Power Distribution for Electric Railroads

Front matter

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Preface

This little book is written in the hope that it may be of service to tliose whose daily work is concerned with the art of transportation, in which electrical traction is to-day so potent a factor. The part it may play to-morrow only the prophet can say.

The author has endeavored to set forth the general principles of the distribution of electrical energy to moving motors, to describe the methods which experience has shown to be desirable in such work, and to point out the ways in which these principles and methods can be co-ordinated in everyday practice. The art of correctly designing systems of distribution requires, more than anything else, skilled judgment and infinite finesse\ it cannot be reduced to formulae in which these terms do not enter as variables. The most that can be done is to sketch the lines of thought that, followed cautiously and shrewdly, lead to good results.

For the most part apparatus is too mutable to describe exhaustively, unless one is writing history. The reader will therefore find little of such detail, save in the frontier region which lies between established tramway practice and that greater field that stretches toward unknown bounds. Along that frontier experiment has blazed paths here and there, and we must note them carefully. We can see whither they lead, but dare not say how far.

The best advice that can be given to the engineer is to keep his eyes and ears open and never to let himself get caught out of sight of experimental facts.

Chapter I. Fundamentai, Principi^ks

Classes of distribution — Fundamental formulae of distribution — Plate I, showing size of conductors for various losses — Losses with distributed and moving loads — Simple and branched lines — Irregular distribution of loads — Center of gravity of load — Location of centers of distribution — Networks and their computation — Variations of load, their nature and magnitude 1-27

Chapter II

thb return circuit.

Nature of the return circuit — Conductivity of rails — Systems of bonding — Arrangement of bonds — Resistance of bonds and bond contacts — Earth resistance — Leakage of current from the rails to earth and other conductors^— Electrolysis, its distribution and amount — Remedies — Supplementary wires — Continuous track — Welded and cast joints — The double trolley — Energy lost by bad bonding — Net resistance of bonded track — Track constants — Formula for complete circuit 28-55

Chapter III. Direct Feeding Systems

Systems of arranging feeders — Maximum and average drop — Load factor of the station — Wandering load — Computation of a feeder system — Extent of lines — Average load on lines — Center of distribution — Maximum loads — Trolley wire and track return — General feeding system — Reinforcement at special points — Plate II, chart for feeder computation — Cost of wasted energy 56-83

Vi CONTENTS.

Chapter IV. Spbciai, Mbthods Op Distribution

Boosters, their proper and improper use — ^Three wire system — Methods of balancing — Self contained three wire system — Advantage of high voltage — Motors in series — Increase of working voltage — Arrangement of feeders — Composite systems 84-103.

Chapter V. Substations

Auxiliary stations — Distributed stations — Substations with power transmission — Cost of power in stations of various sizes — Single station vs, distributed stations — ^A typical auxiliary station — Conditions of economy — ^Typical . distributed stations — ^Typical transmission station — Comparison of substation methods — Relative costs 104-129'

Chapter VI. Transmission Of Power For Substations

Generation of alternating current — Modern alternators — ^Necessity of high voltage — Inner pole machines — Transformers — Transmission lines — Insulators — Synchronous motors — Polyphase generators — Substations with synchronous motors — Motor generators — Rotary converters — I/agging and leading current — Computation of an alternating line — of a three phase line — Operation of the machines. . . 130-164

Chapter VII. Ai^ternating Motors For Raii^way Work

Varieties of alternating motors — Synchronous motors with commutating start — with inductive start — Properties of synchronous motors — Poljrphase induction motors — ^their structure and properties — Regulation of speed — Torque — Tests of polyphase induction motors for railway service — their weak points — The first polj^hase railway — Induction motors on monophase circuits — Methods of working polyphase motors from monophase circuits — Monophase induction motors and their properties — ^Application of alternating transmission to railway work — Its economic relation to other methods of working 165-198:

CONTENTS. Vii

Chapter VIII. Intsrurbak And Cross Country Work

Conditions on interurban roads — Power required — Computation of the feeding system — Economy of various methods of distribution — Light electric roads for country districts — Narrow gauge roads-cost of construction and operation — Bicycle and saddle-back roads-cost of construction and operation 199-226

Chapter IX. Fast And Hbavy Raii,way Skrvick

Kinds of work for which electric power is best suited — Suburban passenger traffic — Conditions of competition between steam and electricity — Power required for operating electrically — Special trolley systems — Computation of the feeders — Cost of overhead system — The third rail system — The Nantasket road — Cost of electric power for suburban work — Very high speeds — ^Air resistance — Other resistances — ^Tractive power required — ^Track for extreme speeds — Methods of operation — ^The braking problem — Computation of the feeding system — Cost of power — Electric elevated roads— The Metropolitan road of Chicago — The Lake Street road of Chicago. Distribution of the power — Special heavy service — ^The Baltimore & Ohio tunnel — Results already attained — Electric passenger locomotive — Methods of power distribution 227-268

CHAPTER I. FUNDAMENTAI, PRlNCIPI^BS

The distribution of electrical energy for use in propelling railway cars is, by nature, a special problem. It deals with magnitudes and distances greater than are usual in other branches of electrical engineering, and, in addition, with the difi&culties of a load that constantly shifts in amount and position. Consequently, the design of a distributing system is of singular difiSculty.

In computing the area of conductors, one ordinarily assumes the load to be the only independent variable, but in this case the distance of transmission must be so considered, and both quantities are of the most erratic character.

The general equations can therefore only be solved within limits, except in special cases, and even then only by very judicious assumptions. It is therefore worth while to investigate these limits, their extent and the causes which impose them.

The conducting system of an electric railway, large or small, consists of three somewhat distinct parts — the working conductor, the return circuit and the feeders. By the first is meant that part of the total circuit from which the moving contact, carried by the car, immediately derives its current. Physically it is a wire or bar, uninsulated as respects the moving contact, and supported in any position — overhead, on the ground or under the ground — that circumstances may require.

The return circuit is, in a large proportion of cases, that which receives current from the wheels of the car, and is composed, partly or wholly, of the rails. In certain cases, conduit roads, double trolley roads and telpher systems, the working and return conductors are alike and of

2 POWER DISTRIBUTION FOR KLKCTRIC RAII.ROADS.

equal resistance. They may therefore be treated alike as parts of the working circuit. The ordinary return circuit calls for special investigation, because it is a heterogeneous conductor, unequal in resistance to the working conductor, and involving unusual complications.

The feeding system in railway work serves the double purpose of reinforcing the conductivity of the working con-

FIG. I.

ductor and equalizing the voltage at various parts of the system. It therefore must be deferred as a practical matter until the working system, which it supplements, has been considered.

Three classes of working systems are common, making the classification according to the nature of the distribution.

!f

The first class is illustrated by the linear system, shown in Fig. I. Ideally it is a straight line, A B, near some point at which the power station is generally situated. It may be modified by bends or curves, as in A^Bi and

FUNDAMENTAI. PRINCIPI^ES.

AgBg , but whether it be a small tramway line along a single street, or a long interurban road, it retains as its main characteristic a single working line, not generally re-curved on itself, and subject throughout its length to fairly uniform conditions of traffic.

The second class is illustrated by the branched type, represented in Fig. 2. As shown, it consists of a main line, A B, into which run two branches, C D and E F. The branched distribution is the one most commonly met with in electric street railways of moderate size, and may assume an infinite variety of forms. It is the legitimate re-

FIG. 3.

suit of growth from the linear type, and, through all its modifications, is noteworthy in consisting of several lines which are neither interlinked, although often overlapping, nor subject to the same traffic conditions. Its conducting system is therefore essentially complex.

Finally, we have the meshed system. Fig. 3. Ideally, it is, as shown, a simple network composed of parallel lines crossing each other at right angles and at nearly equal intervals, and under fairly uniform conditions. Practically, the various lines composing the network cross at all sorts of angles and intervals, and are subject to all sorts of conditions of traffic. All networks however have this property, tnat they are composed of interconnected lines, so that the conducting system of any line can reinforce, and can be reiniorced by, other systems. Fig. 4 shows that portion of

4 POWKR DISTRIBUTION FOR EI.KCTRIC RAII^ROADS.

the Boston network which lies within a mile radius from the Post Office as a center. It conveys an idea, better than any words, of the sort of network that occurs in practice. It differs totally from the networks usually met with in electric lighting, in that, it is without any pretense of symmetry, either in configuration or load.

In all large installations one is likely to find all three types of distribution, usually a network in the center, and branched and linear distribution in the outlying districts. In laying out the system as a whole, each type must conform, as far as practicable, to its own conditions of economy,

while the general feeding system must consider them all.

The starting point in any discussion of a conducting system for any purpose is Ohm's law in its simplest form

■ -4-

In problems of distribution such as we are considering, the term involving R is usually the quantity sought, since the current and loss of potential are generally known or assumed. It is therefore desirable to transform this simple equation into some form which allows the ready substitution of the known quantities to determine the unknown. The resistance of any conductor may be written

R = K--^, in which A is the cross section, L the length A

and K a constant depending on the material considered and the units in which L and A are measured. If L is in feet and A in square inches the constant is obviously different from what it would be if L were taken in miles. The constant is, in practice, so taken that R will be in ohms when

FIG. 4.

FUNDAMKNTAI^ PRINCIPLKS. 5

I. ?iid A are in convenient units. In English-speaking countries it is usual to take L in feet and A in circular mils, i.e,y circles y^^nr of an inch in diameter. The constant connecting L in feet and A in circular mils with the resistance in ohms, for copper wire of ordinary quality at ordinary temperatures, is ii. This is approximately the resistance in ohms of a commercial copper wire one foot long and xuVtt ^^ ^^ ^^^^ i^ diameter. The exact figure is a trifle less, but the ordinary contingencies of temperature, joints, etc. , make it desirable to take 1 1.

Substituting now this value of R in Ohm*s law it becomes, reckoning the area in circular mils,

C =- or, transposing,

iiA— cm,

This is the fundamental equation of electrical distribution. It is like the original form of Ohm's law, strictly a linear equation, so that all the quantities are connected by simple proportions. Doubling E, for example, halves ^.w., while doubling I^ doubles cm. A convenient transposed form is which determines the current which a particular line will carry without exceeding a given loss, and another, is convenient in figuring the actual fall of voltage. Throughout these equations E represents the fall in volts through the conductor under consideration, and 1/ is always the total length of the wire, i.e,^ double the length of the circuit, assuming a uniform return wire. For grounded circuits the equations give correct results for so much of the circuit as is exclusively copper — the grounded portion involves a different constant and must be taken up as a separate problem.

6 POWER DISTRIBUTION FOR KWCTRIC RAII^ROADS.

It is often convenient to have some simple expression connecting the area of a wire with its weight, so that the latter may be readily taken into account. By a fortunate chance, a copper wire, looo c, m.in section weighs almost exactly three pounds per looo ft. So if, in equation (i), we multiply the constant by three, and reckon L in thousands of feet, we obtain directly the weight of conductor per looo ft. Putting Lm for the length, to distinguish it from the former 1, reckoned in feet, we have

Thus, if we wish to transmit loo amperes through 7000 ft. of conductor at a loss of 50 volts, the conductor must

weigh 33QQX 7 =^52 lbs. per 1,000 ft. The total weight

of conductor is evidently Wm lym , and since a simple way of getting the total weight, without reference to wire tables, is often desirable, we may re- write (4), as follows:

which gives the total weight directly. These weight formulae are very easy to remember and apply, and are accurate to about one per cent.

The diagrams of Plate I. put equations (i), (3), (4) in graphic form for ready reference. Four different values of E are assumed, and the unit of power is taken as 100 amperes. The chart is therefore independent of the initial pressure, and serves for transmission at any ordinary voltage. Distances on the horizontal axis represent length of circuit, /. e. , half the total length of conductor. To find area or weight per 1000 ft. of conductor required for a certain distance, take an ordinate at the required point on the distance scale and follow it up until it intersects the oblique line representing the assumed loss of voltage. The area of the necessary wire can then be read off on the left hand scale, and the weight per 1000 ft. on the right. The corresponding sizes of the B. & S. gauge wires are annexed to the former scale. In a similar

FUNDAMENTAI. PRINCIPi;ES.

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8 - POWER DISTRIBUTION FOR RI.KCTRIC RAII.ROADS.

way the distance for which a given wire will carry loo amperes at a given loss can be found, while the loss for a given wire and distance can be rapidly approximated by estimating the position of the intersection of the area and the distance co-ordinates with reference to the oblique lines. By noting that the area of conductor varies inversely with E, one can extend the working range of the chart. Halving the area shown for E = 75 gives, for instance, the area for E = 150, and so on.

Taking up now the case of linear distribution, it has already been shown that the fall in voltage in any conductor is directly proportional to the load and the resistance. If, now, a uniform line, A B, Fig. 5, be loaded at B, the voltage evidently decreases uniformly throughout its length. To make the example more concrete, the length A B is taken as 20,000 ft., and the voltage kept constant at A, e. g,^ 500. Now, if the drop at B under the given load be 100 volts, a straight line drawn from C to D shows the state of the voltage at every point of the line. An ordinate erected at any point of A B and extended to C D shows the voltage of the line at the point selected, and that part of the extended ordinate cut off between C D and C F shows the loss in volts. If the load be transferred from B to some intermediate point of the line, an ordinate there erected will show the drop and the residual voltage at the new point. C E similarly shows the conditions for a terminal drop of 200 volts.

The average drop is evidently half the maximum in each case, since the minimum drop is o, and the voltage varies uniformly.

Now suppose one has to deal with a load moving uniformly back and forth along A B. If the maximum drop be 100 volts, the voltage evidently moves uniformly along C D, and the average voltage is 450, since half the time the voltage is above this, and the other half an exactly equal amount below.

This case corresponds to a line traversed on a uniform schedule by a single car. Such however is not the usual

FUNDAMKNTAI, PRINCIPI.KS. 9

condition of things. The normal condition of an electric road of any kind is a plurality of cars. This means that current is taken from the working conductor at a certain limited number of points. In general, these points represent approximately equal loads and, so long as the time table is maintained, are approximately equidistant. In Fig. 6, the uniform straight conductor, A B, is loaded, not.

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Street Ry.Joonial as in Fig. 5, at one point, but at ten equidistant points, the loads being assumed equal, as they would be quite nearly if each load were a car on a level track.

Here the conditions of fall in voltage are radically different from the conditions of Fig. 5. At the power station, A, the full current for the entire load is supposed to be delivered at a uniform pressure of 500 volts. Assume the total current to be 200 amperes, and the resistance of lO POWKR DISTRIBUTION FOR ICI.ICCTRIC RAII^ROADS.

each of the uniform sections to be 0.05 ohm. The first section carries the whole 200 amperes, and the drop C R is 10 volts. The second section carries but 180 amperes, and the loss is 9 volts, and so on, until the tenth section carries 20 amperes, and the loss has diminished to i volt.

Mapping these successive falls of potential on Fig. 6, the curved line, C D, is formed, showing the consecutive

4 5 6

Points on line

FIG. 6.

9 10 Street Ry. Joarnal values of the potential on A B. C E, a prolongation of the drop in the first section, shows the result of concentrating the whole load at B.

In such a uniformly loaded line the drop is found as

follows : If C is the total current and there are n sections

p in the line, then is the current taken off for each sec-

FUNDAMKNTAI. PRINCIPI.ES. H

C

tion, and r is the drop due to that current, where r

n

is the resistance of each section. The drop in the first

C C

section from A is lo r, in the second section 9-— r

n n

and so on ; i. e, , for the whole n sections the total drop

must be

B»t the sum of this series of integers is well known, being

— ^ — I^. Hence, substituting and reducing, we have 2

This gives the total drop produced by n uniform loads uniformly spaced and aggregating C amperes.

It is generally convenient to have working formulae give the cross section of conductor directly, since that is most frequently the quantity to be determined. Equation (3) can readily be transformed for this purpose as* follows:

But since the R here concerned is the total resistance, and not the resistance per sections, as in (7), we may write,

, II L

Then substituting this value of r in (7) and reducing, we liave

/ N II ciy r^+ 1^

This equation gives the area of conductor required for C amperes supplying a line of known length equally loaded at n points at any required terminal drop.

For a large number of sections ^ approaches unity, so that, for a given current in amperes and a

12 POWKR DISTRIBUTION FOR KI^CTRIC RAII^ROADS.

given terminal drop, the copper necessary for a uniformly distributed load is one-half that required for the same load concentrated at the end of the line. As the number of sections increases, too, the likelihood of obtaining a disarrangement of load sufficient to disturb the terminal voltage much, decreases. The effect of a uniform motion of all the loads on the terminal voltage is small. So long as the schedule is uniform and is adhered to, the worst that can happen is a transformation of the system into half the original number of sections. Suppose in Fig. 6 all the load points of odd numbers to be moving to the right and all those of even number to the left, at uniform speed. Then after each point had moved half a section, there would be five sections each loaded with a pair of coincident loads. Applying (7) to the data of Fig. 6, E = 60, assuming the sections uniform. As, however, the first section would be but three-fourths the length of the others, the real loss would be 55 as before. Another equal movement and the ten sections appear in their original relation. Another and we have the five sections, but with an initial section one-fourth the length of the others and total loss of 45 volts. Next would come a ten-section arrangement, but with the ifirst load at A, and E = 45, and so on. The upshot is that while the terminal voltage oscillates through a range equal to the drop in the first section, the final effect on the average drop of uniformly moving the loads is the same as loading each section at the middle point or increasing n indefinitely. Hence, in a line with uniformly spaced and uniformly moving loads, we may assume

I in (9) and write or, transposing,

2 E That is, the area of the line can be calculated for average

FUNDAM^NTAI, PRINCIPI^ES. I3

terminal drop just as if the load were concentrated at its middle point. Hence, for all practical purposes, by making this assumption, equations (i), (4), (5) can be used in calculating the line.

To keep the voltage approximately uniform over a linear system of distribution is comparatively easy. In the most favorable case, a number of uniform loads moving uniformly, the drop is half that met with in the most unfavorable distortion of the load, i, e, , bunching at the end of the line. This latter condition brings the worst possible load upon the station, barring short circuits. Although long stretches of uniform conductor often occur in railway practice it is usual to reinforce the working conductor by feeders variously arranged, as will be shown later. Such feeders were very necessary in the early days when trolley wire as small as No. 4 was used, but now, when No. 00 is very

■ C

D

FIG. 7.

commonly employed, elaborate feeding systems are less necessary for linear working. The most important linear distributions are likely to come in long interurban roads, which often demand special methods of feeding. Whatever these may be, the uniform working conductor is of sufficient importance in every system to warrant this discussion of its general properties.

As a corollary to this general investigation, it is evident that in dealing with any linear system such as A B, Fig. 6, the best point for the power station is at the middle point of the line, since under the conditions of uniform load supposed, this point would give the smallest average drop. Since ly in such case is one-half of its value when the whole line is fed from A, the total copper by equation (5) is reduced to one-fourth the amount for the same loss.

Considering now the branched type of distribution, shown in Fig. 2, it is best to take it up in the simplest available form. This, Fig. 7, shows a main line, A B D,

14 POWKR DISTRIBUTION FOR BI*SCTRIC RAII^ROADS.

with a branch, B C, which is straightened and made parallel to the main in order to more clearly show their relations. Unless the branch is of such magnitude and position as to require special feeders, it is supplied with current from the main linear system. In a few cases the service on a branch is from B to C and back. More generally it is from C to A and back, a part of the cars being devoted to a through branch route. On the section A B, the load is the sum of those due to each line of cars. Beyond B there are two independent linear systems.

If there are m cars on the route A D, and n cars on the route A C, then the load on A B, due to both lines, will be

AB , AB AD^ AC

and the loads on B C and B D respectively will be

Consequently, if the section A B is computed for this load according to (lo) we shall get the proper conductor for the assumed loss E. The lines B C and B D can then be computed for losses Ei and E2. The values of E, Ej, E2 are usually taken with the condition imposed that E+Ej, E + Eg shall be less than a certain specified maximum. A more general method is that of Fig. 8. Here there is a line, A B, with branches running to C, D, E, F. The loads are /, m, n, o, p, amperes respectively. A B, A C, A D, A E, A F, are now considered as separate, each subject

FUNDAMENTAI, PRINCIPI.KS. 1 5

to its own conditions. Taking now a drop for each line, according to the dictates of economy or convenience, and figuring the conductors from ( lo) with the respective currents, an area is found for the conductor belonging to each line. Then the cross section of copper required from A to the first branch is [cm] i-\- [cmlira -\- . . . . That from the

first to the second branch is [^r w] m 4" [^ ^] n +

and so on. In practice the conductors would be installed of the nearest convenient size, neglecting small variations of E from the calculated amount at the termini of the various lines.

The same procedure applies to all sorts of independent lines radiating and fed from a common center, whether or not these lines have any sections in common.

We have thus far assumed all lines to be uniformly loaded all along their lengths. It often happens how-

•

*-tM c n ever that for some cause a line is loaded unequally. In the long run, grades partially compensate themselves, since as many cars run down -by gravity as go up by the expenditure of extra power, so that their effect shows more in the variations of power required than in the total amount. Not infrequently, however, from the effect of grades, curves or local cars in an extended system, there is a regular demand for extra power at some point of the line. This is shown in Fig. 9. Here the line, A B, is divided into ten sections, each equally loaded, except that at 8 the load is three times the normal. Now it has just been shown that a uniformly distributed load is the same in effect as if it were concentrated at the middle point of the loaded line; that is, the electrical loads, like mechanical ones, act as if concentrated at their center of l6 POWKR DISTRIBUTION FOR EI.KCTRIC RAILROADS.