direct current is therefore restricted to those places where a fairly concentrated load exists, as in large cities; while in the suburbs, and in small cities and villages, where the load is too scattered to reach from one low tension supply point, sufficient customers to load a substation, the alternating current must be used, as it requires merely a step- down transformer which needs no attention. In the interior of large cities, the alternating current system is at a disadvantage, because in addition to the voltage consumed by resistance, an additional drop of volitage occurs by self-induction, or by reactance; and with the large conduc- tors required for the distribution of a large low tension current, the drop of voltage by self-induction is far greater than that by resistance, and the regulation of the system therefore is serious- ly impaired, or at least the voltage regulation becomes far more A difficult than with direct current. second disadvantage of the alternating current for distribution in large cities is, that a considerable part of the motor load is elevator motors, and the alternating current elevator motor is inferior to the direct current motor. Elevator service essentially consists in starting at heavy torque, and rapid acceleration, and in both of these features the direct current motor with compound field winding is superior, and easier to control. Where therefore direct current can be used in low tension distribution, it is preferable to use it, and ito relegate alternating current low tension distribution to those cases where direct i8 GENERAL LECTURES current cannot be used, that is, where the load is not sufficiently concentrated to economically operate converter substations. The loss of power in the low tension direct current system is merely the fr loss in the conductors, which is zero at no load, and increases with the load; the only constant loss in a direct current distribution system is the loss of power in the potential coils of the integrating wattmeters on the customer's premises. In the direct current system therefore, (the efficiency of distribution is highest at light load, and decreases with increasing load. In an alternating current distribution system, with a 2200 volt primary distribution, feeding secondary low tension circuits by step-down transformers, the fr loss in the conductors usually is far smaller than in the direct current system, but a considerable constant, or "no load", loss exists; the coreloss in the transformers, and the efficiency of an alternating current distribution is usually lowest at light load, but increases with increase of load, since with increasing load the transformer core loss becomes a lesser and lesser percentage of the total power. The iV loss in alternating current systems must be far lower than in direct current systems: 1. Because it is not the only loss, and the existence of the "no load" or transformer core loss requires to reduce the load loss or iV loss, if an equally good efficiency is desired. With an alternating current system, each low tension main requires only a step-down transformer, which needs no atten- tion ; therefore many more transformers can be used than rotary converter substations in a direct current system, and the fr loss is then reduced by the greatly reduced distance of second- ary distribution. 2. In the alternating current system, the drop of voltage in the conductors is greater by the self-inductive drop than the GENERAL REVIEW 19 ir drop ; the ir drop is therefore only a part of the total voltage drop ; and with the same voltage drop and therefore the same regulation as a direct current system, the fr loss in the alternating current system would be smaller .than in the direct current system. 3. Due to the self-inductive drop, smaller and therefore more numerous low tension distribution circuits must be used with alternating current than with direct current, and a separate and independent voltage regulation of each low tension circuit that is each transformer, therefore usually becomes impracticable. This means that the total voltage drop, resistance and inductance, in the alternating current low tension distribution circuits must be kept within a few percent, that is, within the range permissible by the incandescent lamp. As a result thereof, the voltage regulation of an alternating current low tension distribution is usually inferior to that of the direct cur- rent distribution in many cases to such an extent as to require the use of incandescent lamps of lower efficiency. While therefore in direct current distribution 3.1 watt lamps are always used, in many alternating current systems 3.5 watt lamps have to be used, as the voltage regulation is not sufficiently good to get a satisfactory life from the 3.1 watt lamps. SECOND LECTURE GENERAL DISTRIBUTION DIRECT CURRENT DISTRIBUTION HE TYPICAL direct current distribution is the system T of feeders and mains, as devised by Edison, and since used in all direct current distributions. It is shown diagrammatically in Fig. 2. The conductors are usually under- f ii t30 /30 I =u 1 24 GENERAL LECTURES ground, as direct current systems are used only in large cities. A system of three-wire conductors, called the "mains" is laid in the streets of the city, shown diagrammatically by the heavily drawn lines. Commonly, conductors of one million circular mil section (that is, a copper section which as solid round conductor would have a diameter of i") are used for the outside conductors, the "positive" and the "negative" con- ductor; and a conductor of half this size for the middle or "neutral" conductor. The latter is usually grounded, as pro- tection against fire risk, etc. Conductors of more than one million circular mils are not used, but when the load exceeds the capacity of such conductors, a second main is laid in A the same street. number of feeders, shown by dotted lines in Fig. 2, radiate from the generating station or converter substations, and tap into the mains at numerous points ; potential wires run back from the mains to the stations, and so allow7 of measuring, in the station, the voltage at the different points of the distribution system. All the customers are connected to the mains, but none to the feeders. The mains and feeders are arranged so that no appreciable voltage drop takes place in the mains, but all drop of voltage occurs in the feeders ; and as no customers connect to the feeders, the only limit to the voltage drop in the feeders is efficiency of distribution. The voltage at the feeding points into the mains is kept constant by varying the voltage supply to the feeders with the changes of the load on the mains. This is done by having a number of outside bus bars in the station, as shown diagrammaitically in Fig. 3, differing from each other in voltage, and connecting feeders over from bus bar to bus bar, with the change of load. For instance, in a 2 x 120 voltage distribution, the station may have, in addition to the neutral bus bar zero, three positive GENERAL DISTRIBUTION bus bars i, i', i", and three negative bus bars 2, 2', 2", differing respectively from the neutral bus by 120, 130 and 140 volts, as shown in Fig. 3. At light load, when the drop of voltage in the feeders is negligible, the feeders connect to the busses i, o, 2 of 1 20 volts. When (the load increases, some of the feeders are shifted over, by transfer bus bars, to the 130 volt busbars i' and 2'; with still further increase of load, more feeders are connected over to 130 volts; then some feeders are connected to the 140 volt bus bars, i" and 2", and so, by varying 2LJ -2 -Z' Fig. 3 the voltage supply to the feeders, the voltage at the mains can be maintained constant with an accuracy depending on the number of bus bars. It is obvious that a shift of a feeder from one voltage to another does not mean a corresponding voltage change on the main supplied by it, but raither a shift of load between the feeders, and so a readjustment of the total voltage in the territory near the supply point of the feeder. For instance, if by the potential wires a drop of voltage below 120 volts is registered in the main at the connection point of feeder A in Fig. 2, and this feeder then shifted from the supply 26 GENERAL LECTURES voltage 130 to 140, the current in the main near A, which A before flowed towards as minimum voltage point, reverses A in direction, flows away from A, the load on feeder and thereA fore increases, and the drop of voltage in increases, while the load on the adjacent feeders decreases, and thereby their drop of voltage decreases, with the result of bringing up the voltage in A the mains at the feeder and all adjacent feeders. This inter- linkage of feeders therefore allows a regulation of voltage in the mains, far closer than the number of voltages available in the station. The different bus bars in the station are supplied with their voltage by having different generators or converters in the sta- tion operate at different voltages, and with increasing load on the station, and consequent increasing demand of higher volt- age by the feeders, shift machines from lower to higher voltage bus bars, inversely with decreasing load ; or the different bus bars are operated through boosters, or by connection with the storage battery reserve, etc. In addition to feeders and mains, tie feeders usually con- nect the generating station or substation with adjacent stations, so that during periods of light load, or in case of breakdown, a station may be shut down altogether and supplied from adjacent stations by tie feeders. Such tie feeders also permit most stations to operate without storage battery reserve, that is, to concentrate the storage batteries in a few stations, from which in case of a breakdown of the system, the other stations are supplied over the tie feeders. ALTERNATING CURRENT DISTRIBUTION The system of feeders and mains allows the most perfect voltage regulation in the distributing mains. It is however applicable only to direct current distribution in a territory of GENERAL DISTRIBUTION 27 very concentrated load, as in the interior of a large city, since the independent voltage regulation of each one of numerous feeders is economically permissible only where each feeder represents a large amount of power; with alternating cur- rent systems, the inductive drop forbids the concentration of such large currents in a single conductor. That is, conductors of one million circular mils cannot be used economically in an alternating current system. The resistance of a conductor is inversely proportional to the size or section of the conductor, hence decreases rapidly with increasing current: a conductor of one million circular mils is one-tenth the resistance of a conductor of 100,000 circular mils, and so can carry ten times the direct current with the same voltage drop. The reactance of a conductor, however, and so the voltage consumed by self-induction, de- creases only very little with the increasing size of a conductor, as seen from the table of resistances and reactances of A conductors. wire No. ooo B & S G is eight times the section of a wire No. 7, and therefore one-eighth (the resistance; but the wire No. ooo has a reactance of .109 ohms per 1000 feet, the wire No. 7 has a reactance of .133 oms, or only 1.22 times as large. Hence, while in the wire No. 7, the reactance, at 60 cycles, is only .266 times the resistance and therefore not of serious importance, in a wire No. ooo the reactance is 1.76 times the resistance, and the latter conductor is likely to give a voltage drop far in excess of the ohmic resistance drop. The ratio of reactance to resistance therefore rapidly increases with increasing size of conductor, and for alternating currents, large conductors cannot therefore be used economically where close voltage regulation is required. With alternating currents it therefore is preferable to use several smaller conductors in multiple : two conductors of 28 GENERAL LECTURES No. i in multiple have the same resistance as one conductor of No. ooo; but the reactance of one conductor No. ooo is .109 ohms, and so 1.88 times as great as the reactance of two conductors of No. i in multiple, which latter is half that of one conductor No. i, or .058 ohms, provided that the two conductors are used as separate circuits. In alternating current low tension distribution, the size of the conductor and so the current per conductor, is limited by the self-inductive drop, and alternating current low tension networks are therefore of necessity of smaller size than those of direct current distribution. As regards economy of distribution, this is not a serious objection, as the alternating current transformer and primary distribution permits the use of numerous secondary circuits. In alternating current systems, a primary distribution system of 2200 volts is used, feeding step-down transformers. The different arrangements are A a. separate transformer for each customer. This is necessary in those cases where the customers are so far apart from each other that they cannot be reached by the same low tension or secondary circuit; every alternating current system therefore has at least a number of instances where individual transformers are used. This is the most uneconomical arrangement. It requires the use of small (transformers, which are necessarily less efficient and more expensive per kilowatt, than large trans- formers. The transformer must be built to carry, within its overload capacity, all the lamps installed by the customer, since all the lamps 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. GENERAL DISTRIBUTION 29 As the core loss in the transformer continues whether the transformer is loaded or not, but is not paid for by the customer, the economy of the arrangement is very low; and so it can be understood that in the early days, where this arrangement was generally used, the financial results of most alternating current distributions were very discouraging. Assuming as an instance a connected load of twenty 16 candle power lamps low efficiency lamps, of 60 watts per lamp, since ithe voltage regulation cannot be very perfect allowing then in cases of all lamps being used, an overload of 1 00%, which is rather beyond safe limits, and permissible only on the assumption that this load will occur very rarely, and for a short time the transformer would have 600 watt rafting. Assuming a core loss of 4%, this gives a continuous power consumption of 24 watts. Usually probably only one or two lamps will be burning, and these only a few hours per day, so that he use of two lamps, at an average summer and winter of three hours per day, would probably be a fair example of many such cases. Two lamps or 120 watts, for three hours per day, give an average power of 15 watts, which is paid for by the customer, while the continuous loss in the transformer is 24 watts ; so that the all year efficiency, or the ratio of the power paid for by the customer, to the power consumed by the transformer, is only 15 , 24 or 38%. By connecting several adjacent customers to the same transformer, the conditions immediately become far more favorable. It is extremely improbable that all the customers will burn all their lamps at the same time, the more so, the greater the number of customers is, which are supplied from the same transformer. It therefore becomes unnecessary to 30 GENERAL LECTURES allow a transformer capacity capable of operating all the con- nected load. The larger transformer also has a higher effiicency. Assuming therefore as an instance, four customers of 20 lamps connected load each. The average load would be about 8 lamps. Assuming even one customer burning all 20 lamps, it is not probable that the other customers together would at this time burn more than 10 to 15 lamps, and a trans- former carrying 30 to 35 lamps at overload would probably A be sufficient. 1500 watt transformer would therefore be 3% larger than necessary. At coreloss, this gives a constant loss of 45 watts, while an 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%, while a 1000 watt transformer would give an all year efficiency of 67%. This also illustrates that in smaller transformers a low coreloss is of utmost importance, while the i~r loss is of very secondary importance, since it is appreciable only at heavy load, and therefore affects the all year efficiency very little. When it becomes possible to connect a large number of customers to a secondary main fed from one large transformer the connected load ceases to be of moment in the trans- former capacity; the transformer capacity is determined by the average load, with a safe margin for overloads; in this case, good all year efficiencies can be reached. Economical alternating current distribution therefore requires the use of secondary distribution mains of as large an extent as possible, fed by large transformers. The distance, however, to which a transformer can supply secondary current, is rather limited by the inductive drop of voltage ; therefore, for supplying secondary mains, transformers of larger size than 30 kw, are rarely used, but rather several transformers are employed, to feed in the same main at different points. GENERAL DISTRIBUTION 31 Extending the secondary mains still further by the use of several transformers feeding into the same mains, or, as it may be considered, inter-connecting the secondary mains of the different transformers, we arrive at a system somewhat similar to the direct current system : a low tension distribution system of 220 volts three-wire mains, with a system of feeders tapping into it at a number of points, as shown in Fig. 4. These feeders 4. Alternating Current Distribution with Secondary Mains and Primary Feeders. are primary feeders of 2200 volts, connecting to the mains through step-down transformers. In such a system, by varying the voltage impressed upon the primary feeders, a voltage regulation of the system similar to that of direct current distribution becomes feasible. Such an arrangement has these advantages over the direct current system: the drop in the feeders is very much lower, due to their higher voltage ; and 32 GENERAL LECTURES that the feeder voltage can be regulated by alternating current feeder regulators or compensators, that is, stationary structures similar to the transformer. It has, however, the disadvantage ithat, due to the self-induction of the mains, each feeding point can supply current over a far shorter distance than with direct current, and the interchange of current between feeders, by which the load can be shifted and apportioned between the feeders, is far less. As a result, it is difficult to reach as good voltage regulation with the same attention to the system; and since this arrangement has the disadvantage that any break- down in the secondary system or in a transformer may involve the entire system, this system of inter-connected secondary mains is rarely used for alternating current distribution, but the secondary mains are usually kept separate. That is, as shown diagrammaftically in Fig. 5, a number of separate secondary mains are fed by large transformers from primary feeders, and usually each primary feeder connects to a number of transformers. Where the distances are considerable, and the voltage drop in the primary feeders appreciable, voltage regulation of the feeders becomes necessary; and in this case, to get good voltage regulation in the system, attention must be given to the arrangements of the feeders and mains. That is, all the transformers on the same feeder should be at about tthe same distance from the station, so that the voltage drop between the transformers on the same feeder is negligible; and the nature of the load on the secondary mains fed by the same feeder should be about as nearly the same as feasible, so that all the mains on the same feeder are about equally loaded. It would therefore be undesirable for voltage regulation, to connect, for instance, a main feeding a GENERAL DISTRIBUTION 33 residential section to the same feeder as a main feeding a business district or an office building. 5. Typical Alternating Current Distribution. In a well designed alternating current distribution system, that is, a system using secondary distribution mains as far as feasible, the all year efficiency is about the same as with the direct current system. In such an alternating current system, 34 GENERAL LECTURES the efficiency at heavy load is higher, and at light load lower, than in the direct current system ; in this respect the alternating current system has the advantage over the direct current system, since at the time of heavy load the power is more valuable than at light load. THIRD LECTURE LIGHT AND POWER DISTRIBUTION A N DIRECT current distribution system, the motor load is connected to the outside mains at 220 volts, and only very small motors, as fan motors, between outside mains and neutral ; since the latter connection, with a large motor, would locally unbalance a system. The effect of a motor on the system depends upon its size and starting current, and with the large mains and feeders, which are gener- ally used, even the starting of large elevator motors has no appreciable effect, and the supply of power to electric elevators represents a very important use of direct current distribution. In alternating current distribution systems, the effect on the voltage regulation, when starting a motor, is far more severe; since alternating current motors in starting usually take a larger current than direct current motors starting with the same torque on the same voltage; and the current of the alternating current motor is lagging, the voltage drop caused by it in the reactance is therefore far greater than would be caused by the same current taken by a non-inductive load, as lamps. Furthermore, alternating current supply mains usually are of far smaller capacity, and therefore more affected in voltage. Large motors are therefore rarely connected to the lighting mains of an alternating current system, but separate transformers and frequently separate feeders are used for the motors, and very large motors commonly built for the primary distribution voltage of 2200, are connected to these mains. For use in an alternating current distribution system, the synchronous motor hardly comes into consideration, since the synchronous type is suitable mainly for large powers, where it is operated on a separate circuit. 38 GENERAL LECTURES The alternating current motor mostly used in small and moderate sizes such as come into consideration for power distribution from a general supply system is the induction motor. The single-phase induction motor, however, is so inferior to the polyphase induction motor, -that single-phase motors are used only in small sizes; for medium and larger sizes the three-phase or two-phase motor is preferred. This however, introduces a complication in the distribution system, and the three-wire single-phase system therefore is less suited for motor supply, but additional conductors have to be added to give a polyphase power supply to the motor. As the result thereof, motors are not used in alternating current systems to the same extent as in direct current systems. In the alternating current system, however, the motor load is, if anything, more important than in the direct current system, to increase the load factor of the system ; since the efficiency of the alternating current system decreases with decrease of load, while that of a direct current system increases. Compared with the direct current motor, the polyphase induction motor has the disadvantage of being less flexible: its speed cannot be varied economically, as that of a direct current motor by varying the field excitation. Speed variation of the induction motor produced by a rheostat in the armature or secondary circuit, in the so-called form "M" motor is accomplished by wasting power : the power input of an induction motor always corresponds to full speed; if the speed is reduced by running on the rheostat, the difference in power between that which the motor actually gives, and that which it would give, with the same torque, at full speed, is consumed in the rheostat Where therefore different motor speeds are required, provisions are made in the induction motor to change the number LIGHT AND POWER DISTRIBUTION 39 of poles ; thereby a number of different definite speeds are available, at which the motor operates economically as "multi- speed" motor. The starting torque of the polyphase induction motor with starting rheostat in the armature (Form L motor) is the same as the running torque at the same current input, just as in the case of the direct current shunt motor with constant field excitation. In the squirrel cage induction motor, how- K ever, (Form motor) the starting torque is far less than the running torque at the same current input; or inversely, to produce the same starting torque, a greater starting current is required. In starting torque or current, the squirrel cage induction motor has the disadvantage against the direct current motor. It has, however, an enormous advantage over it in its greater simplicity and reliability, due to the absence of commutator and brushes, and the use of a squirrel cage armature. > ; j The advantage of simplicity and reliability of the squir- rel cage induction motor sufficiently compensates for the disadvantage of the large starting current, to make the motor most commonly used. In an alternating current distribution system, however, great care has to be taken to avoid the use of such larger motors at places where their heavy lagging starting currents may affect the voltage regulation; in such places, separate transformers and even separate primary feeders are desirable. The single-phase induction motor is not desirable in larger sizes in a distribution system, since its starting current is still larger; in small sizes, however, it is extensively used, since it requires no special conductors, but can be operated from a single-phase lighting main. 40 GENERAL LECTURES The alternating current commutator motor is a single- phase motor which has all the advantages of the different types of direct current motors ; it can be built as constant speed motor of the shunt type, or as motor with the charac- teristics of the direct current series motor : very high starting torque with moderate starting current. It has, however, also the disadvantages of the direct current motor: commu>tator and brushes ; and so requires more attention than the squirrel cage induction motor. Alternating current generators now are almost always used as polyphase machines, three-phase or two-phase, and transmission lines are always three-phase, though in transform- ing down, the system can be changed to two-phase. The power supply in an alternating current system therefore is practically always polyphase ; and since a motor load, which is very desir- able for economical operation, also requires polyphase currents, alternating current distribution systems always start from poly- phase power. The problem of alternating current distribution -therefore is to supply, from a polyphase generating system, single-phase current to the incandescent lamps, and polyphase current to the induction motors. PRIMARY DISTRIBUTION SYSTEMS i. Two conductors of the three-phase generating or transmission system are used to supply a 2200 single-phase system for lighting by step-down transformers and three-wire secondary mains ; the third conductor is carried to those places where motors are used and three-phase motors are operated by separate step-down transformers. In the lighting feeders, the voltage is then controlled by feeder regulators, or, in a smaller system, the generator excitation is varied so as to main- LIGHT AND POWER DISTRIBUTION 41 tain the proper voltage on the lighting phase. At load, the three-phase triangle then more or less unbalances, but induction motors are very little sensitive to unbalancing of the voltage, and by their regulation by taking more current from the phase of higher, less from the phase of lower voltage tend to restore the balance. For smaller motors, frequently two transformers are used, arranged in "open delta" connection. 2. Two-phase generators are used, or in the step-down transformers of a three-phase transmission line, the voltage is changed from three-phase to two-phase; the lighting feeders are distributed between the two phases and controlled by potential regulators so that the distribution for lighting is singlephase, by three-wire secondary mains. For motors, both phases are brought together, and the voltage stepped down for use on two-phase motors. This requires four, or at least three, primary wires to motor loads. 3. From three-phase generators or transmission lines, three separate single-phase systems are operated for lighting; that is the lighting feeders are distributed between the three phases, and all three primary wires are brought to the step- down transformers for motors. This arrangement, by dis- tributing the lighting feeders between the three phases, would require more care in exactly balancing the load between all three phases than two, but a much greater unbalancing can be allowed without affecting the voltage. 4. Four-wire three-phase primary distribution with grounded neutral, and 2200 volts between outside conductors and neutral. The lighting feeders are distributed between (the three circuits between outside conductors and neutral, and motors supplied by three of such transformers. This system is becoming of increasing importance, since it allows economical distribution to distances beyond those which can be reached 42 GENERAL LECTURES with 2200 volts : with 2600 volts on the transformers as the upper limit of primary distribution voltage the voltage between outside conductors is 4500, and the copper economy of the system therefore is that of a 4500 volt three-phase system. 5. Polyphase primary and polyphase secondary distribution, with the motor connected to ithe same secondary mains as the lights. SYSTEMS OF LOW TENSION DISTRIBUTION FOR LIGHTING AND POWER. i. Two-WIRE DIRECT CURRENT OR SINGLE-PHASE no Vows. Fig 6. This can can be used only for very short distances, since its copper economy is very low, that is, the amount of conduc- tor material is very high for a given power. Cu. i. o ^ 6 //Off 6. Two-Wire System. LIGHT AND POWER DISTRIBUTION 43 2. THREE-WIRE DIRECT CURRENT OR SINGLE-PHASE no- 220 VOLTS. Fig. 7. Neutral one-half size of the two outside conductors. The two outside conductors require one-quarter the copper of the no two wires of a volt system; since at twice the voltage and one-half the current, four times the resistance or one-quarter O f Fi. 7. Three-Wire System. the copper is sufficient for the same loss (the amount of con- ductor material varying with the square of the voltage). Adding then one-quarter for the neutral of half-size, = i + r = X gives \ ; or altogether \ jg of the no conductor material required by the two-wire volt system. That is, the copper economy is ^. This is the most commonly used system, since it is very economical, and requires only three conductors. It is, however, a single-phase system, and therefore not suitable for operating polyphase in- duction motors. 44 GENERAL LECTURES 3, FOUR-WIRE QUARTER-PHASE ( TWO-PHASE). Fig. 8. Two separate two-wire single-phase circuits, therefore no saving in copper over two-wire systems. That is, the cop- per economy is : Cu. i. o s^ //L 1. S 6 Fig. 8. Four-Wire Two-Phase System. 4. THREE-WIRE QUARTER-PHASE. Fig. 9. Common return of both phases, therefore saves one wire or one-quarter of the copper ; hence has the copper economy : ^Cu. 3 ^ In this case however, the middle or common return wire carries A/2, or 1.41 times as much current as the other two wires, and when making all three wires of the same size, the A copper is not used most economically. small further saving is therefore ma.de by increasing the middle wire and decreasing the Fi. 9. Three-Wire Two-Phase System. outside wires so tthat the middle wire has 1.41 times the section of each outside wire. This improves the copper economy to: Cu. 0.73 LIGHT AND POWER DISTRIBUTION 45 5. THREE- WIRE: THREE-PHASE. Fig. 10. A three-phase system is best considered as a combination of three single-phase systems, of the voltage from line to neutral, and with zero return (because the three currents neutralize each other in the neutral). Compared thereto the two-wire single-phase system can be considered as a combination of two single-phase circuits from wire to neutral with zero return. 10. Three-Wire Three-Phase System. no In a volt single-phase system the voltage from line to neutral equals -y, in a three-phase system equals -T=J VS The mi -y no ratio ,. of Tj_ voltages . is 110 . -r- -~r~, or 110 x 110 4* 3 and the square of the ratio of voltages equals j; and as the copper economy varies with the square of the voltage, the copper economy for the three-wire three-phase system is : Co.? 6. FIVE-WIRE QUARTER-PHASE. Fig. n. Neglecting the neutral conductor, the five-wire quarter- phase system can be considered as four single-phase circuits without return, from line to neutral, of voltage no. Com- pared with the two-wire circuit, which consists of two single- y phase circuits without return, of volts, No. 6 therefore has twice the voltage of No. i ; therefore one-quarter the copper. 46 GENERAL LECTURES Making the neutral half the size of the main conductor = ^ adds one-half of the copper of one conductor, or g of j + so giving a total of j $2, that is, a copper economy of : t r , 1 \ Fi&. 1 1. Five-Wire Two-Phase System. 7. FOUR-WIRE THREE-PHASE. Fig. 12. Lamps connected between line and neutral. Neglecting the neutral, the system consists of three single- no phase circuits without return, of volts, and compared with t f \ I /wrg* T 12. Four-Wire Three-Phase System. the two-wire circuit of -y between wire and neutral without return, it therefore requires one-quarter the copper. Making the neutral one-half size adds g of the copper, = or g of } 24, and so gives a total copper economy of . _7 5?]T 4 24' LIGHT AND POWER DISTRIBUTION 47 8. THREE-WIRE SINGLE-PHASE LIGHTING WITH THREEPHASE POWER. Fig. 13. Lighting: Half size neutral, same as No. 2, therefore copper economy : = Cu. ^ 16 Power: Three-wire three-phase 220 volts; that is, the same as No. 5, but twice the voltage, thus one-quarter the = copper of No. 5, or \ of | : - 3 Fig. 13. Single-Phase Ughtlng and Three-Phase Power. The systems mostly used are: No. 2. Three-wire direct current or alternating current single-phase. No. 8. Three-wire lighting, three-phase power. Less frequent No. 6. Five-wire quarter-phase. No. 7. Four-wire three-phase. As we have seen, the two-wire system is rather inefficient in copper. High efficiency requires the use of a third conduc- tor, that is, the three-wire system, for direct current or singlephase alternating current. Three-wire polyphase systems, however, are inefficient in copper, as No. 4 and No. 5 ; and to reach approximately the same copper economy, as is reached by a three-wire system with direct current and single-phase alternating current, re- quires at least four wires with a polyphase system. 48 GENERAL LECTURES That is, for equal economy in conductor material, the polyphase system requires at least one more conductor than the single-phase or the direct current distribution system. While the field of direct current distribution is found in the interior of large cities, alternating current is used in smaller towns and villages and in the suburbs of large cities. In the latter, therefore, alternating current does the pioneer work. That is, the district is developed by alternating current, usually with overhead conductors, and when the load has become sufficiently large to warrant the establishment of con- verter substations, direct current mains and feeders are laid under ground, the alternating current distribution is abandoned, and the few alternating current motors are replaced by direct current motors. In the last years, however, considerable motor load has been developed in the alternating current suburban distribution systems, fairly satisfactorily alternating current elevator motors have been developed and introduced and the motor load has become so large as to make it economically difficult to replace the alternating current motors by direct current motors in changing the system to direct current; and it therefore appears that the distribution systems of large cities will be forced to maintain alternating current distribution even in districts of such character as would make direct current preferable. FOURTH LECTURE LOAD FACTOR AND COST OF POWER The cost of the power supplied at the customer's meter consists of three parts. A A. fixed cost, that is, cost which is independent of the amount of power used, or the same whether the system is fully loaded or carries practically no load. Of this character, for instance, is the interest on the investment in the plant, the salaries of its officers, etc. A B. cost which is proportional to the amount of power used. Such a proportional cost, for instance, is that of fuel in a steam plant. A C. cost depending on the reliability of service required, as the cost of keeping a steam reserve in a water power trans- mission, or a storage battery reserve in a direct current dis- tribution. Since of the three parts of the cost, only one, B, is propor- tional to the power used, hence constant per kilowatt output, the other two parts being independent of the output, hence the higher per kilowatt, the smaller a part of the capacity of the plant the output is ; it follows that the cost of power delivered is a function of the ratio of the actual output of the plant, to the available capacity. Interest on the investment of developing the waiter power or building the steam plant, the transmission lines, cables and distribution circuits, and depreciation are items of the character A, or fixed cost, since they are practically independent of the power which is produced and utilized. Fuel in a steam plant, oil, etc., are proportional costs, that is, essentially depending on the amount of power produced. 52 GENERAL LECTURES A Salaries are fixed cost, ; labor, attendance and inspection are partly fixed cost A, partly proportional cost B, economy of operation requires therefore a shifting of as large a part thereof over into class B, by shutting down smaller substations during periods of light load, etc. Incandescent lamp renewals, arc lamp trimming, etc., are essentially proportional costs, B. The reserve capacity of a plant, the steam reserve main- tained at the receiving end of a transmission line, the difference in cost between a duplicate pole line and a single pole line with two circuits, the storage battery reserve of the distribution system, the tie feeders between stations, etc., are items of the character C ; that is, part of the cost insuring the reliability and continuity of power supply. A The greater the fixed cost is, compared with the propor- tional cost B, the more rapidly the cost of power per kilowatt output increases with decreasing load. In steam plants very A frequently is larger than B, that is, fuel, etc. not being the A largest items of cost; in water power plants practically al- ways is far larger than B. As result thereof, while water power may appear very cheap when considering only the proportional cost B which is very low in most water powers the fixed A cost usually is very high, due to the hydraulic development required. The difference in the cost of water power from that of steam power therefore is far less than appears at first. As water power is usually transmitted over a long distance line, while steam power is generated near the place of consumption, water power usually is far less reliable than steam power. To insure equal reliability, a water power plant brings the item C, the reliability cost, very high in comparison with the reliability cost of a steam power plant, since the possibility of a break- down of a transmission line requires a steam reserve, and LOAD FACTOR AND COST OF POWER 53 where absolute continuity of service is required, it requires also a storage battery, etc. ; so that on the basis of equal reliability of service, sometimes very little difference in cost exists between steam power and water power, unless the hydraulic development of the latter was very simple. The cost of electric power of different systems therefore is not directly comparable without taking into consideration the reliability of service and the character of the load. As a very large, and frequently even the largest part of the cost of power, is independent of the power utilized, and therefore rapidly increases with decreasing load on the system, the ratio of average power output to the available power capacity of the plant is of fundamental importance in the cost of power per kilowatt delivered. This ratio, of the average power consumption to the available power, or station capacity, has occasionally been called "load factor." This definition of the term "load factor" is, however, undesirable, since it does not take into consideration the surplus capacity of the station, which may have been provided for future extension; the reserve for insuring reliability C, etc. ; and other such features which have no direct relation whatever to the character of the load. Therefore as load factor is understood, in accordance with the definition in the Standardization Rules of the A. I. E. E., the ratio of the average load to the maximum load; any excess of .the station capacity beyond the maximum load is power which has not yet been sold, but which is still available for the market, or which is held in reserve for emergencies, is not charged against the load factor. The cost of electric power essentially depends on the load factor. The higher the load factor, the less is the cost of the power, and a low load factor means an abnormally high cost 54 GENERAL LECTURES per kilowatt. This is the case in steam power, and to a still greater extent in water power. For the economical operation of a system, it therefore is of greatest importance to secure as high a load factor as possible, and consequently, the cost and depending thereon the price of electric power for different uses must be different if the load factors are different, and the higher the cost, the lower the load factor. Electrochemical work gives the highest load factor, frequently some 90%, while a lighting system shows the poorest load factor in an alternating current system without motor load occasionally it is as low as 10 to 20%. Defining the load factor as the ratio of the average to the maximum load, it is necessary to state over how long a time the average is extended ; that is, whether daily, monthly or yearly load factor. &. 14. Summer Li^htln^ Load Curve. For instance, Fig. 14 shows an approximate load curve of a lighting circuit during a summer day : practically no load LOAD FACTOR AND COST OF POWER 55 except for a short time during the evening, where a high peak is reached. The ratio of the average load to the maximum load during this day, or the daily load factor, is 22.8%. Fig. 15 shows an approximate lighting load curve for a winter day : a small maximum in the morning, and a very high evening maximum, of far greater width than the summer day curve, giving a daily load factor of 34.5%. t \\ 7 Fi&. 15. Winter Lihtin& Load Curve. During the year, the daily load curve varies between the extremes represented by Figs. 14 and 15, and the average annual load is therefore about midway between the average load of a summer day and that of a winter day. The maximum yearly load, however, is the maximum load during the winter GENERAL LECTURES day; and the ratio of average yearly load to maximum yearly load, or the yearly load factor of the lighting system, therefore is far lower than the daily load factor : if we consider the aver- age yearly load as the average between 14 and 15, the yearly load factor is only 23.6%. One of the greatest disadvantages of lighting distri- bution therefore is the low yearly load factor, resulting from the summer load being so very far below the winter load ; econ- omy of operation therefore makes an increase of the summer lighting load very desirable. This has lead to the development of spectacular lighting during the summer months, as represented by the various Luna Parks, Dreamlands, etc. BL^L/A ACWX vf*v \ Jg 6 a /& i Fl^. 16. Factory Power Load Curve. The load curve of a factory motor load is about the shape shown in Fig. 16: fairly constant from the opening of the factories in fthe morning to their closing in the evening, with perhaps a drop of short duration during the noon hour, and a low extension in the evening, representing overtime work. It gives a daily load factor of 49.5%. LOAD FACTOR AND COST OF POWER 57 This load curve, superimposed upon the summer lighting curves, does not appreciably increase the maximum, but very greatly increases the average load, as shown by the dotted curve in Fig. 14; and so improves the load factor, to 65.4^ thereby greatly reducing the cost of the power to the station, in this way showing the great importance of securing a large motor load. During the winter months, however, the motor load overlaps the lighting maximum, as shown by -the dotted curve in Fig, 15. This increases the maximum, and thereby increases the load factor less, only to 41.7%. This is not so serious in the direct current system with storage battery reserve, as the overlap extends only for a short time, the overload being taken care of by storage batteries or by the overload capacity of generators and steam boilers ; but where it is feasible, it is a great advantage if the users of motors can be induced to shut them down in winter with beginning darkness. It follows herefrom, that additional load on the station during the peak of the load curve is very expensive, since it A increases the fixed cost and C, while additional load during the periods of light station load, only increases the proportional cost B; it therefore is desirable to discriminate against peak loads in favor of day loads and night loads. For this purpose, two-rate meters have been developed, that is, meters which charge a higher price for power consumed during the peak of the load curve, than for power consumed dur- ing the light station loads. To even out load curves, and cut down the peak load, maximum demand meters have been developed, that is, meters which charge for power somewhat in proportion to the load factor of the circuit controlled by the meter. Where the circuit is a lighting circuit, and the maximum demand therefore coincides with the station peak, GENERAL LECTURES this is effective, but on other classes of load the maximum demand meters may discriminate against the station. For instance, a motor load giving a high maximum during some part of the day, and no load during the station peak, would be preferable to the station to a uniform load throughout the day, including the station peak, while the maximum demand meter would discriminate against the former. By a careful development of summer lighting loads and motor day loads, the load factors of direct current distribution systems have been raised to very high values, 50 to 60% ; but in the average alternating current system, the failure of developing a motor load frequently results in very unsatisfactory yearly load factors. \ -L hoAp \Cvftvr\ I. Fi&. 17. Railroad Load Curve. The load curve of a railway circuit is about the shape of that shown in Fig. 17 : a fairly steady load during the day, with a morning peak and an evening peak, occasionally a smaller noon peak and a small second peak later in the evening, then tapering down to a low value during the night. The average LOAD FACTOR AND COST OF POWER 59 load factor usually is far higher than in a lighting circuit, in Fig. 17:54.396. In defining the load factor, it is necessary to state not only the time over which the load is to be averaged, as a day, or a year, but also the length of time which the maximum load must last, must be counted. For instance, a short circuit of a large motor during peak load, which is opened by the blowing of the fuses, may momentarily carry the load far beyond the station peak without being objectional. The minimum duration of maximum load, which is chosen in determining the load factor, is that which is permissible without being objectionable for the purpose for which the power is distributed. Thus in a lighting system, where voltage regulation is of fore- most importance, minutes may be chosen, and maximum load may be defined as the average load during that minute during which the load is a maximum; while in a railway system, a half-hour may be used as a duration of maximum load, as a railway system is not so much affected by a drop of voltage due to overload, and an overload of less than half an hour may be carried by the overload capacity of the generators and the heat storage of the steam boilers; so that a peak load requires serious consideration only when it exceeds half an hour. FIFTH LECTURE LONG DISTANCE TRANSMISSION HREE-PHASE is used altogether for long distance fF transmission. Two-phase is not used any more, and direct current is being proposed, having been used abroad in a few cases : but due to the difficulty of generation and utilization, it is not probable that it will find any extended use, so that it does not need to be considered. FREQUENCY The frequency depends to a great extent on the character of the load, that is, whether the power is used for alternating current distribution 60 cycles or for conversion to direct current 25 cycles. For die transmission line, 25 cycles has the advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proportional to the frequency. VOLTAGE 1 1,ocx) to 13,200 volts and more recently, even 22,000 volts is most common for shorter distances, as 10 to 20 miles, since this is about the highest voltage for which generators can be built ; its use therefore saves the step-up transformers, that is, the generator feeds directly into the line and to the step- down transformers for the regular load. The next step is 30,000 volts ; that is, 33,000 volts at the generator, 30,000 at the receiving end of the line. No inter- mediate voltages between this and the voltage for which generators can be wound is used, as 30,000 volts does not yet offer any insulator troubles ; but line insulators can be built at moderate cost for this vokage, and as step-up transformers 64 GENERAL LECTURES have to be used, it is not worth while to consider any lower voltage than 33,000 volts. This voltage transmits economically up to distances of 50 to 60 miles. 40,000 to 44,000 volts is the next step ; it is used for high power transmission lines of greater distance, where reliability of operation is of importance and the use of a conservative voltage therefore preferable to the attempt at economizing by the use of extra high voltages. A number of 60,000 volt systems are in more or less successful operation, and systems of 80,000 to 110,000 volts are in construction and a few in operation. Where the dis- tances are very great, power valuable, and continuity of ser- vice not of such foremost importance, such voltages are justified in the present state of the art In such very high voltage systems, the transformers are occasionally wound so that they can be connected for half voltage, for operating the line at half voltage, until the load has sufficiently increased to require full voltage; or the Y transformers are built for star or connection at full voltage, and at first operated in ring or delta connection, at = 57% of full voltage. rj- The cost of a long distance transmission line depends on the voltage used. The cost of line conductors decreases with the square of the voltage. At twice the voltage, twice the line drop can be allowed with the same loss; at twice the voltage the current is only half for the same power, and twice the drop with half the current gives four times the resistance, that is, one-quarter the conductor section and cost LONG DISTANCE TRANSMISSION 65 The cost of line insulators increases with increase of voltage. The cost of pole line increases with increase of voltage, since greater distance between the conductors is necessary and so longer poles, longer cross arms, and heavier construction, and not so many circuits can be carried on the same pole line. The lower the voltage, the greater in general is the reli- ability of operation, since a larger margin of safety can be allowed. Since a part of the cost of the transmission line decreases, another part increases with the voltage, a certain voltage will be most economical. Lower voltage increases the cost of the conductor, higher voltage increases the cost of insulators and line construction, and decreases the reliability. The most economical voltage of a transmission line varies with the cost of copper. When copper is very high, higher vokages are more economical than when copper is low. The same applies to aluminum, since the price of aluminum has been varied with that of copper. Aluminum generally is used as stranded conductor. In the early days single wire gave much trouble by flaws in the wire. Aluminum expands more than copper with temperature changes, and so when installing the line in summer, a greater sag must be allowed than with copper, otherwise it stretches so tight in winter that it may tear apart. Aluminum also is more difficult to join together, since it cannot be welded. For the same conductivity an aluminum line has about twice the size, but one-half of the weight of a copper conductor, and costs 10% less ; but copper has a permanent value, while the price of aluminum may sometime drop altogether, as the metal has no intrinsic value, being one of (the most common 66 GENERAL LECTURES constituents of the surface of the earth, and its cost is merely that of its separation or reduction. LOSSES IN LINE DUE TO HIGH VOLTAGE The loss in the line by brush discharge or corona effect is nothing up to a certain voltage, but at a certain voltage it begins and very rapidly increases. The voltage at which a loss by corona effect begins is where the air at the surface of the conductor breaks down, becomes conducting and thus luminous. This occurs at a potential gradient of 100,000 to 120,000 volts per inch. The potential gradient is highest at the surface of the conductor. JH Ft&. 18. In Fig. 18 let R = radius of conductor. = 2 d distance between conductor centres. O At a point x from the centre the potential is ; C ^ ~~ d x C 2CX _~_~_ d+x d2 x1 = for:x d R that is, at the conductor surface, it is : Ql=e LONG DISTANCE TRANSMISSION 67 Substituting this in the equation, gives : _c e If hence : c=eR therefore the potential at point x is : 2 Rx d2 x2 e and the potential gradient: = = + g ~~