Engineering Library ALTERNATING CURRENT DESIGN ALTERNATING CURRENT DESIGN BY JULIUS FRITH, M.Sc., M.I.E.E. CONSULTING ENGINEER SPECIAL LECTURER IN ELECTRICAL DESIGN IN THE MANCHESTER UNIVERSITY LONDON AND NEW YORK HARPER 6f BROTHERS 45 ALBEMARLE STREET, W. 1912 (All rights reserved) B. VAN NOSTRAND COMPANY K*W YOKK Engineering Library PREFACE LET me say at once that this book does not, and is not meant to, cover the whole of the subject suggested by its title. It is intended, for instance, to be a companion book to Mr. Cramp's " Continuous Current Machine Design," to which treatise the reader is referred for much of the ground that would otherwise have been twice traversed, as, for example, the sections on Temperature Rise arid Insulation, together with nearly all the purely mechanical parts of design, including works costing. Of the rest, I have perhaps aimed at giving that which I have not found in similar books, and particularly have I aimed at expressing it in a non-mathematical way, endeavouring to emphasize the inward physical meaning rather than the outward mathematical form, to impart ideas rather than information. I hope the book will be useful alike to students and to those engaged in works, and I sometimes dare to hope that my brother designers will find one or two things presented in a new light which may stimulate them even whilst disagreeing. Of those to whom I have become indebted over the compilation of this book I shall have space only to mention a few. My friend and late assistant, VI PREFACE Mr. R. E. Grime, comes easily first, for from his notes I have largely helped myself for material for many of the chapters. The idea of the price curves for cables is taken from a paper by Mr. H. A. Earle, and the idea of sodium as a conductor from Betts. The costs of most of the more usual metals in Chapter XL were obtained for me by Messrs. Carrick & Brockbank of this city, and those of the rarer metals by Messrs. Johnson Matthey of London. I shall at any time be pleased to receive, and if possible to answer, letters of suggestion, criticism or correction. JULIUS FKITH. THE HOMESTEAD, VICTORIA PARK, MANCHESTER, November, 1911. CONTENTS CHAPTBE I ALTEENATING CURRENTS PAGK Elementary alternator The production of an alternating E.M.F. The flow of an alternating current through circuits having resistance, self-induction, and capacity Angle of lag . . 1 CHAPTEE II ARMATUEE REACTION System of vectors used Various fluxes existing in an alternator Ampere turns to drive these fluxes Demagnetizing ampere turns on the stator Numerical values of fluxes and ampere turns Inherent regulation Pre-determination of behaviour of alternator 10 CHAPTER III RELATION OF DIMENSIONS TO OUTPUT Ampere turns per inch diameter Induction in the air space D 2 Z formula Limits of convenience ...... 20 CHAPTER IV EXAMPLE OF THE DESIGN OF AN ALTERNATOR Specification for a 250 KW. alternator Diameter Stator winding " Field effect " The magnetic circuit Synthesis with full load fluxes Magnet winding Open circuit synthesis Rotor ampere turns at various loads and power factors Short circuit Efficiencies Weights and costs of active material . 24 viii CONTENTS OHAPTEE V SYNCHEONOUS MACHINEKY IN PAEALLEL PAGE Stator flux independent of rotor excitation Eelative position of stator and rotor poles Synchronous motors Cyclic irregu- larity Meaning of power factor 40 CHAPTER VI COMPOUND-WOUND ALTEENATOES Compounding by separate windings By action on the exciter By armature reaction itself 46 CHAPTEE VII INDUCTION MOTOES THEOEY Importance of power factor Leakage fields Determination of Angle between the maximum value of current and volts. cos < = power factor. H Magnetic lines of force per cm 2 , in air, in Chapter I. Elsewhere C.G.S. magnetizing force per cm. H.P. Horse-power. H.T. High tension, in Chapter X. I Maximum value of alternating current in amperes, in Chapter I. in. Inches. in 2 ., in 3 . Square and cubic inch. K Cost of material in 's per ton, in Chapter XI, KW.'s Kilowatts K.V.A.'s Kilo-volt-amperes. L Self-induction in henries, in Chapter I. I Length of an active conductor, gross length of stator plates, axial length of stator. Also a length in cms. of a magnetic path. Also the length of a limb of a transformer in Chapter IX. L.T. Low tension, in Chapter X. M.S. Mild steel. mb Function of increase of resistance due to a conductor's own field, in Chapter IV. mm.'s Milimetres. N Magnetic flux linking a coil, or per pole, in Chapter I., etc. Number of slots per pole in "cr" formula, in Chapter VII., etc. P Phosphorus, in Chapter XI. Also number of poles. P.c. Price of copper per in 3 ., in Chapter IX. P.i. Price of iron per in 3 ., in Chapter IX. p Percentage loss per mile in cables, in Chapter XI. p.f. Power factor. Q Maximum quantity of electricity in condenser, in Chapter I. LIST OF SYMBOLS AND CONTRACTIONS USED xiii B Eesistance in ohms. 1 Revolutions per minute. r.p.m.J E.M.S. Square root of mean square of a sine wave, Virtual value of an alternating current or voltage. r length of radial arms of an active conductor, in Chapter I. p Eatio of primary and secondary turns on a transformer, in Chapter IX. Also specific resistance in microhms per cm 3 , at 15 C., in Chapter XI. 5 Tensile strength in tons per in 2 ., in Chapter XI. Sn Tin. Si Silicon, o- 1 + o- is the waste field coefficient of an Induction Motor, in Chapter VII., etc. T Turns per phase. ETj & T 2 Primary and secondary turns on a transformer, in Chapter IX. t Time in seconds since the beginning, in Chapter I. Also depth of copper in transformer coils, in Chapter IX. 6 Angle between the coil and its position of maximum flux, in Chapter I. r Pitch of poles, N. to S., in Chapter VII. V Velocity in cms. per second, in Chapter I. W Watts output, in Chapter IX. W.I. Wrought iron, w.f.c. Waste field coefficient. Zn Zinc, in Chapter XI. o> Eadians per second of elementary alternator, in Chapter I., etc. = 27T~ ~ Eevolutions per second of elementary alternator, in Chapter I. Complete reversals per second of alternating current and voltage. ALTERNATING CURRENT DESIGN CHAPTER I ALTERNATING CURRENTS THE simplest form of alternator possible would be a single conductor supported parallel to a shaft by radial arms and revolved in a uniform magnetic field. It is worth while to study such an arrangement and the laws which can be deduced from its behaviour before considering the more practical forms of alternating current generators (Fig. 1). If the length of the conductor parallel to the shaft be / centimetres, that of the radial arms r cms., the peripheral speed of the conductor V cms. per second, and the uniform magnetic field H lines per square centimetre, then the maximum electro-motive force generated in the conductor will beH.Z.Vx 10~ 8 volts. There is no E.M.F. in the shaft or in the radial supporting arms because they cut no lines of force. If we call the revolutions per second ^ and the radians per second w, then o> = 2^^ and V = ZTTT^ = wr. So that the maximum E.M.F. E = H/wr x 10~ 8 volts. i B * ?" , a" : "jtLTJWATlWG CURRENT DESIGN But x T is the area of the coil in cms 2 , and H . I . r is the maximum number of lines of force ever through the coil ; calling these N, the maximum E.M.F. E = w.N.lO- 8 . This is one of the most universal relations in the whole of alternating current work ; whenever lines of + // ///?es per cm * revo/uf/ons per sec co rad/axs per second ^ FIG. l. force through a coil vary from a maximum N at the rate of ^ complete reversals per second, then the maximum E.M.F. in each turn of that coil is w . N . 10~ 8 where cy = ZTT^. This is true however the lines may be varied, either by revolving the coil, or revolving the field, or magnetizing an iron core which passes ALTERNATING CURRENTS 3 through the coil, or if the lines merely link the coil due to current in the coil itself. It is true whether the lines of force cause the E.M.F., or whether the E.M.F. in being applied to a coil sends such a current through it as will magnetize for that flux N, so that, neglecting only the volts lost in resistance, the reading of a voltmeter is always a measure of the flux. Returning to the elementary alternator, it is seen that at the instant when the E.M.F. is a maximum the number of lines of force threading the coil is zero and vice versd, i.e. that the maximum of the lines through the coil and that of the E.M.F. in the coil are separated by a quarter of a period, or 90 degrees. This result is also true of all cases, just as the former one was. The E.M.F. at any other position of the coil will be proportional to that component of V which is at right angles to the field, the other component not cutting lines. This active component is V sin 9, where 6 is the angle between the coil at any instant and the coil when the maximum number of lines pass through it, i.e. when the E.M.F. is zero. At other times the instantaneous value of the E.M.F. is E sin 0. This is sometimes written E sin (a>t), where o> is the angle in radians turned through per second and t is the number of seconds elapsed since the beginning of movement. cot is thus an angle like 6, but unlike 6 it can be any number of whole revolutions plus any fraction of a revolution. If the coil was not right across the lines at the beginning, but inclined to that position at any 4 ALTERNATING CURRENT DESIGN angle a, then to be quite accurate the instantaneous value of the E.M.F. is written as E sin (a -f cot). For these reasons the curve representing the varia- tion of E.M.F. with time is called a " sine wave/' and, without entering into a mathematical discussion of its properties, we can take a few of them on trust. Most of the usefulness of electro -motive force for purposes of doing work depends on the square of the E.M.F., so that if the E M.F. is alternating, it is the square root of the mean square which is then required, and which is measured on a voltmeter ; for a sine wave this R.M.S. value, as it is written, is the maximum value divided by \/~%. Sometimes, however, we require the simple average current over half a period, and this is the maximum value divided by -. 2i It will be noticed that in the foregoing the pro- duction of an E.M.F. is sometimes attributed to a conductor cutting lines of force, and sometimes to the rate of change of lines linking the circuit, and there are nearly always these two ways of looking at the phenomenon. In some cases one is the more convenient method, and in others the other, but oftener the two points of view together give the best perspective. Now let this E.M.F. send a current through a second coil having a resistance of E ohms and a self- induction of L henries, and let the maximum value of the resulting current be I amperes. The current I flowing through the resistance R, will give rise to a vpltage R . I, but it will also give rise to a number of ALTERNATING CURRENTS 5 lines of force linking the coil, the maximum value of which will be L . 1 . 10 8 , for L is by definition of the unit of self-induction the number of 10 8 lines linking the circuit for each ampere round the circuit. These lines give rise to an E.M.F. of o> . L . I, which we have already seen will be 90 degrees behind the current. The E.M.F. K . I is in phase with the current, that is, has its maximum value at the same instant as the maximum current. The value of the current will so adjust itself that CO. LI R.I FIG. 2. the resultant of these two will equal the impressed E.M.F. So that E = \/(RI) 8 + (o)LI) 2 T E = x/R 2 + LV The root \/E 2 + L V is the impedance of the circuit and takes the place of the plain resistance in direct current work. Now, instead of the circuit having resistance and self-induction, let it have resistance K and capacity F farads ; the capacity of a condenser being the amount of electricity in coulombs required to charge it to a potential of one volt, a flow of one coulomb per second being called an ampere. 6 ALTERNATING CURRENT DESIGN Let Q be the maximum quantity of electricity ever in the condenser at one time. This will occur when the current has been flowing in one direction for as long as possible and is just going to reverse, and therefore equals zero. The potential at the condenser will then be a maximum and equal to Q divided by F, so that it is seen that the maximum potential is 90 degrees from the maximum of current. Q is the quantity of electricity that flows into the condenser during one quarter of a wave, and as there are ** waves per second the time taken is seconds ; 4,-w the average current is therefore 4 ^ Q amperes. This average current is equal to the maximum divided by - ; therefore 2i I = ? X 4~Q = 27r~Q = Q 2t The potential of the condenser = ~ = ^. As before F wY there is an E.M.F. R . I in phase with the current, and the resultant of these two at right angles must equal E, so that or I = the denominator being the impedance of the circuit. ALTERNATING CURRENTS 7 Next consider a circuit having both resistance, self- induction, and capacity. It follows from the above that the potentials at the terminals of the two latter, being both at right angles to the current, are themselves in the same straight line, and it only remains to determine if they are in the same or opposite directions. F.CO R.T. FIG. 3. Consider the instant when the current is just reversing. It has been flowing into the condenser up to now, which is therefore full, and on the current reversing will begin to discharge, aiding the recently reversed current. The lines of force linking the part of the circuit having self-induction, on the contrary, will be just increasing and building up an E.M.F. in opposition to the increasing current. This shows that the two E.M.F.'s are in opposite directions at the terminals of the capacity and self- induction, and therefore which is the general expression for the flow of alternating currents. It is worth while to notice that whichever of the last two terms is the greater, the bracket is always positive ; 8 ALTERNATING CURRENT DESIGN it, however, vanishes when L&> = -^r , when the ex- JDO) pression becomes one of Ohm's Law merely. This means that for every circuit having both self-induction and capacity there is one frequency at which the effects of both vanish and the circuit behaves as if it contained resistance only. If a means exists of supplying the circuit with a variable frequency, this forms a ready means of measuring either self-induction or capacity, the value of the other being known, as the current suffers an extremely rapid variation as the frequency nears the critical value. The foregoing work also defines the power factor, which is the cosine of the angle between the current and the impressed E.M.F. The tangent of this angle is, in the case of resistance and self-induction alone, ^-= ^ , so that the power factor of a K K circuit is seen to decrease as either the self-induction or the frequency increase or as the resistance decreases. In the case of resistance and capacity and the power factor increases as either the frequency, capacity, or resistance increase. ALTERNATING CURRENTS In the most general case of a circuit containing resistance, self-induction, and capacity, and the power factor will be either leading or lagging according as ^ is greater or less than Lo> ; when these are equal the current will be in phase with the voltage, i.e. the power factor will be unity. CHAPTER II ARMATURE REACTION IN the last chapter the effect of the current on the behaviour of the alternator itself was neglected. This is, however, a very important matter which we will now consider. For this purpose a very simple vector diagram will be used. Fixing our attention for the moment on a two-pole revolving field alternator, let us, as it were, point with vectors to the maximum values of the current, voltage, fluxes, etc., as they revolve round the centre ; these vectors by their length will also, to some convenient scales, represent the magnitude of the quantities involved. It is seen that this system of picturing what is happen- ing in the alternator by pointer vectors represents the relation between the various quantities in space, and for this reason must not be confused with any other system of vectors which might endeavour to represent this mutual relationship in time. The angle whose cosine we call the power factor is an example of the former notation, in that it represents the space separating the maximum values of the voltage and current ; to translate such an angle, expressed in degrees, into seconds of time, it is necessary to divide by 360 10 ARMATURE REACTION n times the frequency. Another difference should also be pointed out here, which is that the voltage is taken as residing in the active conductors themselves, and not at the hypothetical centre of a coil formed by two sets of active conductors and their end connections. The most important thing that goes round the alternator is the stator flux, namely, that flux which , Flux Current- Stefor Volte leakage Flux FIG. 5. actually cuts the stator conductors and enters the iron at the back of the stator slots. It is this flux which makes the stator volts, all of which volts are measured by a voltmeter at the terminals of the machine, except- ing only those lost in stator resistance. It is worth while to insist on this statement, as there is so often erroneously supposed to be some larger flux than this in the stator. 12 ALTERNATING CURRENT DESIGN As it is this flux which, by cutting the stator con- ductors, makes the stator volts, these latter are in phase with the former and proportional to it. It follows that the stator flux and terminal voltage can be represented by different lengths of the same vector, measured off each to its appropriate scale. The maximum stator current will be at an angle < Currenr FIG. 6. to the terminal voltage, when cos is the power factor of the outside circuit. The next flux to consider is the stator leakage flux, i.e. that flux which surrounds the stator conductors simply from their own magnetizing force. That this flux is at right angles to the position of the maximum current is shown by the sketch (Fig. 6). The stator leakage flux runs along the roofs of the stator teeth and crosses the air space to the magnets ; ARMATURE REACTION 13 at least, this is the final result. If the fluxes could be built up separately, the leakage flux would first of all travel along the roofs of the stator teeth and enter the stator, and return by the iron at the back of the stator ; then the magnet flux would cross the air space, and part of it, combining with the leakage flux, would form the true stator flux at the back of the stator conductors, and part of it would return to the magnet circuit vid the roofs of the slots, combining with the other part of the leakage flux. FIG. 7. There is also that flux which exists in the magnet circuit but does not cross the air space, leaking from pole to pole of the magnets ; this is the magnet leakage flux, which is generally somewhat mechanically dealt with by means of a leakage coefficient. So it comes about that the magnet circuit proper has to provide three sets of lines of force, one which never crosses the air space but leaks from pole to pole, another which crosses the air space and leaks over the 1 4 ALTERNATING CURRENT DESIGN roof of the stator slots, and a third which, cutting the stator conductors, enters the stator iron and constitutes the working stator flux. This last is the only flux which cuts conductors and therefore which produces volts. If a search coil winding were supported just clear of the pole tips, this would measure a voltage proportional to the air space flux, but as such a winding does not usually exist, it is a mistake to translate these other fluxes into volts at all, it being much simpler to treat them as fluxes. These various fluxes are not, however, all in phase, i.e. do not have their maximum values simultaneously, and so cannot be added arithmetically. The vector diagram shows their relative magnitude and phase. The air space flux is the resultant of the stator flux and the stator leakage flux. The total rotor flux is obtained from the air space flux by multiplying this latter by a waste field coefficient, although, strictly speaking, the magnet waste field or leakage flux is proportional to the excitation and inversely proportional to the reluctance of the leakage paths, and is not connected with the main flux in any very simple way. These three fluxes having been determined, and the areas of the magnetic paths calculated, a synthesis can be made in the usual way, but using the three different fluxes for the stator, the air space, and the magnet circuit respectively. This synthesis will give the ampere turns required to get the full load fluxes through the magnetic circuit, and it now remains to add to these an extra amount to overcome the demagnetizing effect of the ARMATURE REACTION 15 stator currents. To do this draw a vector, representing in length, to some convenient scale, the ampere turns from the combined synthesis, and make its direction parallel to the vector representing the air space flux in the flux diagram (Fig. 5). The demagnetizing stator ampere turns are at right angles to the stator current and parallel to the stator leakage flux (see Fig. 6) ; drawing these to the same scale of ampere turns from the same Sfator demagnetizing AT. 5 FIG. 8. point as the ampere turns from the synthesis, the resultant of the two gives, to the same scale, the total ampere turns required on the rotor for full load at the particular power factor chosen. Let us now consider the actual numerical values of the various quantities we have been using. Firstly the stator flux; this is obtained from the total volts by multiplying these latter by v/2 and 10 8 and dividing by 277^ and the turns in series. The total volts are 1 6 ALTERNATING CURRENT DESIGN simply the terminal volts added to those lost in the stator resistance ; strictly speaking, vector addition should be employed for power factors less than unity, as the lost volts are in phase with the current, and this in reality throws the stator flux slightly out of phase with the terminal volts. In practice, however, the volts lost in resistance are so small a fraction of the terminal volts that this refinement is not worth putting into force, and the total volts are taken as the arithmetical sum of the terminal and lost volts. The stator leakage flux may be arrived at in various ways, the first of which consists in consulting the results of the many excellent published experiments which give the leakage lines of force per inch length of slot per ampere in the slot for various different shapes of slots. The figure for this leakage flux varies from about 50 in parallel to 100 in roofed slots ; this has of course to be multiplied by the length of the slot and by the current flowing in the conductors in the slot. Some allowance should also be made for leakage lines round the end connections, this again being affected by whether all the end connections from one pole are collected together so that each is cut by the lines made by all the others, or whether the end connections are more separated, being cut only by their own or immediate neighbours' lines. The rotor waste field coefficient, though depending on many other things than those mentioned in the following formula, may, in the absence of more definite experimental data, be approximately represented by ARMATURE REACTION 17 / 0*2 x poles 1 + ^y diameter ; the ma g net flux bem S the air space flux x w.f.c., and the diameter being that of the air space in inches. The next quantity to evaluate is the demagnetizing effect of the stator current. In a single-phase stator winding the maximum value of the ampere turns per pole is \/2 X E.M.S. current x turns per pole ; that the magnetic effect of this winding may be split up into two equal parts revolving round the stator in opposite directions with the speed of the field magnets is susceptible to mathematical proof as well as to experi- mental verification. That part which revolves in a direction opposite to that of the magnets has no resulting demagnetizing effect, producing merely a surge in the flux of twice the frequency of the alternator ; that half which revolves at the same speed as the magnets and in the same direction is consequently stationary with regard to the magnet poles and exercises a demagnetizing effect on them, in amount equal to ha]f the maximum ampere turns, and in phase, at right angles to the stator current. In multiphase windings the total turns per pole of all phases are of course taken, V/2 and the demagnetizing ampere turns are --=- x E.M.S. Zi current per phase x total turns per pole on all phases. We have now all the data, not only to determine the requisite strength for the magnet winding of an alternator, but also to predict its voltage regulation at all power factors and loads. o i8 ALTERNATING CURRENT DESIGN The " Inherent Regulation " of an alternating current generator is defined by the British Standards Committee as the rise in terminal voltage on full load being thrown off at the specified power factor, both the speed and the excitation being kept unaltered. This rise can be kept down by two methods, firstly by making the increase of magnetizing force from open circuit to full load small, which may be done either by keeping the stator leakage flux, or the stator ampere turns per pole, or both, low ; and secondly, whilst allowing the full load magnetization to be largely in excess of that required for open circuit, the inductions in some or all of the magnetic circuit may be normally so high that the large number of ampere turns set free on throwing off the load may be unable to produce more than a slightly increased flux, and therefore volts, on open circuit. In most cases the first method mentioned will give rise to an alternator which requires less attention in actual running, but the latter method will, in general, make the cheaper design to build, and would be oftener employed by the designer when working to a given inherent regulation specified in this way, were it not for a certain element of risk which is always present in using these high inductions that a small error may be made in estimating, say, the stator leakage flux or the rotor waste field coefficient, thus making it difficult or impossible to obtain the required voltage, especially at low power factors. Another method of defining the regulation is by ARMATURE REACTION 19 the drop in terminal voltage from open circuit to full load. This is framed to prevent the obtaining of good regulation by high inductions as above, but is, however, unsatisfactory from other reasons, one of which is that " full load " can never be obtained with the open circuit excitation ; in many alternators full load current even would not be reached if the alternator were short- circuited with the open circuit excitation. Obviously, the regulation should not be specified or tested under conditions so far removed as this from actual practice. All interests would be safeguarded by specifying the rise in terminal voltage on throwing off full load, together with the ratio of full load to open circuit excitation. CHAPTER III RELATION OF DIMENSIONS TO OUTPUT ONE of the most obvious limitations which imposes itself on all running machinery, whether for direct or alternating current, is the density of current round the air space, the number of amperes in unit arc of circumference. In this way can be expressed, not only the electro- magnetic effect of so much concentrated current, but also the physical possibility of packing the conductors carrying such current into the space at our disposal. Taking the latter limitation first, it is readily seen that 1000 amperes per inch of circumference, combined with, say, 1000 amperes per square inch of conductor, would require a depth of winding not possibly less than an inch, and with teeth and slots of equal width at 50 per cent, space factor in the latter, 4 inches deep. Not less is it a limit to armature reaction, for the effect of the armature current on the magnet system is obviously proportional to the concentration of the former. Now, the term " amperes per unit arc of circum- ference," although expressing just what is wanted, is 20 RELATION OF DIMENSIONS TO OUTPUT 21 cumbrous, partly because it is the diameter which is usually measured, not the circumference, and also because there seems to be a disinclination to think of current as disassociated from the conductor it is flowing in ; so that the expression has gone through the forms " ampere conductors per unit of circum- ference," " ampere conductors per unit of diameter/' to "ampere turns per inch diameter," the last change from ampere conductors to ampere turns being particularly indefensible, as it is not in the effect of a closed ampere turn that the phenomenon is being studied at all, turns being merely equivalent to " conductors divided by two." Not only do the ampere turns per inch diameter form a limit to every class of revolving electrical machinery, but in all the value of this constant is nearly alike, varying from about 800 to 1200, according to size, etc. The magnetic induction in the air space is another quantity which it is not advisable to vary far from certain prescribed limits, which are, on the one hand, the proper use of material to the best advantage, and, on the other, the maximum allowable induction in the teeth and the limits to magnetizing force on the rotor. The proper compromise between these two may lie some- where about a maximum induction of 8000 lines per square centimetre of air space. Taking this figure in conjunction with one for the ampere turns per inch diameter of 800, we get that the square of the diameter multiplied by the axial 22 ALTERNATING CURRENT DESIGN length of the alternator is equal to the output at one revolution per minute divided by 0'031. For let E = R.M.S. volts C = R.M.S. amperes N = lines of force per pole T .= total turns on stator R = revolutions per minute D = air space diameter in inches L = axial length in inches P = number of poles. Assuming a sine wave distribution of lines over the air space the maximum induction = ^, the averae = -~ X -~ ~T)/ x 6'45 from which PN = DZ x 2 x 6-45 x 8000 CT The ampere turns per inch diameter = -^- =800, or T = x 800 Now N = and ^ 27T~ T PR 120 , ., ^^ E \/2 x 120 x 10 8 irom these two PN = x ZTT Putting in the value of T from above, and equating to the first value of PN, we get that P - = D 2 / x 0-031. RELATION OF DIMENSIONS TO OUTPUT 23 The similar constant for direct- current generators with the same ampere turns per inch diameter, reactance volts of 5, and volts per commutator bar of 10, is 0'034. Besides these two more or less theoretical limitations there are, in alternating- current generators, certain limitations arising out of the least convenient pole pitch which can be used for internally revolving magnets. One would not willingly make the core of the magnet pole less than 3 inches circumferentially ; putting \\ inches of winding on each side of this and allowing 1 inch for insulations and clearance, makes a pole pitch of 7 inches. This can be expressed by saying that the diameter must not be less than the number of poles multiplied by 2*2. The peripheral speed of the magnets imposes a limit in the other direction. If we limit this to, say, 8000 feet per minute, by simple arithmetic the diameter cannot be more than the number of poles multiplied by 250 and divided by the frequency ; which gives, at <^25, 10 times the number of poles, and at ^100, 2*5 times. Comparing this last figure with the statement in the preceding paragraph that the diameter should not be less than 2'2 times the poles, it is seen, what is indeed found to be the case, that at frequencies above 100 either the poles would be crowded or the peripheral speed high. CHAPTER IV EXAMPLE OF THE DESIGN OF AN ALTERNATOR To illustrate the foregoing, we will now proceed to the design of an alternating current generator to fulfil the following specification : Output, 250 kilowatts at any power factor from unity to 0'8 ; 1000 volts 3-phase 50 ^, 375 r.p.m. ; overloads, 25 per cent, for 2 hours, 50 per cent, for 5 minutes. Temperature rise not to exceed 40 Centigrade after 6 hours at 250 KW. at 0'8 power factor. Inherent regulation, not more than 6 per cent, rise at p.f. 1, and 20 per cent, rise at p.f. 0*8 when full load is thrown off, keeping the speed and excitation unaltered. Star wound, the volts per phase will be 577, the current per phase p.f. 1 will be 144 amperes, and p.f. 0'8 180 amperes ; 25 per cent, overload at the lower p.f. is 225, and 50 per cent. 270 amperes. Number of poles is 16 for 50 ^at 375 r.p.m. First, as to diameter, the various guides given in the last chapter are : Firstly, the D 2 Z formula for a length of 10 inches, which would give for 312'5 K.V.A., a diameter of 52 inches ; secondly, the least diameter, from reasons of crowding magnets, would be 48 inches ; and, thirdly, the greatest diameter, from questions of 24 EXAMPLE OF THE DESIGN OF AN ALTERNATOR 25 peripheral speed, would be 82 inches. Obviously, it is not good practice to approach too near to either of the last two limits, and so, in the absence of any guide afforded by the nearest pattern in stock, we will choose a diameter of 60 inches bore of stator plates. The total turns to give 800 ampere turns per inch diameter at 60 inches would be 266, or 89 per phase. For a two-plane winding on the stator there cannot conveniently be less than two conductors per slot, also there must be a whole number of slots per pole per phase. Making this five gives 80 turns per phase, and 240 as the total number of slots. Stator winding, 180 amperes at, say, 1800 amperes per square inch, gives O'l square inch for the area of the copper. Try 0'4" x 0'25" insulated with 0'05" of micanite all round. The covered conductor will be 0'5" X 0'35". A slot 0'4" wide will allow of a slot lining of leatheroid to protect the micanite from the edges of the plates. Two 0*5" conductors and a strip of hard wood will go in to a depth of 1*25". So that we have 240 slots 1*25" x 0*4". The next step is to estimate the resistance of the stator circuits in order to get the total volts and thus the stator flux. This involves knowing the length of the stator plates parallel to the shaft; assume this to be 10". The end connections may like- wise be assumed to form the sides of an equilateral triangle with the pole pitch as base. The pitch of 16 poles at 60" diameter is 12", so that the length of each turn will be about 2 x 10 + 4 X 12 = 68". The resistance of one phrase of 80 such turns, allowing a 26 ALTERNATING CURRENT DESIGN temperature of 60 C. would be 0*042 ohm but for the fact that 20" of the conductor is embedded in iron and cut by its own leakage flux, which produces a local current which circulates along the top half of the embedded conductor and back in the lower half ; this eddy current combines with the main current, adding in the top half and subtracting in the lower half of the conductor, the net result being that the current appears to be crowded up into the top edge of the conductor, thus causing a larger ohmic drop than if it distributed evenly throughout the section. Mr. M. B. Field has published a curve in which the increase of ohmic resistance of the embedded conductor is plotted against a quantity " mb " (see the Journal of the Institution of Electrical Engineers, vol. 37, p. 101). mb = area of the conductor in / "0 13 X ^ sq. in. x / width of conductor" x width of slot " In the present case mb would equal 0*8 ; referring to the curve we find that the resistance of the bottom con- ductor will be increased 4 per cent. , and that of the top conductor 30 per cent. This, of course, only applies to two lengths of 10" each out of a total of 68", so the whole resistance will be increased 5 per cent. The volts lost in resistance at the normal current of 180 amperes will therefore be 8 per phase, making a total of 585, which corresponds to a stator flux of \/2 X 585 X 10 8 27T X 50 x 80 = 3 ' 3 X 10 lmes P er P le ' The area required for the teeth to carry this flux at a maximum induction of 17,000 lines per cm 2 , is 30 sq. in. EXAMPLE OF THE DESIGN OF AN ALTERNATOR 27 If the width of the pole face is such that the winding of one phase occupies the gap between the poles at one 0-24*|0 6 FIG, 9. instant, then there are 1 1 teeth to carry the lines from 28 ALTERNATING CURRENT DESIGN each pole. The pitch of 240 teeth at 60" diameter is 079", the slot is 0'4" of this, leaving 0'39" for the tooth ; the length of iron required is therefore the 30 sq. in. divided by 11 times 0*39" =7". Using plates 0'014" thick for the stator, and in- sulating them with O'OOl" varnish each side, the insulated plates will measure 8" ; putting three |" ventilation spaces into this makes 9*5" overall length of core plates. The area required for an induction of say 8000 at the back of the slots, is 32 sq. in., which divided by the net length of iron gives 4 "6" depth radially. The outside diameter of the stator plates would then be 60 + 2 x T25 4- 2x4-6 = 717"; make this 72", which gives an induction of 7700 lines per cm 2 . The slot leakage flux, assuming 50 lines per ampere per inch length of slot, at a current of 180 amperes, amounts to 50 x 180 x A/2 x 9'5 = 0'24 x 10 6 . The angle whose cosine is 0'8 is 37 degs., so that the stator flux and the stator leakage flux are at an angle of 90 4- 37, or 127 degrees. Drawing the two vectors 3*3 x 10 6 and 0'24 x 10 6 at this angle, the resultant is found to be 3*45 X 10 6 , which is the flux in the air space. The waste fieM coefficient, indicated by the formula in Chapter II would be 1*22, say 1*25 for safety. The rotor flux is then 4*3 X 10 6 . To accommodate this in steel at B = 17,000 needs 39 sq. in. 5" X 9" with semi- circular ends gives 39*6 sq. in. and 16,700 lines per cm 2 . Before settling on these dimensions for the pole, it is EXAMPLE OF THE DESIGN OF AN ALTERNATOR 29 wise to see if they allow sufficient room for the magnet winding. Assuming a 6" length for the pole, and J" a side for the clearance between stator and rotor, the out- side diameter of the yoke is 47|", making the pole pitch there 9*3". Allowing J" clearance between coil and pole and J" between coils, the minimum depth of the coil is 1*7", and assuming a depth of l" for the pole FIG. 10. tip the maximum depth of the coil is 2' 6" and the height 4*5", which gives an area for winding of 9*7 sq. in., which should be sufficient (Fig. 10). The thickness of the pole tip next deserves attention. The pole arc has already been settled at two- thirds of the pole pitch, or 7*8". The flux from this to the air space is, we have seen, 3*45 X 10 6 lines, whilst the flux in the magnet core is 4*3 X 10 6 . Two assumptions are now made, each on the safe side ; firstly, that the 30 ALTERNATING CURRENT DESIGN flux to the air space is uniformly distributed over the pole face, and secondly that all the rotor waste field passes through the pole tips, so that the flux which does not do so is A. of 3-45 x 10 6 = 2 '2 X 10 6 . The rest, or 7*8 4*3 2*2 = 2*1 X 10 6 lines, must pass into the pole tips from the magnet core ; at 18,000 B this requires 18 sq. in., or 9 sq. in. each side ; the length of the pole tip is 9j", so that l" thickness at the centre will be satisfactory. The yoke ring, if of cast iron may be worked at about 8000 lines per cm 2 ., and would then require an area of 42 sq. in. or say 12" x 3j". If this is done, some provision must be made for the lines, which are at an induction of 17,000 in the steel, to enter the cast iron at not more than half this. This may be done by providing the steel poles with enlarged bases where they abut against the cast iron ; these could be 9" x 9" X l" thick in this case. Or again, the steel poles could be recessed into the cast iron. In the former case the pole tip would have to be separate, and might very well be laminated in the same plane as the stator plates. This finishes the outward design with the exception of the magnet winding ; for this a synthesis of the mag- netization is required. This differs from the ordinary only in the use of the three fluxes already obtained for the stator, air space and rotor circuits respectively. The area of the teeth is taken as that at one-fifth of their length from the small end, and the area of the air is one-fifth of the way between the pole face and the tops of the teeth, EXAMPLE OF THE DESIGN OF AN ALTERNATOR 31 i.e. four times the pole face area is added to the minimum tooth area and the sum divided by 5. This process has no theoretical basis, and its only justification is that it usually checks very closely with the observed facts. SYNTHESIS OF MAGNETIZATION AT FULL LOAD P.F. 0'8. Magnetic circuit. HxZ Length cms. Area cms 2 . Flux X 10 6 . lines per cm". H per cm. C.G.S. units per 2 poles. Stator core X 2 33-5 430 3-3 7,700 2 67 Teeth 1 6-85 197 3-3 16,800 36 228 Air space \ 1-27 420 3-45 8,210 8210 10,430 Magnet cores 31-0 256 4-3 16,800 61 1,890 Yoke X 2 20-0 540 4-3 8,000 26 520 Magnetizing force = 5,250 A.T.'s per pole = 13,135 To these 5250 ampere turns per pole must be added, at the proper angle, the ampere turns to com- pensate for armature reaction; these, from Chapter II. 180 x * = 1910 A.T.'s. Putting these on to the vector diagram, Fig. 9, measuring one off on the direc- tion of air space flux and the other on the direction of stator leakage flux, we arrive at the result that 6650 ampere turns are required per pole on the rotor when the alternator is doing 1000 volts 180 amperes at 0'8 power factor. But the alternator has also to give for five minutes a 50 per cent, overload ; the rotor winding will therefore have to magnetize for this. The increase in the stator flux brought about by the increased resistance drop may be neglected, but the stator leakage flux is increased 50 per cent, to 0'36 X 10 6 32 ALTERNATING CURRENT DESIGN lines ; this increases the air space flux to 3*53 X 10 6 and the rotor flux to 4*41. If the combined synthesis is worked out for these new fluxes, the ampere turns are found to have increased from 5250 to 5550 per pole. The demagnetizing A.T.'s are increased 50 per cent, to 2860, which on the vector diagram results in 7750 A.T.'s total for 50 per cent, overload at a p.f. of 0'8. The rotor winding should give, therefore, at least 8000 A.T.'s when warm, for a few minutes, and 6650 A.T.'s under the temperature rise specification. The mean depth of the magnet coil is 2*15". This is wound round a core 9" x 5" with semicircular ends, with J" clearance from the steel ; this makes the length of the mean turn 2 x 4 + TT x 7*65 = 32". Now the ampere turns are dependent on the area of the wire only and not on the number of turns, so that if we excite from a 100- volt circuit the resistance of one turn per pole must be such as to allow 800 amperes to flow; i.e. 16 x 32 = 512 inches must have a resistance warm of 0*0125 ohm, so that the area required is 0'0315 sq. in. In round wire the diameter would be 0*2", or double cotton-covered 0'216". This at 1000 amperes per sq. in. will carry 31*5 amperes, which current gives the required full load excitation of 6650 A.T.'s with 210 turns. The space required for this would be 210 x 0'216* = 9'8in 2 . The space available is 9'7 in 2 ., into which 200 turns of such wire will go nicely. The resistance of 16 poles in series will be 2*17 EXAMPLE OF THE DESIGN OF AN ALTERNATOR 33 ohms cold, or 2*5 ohms at 60 C. The loss in the magnets at full load will be 2'5 x 33'25 2 = 275 KW., which is 0'88 per cent, of the K.V.A. output. Before the entire behaviour of the alternator can be predicted an open circuit magnetization curve must be worked out. This is done on the same lines as the previous synthesis, but with no stator leakage flux, the same waste field coefficient being used for the magnet circuit. Four points, if well chosen, will be sufficient to draw this curve through. Take 2, 3, 3 '5, and 4 million lines in the stator, corresponding to 615, 920, 1080, and 1230 line volts at 375 r.p.m. respectively. The areas and lengths of the magnetic circuits are, of course, the same as for the last synthesis, and are not here repeated. OPEN CIRCUIT SYNTHESIS. Line volts 615 920 1080 1230 Flux X 10 8 2 3 3-5 4 B and H, Stator Teeth Air Magnets Yoke 4,650 - 1 10,100 - 3 4,760 9,750 - 3-5 4,630 - 13 7,000 - 1-5 15,200 - 13 7,140 14,600 - 17 6,950 - 20 8,150 - 2 17,700 - 82 8,330 17,000 - 68 8,100 - 27 9,300 - 2-5 20,200 - 300 9,520 19,500 - 300 9,250 - 36 H X l, Stator Teeth Air Magnets Yoke 33 19 6,050 108 260 50 82 9,070 527 400 67 520 10,580 2,110 540 85 1,900 12,090 9,300 720 C.G.S. per 2 limbs 6,470 10,129 13,817 24,095 A.T.'s per pole 2,590 4,050 5,530 9,640 34 ALTERNATING CURRENT DESIGN Fig. 11 shows the result, line volts at 375 revolutions per minute being plotted against ampere turns per pole. This curve shows that the full load 0'8 power factor excitation of 6650 A.T.'s gives on open circuit 1150 volts, or 15 per cent, rise on throwing off this load, which is 5 per cent, within the guarantee. OPEN CIRCUIT MAGNETIZATION CURVE. 1500 1400 1300 1 200 1 100 1000 ! 9 ~ 1C 800 CO rt 700 > 600 . 5 oo 400 300 T 3000 4000 5000 6000 7000 Ampere Turns per pole on Rotor. FIG. 11. 8000 9000 Allowing a 3 per cent, rise in speed on open circuit, the excitation per 1000 volts is seen to be 4400 A.T.'s ; to get this from the 100 volt supply would need a resist- ance of 2*36 ohms in series with the magnets, graduated to carry a current of from 22 amperes when all in circuit to 40 amperes on the last point. We have already enough data to draw the curve, EXAMPLE OF THE DESIGN OF AN ALTERNATOR 35 which is very nearly a straight line, between the current per phase and the ampere turns required on the magnets to maintain 1000 volts at 0*8 power factor at 375 r.p.m. The points are these : No current, 4650 A.T.'s; 180 amperes, 6650 A.T.'s ; 270 amperes, 7750 A.T.'s (Fig. 12). LOAD CURVES. 300 tn ioo 3000 4000 5000 6000 7000 8000 Ampere Turns per pole on Rotor. FIG. 12. 9000 10,000 At unity power factor, full load current is 144 amperes, the stator flux 3*29, and the stator leakage 0'19 x 10 6 lines; these two at right angles result in an air space flux of 3 '3 X 10 6 . As these are so nearly alike, it will be quite accurate to lookup 3*3 x 10 6 lines, which are equivalent to 1015 line volts, on the open circuit magnetization curve, where it corresponds to 36 ALTERNATING CURRENT DESIGN 4800 A.T.'s. The demagnetizing ampere turns for 144 amperes are 1540; these two, on the vector diagram, have a resultant 5150 A.T.'s, which is therefore the magnetization required for full load power factor unity. 5150 A.T.'s on the open circuit curve correspond to 1050 volts, or a rise of 5 per cent, on unity p.f., which is 1 per cent, within the guarantee. It is interesting to see what would happen on zero power factor. Here the stator and stator leakage fluxes would add; taking the 144 amperes the fluxes are 3'29 + 0'19 = 3'48 x 10 6 for the air space flux. We have a combined synthesis worked out for 3 '4 5 X 10 6 lines on the air space, which gave 5250 A.T.'s, so we may take 5350 A.T.'s for 3'48. These again add to the 1540 demagnetizing A.T.'s, making a total of 6890 ampere turns per 1000 volts 144 amperes at zero power factor. On Fig. 12 are plotted these three curves connecting amperes per phase in the stator with ampere turns per pole on the rotor to maintain 1000 terminal volts at power factor zero, 0'8 and unity respectively. From these can be plotted curves connecting A.T.'s per pole on the rotor with the power factor of some constant current from the stator. Two of these have been drawn for 144 and 180 amperes, they serve to show how very fast the excitation has to be increased for the first small falling away from unity on the part of the power factor ; for instance, on the 180 ampere curve, the alteration from unity to 0*85 p.f. is greater than from 0'85 to zero. EXAMPLE OF THE DESIGN OF AN ALTERNATOR 37 It is often necessary to know what current would result if the alternator were short-circuited at its terminals with full load excitation. The converse of this is easier to calculate, i.e. the excitation for a certain current on short circuit. As the short-circuit current is very nearly proportional to the excitation, it is immaterial what is the particular current chosen, so take 500 amperes. The terminal voltage being zero, the only flux in the stator is that required to generate sufficient volts to overcome the stator resistance. At 500 amperes this is 22 volts per phase, which requires a stator flux of 0*125 X 10 6 lines. The stator leakage flux will be 0'67 x 10 6 , the resultant of these at right angles is 0'682 x 10 6 , which corresponds to 208 line volts, which, on the open circuit curve, requires 850 A.T.'s. The demagnetizing A.T.'s for 500 amperes are 5300 ; the resultant of these two on the vector diagram is 6100. The full load 0'8 p.f. excitation is 6650, so that the short-circuit current will be larger than 500 in that ratio, or 540 amperes. This is exactly three times the normal current of 180. In calculating the efficiency of an alternator the most difficult of the losses to estimate is that in the stator plates. The theoretical value of the hysteresis and eddy current loss is always largely exceeded, due partly to the imperfect insulation between the plates, partly to the fact that the magnetic lines of force are not always in the plane of lamination and still more to the treatment to which the plates have un- avoidably to be subjected during the building up and 38 ALTERNATING CURRENT DESIGN winding of the stator. Any filing or rough treatment of the teeth adds very largely to this increased loss. The designer has, therefore, to fall back on the use of total loss curves, which connect the sum of the hysteresis and eddy current losses per pound of plates with the induction, at some fixed frequency and thick- ness of plates, at other frequencies the assumption being that the induction may be varied inversely with the frequency for the same total loss per pound. As these curves are drawn from actual measured losses in normal machines, they may be relied on to give a very fair indication of the losses in other cases where the conditions are also normal. At 50 cycles per second and plates of about 0*015" thick, the total loss at an induction of 4000 lines per cm 2 , may be taken at about one watt per pound ; the loss about doubling at 7000, and again doubling to 4 watts per pound at an induction of 10,000 lines per cm 2 . The fact that the induction is higher in the teeth than in the plates at the back of the slots can be roughly allowed for in calculating the weight of plates by not subtracting the weight of the material from the slots, i.e. taking the weight of the blanks before stamping out the slots. This, in the case of the alternator under consideration, works out to 2440 pounds. The induction is 7700, which, on the above scale, corresponds to a loss of 2*3 watts per pound, making a total of 5' 6 KW. or adding 25 per cent, for windage and friction, 7 KW. The magnet current for 1000 volts at 375 r.p.m. is EXAMPLE OF THE DESIGN OF AN ALTERNATOR 39 23*25 amperes on open circuit, and can be read off from the curves on Fig. 12 for other loads. The magnet resistance, allowing a temperature of 60 C., is 2*5 ohms. The stator resistance per phase, allowing the same temperature and also for the " Field " effect, is 0*044 ohm. EFFICIENCY AT UNITY POWER FACTOR. At Core loss and friction Sbator C 2 R Rotor C 2 R Sum losses Output Input Efficiency Stator C 2 R Rotor C 2 R Sum losses Input Efficiency \ \ i full 1| l.J load. 7-0 7-0 7'0 7-0 7-0 7-0 0-17 0-69 1-54 2-75 4-3 6-2 1-44 1-47 1-6 1-66 1-76 1-88 8-61 9-16 10-14 11-41 13-06 15-08 62-5 125-0 187-5 250-0 312-5 375-0 71-11 134-16 197-64 261-41 325-56 390-08 87-9 93-2 94-9 95-6 96-0 96-1 % AT POWER FACTOR 0-8. 0-27 1-08 2-4 4-3 6-7 9-7 1-66 1-99 2-35 2-75 3-22 3-75 8-93 10-07 11-75 14-05 16-92 20-45 71-43 135-07 199-25 264-05 329-42 395-45 87-5 92-5 94-1 94-7 94-8 94-8 % WEIGHTS AND COSTS OF ACTIVE MATEBIAL. Stator stampings Stator winding Rotor pole pieces Rotor pole cores Rotor winding Yoke ring Material. Weight in Ibs. Rate. Cost . M.S. 2200 30/- cwt. 29-5 Cu 520 I/- Ib. 26-0 W.I. laminated 300 20/- cwt. 2-7 C.S. 900 18/- cwt. 7-2 Cu 1030 lOd. Ib. 43-0 C.I. 1600 10/- cwt. 7-1 115-5 In general, an alternator can be sold at a profit for four times the cost of the active material in it, in this case for, say, 460. CHAPTER V SYNCHRONOUS MACHINERY IN PARALLEL WHEN a synchronous machine, such as is described in the last chapter, is run in parallel with other generators, there are one or two problems which present them- selves which can be simply solved by means of the flux and ampere turn diagrams already used. Let us assume that the other machinery is sufficiently large and powerful to maintain constant, or practically constant, voltage on the common bus bars. This means that the stator flux of the machine under consideration is fixed and is not therefore altered by altering the rotor excitation ; let this latter be set at the value obtained from the open circuit magnetization curve, to give the bus bar voltage, and let sufficient steam be admitted to the engine driving it to supply the friction and core losses. The alternator will now neither receive nor give power, and the current will, of course, be zero. The magnet poles will keep exactly in the centre of the revolving stator poles. Now admit more steam to the engine. The speed is fixed by the frequency of the station ; the magnet poles will now, however, run round slightly in advance of the stator poles. This is the condition for power to 40 SYNCHRONOUS MACHINERY IN PARALLEL 41 be given by the alternator to the bus bars. The amount of this power is a function of the angle by which the rotor poles lead over the stator poles, and is affected solely by the steam pressure behind the pistons of the engine. There is obviously a limit to the possible amount by which the magnet poles can lead over the stator poles ; if this process is pushed too far the alternator will fall out of step. If, instead of this, the steam were cut off and the alternator made to do external work on the engine or in other ways, the rotor poles would be held back, and whilst still running the same number of revolutions per minute, would lag by a certain angle behind the stator poles. The machine would then be a synchronous motor, and would take power from the bus bars. If more mechanical resistance were offered to the revolution of the motor, the angle between the rotor and stator poles would be increased until as before a limit was reached and the motor fell out of synchronism. There is therefore for each excitation a certain angle forward and backward from the mean position beyond which the magnet pole must not go. For an engine which has not a uniform turning moment throughout the revolution this angle becomes interesting. The condition for successful running is that the magnet pole shall not be separated from the stator pole, supposing the latter to be running uniformly, by more than a certain fraction of its distance from the next pole. The first thing to be noticed is that this condition 42 ALTERNATING CURRENT DESIGN becomes harder to satisfy the larger the number of poles, and that the slow-running prime movers, requiring therefore the largest number of poles for a given frequency, are the gas engines, which are the most apt to suffer from cyclic irregularity, and that for the highest speeds, where the pole pitch is very large, the turbines are almost perfect in this respect. The cyclic irregularity of an engine is usually stated by its makers as a percentage variation in speed throughout the revolution, but this, before it can be of use to the electrical designer, has to be translated into maximum error in position of its flywheel expressed in fractions of a pole pitch. This cannot be done without knowing the number of impulses received per minute, as the error in position depends on for how long the incorrect speed continues in the same direction. For example, suppose a 10 -inch pole pitch and a peripheral speed of 5000 feet per minute ; let us say that the maximum error allowable is ^V of the pole pitch from the mean position, which would permit a total dis- placement of 1 inch. If the engine were running uniformly only to within 1 in 300 in speed, the maximum error in velocity would be ' 3 oo of 500 feet per minute, or 200 inches per minute, which could only be allowed to continue for 2~oo of a minute to result in 1 inch error; i.e. if the engine ran at 100 r.p.m. it must have at least two impulses per revolution to make the time between the impulses 200 minute. All this time we have not considered the excitation of the alternator. Unlike the case of direct current SYNCHRONOUS MACHINERY IN PARALLEL 43 generators in parallel, the excitation is powerless to determine which alternator shall take the load, or indeed whether a particular alternator shall run as generator or motor ; for if the engine were tending to run faster than synchronism, the machine would generate with a very weak field, or if there was a mechanical resistance to its turning it would run as motor with a strong field. Considering any group of alternating current machinery, generators or synchronous motors, running in parallel, they jointly require a certain amount of magnetizing force, and this can be supplied by all or any, generator or motor. If one generator or motor be over-excited it will relieve the others of some of their magnetizing work ; the medium by which this is transferred being, of course, the phase of the current in respect to the E.M.F. Take the case of a synchronous motor driving on to a steady load and taking power from constant potential mains, then the stator flux, the speed and the KW. input are all fixed. On the vector diagram (Fig. 13) let 0V represent the stator volts and likewise the stator flux to convenient scales. As the machine is acting as a motor, the current will in the main oppose the voltage ; let it be represented by OC. The power input is 0V X OC X cos <, which, being fixed, means that C must always be on the line AB. The stator leakage flux OS is, as before, at right angles to the current, and the air space flux is the resultant of this and the stator flux 0V, namely VS. Measure along SV a length ST, representing the ampere 44 ALTERNATING CURRENT DESIGN turns obtained from the synthesis using the stator, air space, and magnet fluxes as before. The demagnetizing ampere turns, which are proportional to OC, are also at right angles to the current ; let SB, represent them on the same scale, then TR represents the total rotor excitation. This length TR is the thing we have control of. By adjusting the excitation, OC can be brought into line with 0V, when the power factor will become unity and the current for that particular load on FIG. 13. the motor is a minimum, as are also the lengths of OS and SR. If the excitation be reduced from this value the current OC swings to the other side, the power factor becomes less than unity, and OS and SR again increase. When C is toward A the motor is magnetizing for the rest of the circuit, and from the point of view of the generator supplying it, takes a leading current. When C is toward B the motor is only partly magnetized by its own rotor and partly by the alternating current, SYNCHRONOUS MACHINERY IN PARALLEL 45 which would then form a lagging or demagnetizing current for its generator. In fact, as ampere turns are taken off the motor's magnets they have to be put on to some other magnets, or the voltage of the system will suffer. Just the same reasoning applies if the machine, instead of being a motor on constant load, were a generator in parallel with others and driven by an engine with fixed steam admission. The alternator could be made to do more or less of its share of magnetization, i.e. give a lagging or leading current, by alteration of its excitation. CHAPTER VI COMPOUND WOUND ALTERNATORS IT has been seen that it is, in general, the inherent regulation of an alternator which most seriously limits the output to be obtained from a given size of carcass ; the heating limit can usually be overcome by efficient ventilation, and space can generally be found for more copper on both stator and rotor ; also, by reason of the variation of voltage caused by changes of current, the full load output has frequently to be fixed below that at which the maximum efficiency occurs. The direct current generator meets this difficulty by placing an additional winding on the magnets in series with the armature, and it was on this analogy that the first attempts were made to effect a similar result in the alternating current generator. The problem is, however, in this latter case, com- plicated by two different difficulties, the first being that the output is in the form of alternating current, and therefore unsuitable as it stands for energizing magnets ; and secondly that the voltage drop in an alter- nator, and therefore the extra magnetization needed, depends, not only on the amount of current, but also on its power factor ; in fact, it depends much more on the 46 COMPOUND WOUND ALTERNATORS 47 power factor of the current than on its actual amount in amperes. There are, however, some classes of load in which the power factor does not vary much, or, better still, improves as the load on the alternator increases. Such cases can be dealt with by the simple method of rectifying a portion of the main current, usually by a commutator attached to the alternator itself, and by means of additional slip rings, sending this rectified current round a separate winding on the magnets exactly like the direct current analogy. The com- mutator used to rectify the current is, however, rather liable to give rise to sparking troubles, which can, nevertheless, be eliminated by careful design and adjustment. The use of small auxiliary transformers enables voltages at different angles to be combined, and the resultant of them, after passing through the rectifying commutator, employed for the purposes of excitation. This resultant voltage can be made to increase either as the current output increases or as the power factor decreases ; in a three-phrase circuit, for instance, the current in one phase and the voltage across two phases are at an increasing angle as the power factor decreases, and therefore the resultant will increase as above, and can be used to supply the additional magnetization required for both these causes of the voltage drop. To overcome the disadvantages inherent to the use of rectifying commutators, and also the complication of two separate windings on the magnets, each with its 48 ALTERNATING CURRENT DESIGN own slip-rings, a method has been developed by which the alternating current output is made to increase the voltage of the exciter itself, and thus automatically to increase the excitation. To attain this end, the armature winding of the exciter is provided with slip rings just as if it were a rotary converter, the number of poles being arranged to give the same frequency as the main alternator. If now these slip rings are fed from a series transformer in the feeder circuit there will be produced in the air space of the exciter a magnetic field which, if the armature were stationary, would revolve just as the field of an induction motor revolves. But as the armature is itself revolving at the same speed in the opposite direction, this field is really stationary in space, exactly like the field produced by the exciter's own magnets ; if these latter are capable of adjustment by turning round on their own bearings, the centres of the two sets of poles can be made coincident and aiding each other ; let this be so only when the power facter is as low as is likely to occur in practice, for that particular load. If now the power factor improves, the current will reach its maximum earlier in point of time, which means that the resulting pole will be displaced in relation to the field magnet pole of the exciter, and the two no longer being coincident, the result will be a weakening of the air space induction, and therefore, of the exciter voltage. It is seen that the conditions for automatic voltage regulation are thus fulfilled, for if the current increases COMPOUND WOUND ALTERNATORS 49 with constant power factor the pole strength increases, the pole remaining fixed, whereas if the power factor decreases with constant current, the pole, whilst remain- ing constant in strength, is moved round to more nearly coincide with the field pole, and so the effect of the two is increased. All the methods hitherto described suffer from the defect that they are not instantaneous in their action. To take the last described as an example, although increased magnetizing force is applied to the exciter directly the current in the alternator increases or the power factor decreases, the flux through the exciter is only built up by a process that takes time. When this flux is increased the exciter voltage is indeed immediately increased, but this voltage can only affect the alternator magnet current gradually, which in its turn can only raise the alternator voltage by means of the comparatively slow increase of the alternator flux. On the other side, there is only one process to balance all these, i.e. the drop in terminal voltage does not instantaneously follow the increased output, but only through the reduced total excitation lessening the alternator flux. Processes such as described above must of necessity be slow, because the force producing them is in every instance only just sufficient to give the required result as a steady condition, the exponential term, under such conditions, never really disappearing. This fact is realized by such devices as the Entz booster and the Tyrrell regulator, which are alike in applying forces E So ALTERNATING CURRENT DESIGN many times greater than those finally required, and thus accelerating matters by making the whole process merely the initial stages of a far greater change, which however, is again checked as the required result is attained. There are other methods of compounding alternators which aim at cutting out all these subsidiary stages, and making the armature reaction itself counteract its own evil effects. One of these methods, due to Mr. Miles Walker, employs rotor poles made up of two parts, magnetically in parallel. The magnet winding is wound on one of these only, which in consequence becomes highly saturated. The effect of the armature reaction is to weaken one pole tip and to strengthen the other. Things are so arranged that the one to be weakened is the highly saturated part, which conse- quently is not much affected, whilst the other un- saturated pole becomes strengthened and adds to the total flux, and therefore to the voltage of the machine. At unity power factor this can be made to over-compound the alternator, the voltage actually increasing as the current increases, but the effect becomes less as the power factor decreases. CHAPTER VII INDUCTION MOTORS THEORY IN the synchronous machines dealt with in the last chapter the magnetization of the circuit was obtained wholly or in part from a system of direct current magnets. As we have seen, this gives a ready method of controlling the phase relations of the current and the E.M.F. The power factor, however, of an alternator is a function, not primarily of its own, but of the circuit which it supplies with energy. Induction motors, on the other hand, derive their magnetization from the alternating current generators from which they are driven, and therefore always form for these latter a load having a power factor less than unity, lagging. It is of the utmost importance, from all points of view, that this magnetization be done in the most efficient way possible in other words, that the power factor of the induction motor should be as high as possible, For a low power factor not only, as we have seen, affects the voltage regulation of the generators, their heating and efficiency, together with the earning capacity of the cables connecting the two, but also to a still greater degree, the behaviour of the motor itself. 5' 52 ALTERNATING CURRENT DESIGN Compare two induction motors with the same input and therefore with approximately the same cost of materials, the one with a maximum power factor of 0*8, the other 0*9. The latter will not only do 12| per cent, more horse-power, but will have an overload capacity of more than double the former's. These facts make the predetermination of power factor of preponderating importance in the design of induction machinery, and we shall therefore examine into this question at some length. Unlike the alternator, the induction motor starts with a certain fixed stator flux depending only on the voltage and frequency of supply, and on the number of turns on the stator winding ; as these are all fixed quantities, so also is the stator flux. Now it is only that portion of this flux which penetrates into the rotor, and is cut by the rotor conductors, which is used in the production of brake horse-power, so that any leakage of lines that occurs in the process must be taken from the available fixed supply, and the problem develops into a study of waste fields. When the motor is running light, the very small stator currents drawn from the supply mains are only those used to magnetize the circuit and to cause sufficient lines to flow round to produce a counter E.M.F. almost equal to that of supply. Under these conditions the waste field is very small, and most of the stator flux finds its way into the rotor. But as an increasing load is put on, the rotor conductors lag behind INDUCTION MOTORS THEORY 53 the revolving field, are cut by it, and consequently have current induced in them ; these currents tending to oppose the magnetizing currents in the stator, the latter are increased proportionately to their respective turns. All these currents give rise to waste fields, which have ultimately to be supplied from the stator flux. As the load on the shaft of the motor increases this process continues, until by the increase of the leakage fluxes the portion penetrating into the rotor is no longer sufficient to provide the torque demanded, and the motor falls out of step. The various leakage fluxes naturally fall under three descriptions : there is the true slot leakage, i.e. the lines caused by the magnetizing power of the currents in the slots, and which jump across from the sides of the teeth without entering the air space ; there is a somewhat similar leakage flux round the conductors forming the end connections. These are not helped by the existence of teeth, and so have most of their path in air. Their amount depends to some extent on whether the end connections are bound down on to an iron flange, and also on the way in which the end connections are grouped, as already mentioned in considering the analogous case of an alternator. These two leakage fluxes exist in both stator and rotor separately, but there is a third, which is caused by their joint action on the opposite sides of the air space. If the tooth leakage lines be drawn coming out from the tops of the teeth and bending round, it will 54 ALTERNATING CURRENT DESIGN be seen that those from stator and rotor will combine, especially when the tooth of one is opposite the slot of the other, and form a flux which zigzags across the air space, obtaining its magnetization alternately from stator and rotor currents. FIG. 14. In some such way as this various writers have essayed to build up an expression for the total waste field in terms of the stator flux. This fraction total leakage flux over total stator flux is usually called cr. Expressions for cr generally contain three terms repre- senting the three sources of leakage, viz. zigzag, slot, and end connections. Unfortunately, the calculation of waste fields from first principles, although it can be used to give the general form to the expression, is too difficult and uncertain to rely upon solely for the numerical values of the constants deduced, which latter must always chiefly rest on empirical authority. With these remarks we will proceed to show how the three terms of such an expression for cr are arrived at. INDUCTION MOTORS THEORY 55 In a two-pole induction motor, let N be the number of slots per pole, total. T be the number of turns in series per phase. 8 be the radial clearance between stator and rotor in cms. T be the pole pitch, north to south, in cms. / be the gross length of plates, exclusive of ventilation spaces, in cms. C be the stator current in R.M.S. amperes. The area of the air space, allowing, say, 15 per cent, for slot openings, is 0*85 . 1 . T cms 2 ., and its length 8 cms. \/2CT The maximum ampere turns driving the flux are- t fer the \ 2 Assuming a sine wave distribution of flux over the surface of the pole, the maximum induction is - times the average ; allowing, say, 20 per cent, extra magne- tizing force for the iron parts of the magnetic circuit, the stator flux produced is X/2CT 0-85/r 2 1 0;4CTZr 2xO'8 X 8 X 7T X 1 7 2~ 8~ For the zigzag leakage the current in each slot magnetizes for that section. The current per slot is 3TC T *r- . The area of the path of the lines is J x JT x ^, and its length is 28. The flux produced is therefore : 3\/2CT 1 T I 0-8N X 2 X N X 2S~ N 2 8 56 ALTERNATING CURRENT DESIGN This expressed as a fraction of the stator flux above is CT/T S 1'3 3 SN 2 For the slot leakage from the sides of the teeth a figure can be found giving the lines per cm. of slot per ampere in the slot, much as for the alternator already discussed ; this figure is in the neighbourhood of 1, which makes the slot leakage flux 3 _ or as N a fraction of the stator flux 3>/2CTJ 8 108 N < 0-4CT/T ~ sa7 NT The end connections have to be treated in much the same way. Let us say that they have half a line per ampere per cm., and that they form a semicircle each side on the pole pitch as diameter. The waste field due to this cause will be then \/2CT x TTT x 0'5, 58 and as a fraction of the stator flux, -j~ Gathering together these three terms, we may write 3 108 58 But, as before stated, the whole rests on an entirely empirical basis, and the constants must be made to fit the experimental results, even if a certain amount of violence is done to theoretical basis of the formula. It is only as the expression succeeds in interpreting the INDUCTION MOTORS THEORY 57 results of past work that it has any claim to predetermine future results. To give some idea of how the three terms of the expression work out in practice, we may take a fairly typical case, where N = 12, T = 10, 8 = 0-1, and I = 20 ~"*~ 20 Then 144 120 = 0-0208 + 0-0083 + 0'025 = 0-054 In the case of motors having squirrel-cage rotors, the last term is usually some 30 per cent. less. FIG. 15. Having obtained a value for cr, we can construct the Heyland diagram, Fig. 15, in which OB represents the total stator flux, and OA the leakage flux at no OA load, AB being therefore the rotor flux and being cr. At any other load the leakage flux is, to the same scale, represented by OP and the rotor flux by PB, where 58 ALTERNATING CURRENT DESIGN P is any point on the semicircle which is drawn on AB as diameter. As P moves round the semicircle from A to B the leakage flux is seen increasing and the rotor flux decreasing until, as previously stated, the motor has not sufficient rotor flux to maintain the load and consequently falls out of step and stops, in which case the stator flux is all leakage and both are represented by OB. Exactly the same diagram represents the currents in the motor. OA is the stator current on no load to some suitable scale, any other stator current being represented by OP ; this becomes equal to OB when the rotor is standing and short-circuited. PA is pro- portional to the rotor current, the actual rotor current being obtained by multiplying the length of PA by the ratio stator turns over rotor turns. The direction of the voltage vector is 0V at right angles to OAB, so that the cosine of the angle VOP is the power factor, and the maximum value this can reach is when OP is a tangent to the semicircle, when it follows from the geometry of the figure that 1 cr 1 cos max. cos max. = 1 . or cr = - -7 - 1 + cr 1 + cos

; i i / r\-rt i A.13 Go the maximum value of Or cos

K )O An Pi ape a. res 16 2C O 3 cx input is \/3 x 500 X inphase component of stator current. The output is this minus the total loss, and the brake horse-power is the output divided by 0746. The slip is the rotor copper loss divided by this loss plus the motor output. The efficiency of the motor output over input for each current, can also be written down. EXAMPLE OF DESIGN OF AN INDUCTION MOTOR 69 b ** II l-e- t - if &.. f. W M 1 O ft >-4 25 8 ^ li li IS P3 f I q I B 1 .2 *s 0> 15 7-0 0-47 o-i 7-0 0-03 1-13 6-08 4-95 6-6 0-6 81-5 90 14-0 0-7 0-18 14-0 0-11 1-29 12-16 10-87 14-6 1-0 \ 89-4 30 25-5 0-85 0-4 25-5 0-38 1-78 22-0 20-2 27-0 1-8 91-9 40 35-5 0-885 0-72 35-5 0-73 2-45 30-7 28-2 37-9 2-5 92-0 50 45-0 0-9 1-12 45-5 1-2 3-32 39-0 35-7 47-9 3-3 91-5 60 54-5 0-91 1-62 56-0 1-82 4-44 47-4 42-9 57-4 4-0 90-6 80 72-5 0-905 2-87 76-0 3-34 7-21 63-0 55-8 I 74-7 5-7 88-5 100 89-0 0-89 4-5 95-0 5-22 10-7 77-0 ; 66-3 i 88-8 7-3 86-1 125 106-0 0-85 7-0 119-0 8-2 16-2 92-0 75-8 102-0 9-8 82-4 150 120-0 0-8 10-2 143-0 11-9 23-1 104-0 : 80-9 108-0 12-9 78-0 175 129-0 0-74 13-8 168-0 16-4 31-2 112-0 80-8 108-0 16-9 72-0 200 132-0 0-66 18-0 190-0 20-9 39-9 114-0 74-1 100-0 22-0 65-0 These results are plotted, not against stator current, but against B.H.P, The curves will then show the s 6 KH i5ht-H- .40 O 10 20 30 40 50 60 70 80 90 100 1 10 120 130 I4O 150 B.H.P. FIG. 17. efficiency, power factor, slip and stator current for any particular H.P. 70 ALTERNATING CURRENT DESIGN From these curves it is seen that for 50 B.H.P. the stator current is 52 amperes, the efficiency is 91*3, and the power factor 90*3 per cent. The full-load slip is 3*4 per cent., which makes the full-load speed 725 r.p.m. The curves begin to bend back at 109 H.P., and are commencing to show instability soon after 100 H.P. The power factor running light is got from the fact that the input is about 1*1 KW. allowing O'l KW. for stator and rotor C 2 R loss whilst the imput inK.V.A.is X/ 3x500xl2-8 =11> The power factor 1000 is therefore about 10 per cent. The maximum power factor, from the diagram, is 91 per cent., and occurs at a stator current of 60 amperes. The efficiency is a maximum at about three-quarter load, and is over 90 per cent, from about 15 to 65 H.P. WEIGHTS AND COSTS OF ACTIVE MATERIAL. Material. Weight in Ibs. Rate. Cost. Stator plates Rotor plates Stator winding Botor winding M.S. M.S. Cu Cu 370 190 160 140 30/- cwt. SO/- cwt. I/- Ib. I/- Ib. 4-95 2-55 8-0 7-0 Total cost of active material 22-5 As for the alternator, this motor would probably be sold at a profit for four times this, or 90. CHAPTER IX STATIC TRANSFORMERS AFTER the study of generators and motors, it is quite in place to look to transformers. The two oldest forms of static transformers are the ring of iron with primary and secondary windings wound round it, and the induction coil with a single straight core with both windings upon it. The first has given rise to the core type of transformer, but now has its parts rectangular ; and the latter to the shell type, so called from the iron which completes the magnetic circuit enclosing the windings. Consider a simple transformer of, say, the core type, with two windings of T x and T 2 turns respectively, having resistances R x and R 2 ohms. Call the ratio of turns, T! over T 2 p. If, the secondary winding being on open circuit, an alternating voltage is impressed on the primary, current will flow in increasing strength until its magnetizing force is sufficient to drive a flux through the iron core, of such a magnitude that the voltage induced thereby in the T x turns is equal to the impressed voltage less that used up in the resistance E x of the windings. 71 72 ALTERNATING CURRENT DESIGN This current, in comparison with the full-load current, will usually be very small indeed. A voltage corresponding to the turns and the flux threading it will also be induced in the secondary coil. Any current taken from this will be a demagnetizing current, and the primary coil will therefore take an increase of current in the ratio of the turns T 2 to T 1? so that the algebraic sum of the two ampere turns will always be that needed to magnetize the circuit. On open circuit, the ratio of the secondary voltage to the impressed voltage will be that of the turns T 2 to TU but on current being taken from the secondary its terminal voltage will fall, for three reasons : firstly, due to the pressure lost in sending its own current through the resistance of its own windings ; secondly, due to the flux through it having been reduced owing to the corre- o o o spending resistance drop on the primary winding ; and, thirdly, due to the fact that both primary and secondary currents set up leakage fields which do not thread the others' coils. In order to be able to represent the effect of these leakage fields on the same diagram as terminal voltages and volts lost in resistance, it is convenient to translate them into voltages too, remembering that really the leakage fluxes combine with the working fluxes, forming one resultant flux which produces one voltage only in each coil. To represent both primary and secondary effects on the same diagram one must be brought to terms of the other. Let A! and A 2 be the primary and secondary currents STATIC TRANSFORMERS 73 respectively. The current A x in the resistance Ej causes a drop 1 at the secondary terminals, which adds to P the secondary's own resistance drop of R 2 A 2 . As the magnetizing current is so small in comparison with the load currents, we may write A x = ; so that P the total drop on the secondary side due to the resistances of both windings is e r = A. 2 lR 2 H 2 l J ; this is in phase with the current. The reactance voltage drops due to the leakage fields are also proportional to the current, but at right angles to it. The amount of the waste field is as usual very difficult to calculate, as the leakage paths are quite undefined. The total drops due to this cause can, however, readily be measured in terms of the secondary voltage by short-circuiting the primary winding and supplying the secondary winding with sufficient voltage to cause full-load currents to circulate in both. This applied voltage is the resultant of the resistance and reactance voltages at right angles ; the former is, of course, easily calculated from the measured resistances, and hence the reactance drop is known. In a new transformer the result can be predicted from the data obtained from somewhat similar ones on test. On power factors of unity, or less than unity, lagging, both these causes reduce the secondary voltage. Let, in Fig. 18, E 2 represent the secondary terminal 74 ALTERNATING CURRENT DESIGN voltage. Draw A 2 to represent the direction of the secondary current at an angle to E 2 , where cos < is the power factor of the circuit supplied by the trans- former. In the same straight line as A 2 draw e r to represent the combined primary and secondary resist- ance drop, to the same scale as E 2 . This is in phase with the current. At right angles to this draw e st to represent the combined reactance drop. The vector FIG. 18. joining the end of this with the end of E 2 is propor- tional to the primary terminal voltage and equal to it if multiplied by p. If e r and e s are small compared with Ej and E 2 , then EX E 2 = e r cos < + e s sin < ; that is, the total drop of the secondary voltage from all causes is e r cos + e s sin (f>. This is seen, by the geometry of the figure, to be a maximum when the power factor of the circuit is a such that tan <> = -*. STATIC TRANSFORMERS 75 Before leaving this diagram it is interesting to note what happens if the power factor is less than unity but on the leading side of E 2 . In this case it is seen that, especially if the magnetic leakage is fairly high, the secondary voltage may be increased instead of diminished as the load increases, and still more so if the current tends to lead more on the pressure as the former increases. This fact is made use of in the operation of rotary converters, which by nature of the odd value of the alternating voltage required, if for no other reason, are practically always fed through transformers. If it is remembered that a rotary is essentially a synchronous motor, and the paragraphs at the end of Chapter V. be read in that light, it is seen that the provision of a compound winding on the magnets of a rotary converter carrying the main direct current pro- vides an increasing excitation, and therefore a power factor tending from lagging to leading as the load increases. This enables the transformer feeding it to raise its secondary voltage although itself fed from constant potential mains. So that, although the rotary converter operates with a fixed conversion ratio of DC to AC volts, the net result is that the addition of series turns on its magnets raises the voltage on the direct current side with increasing load, exactly like any other over-compound-wound D.C. generator, though really from a very different cause. If necessary the transformers for use with rotaries are made with specially large magnetic leakage in order to effect this end. 76 ALTERNATING CURRENT DESIGN The voltage regulation of transformers may be made as close as desired. The resistance drop is a question simply of quantity of copper used, and the reactance drop one of sufficiently interleaving the primary and secondary windings so that the lines made by the one are bound to cut the other also. As both these processes, however, cost money, and are increasingly expensive the further the result is pushed, it is worth while to consider if there are no other corresponding dis- advantages. One other disadvantage, besides the cost, to very close voltage regulation is the difficulty, when running such transformers in parallel, of ensuring that the load divides equally between them. Take the case of two transformers, one having a 9 and the other a 10 per cent, drop ; if these are in parallel it is obvious that they must have the same secondary voltage and there- fore the same drop, say 9| per cent., when one will be 5 per cent, under- and the other 5 per cent, over-loaded, which is not of much consequence. But now suppose that the regulation of the two is 2 and 3 per cent, respectively, and say 2| per cent, when in parallel, one will have 50 per cent, more load than the other, the one being 17 per cent, under- and the other 25 per cent, over-loaded. The design of transformers is rendered more than usually difficult on account of the apparently unlimited choice which is offered by varying the relative pro- portions of the iron and copper used. For instance, a 100 V. 50 ^ transformer might have one turn of copper STATIC TRANSFORMERS 77 and a flux of 45 million lines, or a million turns and 45 lines of force. Experience has shown, however, that there exists in well- designed transformers a fairly definite ratio between the flux and the ampere turns, though the value of this ratio naturally depends somewhat on the size and type. There is then the further choice of the lines per square centimetre in the iron, and the amperes per square centimetre in the copper ; the values for these are largely dictated by the efficiency aimed at and by the methods employed to carry off the heat generated ; for, whilst in small apparatus, natural cooling may be sufficient to carry off the heat corre- sponding to quite a moderate efficiency, yet the output increases so much faster than the linear dimensions that in large units, even where quite extraordinarily high efficiencies are obtained, some artificial method of cool- ing is called for to prevent an altogether abnormal rise of temperature, This artificial cooling may take the form of a blast of air forced through and round the transformer by an auxiliary fan, or again the whole apparatus may be immersed in oil, which itself may be cooled either naturally or artificially. The former method is cleaner and in some ways more direct, inspection is easier and the heat generated can readily be led out of the building or transformer chamber. The advantages of oil cooling are that the air circulation is dependent on running machinery, which may fail ; the air may be damp or dust-laden. Of the 78 ALTERNATING CURRENT DESIGN two, the fire risk with air is greater than with oil cooling. In very high-tension apparatus static dis- charges may occur in air which combine the nitrogen and oxygen of the atmosphere, forming nitric acid, which deteriorates the insulation and corrodes the copper. Owing to the larger specific heat of oil the overload capacity is greater than with air cooling, and oil is a very good insulator by itself and is self-healing in case of a discharge taking place. The material used for the electrical circuits is always copper having a fairly constant quality, but the magnetic circuits may be made of different classes of iron or of various alloys of iron containing small proportions of other ingredients. The correct proportions of iron and copper to use for any transformer will vary with the relative cost of the two metals. Let PC be the price of copper per cubic inch Pi be the price of iron per cubic inch I be the length of the core in inches d be the diameter of the core in inches t be the depth of copper a side in inches A be the amperes per square inch and B be the lines per square centimetre ; Then, neglecting the space factors for both iron and copper, which, for circular coils at any rate, are not far different, the volume of the iron is - d*l, and that of 4 the copper ir(d + t)lt, and the total cost of the two will be these expressions multiplied by Pi and PC respectively. STATIC TRANSFORMERS 79 The volts in a coil are equal to the flux x /= X 10~ 8 x turns in the coil. The flux is ^d 2 ~B x 6'45. The output W = volts x amperes. The ampere turns are /A and the amperes this divided by the turns, there- fore W= d*R~ X lt& x 22'5 X 1CT 8 . Putting this expression into the one for the total cost, we have W Pi id + t Total cost = A~ which is a minimum when t 1 /Pi PC This gives the best relation between the depth of copper and the diameter of iron core when the ratio of the costs of iron and copper is known. For iron plates at 20 shillings a cwt. and copper wire at a shilling a Ib. and densities 7 '8 and 8 '9 respectively, PC = 6 '4 Pi, and the best depth is when t = . If, however, we use "stalloy" at twice the o price of iron, the minimum cost occurs when t = 3'6 Taking the first value, i.e. that the depth of the copper is one-fifth the diameter of the core, and making a few assumptions such as that the length of the core is twice its diameter and that B = 7000 lines per cm 2 , and A = 1000 amperes per in 2 ., the value of the ratio flux to ampere turns mentioned 8o ALTERNATING CURRENT DESIGN before works out to about 180 to 1, which is actually very near the figure met with in practice ; the ampere turns being those due to one of the two windings, not both. The expression for the total cost shows also that this is proportional to the output, but inversely proportional to the induction, the density, and the frequency. CHAPTER X EXAMPLE OF THE DESIGN OF A TRANSFORMER WITH the help of the theory discussed in the last chapter we will now design a three-phase 350 KW. transformer of the three circular core type with common yoke. Primary voltage 2200, secondary 415 volts, 50^, to work on a power factor of 0*85. The secondary full-load current corresponding to 412 K.V.A. is 573 amperes, and at 98 per cent, efficiency the primary current is 110 amperes, both star connected. Taking the ratio of flux to ampere turns as 180 to 1, and calling the secondary turns T 2 , then 415 x v 2 x 10 8 1 573 T \/3 27r x 50 T 2 and T 2 = 32*3, say 32 turns per phase in 4 coils of 8 turns each. The flux will be 3*4x 10 6 lines in each core. The area for this at B = 7000 is 75 ins 2 , using plates 0*013" thick and varnished to 0*015", the gross area is 86 ins 2 . This may be made up of two blocks 11" x 3" and two blocks 5j" x 2", which, with half an inch ventilation spaces between each, just fit into a circle of 12f" diameter and give 88 ins 2 ., the net area of iron being 77 ins 2 , and the induction 6850 lines per cm 2 . 8r G 82 ALTERNATING CURRENT DESIGN The low-tension winding at 1000 amperes per in 2 , requires 0*573 sq. in. ; wind this with a number of fairly small square conductors in parallel, say six, each " square, which gives 0*585 in 2 , and 980 amperes per in 2 . Cover it to say 0*33 5" with double cotton. IE! FIG. 19. Eight turns of this combined conductor would occupy a space 2" x 2f " deep. Allowing |" from iron to copper, the inside turn would have a diameter of 13 75" and the mean diameter of the coil would be 16'5' ; , making the mean turn 52". The resistance of 32 such turns would be 0*0019 ohm per phase, and the total weight on three phases 936 Ibs. EXAMPLE OF THE DESIGN OF A TRANSFORMER 83 In fixing the number of primary turns, allow for 420 secondary volts, or 5 volts drop ; the high tension turns are then 32 x =168. The density should be rather lower here owing to the additional insulation. Two conductors J" square in parallel would give an area of 0*125 in 2 , and a density of 880 amperes per in 2 . Cover the conductor to 0*275" and wind nine layers deep, or 2j". The three coils in between the low-tension coils can then have 10 conductors side by side, which will take up 2*75" in width, leaving two coils at the two ends each of four conductors wide, or 1*1". The resistance of the 168 turns is 0*0465 ohm per phase, and the total weight 1048 Ibs. Allowing 1 in. between the coils and at each end, the length of the windings is 28*45", so make the iron core 30" long. The distance between centres of the three cores is 20*25", made up of 1275" for the iron, 5*5" for the coils, and 2" in clearance space. The total length of the yoke is 2 x 20*25" + 11" = 51*5". The area of the yoke is the same as that of the core, and is similarly arranged. The total weight of iron is 4150 Ibs., the maximum induction 6850 lines per cm 2 . In transformer iron, partly on account of its use in rectangular sheets with- out teeth, and partly that it need not be subjected to so much ill treatment in manufacture as are core plates for alternators or motors, the loss per pound at similar inductions is much less. In the present case this should not exceed 0*7 watt per pound, or say 3 KW. total. 84 ALTERNATING CURRENT DESIGN The copper losses warm are H.T. 1*9 KW. and L.T. 2-1 KW., making a total loss at full load of 7 KW. in an input of 357, or a full-load efficiency at 0*85 power factor of just over 98 per cent. At unity power factor the total loss at 350 KW.'s is reduced to 5'9 KW., and the efficiency works out to 98*3 per cent. The efficiencies at different loads are shown in the following columns : full \l l|load. Power factor 0-85 Iron loss 3-0 3-0 3-0 3-0 3-0 3-0 Copper loss 0-25 1-0 2-25 4-0 6-25 9-0 Total loss 3-25 4-0 5-25 7'0 9-25 12-0 Output 87-5 175-0 262-5 350-0 437-5 525-0 Input 90-75 179-0 267-75 357-0 446-75 537-0 Efficiency, per cent. 96-4 97-8 98-0 98-0 97-9 97-8 Power factor unity Copper loss 0-18 0-72 1-62 2-9 4-53 6-53 Total loss 3-18 3-75 4-62 5-9 7-53 9-53 Input 90-68 178-72 267-12 355-9 445-03 534-53 Efficiency, per cent. 96-5 97-9 98-3 98-3 98-3 98-2 The cost of active material is : for plates, 4150 Ibs. at 205. per cwt., 37 ; for copper, 2000 Ibs. at Is. per lb., 100. Total cost of active material, 137. The magnetizing current is calculated on the assumption that each phase magnetizes for its own core and the yoke halfway to the next, 30" and 20" respec- tively in length. The joints at each end of the core are taken as equivalent to 0*1 mm. of air. H x / for air = 6850 x 0'02 = 137 for iron = 2 x 127 = 254 Total 391 The magnetizing current is therefore 391 x 0*8 168 x \/9 = 1>3 -R" M.S. amperes per phase. EXAMPLE OF THE DESIGN OF A TRANSFORMER 85 For purposes of the calculation of voltage regulation, it is assumed that previous experience with similar transformers would lead one to expect a reactance drop of 3 per cent. The resistance drop in the secondary when warm is 0'0019 X T15 X 573 = 1 '2 5 volts, which is 0*52 per cent, in the star voltage of 240. In the primary the corresponding figure is 0*065 X 1*15 x o'4 o'6 Power factor. 0-9 FIG. 20, 110 = 5 '9 volts, or 0'47 per cent. The total resistance drop is therefore, say, 1 per cent. The total voltage drop from both causes is then 1 cos (j> 4- 3 sin , where cos (/> is the power factor of the circuit fed from the secondary. The power factor at which this drop is a maximum is when tan < = 3 or cos (f) = 0'32, when the drop is 3'16 per cent. 86 ALTERNATING CURRENT DESIGN The following table gives the total drop for other values of the power factor : COB<. $ in degrees. Sin $ X 3. Total percentage drop. 1-0 o-o o-o 1-0 0-95 18-2 0-93 1-88 0-85 31-8 1-58 2-43 0-6 53-1 2-4 3-0 0-4 66-4 2-75 3-15 0-2 78-5 2-94 3-14 o-o 90-0 3-0 3-0 CHAPTER XI TRANSMISSION LINES THERE follows naturally from generators, motors and transformers the question of transmission of electrical energy. Firstly comes the question as to what system of generating electricity is best adapted for its transmis- sion. A simple comparison can be made of the various systems, on the basis of equal power transmitted for a given distance with a given loss, the pressure at the receiving end being kept the same for all. For the sake of example, take 100 KW. delivered one mile away with a 10 per cent, loss, the pressure at the delivery end to be 200 volts. Firstly, on the direct- current two- wire, or single- phase two-wire systems, the current would be 500 amperes. The loss in each line is 5 KW., which requires an area of 2*1 ins 2 , of copper and a total weight of 38 tons. The density would be 240 amperes per in 2 . Secondly, direct- current or single -phase three wires with the middle wire 10 per cent, of each outer, but carry- ing no current. The current in the outers is 250 amperes, the loss in each is as before, 5 KW., which makes the 87 88 ALTERNATING CURRENT DESIGN area of each 0'525 in 2 , with a density of 480 amperes per in 2 . The total weight of copper is 10 tons. Thirdly, two-phase four wires, which gives the same total weight as for a single-phase, 38 tons. Fourthly, two-phase three-wires. The current in each outer is 250 amperes and in the middle wire 354. The density is the same in all these, i.e. 280 amperes per in 2 . The area of each outer is 0*895 in 2 , and of the middle 1*26 ins 2 . The total weight is 27 '6 tons. Fifthly, three-phase mesh, with 200 volts between each of the three wires. The current in each wire is 288 amperes, the area 1*05 ins 2 ., the density 274 amperes per in 2 ., and the total weight 28*8 tons. Sixthly, three-phase star, with 200 volts between each wire and the star point. The middle wire to be 10 per cent, of each of the outers, but carrying no current. The total weight of this arrangement is 9*8 tons. Seventhly, three-phase star, but transforming down to 200 volts at the receiving end. The voltage to be such that the 10 KW. loss is combined with a density of 1000 amperes per in 2 . At this density the drop is 42 volts per mile in each wire, so that the receiving voltage must be 420 star volts, or 730 volts between lines, and 803 volts at the generator end. The current per line is 79 amperes, and the section of each wire 0*079 in 2 . The weight of the three wires (the transformers supply the middle wire) would be 2*15 tons. TRANSMISSION LINES 89 Below is a summary of these results : 1 MILE TRANSMISSION. 100 KW.'s delivered at 200 volts with 10 KW. loss. System. A amperes per cm-. Total weight in tons. Per cent, of D.C. 1. D.C. or single phase 240 38-0 100-0 2. D.C. 3 wires, 480 10-0 27-0 3. 2-phase, 4 wires 240 38-0 100-0 4. 2-phase, 3 wires 280 27'6 73-0 5. 3-phase, mesh 274 28-5 75-0 6. 3-phase, star 480 9-8 26-0 7. 3-phase, star, with transformers 1000 2-15 5-7 The last case introduces the question of the cheapest voltage to transmit at, because, if the cables be covered, the increased cost of insulation may more than balance the reduced cost of copper. To obtain this cheapest voltage, certain assumptions have to be made. Few manufacturers will guarantee their cables if worked at more than 1000 amperes per in 2 , on account of temperature ; this is not a very scientific basis, but it is worth while to see what results it will lead to. Another basis of comparison would be equal efficiencies, which can be expressed as equal percentage pressure drop per mile. In general, manufacturers' catalogues have to be re- arranged in order that the cheapest voltage at which to transmit a given load, at either constant density or constant efficiency may be apparent. For example, let us assume that we have prices for three-core lead-covered and armoured cables for three voltages and for three sizes at each voltage, as under : Cables of 0*01 in 2 , area per core insulated for 1000, ALTERNATING CURRENT DESIGN 6000, and 10,000 volts between cores and to the sheath, <215, 310 and 425 per mile respectively ; for 0'05 in 2 , per core for the same voltages, 450, 550 and 700 per mile ; and for O'l in 2 ., 720, 825 and 1000 per mile. Plot these on the same sheet and to the same horizontal scale of 's per mile, one vertical scale being volts and the other square inches area per core. From the Volts. Square inches. 10,000 ,g 5000 TL I ___ __ . -4 K l I ;'s per mile. FIG. 21. constant area curves, points can be read off for the price curves at constant volts of 3500 and 8000. Now the area of each core of a three-core cable delivering KW. kilowatts at E volts between cores, with a loss of p per cent, of these kilowatts per mile trans- mitted, at 15 C. is 4224. ins . P E 2 TRANSMISSION LINES 91 To do the same as above, but at a density of A amperes per square inch instead of at a loss of p per cent., the area of each core would be KW 588 . v . 2 AA = ^- ms 2 . The areas required for 10, 50, 100, 500 and 1000 kilowatts at a loss of 2 per cent, per mile, as calculated by the above expression, are as follows : KW.'s at 1,000 3,500 6,000 8,000 10,000 volts. 10 0-021 0-00172 0-00058 0-00033 0-00021 ins. 2 60 0-105 0-0086 0-0029 0-00165 0-00105 100 0-21 0-0172 0-0058 0-0033 0-0021 500 1-05 0-086 0-029 0-0165 0-0105 1000 2-1 0-172 0-058 0-033 0-021 The prices of these read from the price curves are as follows : KW.'s at 1,000 3,500 6,000 8,000 10,000 volts. 10 280 210 255 . 50 750 250 275 315 360 100 305 285 320 370 500 700 430 415 430 1000 605 515 500 These are plotted on Fig. 22. It is seen from this that each load has a cheapest voltage, and also how this " cheapest voltage" increases with the KW.'s to be transmitted. If, instead of the loss, the density were kept constant, a similar set of figures would be obtained, but giving a slightly different " cheapest voltage." Although, with the exception perhaps of telegraph wire, the material almost universally used for electric conductors is copper, there are other metals which have certain claims for consideration as possessing advantages in one way or another over copper. 92 ALTERNATING CURRENT DESIGN In order to make a comparison, one must be sure of the basis of comparison selected. In general the problem is one of transmitting a certain quantity of electrical energy a certain distance with a given loss in the process ; thus the comparison might be in the IOOO 's per mile. cost of a conductor one mile long having a resistance of one ohm. There are other considerations, of course, besides the one of cost. The diameter of the conductor is important as affected by wind and snow. The weight TRANSMISSION LINES 93 of the conductor has a direct bearing on the cost of poles, and its strength must be considered in this connection, in relation to its weight. For the solution of the problem as stated above, four of the properties of the material of the conductor must be known, namely, its specific resistance, its density, its tensile strength, and its cost per ton. If p be the specific resistance in 10~ 6 ohms per cm. length per cm 2 , area at 15 C., and 8 be the density in grammes per cm 3 ., S be the tensile strength in tons per in 2 ., K be the cost in 's per ton, then the diameter of the conductor of one ohm per mile will be 0'178\/p inches. g The weight per mile will be * tons, and the O*7 O ., p x 8 x K p , cost per mile c s. 39'3 The strength of the conductor considered in relation to its weight may be expressed as the number of miles of itself that the conductor would support vertically ; n this = - very nearly indeed. In the table on next page are given a few of the possible metals of which conductors might be made, with their four physical properties as above, from which are worked out the particulars of the one ohm per mile conductor. It should be noted that the cost given is for the material of which the conductor is made, and does not 94 ALTERNATING CURRENT DESIGN include the cost of making it into a wire or other suitable form ; for instance, sodium would probably have to be contained in an iron tube. Conductor 1 mile long " a o - 1 ohm resistance at 15 C. *^ .0 JS c 55 * p< 92 | Material. jr S tt! ft 1 | L 2 as ' O.CC .3 % 42 o Cost. 3 H 5 1 I |f P 8 S K c i i ! Aluminium 2-84 2-6 15-0 74 0-3 0-188 5-8 14 Antimony 37-0 6-7 0-4 28 1-08 6-3 0-06 176 Bismuth 136-0 9-8 3-8 896 2-08 34-0 0-39 30,500 Brass, Cu f Zn 6-5 8-4 22-0 48 0-455 1-39 2-6 67 Bronze, Cu, Sn, P or Si 3-3 8-9 40-0 69 0-324 0-75 4-5 52 Cadmium 10-6 8-6 5-2 336 0-58 2-32 0-6 780 Copper 1-67 8-9 26-0 59 0-23 0-38 2-9 22-4 Gold 2-32 19-3 17-5 139,000 0-271 1-14 0-9 158,000 Wrought iron 10-5 7-8 40-0 6 0-57 2-09 5-1 12-5 Cast iron 100-0 7-2 9-0 3 1-78 18-3 1-25 55 Lead 21-0 11-4 1-4 13 0-82 6-1 0-12 79 Magnesium 4-6 1-7 12-0 672 0-382 0-2 7-0 134 Mercury 95-3 13-6 250 1-74 33-0 8,250 Nickel 13-4 8-9 39-0 171 0-65 3-04 4-4 520 Platinum 9-3 21-5 22-0 238,000 0-544 5-1 1-02 1,220,000 Silver 1-56 10-5 19-0 3,460 0-222 0-42 1-8 1,450 Sodium 5-2 0-97 0-01 90 0-406 0-128 0-01 11-5 Steel 15-0 7-8 60-0 5 0-69 3-0 7-7 15 Tantalum 16-5 16-5 27-0 13,000 0-725 6-9 1-6 90,000 Tin 13-8 7-3 2-0 157 0-66 2-56 0-27 40-5 Tungsten 10-7 19-1 11-0 560 0-58 5-2 0-58 2,900 Zinc 6-1 7-1 3-4 24 0-44 1-1 0-48 26-4 Below are given eight of the more interesting metals arranged in order of merit under the four different counts. For the sake of comparison, copper has been taken as a standard and called one, the others being compared with copper. TRANSMISSION LINES 95 Size. Weight, Strength (in length of itself it will support). Cost. Silver 0-97 Copper 1*0 Aluminium 1'3 Bronze 1'4 Magnesium 1-66 Sodium 1-76 Wrought iron 2-47 Steel 3-0 Sodium 0-34 Aluminium - 5 Magnesium 0-53 Copper 1-0 Silver 1-1 Bronze 2*0 Wrought iron 5-5 Steel 7-9 Steel 2-6 Magnesium 2-4 Aluminium 2-0 Wrought iron 1-8 Bronze 1'5 Copper 1-0 Silver 0'6 Sodium 0-003 Sodium 0-52 Wrought iron 0'56 Aluminium 0-63 Steel 0-67 Copper 1-0 Bronze 2-3 Magnesium 6-0 Silver 65-0 All compared for a conductor of equal resistance per mile. It will be noticed that the somewhat curious result is arrived at that sodium forms both the cheapest and the lightest conductor, whilst aluminium is better than copper in everything but size ; wrought iron and steel are cheap and strong, but very heavy and large. By far the most costly conductor of all is platinum, although it is for the purpose of an electrical conductor that the largest part of the world's output of platinum is used, namely, in the manufacture of electric lamps. CHAPTER XII CHOKING COILS IT sometimes happens that it is required to reduce the amount of current flowing in a circuit. In direct- current work this would have to be done by inserting a series resistance, with its consequent waste of energy ; a back electro-motive force would do the work better and more economically, but is difficult to arrange. In alter- nating-current work, however, a method exists of readily manufacturing this back E.M.F on the spot in the piece of apparatus known as a choking coil. This consists of a magnetic circuit, either wholly of iron or partly of iron and partly of air, round which is wound the conductor carrying the main current. The current flowing round the iron magnetizes it, thus causing an alternating flux to flow, this in its turn creates an alternating E.M.F. in the conductors encircling it. Such a number of turns is wound round the iron as will, multiplied by the maximum value of the current, give the ampere turns needed to send that flux round the circuit which will give the required back E.M.F. It follows from the principles discussed in the first chapter of this book that this back E.M.F. is at right angles to the current. 96 CHOKING COILS 97 Suppose that it is required to work a 50-volt 10-ampere arc lamp from a 100-volt circuit ; the current of an arc being in phase with the voltage across it, the choking coil voltage is at right angles to this latter, the supply voltage being the resultant of the two. The choking coil will therefore be required to give a voltage equal to vToo 2 50 2 or 86*5. Assuming a 50 ^ circuit, the product of the flux and the turns will equal 86 ' 5 x _^ x 10 8 = 39 x 1Q6> 2?r X 50 Taking the relation established for a transformer that the flux should be of the order of 90 times the total ampere turns, the flux would be 187,000 lines and the turns 208. To carry these lines at an induction of, say, 10,000 lines per cm 2 , requires 2'9 ins 2 ., or say 2" X 1*65", allowing for insulation between the plates. Ten amperes at 1500 amperes per in 2 , requires 0*0067 in 2 ., or 0*092" diameter, which covered to 20 mils, equals 0*112". Winding this to 7 layers and 15 convolutions per layer on each coil, gives a coil 0*8" deep and 1*8" long. The inside dimensions of the stamping will -be 2" x 2" and the outside 6" x 6". The yoke piece would, of course, be separate, in order to slip the coils over the two limbs. The mean path of the lines in the iron would be 14" = 36 cms. H for B = 10,000 is about 3, making H x I = 108 for the iron. The total magnetizing force of the two coils carrying 10 E.M.S. amperes is H 98 ALTERNATING CURRENT DESIGN - X + 2Q8 = 3660, which leaves 3552, which can 0*8 be used up in the air space between the removable yoke and the two limbs. The induction in this air space is also 10,000, which means 0'055 cm., or from 1| to 2 millimetres a side, which can take the form of mica packing and is readily adjustable to obtain the exact back E.M.F. required. The mean turn of the coil is about 11 inches, so that the resistance of the 208 turns is 0'23 ohm cold, and the copper loss warm with 10 amperes is 26 watts. The weight of the iron is 13 Ibs., which at 2 watts per pound also gives a loss of 26 watts, or 52 watts lost in all. The volt ampere input to the choking coil is 86*5 x 10 = 865, from which the power factor is 0'06. The power factor of the whole circuit consisting of arc and choking coil would be 0*55, the total power being 500 watts for the arc and 52 for the coil, and the input being 1 K.V.A. In the continuous current analogy a series resistance of 5 ohms and a loss of 500 watts, or nearly ten times as much, would have been necessary. At currents less than 10 amperes the back E.M.F. of the choking coil will be sensibly proportional to the current, but at much higher currents the iron will saturate : to give double the back E.M.F. would require an induction of 20,000 lines per cm 2 . H would then be 290, making H x I for the iron = 10,400, and 7100 for the air, total 17,500 C.G.S. units or 48 amperes. CHAPTER XIII ADDITIONAL EXAMPLE OF THE DESIGN OF AN ALTEENATOE THE alternator designed in Chapter IV. fulfils the requirements of a constant pressure generator with a good inherent regulation, but there may be uses for an alternator when these small pressure drops are out of place. For instance, in the case of an alternator for use with a resistance type of electric furnace it is more important to keep the KW. input to the furnace as nearly constant as possible with wide variations of the resistance offered by the furnace. This means that as the current increases the voltage should decrease in nearly the same proportion. This result can be approached by the use of a large stator reaction combined with a large stator leakage flux ; and it so happens that both these tend to cheapen the manufacturing cost per KW. To illustrate this, let us consider the design of a two -phase alternator for furnace work giving, say, 500 K.V.A. total, at 130 volts per phase, frequency of 25, speed 100 r.p.m., 30 poles. The full-load current per phase will be 1920 amperes. 99 ioo ALTERNATING CURRENT DESIGN A stator reaction of something like 1500 ampere turns per inch diameter will be possible ; putting this value into the expression in Chapter III. gives D 2 / = 86,000, which for a length of about 10" gives a diameter of about 100 inches. The corresponding peripheral speed for this is 2600 feet per minute, and the pitch of the poles is 10' 5 inches. All these figures are quite satisfactory. The conductors per pole per phase at 1500 total ampere turns per inch diameter and 100 inches diameter and 1920 amperes per phase are 2*6. Call this 3; putting each conductor in a tunnel would mean 6 tunnels per pole, or 180 total ; the pitch of the teeth would be 174". The stator conductor for a density, say, of 2500 amperes per in 2 , would be 077 in 2 . ; this, at any rate for the conductor embedded in the tunnel, would have to be stranded, as otherwise the " Field effect " would nearly double the RC 2 loss in that portion. The stranding will increase the bulk of the conductor from 15 to 20 per cent, for the same conductivity. The length of the turn on the stator is about 57 ins., which would make the resistance of the 45 turns per phase 0*0022 ohm cold, the lost volts warm 5, the total volts per phase 135, and the stator flux 27 X 10 6 lines per pole. In the design of the whole magnetic circuit we must allow for the voltage increasing as the load on the alternator falls, in order to keep the output to the furnace as nearly constant as possible, thus the induction ADDITIONAL DESIGN OF AN ALTERNATOR 101 in the teeth should not exceed, say, 15,000 lines per cm 2 , at full load. In a two-phase machine the pole arc should not be much more than half the pole pitch, so as to allow of one phase being entirely out of the field at one time. To do this in this case allows the pole a width of 3 teeth and 4 slots, or say, 6". The net length of iron in the 10" length, allow- ing for three |" ventilation spaces and plates 0*015" thick, with 1 mil. of varnish on each side, is 7*5". The teeth are then '9 3" wide, leaving 0' 81" for each tunnel. The copper could be 1*3" x 0*7", insulation all round with 0*05" of, say, silesia varnished and ironed on ; the tunnels could then be 1*5" deep. The iron at the back of the slots for an induction of say 12,500 would be 2*25" deep each side, making the outside diameter of the stator plate 107 "5". The stator leakage flux, taking for tunnels 100 lines per ampere per inch, at a current of 1920 amperes, is 27 x 10 6 , or curiously enough exactly equal to the stator flux. It is safer to allow for a power factor of 0*95, which, however, is mostly accounted for by the leads and not by the furnace itself. The air space flux at this angle by the vector diagram is 4*4 X 10 6 . The rotor leakage factor is probably about 1*2, so that the rotor flux is 5*3 x 10 6 , to accommodate which in cast steel at 16,000 lines per cm 2 , requires 51 ins 2 . Make the pole, say, 10" x 5" and assume a length of pole of 6". The yoke itV&T&fY? - *** s.'ft*., i ALTERNATING CURRENT DESIGN 102 if cast steel should be rather more than half this area, say, 10" X 3". Take the radial clearance as ". We have now all the data for the calculation of the full load magnetization, which works out as follows : SYNTHESIS AT 130 VOLTS, 1920 AMPEBES, 0-95 POWER FACTOR. Length cms. Area cms 2 . Flux xio 6 . B H lines cm 2 , per cm. HxZ C.G.S. Ampere turns per pole. Stator core ... Teeth Air space Magnets Yoke 28-0 7-6 1-27 30-0 22-0 217 182 387 323 387 2-7 2-7 4-4 5-3 5-3 12,500 ! 6 14,800 11 11.400 11,400 16,400 i 47 13,700 ; 6-5 168 84 14,480 1,410 143 16,285 6,500 The demagnetizing ampere turns on the stator are 1920 x 45 x 2 x \/2 2 3Q -=4100 These two combined on the vector diagram give the rotor ampere turns at the above full load as = 10,100. The rotor magnet winding may very well take the form of copper strip on edge. Exciting from 100 volts and allowing 36 inches for the length of one turn, the area for 10,100 ampere turns is 0*084 in 2 ., say 1^" x 0*067". This would carry 126 amperes at 1500 amperes per in 2 . The turns would be 80 per pole. Separating these with 5 mil. paper, the winding would occupy 5*85" radially : the magnet pole should be 6j" long. The resistance cold of the 30 poles in series is 0*69 ohm, the loss warm 12*6 KW. or 2*5 per cent, of 500 KW. The next thing required is the open circuit magneti- zation curve. Using the areas and lengths of the ADDITIONAL DESIGN OF AN ALTERNATOR 103 magnetic circuit from the full-load synthesis, and taking four points, this works out as follows : Line volts at 100 r.p.m. 100 150 175 200 Stator flux X 10 6 ... 2 3 3-5 4 B and H Stator Teeth Air Magnets ... Yoke 9,200-3 11,000-4 5,200 7,400-2 6,200-1 13,800-8-5 16,500-28 7,800 11,200-5-5 9,300-3 16,200-23 19,200-200 9,100 13,000-9 10,800-5 18,400-130 22,000-650 10,400 14,800-18 12,400-8 H x I Stator Teeth Air Magnets . . . Yoke 84 30 6,600 60 22 238 213 9,900 165 66 644 1,520 11,550 270 110 3,640 4,950 13,200 540 176 C.G.S. per 2 poles ... 6,796 10,582 14,094 22,506 Ampere turns per pole 2,720 4,240 5,640 9,000 This curve is drawn on Fig. 23 ; from it is found that the full-load magnetization would give 204 volts on open circuit, or a rise of 57 per cent. The short circuit current for 10,100 ampere turns on the rotor is 2500 amperes. We have now three points on the load curve connect- ing volts and amperes at constant speed, power factor, and rotor excitation namely, 204 volts amperes, 130 volts 1920 amperes, and volts 2500 amperes. Drawing through these points the best curve we can (Fig. 24), it would be as well to check two more points, say, 188 volts 1000 amperes and ^70 volts 2300 amperes; these 104 ALTERNATING CURRENT DESIGN Volts per phase. _L__ ; 2500 5000 Ampere turns per pole. FIG. 23. 7500 Volts per phase. 300 2000 Amperes per phase. FIG. 24. 3000 ADDITIONAL DESIGN OF AN ALTERNATOR 105 are both found to require very nearly 10,100 ampere turns on the rotor. On the same sheet is drawn the volt ampere curve for 500 K.Y.A., which shows that for voltages between 100 and 200, the two curves do not widely differ. The losses at full load are approximately as under- iron loss, 2580 Ibs. at 1-75 watts per Ib 4-5 KW. Stator copper = 2 X 0-0022 X 1-15 X 1920 2 18-6 Rotor copper = 0-69 X 1-15 X 126 2 12-6 Total loss 35-7 Output = 500 X 0-95 475-0 Input 510-7 Efficiency 93 per cent. This rather low efficiency is not so much due to the peculiarities of the design as to the low speed for the output, necessitating a large amount of active material. The weights and costs of active material are Stator Iron 2,120 Ibs. at 30s. cwt. 28-5 Stator copper 1,270 Is. Ib. 63-5 Rotor poles 3,000 18s. cwt. 24-0 Rotor copper 2,320 lOd. Ib. 97-0 Yoke ring 2,170 18s. cwt. 17'5 10,880 Ibs. 230-5 This could probably be sold at a profit for 900. If this is compared with the 250 KW. constant pressure alternator at 375 r.p.m. and 0*8 power factor, it is seen to be about one-third the cost on the basis of the K.V.A. at one r.p.m. CHAPTEK XIV DESIGN OF A SMALLER TWO-PHASE SQUIRREL-CAGE INDUCTION MOTOR AND AUTO-STARTER THE design of the 50 H.P. wound-rotor motor described in Chapter VIII. may be supplemented by that of a smaller squirrel-cage motor ; this, of course, will suffer from the disadvantages of such a rotor winding : firstly, in starting, it will take a larger current from the mains, and even then it will not start up against such a large load in comparison with its rated H.P. ; and secondly, it will not be capable of speed regulation ; it will, however, have a slightly better power factor than the corre- sponding wound-rotor motor, and it will be considerably cheaper to build owing both to the simplicity of its rotor winding, and to the absence of slip rings and brush gear. For the sake of example, let us take a 5 -H.P. motor to work from a 50^w, 2-phase, 3-wire circuit at 220 volts per phase. Speed light, 1500 r.p.m., i.e. 4 poles. The motor to stand 50 per cent, overload for a few minutes, and full load for 6 hours with a temperature rise of not more than 40 C. The full load efficiency of such a motor should be about 85 per cent, and the power factor about 90 per 106 INDUCTION MOTOR AND AUTO-STARTER 107 cent. The current per phase on this basis is about 11 amperes. To obtain a power factor of 90, cr would = ^-^ = 0-053. Take for a first approximation 4 slots per pole per phase in the stator, making 8 per pole and 32 total. The rotor slot number should be as dissimilar as possible from this, and also as high as practicable ; try 45. N in the cr formula would then be 9*6 and the first term 0*0325. S, the radial clearance, could be as low, with good mechanical workmanship, as 0*5 mm. Making the length 12 cms. and taking advantage of the 30 per cent, decrease in the third term of the cr expression due to the squirrel-cage winding, the value of o- = 0*053 would be satisfied with a pole pitch of anything over 9 cms. Taking 300 ampere turns per cm. diameter, with 11 amperes per phase and 9 cms. pole pitch, the air space induction would work out to about 10,800 ; reducing this to 5000 would give pole pitch of 13*2 and a diameter at the air space of 17 cms. nearly. On the foregoing assumptions the total turns for 17 cms. diameter are 464, which is 29 conductors in each of the 32 slots, making 232 turns per phase. To carry 11 amperes at about 4 amperes per mm 2 , requires 275 mm 2 . No. 15 S.W.Gr. is 2*63 mm 2 , area, which would make the density 4*2. The average length of a turn on the stator would be io8 ALTERNATING CURRENT DESIGN about 68 cms., the resistance per phase cold would therefore be 1 ohm, or about 13 volts lost, warm. The total flux per pole in the stator will be 0*42 x 10 6 lines. 3 10 x 0-05 3;5 X CK)5 - + 9^TxT3 : 4 H 12 = 0-051 which makes the rotor flux 0'4 x 10 6 . The 12 cms. length will have one ventilation space 1 cm. wide, and will have a net length of iron of 10 '6 cms. The width of each tooth for the induction never to exceed 17,000 lines per cm 2 , will be 4 '6 mm., which makes the slot 12 mm. wide. Insulating this with 0*5 mm. a side, leaving O'o mm. margin, and insulating the wire to 0*25 mm. on its diameter with, say, varnished silk, 5 wires will go in abreast. The overall depth of the slot will therefore be about 17 mm. with a 2 mm. opening. The radial depth of iron at the back of the stator slots for, say, B = 7000 is 2*8 cms., making the outside diameter of the stator plate 26 cms. The rotor copper per slot for a density of about 5 amperes per mm 2 , is approximately 32 x 29 x 2'63 4'2 x = 46 mm 2 . 45 5 This, in a round bar, has a diameter of 7*6 mm., which would go through a hole in the rotor plate of 8 mm. diameter, no insulation being necessary. The INDUCTION MOTOR AND AUTO-STARTER 109 minimum width of tooth would then be 3 '4 mm., which is ample to carry the flux. The rotor plate could have a hole in its centre up to 1 1 "5 cms. in diameter for the induction not to be over 10,000 lines per cm 2 . The end ring should have a cross-sectional area of a little less than half the rotor bars per pole, in this case about 15 mm. square. The synthesis of the magnetic circuit works out as follows : Length. Area. Flux. B. H. HxZ. Stator core X 2 ... 12-3 60 0-42 7,000 2 25 Stator teeth 3-4 46 0-42 14,400 10 34 Air 0-1 150 0-41 4,300 4300 430 Rotor teeth 1-6 42 0-4 i 15,000 12 19 Kotor core X 2 ... 7'2 40 0-4 10,000 3 22 Total C.G.S. per 2 poles 530 Ampere turns per pole 212 From this the magnetizing current per phase is 212 x 4X2 \/2 x 2 x 232 212 x 4 x 2 Toon = 2 ' 6 amperes. The static current is this divided by cr = 51 amperes. The Heyland diagram (Fig. 25) is drawn from these two currents. The stator iron loss is approximately given by 55 Ibs. of iron at 2 watts per pound = 110 watts ; add to this 30 watts for windage and friction and the fixed loss becomes 140 watts. For the squirrel-cage rotor loss, the best we can do is to say that from actual data on similar motors the no ALTERNATING CURRENT DESIGN full load slip will be about 5 per cent., which gives a rotor C 2 R loss at full load of about 200 watts. Amps. 35 ^ ' 8T -, >f x^ >o s> X / s,, / \ / 6 \ 1 \ / \ \ / a \ 5 s \ 3 _ \ 25 FIG. 25. 75 With the help of the Hey land diagram we can now work out the whole behaviour of the motor as under : ti tf 1 rt | ^ 11 Jl || 6 S 111' ? 1 I 1 0* W 3 s oo i *! 1 r g s I " o PQ 02 ^ 3 1-5 0-5 ! 21 1-5 4 165 660 495 0-7 0-8 75-0 5 4-0 0-8 ! 58 4-0 32 230 1760 1530 2-1 2-0 87-0 8 7-0 0-88 i 148 7-0 98 386 3080 2694 3-6 3-5 87-5 11 9-9 0-9 280 10-0 200 620 4360 3740 5-0 5-1 86-0 16 14-2 0-87 590 15-0 450 1180 6200 5020 6-7 8-2 81-0 25 20-5 0-82 1440 23-5 1100 2680 9000 6320 8-5 14-8 70-0 30 23-0 0-77 2070 28-5 1620 3830 10200 6370 8-5 20-0 63-0 35 24-0 0-69 2840 33-0 2170 5150 10600 5450 7-3 28-0 51-0 These are plotted on Fig. 26. For the power factor running light the losses are 140 + 16 for C 2 R = 156 ; the volt-ampere input is 2 x 220 X 2*6 = 1140, which makes the power factor about 14 per cent. Per cent, and amps. INDUCTION MOTOR AND AUTO-STARTER WEIGHTS AND COSTS OF ACTIVE MATEBIAL. in Stator plates Rotor plates Stator copper Rotor copper 43 Ibs. at 30s. cwt. 18 at 30s. cwt. 16 at Is. Ib. 10 at 9d. Ib. 0'58 0-24 0-8 0'38 90 So 60 P.f B.H.P? FIG. 26. Auto-starter for the above motor. To prevent the undue rush of current which would result from switching the stator of such a motor straight on to the mains an " auto-starter " is employed. This device performs two functions, firstly, it causes a reduced voltage to be applied to the motor when starting up, H2 ALTERNATING CURRENT DESIGN which consequently reduces the current sent into the motor ; and, secondly, by doing this by means of a transformer, the actual current demanded from the mains is less than the current sent into the motor by nearly the same proportion in which the voltage on the motor is reduced from that of the mains. If a coil of wire is wound round an iron core and an alternating voltage applied at its ends, the voltage will be divided up proportionately to the turns, i.e. a point halfway along the coil will give half the line voltage from that point to either end of the coil ; but not only this but the half number of turns will act in every way as the secondary windings of a transformer on the same core, and, neglecting the small loss in the core and winding, will deliver the same volt amperes as are supplied by the mains, giving a greater current as the voltage is reduced. This is just what is wanted for the starting up of a squirrel-cage induction motor. A suitable switch will apply consecutively higher voltages to the motor as its speed increases, finally leaving the motor straight on to the mains with the auto- transformer coil switched off. The two phases must, of course, be wound on separate iron cores, but can share a common yoke like the three-phase transformer, but unlike this, must have an iron circuit to take the resultant flux, which in the two-phase case is \/2 times the flux of each phase, whilst in the three-phase case the resultant flux, of course, vanishes. In the case under review the voltage per core is 220 and the frequency 50. If the motor is tapped on to the INDUCTION MOTOR AND AUTO-STARTER 113 middle of the winding, each half will contribute current equally, so that if we wind with a conductor which will carry the full-load current of the motor at, say, 5 amperes per mm 2 ., it will enable the motor to have two or three times its normal current whilst starting up with safety. Eleven amperes at 5 amperes per mm 2 , requires 2-2 mm 2 ; 16's S.W.G. is 2-1 mm 2 . The wire will have to be well insulated, as the voltage per turn is high. As the auto-transformer is only used for short times together, the induction in the iron core can be as high as about 17,000 lines per cm 2 . A core 5 cms. x 4, built, of course, of laminated iron, will carry 0*3 x 10 6 lines, which will require 330 turns for 220 volts. 16's S.W.G., insulated to 0*5 mm., is 2'13 mm. in diameter ; 330 turns would make a coil 7*5 cms. long and 2 cms. deep. The iron cores would be 8 cms. long, the yoke 4 cms. high, and the unwound iron return in the centre 5*5 cms. wide, all being, of course, the 5 cms. deep. APPENDIX EQUIVALENTS OP ENGLISH AND METRIC MEASURES. 1 inch = 2*54 centimetres. 1 square inch = 6 -4 5 square centimetres. 1 cubic inch = 16'39 cubic centimetres. DENSITIES OF METALS. Copper : 1 cubic inch weighs O32 pound. Iron : 1 cubic inch weighs O28 pound. RESISTANCE OP COPPER. 1 inch of copper conductor of 1 square inch area has a resistance of | x 10- 6 ohms at 60 Fahrenheit. 1 centimetre of 1 square centimetre area = 1-7 X 10- 6 ohms at 15 C. 15 per cent, increase in resistance allows for a temperature rise of about 70 F. or 40 C C. SPEEDS OF SYNCHRONOUS ALTERNATING CURRENT MACHINES. POLES. Frequency. 2 4 6 8 10 12 14 16 18 20 22 24 25 30 40 50 60 100 1500 1800 2400 3000 3600 6000 750 900 1200 1500 1800 3000 500 600 800 1000 1200 2000 375 450 600 750 900 1500 300 360 480 600 720 1200 250 300 400 500 600 1000 214 257 343 429 514 857 188 225 300 375 450 750 167 200 267 333 400 667 150 180 240 300 360 600 136 164 218 273 327 545 125 150 200 250 300 500 114 APPENDIX POLES. Frequency. 26 28 30 40 50 60 70 80 90 100 120 150 25 115 107 100 75 60 50 43 38 33 30 25 20 30 138 129 120 90 72 60 51 45 40 36 30 24 40 185 171 160 120 96 80 69 60 53 48 40 32 60 231 214 200 150 120 100 86 75 67 60 50 40 60 277 257 240 180 144 120 103 90 80 72 60 48 100 462 429 400 300 240 200 171 150 133 120 100 80 H.-B. CURVE USED IN EXAMPLES OF DESIGN. FIG. 27. INDEX AiR-cooled transformers, 77 Air space induction, 21 Alternators, compound, 46 ,, furnace, 99 250 K.W., 24 ,, simple, 1 Aluminium as a conductor, 94 Ampere, definition of, 5 Ampere-turn per inch diameter, 21, 60 Antimony as a conductor, 94 Arc-lamp, choking coil for, 97 Armature-reaction, 10 Automatic voltage regulation, 48 Auto-starter, 111 B.-H. CURVES, 115 Bismuth as a conductor, 94 Brass as a conductor, 94 Bronze as a conductor, 94 CADMIUM as a conductor, 94 Capacity, 5 Cast iron as a conductor, 94 Cheapest voltage for transmission, 89 Choking coils, 96 Compound winding rotaries, 76 Compound wound alternators, 46 Condensers, 5-6 Converters, rotary, 75 Copper as a conductor, 94, 114 Cost of alternator, 89, 105 ,, induction motor, 70, 111 ,, metals, 94 ,, transformer, 84 Coulombs, 5 Cramp, William, v. Current, average, 4, 6 ,, magnetizing, 58, 84 ,, no-load, 59 Cyclic irregularity, 42 D 2 Z FORMULA, 22 Demagnetizing A.T.'s, 17 Densities of metals, 94, 114 Depth of transformer coils, 78 Dimensions, relative to output, 20 EARLE, H. A., vi. Efficiency of alternators, 39, 105 ,, induction motors, 69, 110 Efficiency of transformers, 84 E.M.F., production of, 2-4 Entz booster, 49 Equivalents of English and metric measure, 114 FIELD, M.B., 26 Frequency, 1 Furnace alternator, 99 GOLD as a conductor, 94 Grime, R.E., vi. H.-B. CURVES, 115 Heyland diagram, 57 IMPEDANCE, 5 Induction in air space, 21 Induction motor theory, 51 50 H.R, 61 5 H.R, 106 Inherent regulation, 18 Iron as a conductor, 94 losses, 36 LAG, angle of, 8 Lead as a conductor, 94 Leakage flux, stator, 12, 16 rotor, 13, 16 ,, ,, in induction motors, 53 Lines, transmission, 87 117 n8 INDEX Load curves of alternators, 35, 104 Loss, iron, 36 MAGNESIUM as a conductor, 94 Magnetizing current of induction motor, 59 Magnetizing current of trans- former, 71-72 Mercury as a conductor, 94 Motor, induction, theory, 51 50 H.P., 61 5 H.P., 106 synchronous, 43 NICKEL as a conductor,, 94 No-load current, 59 OIL cooling for transformers, 77 PARALLEL running alternators, 40 Platinum as a conductor, 94 Pole-pitch, least, 23 Pole-tip thickness, 29 Power factor, 8, 9 ,, ,, zero, 36 Price of metals, 94 QUANTITY of electricity, 6 KEACTANCE voltage of transformers, 73 Eeaction, armature, 10 Rectifying commutators, 47 Regulation, inherent, of alter- nators, 18 Regulation of transformers, 72, 76 Resistance of copper, 94, 114 ,, ,, metals, 94 Resonance, 8 Rotary converters, 75 SELF-INDUCTION, 4 Short circuit current of alternators, 37, 103 ff formula, 55 Silver as a conductor, 94 Sine curve, 4 Slip of induction motors, 68 Slots per pole per phase, 25, 55, 61. 107 Sodium as a conductor, 94 Specific resistances, 94 Speeds of alternators, 114 Squirrel-cage motors, 106 Stalloy for transformers, 79 Starter, auto, 111 Steel as a conductor, 94 Strength, tensile, 94 Symbols used, xi. Synchronous alternator speeds, 114 ,, motors, 43 TANTALUM as a conductor, 94 Tensile strength of metals, 94 Tin as a conductor, 94 Total loss curves, 36 Transformers, theory, 71 350K.W., 81 Transmission lines, 87 Tungsten as a conductor, 94 Tyrrell regulator, 49 VECTORS, 10 Voltage, cheapest to transmit at, 89 Voltage drop in alternator, 18 ,, regulation of transformers, 76 WALKER, MILES, 50 Waste field, rotor, 16 ,, ,, induction motors, 55 Weights of material of alternator, 39, 105 Weights of material of induction motor, 70, 111 Weights of material of transformer, 84 Wrought iron as a conductor, 94 ZIGZAG leakage flux, 54 Zinc as a conductor, 94 PRINTED BY WILLIAM CLOWES AND SONS, LIMITED LONDON AND BECCLES HARPER & BROTHERS, Standard Works on Electricity, Engineering, &c. ELECTRIC PROPULSION OF SHIPS. By H. M. HOBART, M.I.C.E. Demy 8vo. 44 Illustrations. 53. net ; post free, 55. 4d. Explains fully the various systems of propulsion, deals with such matters as "Size and Power," "Fractional Resistance," "Momentum," "Gearing," " Efficiency of Propellers," &c., and shows that with electrical machinery in the equipment a turbine-engined ship can excel the piston-engined ship both in economy and in manoeuvring capacity. MOTOR BODIES AND CHASSIS. By H. J. BUTLER. With a Foreword by the Rt. Hon. the LORD MONTAGU OF BEAULIEU, Editor of The Car Illustrated. Demy 8vo. 39 Illustrations. 6s. net ; post free, 6s. $d. A comprehensive work, dealing with the construction of the entire motor-car bodywork as well as mechanism. "The Petrol Engine," "Ignition," "Transmission," "Brakes," "Gears," "Upholstery," "Decoration," "Painting, " Accessories," &c. Body Design various type fee.," "Wheels," "Tyres," and ELECTRIC TRAINS. By H. M. HOBART, M.I.C.E. Demy 8vo. With many Illustrations and Diagrams. 6s. net ; post free, 6s. 4d. 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