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Salomons' Electric Light Installations. Vol. I.— ACCUMULATORS. 5s. Vol. II.— APPARATUS. Ts.M- YOL. III.— APPLICATIONS. 5s. Russell's Electric Light Cables. 7s. 6d. Mayeoek's Alternating Current Circuit. 2s. 6d. Maycoek'g Electric Lighting and Power Distribu- tion. 2 Vols. Vol. I. 6j. London: WHITTA.KER & CO., Paternoster Square, E.G. ALTERNATE CURRENTS IN PRACTICE TRANSLATED FROM THE FRENCH OF LOPPE AND BOUQUET BY FRANCIS J. MOFFETT, B.A.(Lond.) ELECTRICAL ENGINEER TO THE COLONY OF LAGOS, WEST AFRICA ASSOCIATE MEMBER OF THE INSTITUTION OF ELECTRICAL ENGINEERS LATE SCHOLAR OF THE UNIVERSITY ^COLLEGE OF N. WALES WITH 288 ILLUSTRATIONS WHITTAKER & CO. 2 WHITE HART STREET, PATERNOSTER SQUARE, LONDON AND 66 FIFTH AVENUE, NEW YORK. 1898 PRINTED BY SrOTTISWOODE AND CO., NEW-STREET SQUARE LONDON PREFACE This translation of the work of MM. Lopp^ and Bouquet has been made under the impression that it will fill a gap in Electrical Engineering Literature. To the best of my knowledge there is no work in existence in England at the present time which treats in a practical manner the whole range of Alternating Currents of Electricity. MM. Loppd and Bouquet systematically traverse the entire field, as will be seen on reference to the table of contents, and derive their information impartially from English, French, German, and American sources. Enghsh readers will thus be enabled to inform themselves of the current practice in other countries beside their own. I have to request the indulgence of my readers to any errors in the text, as the proofs have been corrected during residence in tropical Africa, where there is a great tendency for one's E.M.F. to drop. FRANCIS J. MOFFETT. Lagos, West Africa : December, 1897. CONTENTS CHAPTER I Alternators SECT. PAGE 1 Relative Dimensions of Coils and Pole Pieces . i 2 Influence of Self-induction ... ... 9 3 Armature Reaction ... ... 14 4 Determination of the Efficiency .... . . 18 5 Single-phase Alternators with Revolving Field-magnet and Sta- tionary Armature 20 6 Single-phase Alternators with Stationary Field-magnet and Re- volving Armature . 34 7 Alternators with both Field-magnet and Armature Stationary . 45 8 Polyphase Alternators .... . . 53 9 Parallel Running ... 74 10 Alternator Design ... .... 79 CHAPTER II Motors 1 Revolving Fields in Practice .... . . 93 2 History and Classification of Motors . ... loi 3 Single-phase Synchronous Motors 102 4 Polyphase Synchronous Motors . . . .111 5 Theory of Asynchronous Motors 113 6 Asynchronous Motors with Revolving Field 125 7 Asynchronous Motors with Simple Alternating Field . . . 152 8 Design of Alternate Current Motors 164 9 Influence of the shape of the E.M.F. Curve qf the Generator on the Efiiciency of a Motor 175 a CONTENTS CHAPTER III Transformers and Condensers SECT. PAGE 1 General Properties of Transformers 178 2 Classification of Transformers . . 194 3 Different Methods of Using Transformers 198 4 Description of Transformers in Common Use . . . . 200 5 Transformers for Polyphase Currents 226 6 Transformer Testing 234 7 Transformer Design 235 8 Condensers 241 CHAPTER IV Transformation of Current 1 Comparison of the Different Systems from the Point of View of the Conductors 248 2 Transforming of Currents 250 Transformation of Continuous Current into Single-phase Alternate Current, and Vice-versa 250 4 Transformation of Continuous into Polyphase Currents and Vice- versa 259 5 Transformation of Single-phase Currents into Polyphase . . 262 6 Transformation of Triphase" into Biphase Currents and Vice-versa . 265 CHAPTER V Distribution Mains . I Effective Resistance of Conductors of Circular Section 268 2 Influence of Heat and Cold 269 3 Influence of Capacity and Self-induction . . 274 4 Loss of Energy in Armed Cables .281 5 Insulation of Conductors ... 284 6 Cables 290 7 Underground Mains *2q6 8 House Wiring . ,q . 9 Measures of Precaution „^^ 10 Treatment of Persons Suffering from Shock . ,14 CONTENTS CHAPTER VI Current Distribution SECT. PAGE 1 Selection of the Frequency .... ... 316 2 Classification of the Systems of Distribution 3iii 3 Direct Distribution 318 4 Distribution with Transformers . . . .321 5 Distribution with Condensers . . 336 6 Distribution by Polyphase Currents . . . 337 7 Mixed Distribution 342 8 Secondary Circuits . 343 9 Special Apparatus employed for Alternate Currents . . . 348 CHAPTER VH Industrial Measurement of Alternate Currents 1 Measurement of Effective Potential Difference .... 355 2 Measurement of the Current . . ■ • 357 3 Measurement of the Power . . ... . 359 4 Measurement of Instantaneous Current Values and Tracing of Current Curves . . . . . . . . . 361 5 Measurement of Phase Difference ... . . 363 6 Measurement of Self-induction . 364 7 Determination of the Quality of Iron ... ... 367 8 Measurement of Efficiency. . . -371 Index . ... . . .373 ALTERNATE CURRENTS CHAPTER I ALTERNATORS § I. Belative Dimensions of Coils and Pole-pieces In works on the theory of alternating currents it is shown that the electro-motive-force of an alternator fluctuates very nearly according to the law of sines, and the formulae for finding the average and maximum induced ele'ctro-motive-forces are there deduced. We shall examine in greater detail the form of the curve in the case of a disc alternator, on the supposition that the magnetic flux passes directly from one pole-piece to the other without any leakage, and that the curve may exhibit sudden varia- tions, which in practice are flattened out by the self-induction. The name ' pitch ' has been assigned to the distance between, the axes of two consecutive pole-pieces. The form of the curve depends on the relative breadths of the pole-pieces and coils compared with the length of the pitch. Mr. Kapp has investigated the question in the following manner : Suppose that the breadth of the pole-pieces is equal to half the pitch (figs. I, 2, and 3), that is to say, the intervals which separate these pole-pieces are equal to their breadth. If the coils are formed of very fine wire, which encloses a space the section of which has exactly the same breadth as the pole-pieces, it is easy to see that the electro-motive-force curve has the shape shown in fig. i. B 2 ALTERNATE CURRENTS If the copper of the coils has the same breadth as the pole- pieces and does not enclose any space inside, curve c (fig. 2) will be the result. If the space inside has a certain breadth, in addition to the breadth of the copper, so that the coil is of larger cross-section than the pole-piece, curve c (fig. 3) will be obtained. ^ YMuamsM ® ■A'mMmfmj. '^ v,/^ V/MU//»//^ yi/>w/»m i/iiiiiiMim rm. js m?/»inmA'/. jj miiw/i///'//' g ™'- ttme Fig. It is possible in the same manner to trace out the curves for a ring alternator. If 2 M be the number of magnetic fields in the case of an alternator with reversed fields (figs, i, 2, and 3) ; b the number _ W/W/WWA W/J-^M»m WWWM/A vf/i s vwwju^MTy- Mr 'Wiiiiuu/fiyi S !fe» time Fig. 2 of lines of force emanating from one pole ; m^ the number of armature coils; n-^ the number of turns of one coil; n the number of revolutions per minute of the alternator ; and f the frequency, F = i, T ALTERNATORS T being the time taken by one complete alternation. Substituting we get MN F = 60 The variation in the flux of induction through a coil whilst passing from o to o' will be B — (— b) = 2 B. The time taken being -, the average E.M.F. will be for one turn ; 2 2B 2 V///>/>/l/y/iA W/W/M/lii V/'''1L""\— . Fig. 3 For the «, turns of one coil, and for the mi coils we shall have N e^ ^4 BM»«i«i 60 N =4BM« -^, 60 n being the total number of turns in series. Expressing the average E.M.F. in volts we shall have tf^ = 2 B (2 m) « ^- io~'. 60 In the case of an alternator, the magnetic fields of which are not B2 4 ALTERNATE CURRENTS reversed, as in the Mordey type of machine (fig. 4). if/ denotes the number of pairs of pole-pieces, or the number of magnetic fields, we shall have pn t 60 T The variation in the magnetic induction through the coil between o and o' will be b, and the average E.M.F. will be expressed as B - 2 B N " - T ^60 ^a^(M/A KtmrnfA K,j,„,„/A Fig. 4 The total average E.M.F. expressed in volts will be N «a = 2 B * « — IO~°. 60 The values of the eflFective and maximum E.M.F. in relation to the average E.M.F. depend on the shape of the curve. In all cases it is possible to denote the effective E.M.F. by the following expression : «, = K B (2 m) « iL io-», or in general 60 = KA, K being twice the ratio of the effective to the average E.M.F. ALTERNATORS 5 In the case in which the curve is sinusoidal, we get «, = *-?-= riie„ 9 .-. K ^ 2"22. If the curve has the shape indicated by figs, i and 4, we get «. = «» = e„ K = 2. If the curve has the shape indicated by fig. 2, we get «m = 2"0 «« K = 2-32. Mr. Kapp has arranged in a table the different values of k when the dimensions of the pole-pieces and coils vary in relation to the pitch. No. Breadth in relation to the pitch Value of K Of the pole-pieces Of the coils I 2 3 4 S 6 7 8 I-oo I-oo I-OO •62 -50 •SO ■33 ^. Sinus I-OO I-oo •so •so I-oo ■so •33 oidal i-ooo •S8o •817 2-060 i^63S 2-310 2-830 2 -220 In the case of a Mordey machine the pitch is half the distance between two adjacent pole-pieces. In practice the self-induction considerably flattens the abrupt variations of the curves, and it may be assumed without much inaccuracy that the curve is a sinusoidal one, so long as the ratios between the breadth of the pole-pieces and coils approximate to those given in the sixth line of Kapp's table. Different methods are used to trace the E.M.F. curve of an alternator, and we shall investigate them in a subsequent chapter. 6 ALTERNATE CURRENTS When there are twice as many coils as pole-pieces, the latter are equal in breadth to half the pitch. Elihu Thomson has found that when there are just as many coils as pole-pieces, it is an advan- tage to make the core of the coils a Uttle less than the breadth of the pole-pieces, so that the total breadth exceeds half the pitch. The armature, instead of being provided with coils, may be furnished with a bar — i.e. with a drum wind- ing ; this arrangement is used espe- cially for low-potential polyphase alternators. When this is the case the pole-pieces, whether inside or outside the armature, must neces- sarily produce reversed magnetic fields. Fig. 5 gives the plan of con- nections of a 4-pole machine, and fig. 6 shows the variation of the E.M.F. If B is the total number of lines of force emanating from one pole, F the frequency, n the number of revolutions per minute, and/ the number of pairs of pole-pieces, we get c D Fig. s F T _ /N 6o «« B 2 2B/ N Si It is easy to see that the effective E.M.F. is equal to the average E.M.F., on examining the curve of fig. 6, and we have therefore N e, = 2 B/ 6o" As there are 2/ bars, the total E.M.F. expressed in volts will be 4B/2 ji 10-8. 60 The maximum E.M.F. will be-^' e^. ALTERNATORS 7 It is possible to place several bars side by side or on the top of one another, and it is easy to see that the whole armature space be > -2 ao). The self-induction in any given armature varies with the excitation, for the magnetic resistance varies in proportion tp the amount of magnetic induction through the iron. Professor Ayrton found that the self-induction of a Mordey alternator was from '036 to -038 of a quadrant when the machine was not excited, and that it decreased by 14% when the field was excited. The coefficient of self-induction varies according to the relative positions of the armature and poles. At the Gratz Technical College, experiments were made with a little alternator, a section of which is shown in fig. 15. The particulars of the machine were as follows : Normal power Number of poles . Frequency Induction through air-gap Resistance of armature . 400 watts 4 100 5,000 C.G.S. units I '6 ohm. 12 ALTERNATE CURRENTS Measuring the coefficient of self-induction in six positions by Maxwell's method, the following results were obtained : Position of armature Coefficient of self-induction Position of armature CoefEcient of self-induction I 2 3 527 X 10* cms. SI '2 X 10* „ 47-1 X 10* „ 4 s 6 47-1 X 10* cms. 50-9 X IO» „ 527 X ID' „ The mean value is 48-8 x 10* cms. = -00488 quadrant. The values in different positions are given by the following expression : io« (48-8 + 3-9 cos 4 o) cm. a representing the angular distance through which the armature is moved from the first position. The variations are thus 8% above and below the mean value. These variations must cause a defor mation of the curves of E.M.F. and current, and consequently the lag of the current behind the E.M.F. varies at each instant. Influence of the Frequency.— We will compare two alternators A and B of the same type, the same power and number of revolutions, and we will suppose that the current furnished by a has double the frequency of that of b. If the alternator a has a frequency f, jj be the number of revolutions, and 2 m, the number of fields,, we shall have : j,_£_M, N M, = T 60 60 F N For the alternator b, the frequency will be -, and the number of 2 poles 2 Mj will be given by the equation : F _ Ma'N 2 60 A therefore will have twice as many magnetic fields as b, and also twice as many armature coils. ALTERNATORS 13 The effective E.M.F. being the same, we have (s, Sj = areas, *i *j = induction) For A : — e, = K Sj *, (2 m,) m^ «, ii lo"' volts. 60 For B : — e, = K $2 *2 (2 Mj) m^ n^ ^ 10"' volts. 60 whence Si *, (2 M,) Wi «i = Sa 2 (2 Mj) Wj «2- We know that M, ^ 2 M2, and w, ^ 2 W2, ««, and »?2 being the number of armature coils ; whence 4S1 *i«i = S2*2«a- If we take *, = #2> we shall have 4 S, «| = S2 «2' If, in order to satisfy this equation, we make Wj = 4 «ij that is to say, if we place on an armature coil of b four times as many turns as on a coil of a, the self-induction will be four times as great ; the same will be the case if we make S2 = 4 s,. The self-induction of a coil of b will be four times the self- induction of a coil of A : and as a has twice as many coils as b, the total coefficient of self-induction of b will be twice that of a. If we make the section of the pole-pieces of b four times that of a, keeping the same number of turns per coil, the pitch must be doubled : the external diameter of the alternators will be the same. The wire wound on an armature coil of b will be twice the length of wire wound on a coil of a, and as the connecting wires will be twice as long for b, we shall have exactly the same length of wire on the two armatures, so that the resistance will be the same. The same will be the case with the field-magnet and the cost of excitation will be the same for b as for a. If we adopt the same section for the pole-pieces, we must double the number of turns of each armature coil of b ; the pitch will be the same for both, and the external diameter of b will be half that of a. The resistance of the armature will be almost the same for b as for A (the length of the connecting wires of a will be double 14 ALTERNATE CURRENTS those of B, but, on the other hand, the wire on the coils of b will be a little longer owing to the increased diameter of the outer turns), whilst the length and resistance of the wire on the field- magnet coils of A will be twice those of b : the cost of exciting b will therefore only be half that for a. If the alternators both supply current to a circuit without self- induction, the lags will be the same for both. The angle of lag for the alternator a will be : for the alternator b, ^ R V 60 2 / Since 2 Lj = Lj, we have ^| ■= *i) since the loss due to hysteresis will be less. § 3. Armature Eeaction The following investigation clearly demonstrates that the armature reaction depends on the self-induction of tlie armature and external circuit. ALTERNATORS 15 Suppose the armature of a disc alternator to be displaced in the direction of the arrow f (fig. 16), the arrows i, 2, 3, &c., indicating the direction of the magnetic induction. From a to b the magnetising force decreases, and consequently a current will flow through the armature coil in such sense as to create a field of the same sign as the magnetising force, that is in the direction of the arrow i. It is easy to see that from b to c the current through the coil will still create a field in the direction of arrow r, since, although the magnetising force is now increasing, it has changed to the direction indicated by arrow 2 : from c to e the current will Fig. 16 flow in such sense as to produce a field in the opposite direction as shown by arrows 2 and 3. If the armature circuit possesses no self-induction, the current for each position of the coil will be represented by the sine curve a, b, c, d, e, which will be cophasal with the curve of E.M.F. ■When the coil is moved from a to b and from c to d, the magnetising force and the induction through the armature coil are in the same direction : whilst when it is moved from b to c and from D to E the magnetising force and the induction through the armature coil are in opposite directions. As the lengths a b, b c, i6 ALTERNATE CURRENTS c D, and D E are equal, it will be seen that there is, on the whole, no armature reaction. If the armature circuit possesses self-induction the current will lag behind the induced E.M.F. and will be represented by the curve g, h, i, k, m. It is easy to see that from a to g, from b to i, and from d to m, the induction through the armature coil is opposed to the magnetising force, whilst from g to b and from i to D the induction and magnetising force are in the same direction. If the lag is 90° the magnetising force and the induction through the armature coils will be continually opposed to one another, and the demagnetising effect will be a maximum. By inserting in the circuit a condenser it is possible to decrease the lag of the current behind the E.M.F. and so reduce the excitation necessary. In alternators with armatures containing iron, the flux of induction from the pole-pieces undergoes varia- tions which arise from the differences in the permeability of the magnetic circuits ; whenever a coil with iron core is between two poles the magnetic resistance of course decreases. The exciting current varies therefore considerably in its instantaneous value. Calculation of Armature Reaction. — This is a very complex question, but it is clear that the reaction is proportional to the value of the armature current. As we have just seen, an increased lag increases the demagnetising effect, but it is not possible at first sight to determine whether the reaction is simply proportional to the angle of lag. The shape of the coils and of the pole-pieces, as well as the amplitude of the current curve, will naturally have their effect on the reaction. The value of the reaction is not constant but is a periodic function of the time ; as the exciting circuit, however, possesses, necessarily, a large coefficient of self-induction, we shall not be far wrong in assuming it to have a constant value. The de- magnetising effect, or back ampfere-turns, may therefore be deter- mined by integrating the instantaneous values for a whole period. If X represent the back ampfere-turns at a given moment, the total ampfere-turns to be added to the field circuit will be J -x-dt. ALTERNATORS 17 It should be pointed out that x is the product of the instantaneous value of the current into the number of turns which occupy such a position on the armature that the current through them exer- cises a demagnetising effect on the field magnet cores. The solution of this integral is often complicated, if not impossible, but in the simple case when the breadth of the pole-pieces and coils is equal to |-pitch (which is the case with most alternators in practice), it is possible to obtain an approximate solution. If (/I is the angle of lag and n the total number of turns of an armature coil, we get as the total number of ampere-turns to be added to one coil : Xj = — I ^ — a 1 sm u. Integrating this for a whole period : Xj = ni^~z ^ IT I being the effective current. Expressing

fl Fig. 33 may be employed. The power necessary to excite the alternator is very small, for the magnetic resistance is reduced to that of the air-gap, which is very short. ■ In order to obviate all lateral movement of the field-magnet, the spindle revolves in collar bearings. 32 ALTERNATE CURRENTS As there is no iron in the armature, the self-induction is very small, and the machine is almost self-regulating when the load has no self-induction. Fig. 34 gives the characteristic curve of a 9 -pole alternator, the exciting current and speed being kept constant. Tests were made on a 250 k.w. alternator supplied to the Newcastle-on-Tyne Electric Supply Co., and it was found that, when the machine was excited with a constant current of 28 ampferes, the fall of potential between full load and open circuit was 4i%. When the machine took the full-load exciting current ■ ■'■ T Volts20oo::::::::::::::::::: :::::::::; iil 1 .■.<■ Speed and excitation ,nnn _ Uons ant . — . — _ 10 Fig. 34 aoinnieies of 36-5 amperes, the rise of potential on open-circuit was 12%. The electrical efiSciency at full load, including excitation, was 97%, and the guaranteed commercial efficiency 93%. Patin Alternator.— M. Patin, who was for a long time a fellow- worker with Mr. Ferranti, has built an alternator (fig. 35) the field-magnet of which may be used as a flywheel. The field-magnet coils are placed, half on the inside of the outer ring frame, and half on the outside of an inner ring,' so that the two sets face one another. The pole-pieces, rectangular in section, leave a narrow space between them, in which the armature is placed. Consecutive ALTERNATORS 33 Fig. 33 34 ALTERNATE CURRENTS poles on either ring are of opposite sign, and poles which face one another on the two rings are also of opposite sign. It is easy to see that the flux of induction from any one pole-piece is divided into two parts in the rings, and traverses the magnet coils on either side of the coil in question. The flat armature coils are formed of copper ribbon, wound on a hollow gunmetal core, the turns being carefully insulated from one another. These coils are fixed by means of bolts on two gunmetal rings, from which they are insulated. They are all wound in the same direction, and connected as shown in fig. iZ- The armature is supported by 4 arms, which radiate from a sleeve fitting on the spindle : a screw turned by a hand wheel provides for the withdrawal of the armature, so as to examine and, if necessary, repair it. § 6. Single-phase Alternators with Stationary Field- magnet and Revolving Armature In these alternators the current is collected by means of brushes, rubbing on two rings, which are connected to the terminals of the armature coils. Ferranti Alternator.— The field-magnet is formed of two sets of coils with their axes horizontal, facing one another, consecutive pairs of poles being wound in opposite directions. The iron cores of these coils are supported by cast-iron cheeks ; the two halves are separate and may be drawn apart on slide-rails, so as to admit of examining the armature. When the two halves are in position, the magnetic attraction renders unnecessary any other means of holding them together. The armature, which contains no iron, is a flat ring : it revolves between the two sets of pole-pieces, which are very close together (generally about f inch apart in large machines). In small machines, the armature consists of cojls formed of a single copper ribbon, as shown in fig. 36. The coils of large machines have the shape indicated by fig. 37. The cores are formed by strips of brass, insulated from one another.: they are separated at one end, and joined at the other end to a piece of brass with a hole drilled through it, The coil is formed of copper ALTERNATORS 35 ribbon, the diflferent turns being insulated from one another by means of strips of vulcanised iibre. The inner end of the winding is soldered to the brass core. Two coils are fixed on one gunmetal piece provided with Fig. 36 Fig. 37 bolt-holes (fig. 38) : they are insulated from one another by a strip of vulcanised fibre, and from the gunmetal piece by leaves of mica. The inner ends of the windings of the two coils make connection # through the holding bolts and the gunmetal piece. The outer ends of the windings of two adjacent coils, which are fixed on different gunmetal pieces, are soldered to one another. The connections are therefore as shown in fig. 33, i.e. the windings of 36 ALTERNATE CURRENTS two consecutive coils are reversed ; this must necessarily be the case, since there are as many armature coils as magnetic fields. As the gunmetal pieces or carriers are electrically connected to the armature winding, they must be very carefully insulated. On the lower side of the carrier a stud is inserted, the end of which is either drilled for a lynch-pin or screwed to take a nut. A porcelain collar is slipped on the stud, which is then in- serted in a hole, of larger diameter than itself, drilled in the rim of the centre boss, and held in position by the lynch- pin or nut. It is arranged so that the stud does not make electrical contact with the boss, and a mixture of sulphur and powdered glass is poured round the stud, to hold all firm. Generally the whole number of coils is divided into two equal parts, which are connected in parallel, as shown in fig. 39 : the Fig. 39 Fig. 40 collecting rings and brushes are placed at one end of the spindle, and are enclosed in a glass case. Fig. 40 gives the longitudinal section of a Ferranti alternator ALTERNATORS 37 Fig. 41 of 1,250 h.p. at 10,000 volts. It makes 120 revolutions per minute, and each cheek carries 48 pole- pieces. It is driven by means of a rope pulley. The bearings have a large surface and are automatically supplied with oU, by means of a pump worked by an eccentric on the spindle. Eapp Alter- nator. — This al- ternator, which is built at the Oerlikon works, is constructed as described below. Two sets of magnets are fixed to vertical cast- iron cheeks, which are held together by bolts. The poles of one set of magnets are alternatively N. and S., while a N. pole of one set faces a N. pole of the other set, so that the flux of induction takes place from one pole to the next of the same set : as a result there are two sets of magnetic fields. The armature core is formed of a ribbon of charcoal iron, wound on a gunmetal disc, with paper insulation : the ring formed of this iron ribbon is fixed to the central gunmetal boss by means of radial bolts, as shown in fig. 41. The core of the coils formed in L this way is carefiiUy insulated with mica and paper, and the winding- is put on so that the turns are in planes passing through the spindle of the machine, as shown in fig. 42. The Fig. 42 38 ALTERNATE CURRENTS angular breadth of a coil is the same as the pitch of the alter- nator. Labour Alternator. — The Labour alternators, which the Soci^t^ I'Eclairage Electrique formerly constructed, were high potential machines of a type similar to the Siemens. The Soci^te Fig. 43 having come to the conclusion that it was more advantageous to use low potential alternators and raise the potential on the line by means of a transformer, M. Labour, electrical engineer to the Company, designed the type of machine which we shall now describe. He did his utmost to obtain in this alternator a curve of E.M.F. as nearly as possible sinusoidal. ALTERNATORS 39 The field-magnet coils, the cores of which are formed of thin iron plates, insulated from one another, are arranged on the inside of a cast-iron ring (fig. 43). These coils are wound so as to make consecutive poles of opposite sign. The pole-pieces have very large polar expansions, the space between two pole-faces being at_ the most equal to twice the air-gap. Fig. 44, which is borrowed from an article in the ' Lumibre Electrique,' by M. Guilbert, shows the method of arrangement. The edges or horns of the polar expansions are saturated magnetically, so that the induction through the air-gap is a maximum near the axis of a field-magnet Field magnets Fig. 44 coil and diminishes towards the horns of the pole-pieces. The space in which there is no induction is very small, so that there is no abrupt variation of the induced E.M.F. The armature core is formed of a ring of laminated iron, with teeth on the periphery, exactly similar to a Rechniewski dynamo. As in these latter machines, there is a variation in the magnetic resistance, and in consequence a fluctuation in the induction through the field-magnet cores : but as the teeth are of small size and the pole-pieces laminated, the eddy current losses are negligible. 4<5 ALTERNATE CURRENTS The armature coils are wound as shown in fig. 49 = each slot contains one or more turns, and it will be observed that the outer turns of each coil surround a greater area of core than the mner turns. In an alternator built for the Lighthouse Commissioners, which was an 8-coil machine, the armature had 72 teeth, so that there were 9 teeth to a coil. The winding was arranged as follows : Suppose the 9 teeth to be numbered i, 2, 3, 9, There were 8 turns round tooth No. 5 „ „ 8 „ „ teeth Nos. 4 and 6 „ 8 „ „ „ Nos. sand; „ 8 „ „ „ Nos. 2 and 8 „ 4 „ „ „ Nos. I and 9. M. Blondel traced the current and E.M.F. curves of this alter- nator (fig. 45). It will be noticed that the curves are very regular : I is the curve of current, and E that of E.M.F. The pre- cautions taken to insure the regularity of the E.M.F. curve resulted in the com- plete absence of the usual humming sound. M. Labour tried several arrangements for exciting the alternator : he first con- nected a rectifier to the main winding, but finding it in- convenient to have only one circuit both for direct and al- ternating currents, he placed a second winding (Gramme) on the armature ring. As a rule the exciting current is furnished by a small direct current dynamo on the alternator spindle. This dynamo is provided with a rheostat in its field-circuit, by means of which the current sent through the field-circuit of the alternator may be regulated. There is another rheostat directly in the field-circuit of the alternator, the object of which is to reduce the r \ / \ / r A / / \ ■s '" /, / \ ■^ // \ « \\ / / 1 \^ \ // \ \ / \ \ H \ /e 120 V Fig. 45 ALTERNATORS 41 exciting current at light load. When the alternator is fully loaded this latter rheostat is short-circuited, and regulation is effected by means of the rheostat in the iield-circuit of the exciter. An alternator, giving 300 amperes at no volts, and making 500 revolutions per minute, requires an exciting current of 14 amperes at full load. The speed and excitation being kept constant, the variation between the E.M.F. on open circuit and at full load is 10 per cent. : the exciting current on open circuit is eight or nine ampbres. Fig. 46 gives the characteristic curve of an 8-kilowatt Labour alternator of 84 per cent, commercial eflSciency. The ordinates represent volts and the abscissae ampere-turns. ^tea Iwo 5555 ^ooa~ Ampere-turns Fig. 46 Fig. 47 Siemens Alternator. — The field-magnet is formed, hke that of the Ferranti machine, of two sets of horizontal pole-pieces fixed to vertical cast-iron cheeks. Opposing poles of the two sets are of opposite sign, as also are adjacent poles of the same set. The coils are wound first on brass formers and then slipped over the cores. The armature coils (fig. 47) are fixed on a disc, which is keyed on the spindle : they are formed of copper ribbon wound on a wooden core, the insulation between the different turns being Special paper or fibre. The coils are fastened to the disc by means of plates of German silver, which, in consequence of its 42 ALTERNATE CURRENTS high specific resistance, does not cause any appreciable loss in Foucault currents. These plates are bolted to the disc and also to the cores : they are insulated from the coils. Connection between consecutive coils is made by means of bolts, insulated from the German silver plates and joined by a piece of wire : the coils are connected in accordance with fig. 38. A chain, composed of a number of links of brass, is fitted over the outside of the coils, from which the links are insulated : the object of this chain is to assist the coils in resisting the action of centrifugal force. Thomson-Houston Alternator. — The pole-pieces, of cast-steel, are arranged on the inside of a vertical ring, which, for con- z Rheostat ^ 1 line Exciter i Rheostat 3 Fig. 48 venience of repairs, is divided into two halves along a median horizontal plane. The armature is formed of a cylinder of laminated iron on which the coils are fixed. The cores of the coils are of insulating material, and the winding is composed of copper wire of rectan- gular section. The armature coils, of which there are as many as there are pole-pieces, are bent on a former so as to fit the cylindrical surface of the core : they are insulated from the core by sheets of mica. Bands of German silver hold the coils in position on the armature. The Thomson-Houston Co. builds three types of machines. ALTERNA TORS 43 1. Self-exciting alternators. 2. Separately excited alternators. 3. Compound alternators. The compound alternator is designed to keep a constant p.d. on the external circuit. With this end in view either a certain number of the magnet coils are traversed by direct current from the exciter, and the rest by rectified alternating current, as shown in fig. 48 : or each of the magnet coils has two windings, one of which is traversed by the current from the exciter, and the other by the rectified alternating current as indicated by fig. 49. The rectifying commutator c, which has as many segments as there are coils, is connected as a shunt to the main circuit of the alternator. Fig. 49 The rectified current increases with the main alternating current : therefore the exciting current and the terminal E.M.F. also increases, so that the p.d. at any point on the line may be kept constant. Rheostats i and 2 allow of the regulation of the current from the exciter, and rheostat 3 of the regulation of the rectified current. By suitably adjusting these rheostats the alter- nator may be made self- regulating. Westinghouse Alternator. — The pole-pieces are arranged on the inside of a cast-steel ring ; the magnet coils are held in position on the pole-pieces by means of bolts, and are wound so that consecutive poles are of opposite sign (fig. 50). 44 ALTERNATE CURRENTS The armature core consists of thin iron discs (fig. 51), in which holes are stamped out for ventilation ; they are threaded on the spindle and clamped by bolts between two end-plates. The laminae are not insulated from one another by paper, as the rust is Fig. 50 Fig. sufficient to prevent the formation of eddy currents. The flat armature coils are wound on a wooden core (fig. 52) : the straight part is just the same length as the armature cylinder, and the curved end parts are bent over the end-plates. The coils are placed on the cylinder, from which they are insulated, and the ^ Fig. 52 Fig. S3 whole cylinder is covered with a winding of brass wire. The ends of the coils, which are turned over, are held by flat rings of gun- metal, and at one end there is a disc, fitted with blades, which ventilates the armature by driving air through the holes in the laminae. The connections between the coils are shown in fig. 53 : the ALTERNATORS 45 whole number of coils is divided into two halves, which are joined up in parallel to the collecting rings. The Westinghouse Co. builds alternators which are self- regulating for constant current. The armature core consists of iron plates of the shape shown in fig. 54. The faces of the armature teeth are wider than the pole-pieces. The proportion between the armature and field-magnet windings is such that at the moment when the armature current is a maximum, the Fig. 54 Fig. ss number of ampfere-turns of the armature is equal to the number of ampfere-tums of the field : it therefore follows that if at the moment the axes of the teeth of the armature coincide with the axes of the pole-pieces the armature current is a maximum, then the E.M.F. developed is very small. As the teeth of the armature are wider than the pole-pieces (fig. 55), the self-induction increases very much when the former are approaching the latter, and con- sequently the armature reaction is very large : this also tends to reduce the terminal E.M.F. § 7. Alternators with both Field-magnet and Armature Stationary In these alternators, which are called in England ' inductor alternators,' the variation in the flux of induction through the armature coils is eifected by varying the resistance of the magnetic circuits. A great number of engineers have built alternators with variable magnetic resistance, amongst others Mordey, Ehhu 46 ALTERNATE CURRENTS Thomson and Kennedy. We shall examine three types of these alternators, viz. : the Cail-Helmer, the Kingdon, and the Thury. Cail-Helmer Alternator.— As will be seen from fig. 56, which shows a 4-pole alternator, the pole-pieces are placed radially inside a ring. Both the field-magnet and armature windings are placed on the pole-pieces. The field-magnet winding is close to the ring and is connected so as to make consecutive poles of opposite sign. The armature winding is very near the pole-faces, so as to be as close as possible to the revolving inductor, which is shaped as shown in fig. 56. When the inductor is in the position shown in the figure, the magnetic resistance is a minimum, and the flux of Exciting circuity Line Fig. 56 induction a maximum : when the inductor has rotated through an angle of 45°, the magnetic flux is a minimum. Fig. 57 represents a little experimental alternator, the output of which is 12 kilowatts at 1,800 revolutions per minute. The power wasted by the inductor is very large, being 1 2 per cent, of the total power : the reason is that the difference in magnetic resistance is slight The maximum induction in the iron is 6,200 C.G.S. units. Fig. 58 gives the theoretical E.M.F. curve, assuming that there is no magnetic leakage or self-induction. When the middle of a tooth of the inductor passes from o to o', the induction through the coil A diminishes. When the middle of the tooth is at o', the induction is a minimum : it then begins to increase. The curve therefore has the shape shown at c. ALTERNATORS 47 Fig. 57 ft/t/ffff /i ^ Fic. 58 48 ALTERNATE CURRENTS If 2p be the number of poles, f the frequency, t the time of one complete alternation, and n the number of revolutions per minute, we get : T 60 If (I> be the difference between the induction through the coil a, when in the two positions o and o', the mean E.M.F. in C.G.S. units induced in one turn of the coil a will be T T 60 2 As K = 2, if there are n^ turns per ceil, the effective E.M.F. in volts for the 2/ coils in series will be : 8*/2«,ii 10-'- 60 Fig. 59 Eingdon Alternator.— The field-magnet and armature coils, which are wound on laminated cores, are arranged on the inside of a ring (fig. 59). The field-magnet and armature coils are not ALTERNATORS 49 both wound on the same core, but one core is wound with a field- magnet coil, and the next with an armature coil, so that the two sets of coils alternate with one another. Consecutive coils of both sets are wound in opposite directions. Inside the ring a gunmetal disc revolves, carrying on its periphery laminated iron teeth, equal in number to the field- magnet coils. Each of these teeth is of such width as to exactly cover two adjacent pole-pieces. When the disc revolves there is a change in the induction through the armature cores, and in consequence an alternating E.M.F. is produced. Suppose the ring developed as shown in fig. 60, b a being one of the teeth of the inductor, Aj Aj two armature coils (wound in }..- --p.. "1 •■ i ■■■■' C CL ^J is 9 A, ■ jsr -AL -i- 5; -ir^ qL. Fig. 60 opposite directions). The breadth /j of an armature coil being equal to the breadth of a pole-piece, and ^2 being the width of the interval between two consecutive coils, if /i is the pitch of the alternator, we get : /, = 2 (/i -I- 4)- When the inductor tooth is in the position shown in the figure the E.M.F. is zero. While a is moving to /the induction through the coil Ai diminishes, and the E.M.F. induced is constant in value, viz. — o' h. When a has reached/ and b has not yet reached c, the core of the coil Ai is subjected to two fluxes of induction in E 50 ALTERNATE CURRENTS opposite directions, one flux increasing and the other decreasing : the E.M.F. is consequently constant in value, and is twice as great as between e and/ When b has passed c, the core of coil A, is only subject to induction from the S. pole, which is increasing regularly : consequently the induced E.M.F. in the coil a, is the same as it was from e \.o f. When the centre of the tooth is at o,, the direction of the E.M.F. is reversed. Curve c represents the variation of the E.M.F. : of course the self-induction and magnetic leakage would exert a flattening effect on the angles of this curve. If 2 / be the number of field-magnet coils, n the number of revolutions per minute of the inductor, and f the frequency, we get: P_2i>N If * be the difference between the total number of lines issuing from one pole when the tooth is in the position shown in the figure and the number of lines when the tooth is removed, it is easy to see that o' h represents the E.M.F., viz. : * 2$ . . . N — = — = 2'I>r = 4^ — T T 6o 2 and ij represents a double E.M.F., viz. : 6o we have : o' o', = — , and ik=-ly — l^. The mean E.M.F. induced in one turn will be : ^•^^{■-^^}- If /) = 4, the second term disappears, and it will be seen that the curve then consists of a series of rectangles, placed alternately above and below the axis. It is easy to determine k, and we get therefore as the effective E.M.F. in volts : 2 K */ « il i I -t- ? (A - h) 1 jQ -s 6o L /i J ALTERNATORS 51 n being the product of the number of coils into the number of turns per coil Thury Alternator. — This alternator consists of a stationary magnet of ring shape, with a single field winding as shown in figs. 61 and 62. The field-magnet winding, which consists of two or three coils of copper ribbon, with a space between the coils for ventilation, is placed as the figure shows at the inner end of the groove in the ring, which is shaped like an elongated C. The inductor, of bell shape, is keyed on a spindle, the axis of which coincides with the axis of the magnet ring. The outer sur- face of the bell-shaped inductor is smooth, while the inner face, Fig. 61 Fig.- 62 which is between the lips of the C-shaped groove, is provided with a number of projectors like a spur wheel. The armature winding, which is formed of flat coils, is secured by means of bands, on the lower lip of the c-shaped groove. The inductor by its rotation produces a variation in the flux of induc- tion through the air-gap, and an alternating E.M.F. is produced. By means of a ratchet the magnet ring may be moved along the bed-plate in the direction of the axis of the spindle, so as to allow the field-magnet and armature coils to be inspected. Tests of two Thury alternators of 400 h.p., at Turin, showed : (i.) That the power used in exciting was less than 5 per cent, of the total output. 52 ALTERNATE CURRENTS (ii.) That the commercial efficiency is from 93 per cent, to 94 per cent., and the electrical efficiency 97 per cent, (iii.) That these machines are very easily synchronised, run well in parallel, and do not fall out of step. The shaded parts in fig. 63 show the width of the armature coils ff, «!, which are wound in opposite directions. The inductor teeth are the same width as the coils. It is easy to see that the curve of E.M.F., leaving self-induction and magnetic leakage out of account, has the shape shown at c. If * be the total flux of Fig. 63 induction through one tooth, the mean E.M.F. induced in one turn of an armature coil in C.G.S. units will be : * 2 ^ - =: = 2 F. T T 2 If d be the number of teeth We get, therefore, as the mean E.M.F. in one turn of the coil 2 *(/ 6o' If « be the total number of turns in series, the mean E.M.F. in volts is : 2 ^ an — . 60 ALTERNATORS 53 From the shape of the curve it is possible to calculate k, and we have, for the effective E.M.F. in volts, the expression K c 4 1 V 5 1 e \st Circuit 1 2nd Circuit 8 ,' Fig. 68 circuit as there are pole-pieces (in the latter case adjacent coils in each circuit will be wound in opposite directions). Figs. 67, 68, 69, 70 show the method of winding bar armatures for biphase and triphase currents : if it is required to place several bars side by side in each circuit, they will be con- nected as shown in figs. 9 and 10. It will be seen from figs. 67 and 68, which give the method of connection for biphase currents, that one ar- mature circuit is formed of bars I, 3, 5, 7, and the other of bars 2, 4, 6, 8. Figs. 69 and 70 show the method of connection for tri- phase currents : the first arma- ture circuit is formed of bars I, 4, 7, 10, the second circuit of bars 3, 6, 9, 12, and the third of bars 5, 8, 11, 2 ; bars 10, 12, and 2 are joined to a common return wire. ALTERNATE CURRENTS Polyphase alternators may be made self-regulating for constant E.M.F. even when the outside circuit possesses self-induction. 1st Circuit 1 \ 2nclCiri 2 ■ ■uit 3 4 1 A j 3«/ Circuit 5 1 —^^~ 6 ___ J i^ f 2 V Common return^--.,^ \ ^ \ \ \ 1 8 ■ T 1 9 ~ — i- N^, 10 s 11 12 1 Fig. 70 The Thomson-Houston Co. employ the. following arrangement for the purpose. The exciter is driven by a motor f with revolving Fig. 71 field, connected in shunt to the alternator circuit. As the currents in the external circuits increase, the impedance of the shunt circuits supplying the motor decreases ; consequently the ALTERNATORS 57 power supplied to the motor increases, the exciting current becomes lai^er, and the E.M.F. is raised in proportion to the load. A belt p serves to drive the exciter at starting up. The method by which the impedance of the motor circuits is diminished in proportion as the external load grows larger will be understood on reference to fig. 71. In each of the three circuits ISO »M) ^ J -^ ^V^ -^ 5 IM ^ "-^ _ no '~- — — "*■ ( ) ! I 1 Fig. 72 2 25 30 a cofl, with la:^e coefficient of self-induction, is inserted : these coils have two windings d and e in opposite directions, and the windings d are traversed by the main currents, whilst the windings e are in the shunt circuits of the motor. Naturally the choking effect of the coils on the motor currents diminishes as the main currents increase. Fig. 73 The upper curve of fig, 72 shows the results obtained with a triphase alternator for different loads when using the compensat- ing apparatus. The E.M.F. at the terminals \'aries from 114 volts on open circuit to 148 volts at full load. The lower curve gives the E.M.F. for different loads when the compensating apparatus is not used. 58 ALTERNATE CURRENTS Brown Alternator. — The field-magnet consists of a cast-iron ring, carrying, on its inner surface, the pole-pieces with rectangular faces. The armature is formed of a laminated soft iron drum, on the surface of which the flat armature coils are placed. The coils of 1 Fig. 74 the different circuits are superposed, and are insulated from one another and from the core by means of paper (fig. 73) : the whole is held together by brass wire bands. The coils are wound with cotton-insulated wire of elliptical section, the larger diameter being in the plane of the coil ; as will be seen from fig. 75, the turns are placed on the top of one another, not side by side. The Wehyer and Richemond Co. build single-phase alternators of the same type. In this case two coils, with the windings in opposite directions, are placed on the top of one another and connected as shown in fig. 76. After the coils are in position, the armature is as shown in fig. 74. ' '^ Fig. 77 gives the plan of the connections of the _»L coils in the case of a biphase alternator, and fig. 78 the same for a V^ single-phase alternator. In fig. 77 the two outer circles represent one pair of collecting rings, and the two small inner circles the other pair; in fig. 78 the small inner circle represents one collecting ring, and the large circle the other. M, Boucherot has measured the losses in a 75 k.w. biphase Nf^ In Os ^ W Fig. 75 J 'J s y 'J Fig. 76 ALTERNATORS 59 alternator with 8 poles; it made 600 revolutions per minute, and furnished in either circuit 165 ampferes at 150 volts. He used the same method as for continuous-current dynamos, which Collecting rings for one phase Collecting rings for the other phase Fig. 77 consists, firstly, in measuring the value of the exciting current necessary to give the normal voltage at full load ; secondly, measuring the hot resistance of the armature circuits ; and finally. Collecting rings Fig. 78 determining the power absorbed by the machine when revolving at the same speed and with the same excitation as that which gives the normal voltage on open-circuit. 6o ALTERNATE CURRENTS This last power loss is due to friction, air resistance, hysteresis and internal Foucault currents. By varying the speed, he was able to determine separately the losses due to hysteresis (proportional to the speed) and the losses due to Foucault currents (proportional to the square of the speed). This method of investigation is quite legitimate, for, as we saw at the beginning of this section, there are no Foucault currents induced in the pole-pieces. The results of the tests are given in the following table : Watts at full load Watts at half load Watts at -is load Loss in armature .... Loss in field-mj^net . . . Frictional losses Hysteresis losses Foucault current losses . . . Useful power Total power Efficiency 1,700 1.370 540 390 I.SSO 50,000 SS.SSO •9 420 1,250 540 380 1,500 25,000 29,090 •86 20 1,160 540 370 1,460 5,000 S.SSo ■58 Alternator of the Fives-Lille Co. — The Fives-Lille Co., who are the licensees in France of the patents of the 'AUgemeine Electricitats-Gesellschaft,' build alternators of the type shown in figs. 79 and 80. The field-magnet of laminated iron is of ring shape, and is fixed to the bed-plate : it carries on its inner surface the pole- pieces, also of laminated iron. The armature consists of a cylinder, composed of iron discs, which is provided with a bar winding. In triphase machines, one of the ends of each of the windings is connected to a collecting ring, and the other ends of the three windings, which are joined together, are connected to a fourth collecting ring.. The fourth collecting ring may be either put to earth or joined to the fourth wire of the external circuit. Forbes Alternator. — These machines are for the utilisation of the power of the Niagara falls. They generate current at 2,000 volts, and are constructed by the Westinghouse Co., of Pittsburg. They are driven direct by horizontal turbines, of the Faesch and Picard system. The number of revolutions per minute is 250, and the revolving 62 ALTERNATE CURRENTS field-magnet has 8 poles : there are 8 coils in each of the armature circuits, and the frequency is therefore i— - — 5_ = 16-67. 00 The magnet core, formed of a ring b of cast-steel (figs. 81 and 82), is fixed by 16 bolts to an 8-armed spider d, which is keyed on the top of the turbine shaft. On the inside of the ring the 8 pole-pieces are fixed by bolts : each pole-piece is surrounded by 2 coils of copper strip, with an air space between them for ventilation. The exciting current is conveyed to the Fig. 81 magnet coils by means of two brushes g, rubbing on two rings arranged on the under side of the spider. A cast-iron cylinder a, resting on. the bed, supports the armature, as well as the two bearings of the turbine shaft. These bearings have oil circulating through them, and a thermo-electric couple is so arranged that it actuates a relay when the temperature rises above a certain limit : the engineer in charge then sends a stream of water through a jacket surrounding the bearings, so as to cool them down. The armature core of thin iron plates, in which there are apertures for ventilation, is clamped by two flat gun- metal rings. It is fixed in a horizontal groove in the cylinder a AL TERN A TORS 63 by means of 16 bolts of nickel steel. This steel, which contains about 25 pter cent, of nickel, has a large specific resistance. The armature coUs have 72 turns of copper wire, No. o B. and S. gauge : these turns are insulated by mica, and are enclosed in conduits through which oil circulates. These conduits are formed of an insulating material, which is not acted on by oil or destroyed by heat The coils are placed in channels in the periphery of the armature : these channels, for convenience in removing the coils, are not cut out radially but are parallel to one another. The coils Fig. 83 Fig. 8a F of one of the circuits are flat, while the ends of those of the other circuit are turned over at the top and bottom. Oil is supplied firom a reservoir, placed at a certain height in the engine room, and flows through pipes to the bottom of the coils of the armature (fig. 83). It leaves the conduit at the top of the coils and returns to a refiigerator, whence it is pumped back to the elevated reservoir. Oerlikon Alternators. — r. Low-texsios Alternators. — ^The 300 h.p. biphase alternator used for the transmission of power from Lauffen to Frankfort in 189 1 was of this type. The revolving field-magnet is formed in the following manner : 64 ALTERNATE CURRENTS On the outer surface of a cast-iron wheel, a channel, about 7 inches deep, is cut : in this channel the field-magnet winding is placed, consisting of 496 turns of copper wire -2 inch in diameter. On either side of the rim of the wheel (figs. 84 and 85) rings of soft steel are fixed, each of which is provided with 16 pole-pieces. The pole-pieces of the two rings alternate, those of the left ring pointing towards the right, and those of the right ring towards the left : consecutive poles are therefore of different sign. (The dimensions in figs. 84 and 85 are in mm.) The stationary armature consists of a ring of laminated iron plates, insulated from one another by paper : this ring has an external diameter of 6' 3", and an internal diameter of 5' 10", the *- 3Sa 'f y/^^'////frl',*/,'///,V/,>,i'.'//r','//,',V/ Fig. 85 Fig. 84 width being i' 3" Close to the internal surface of the armature, 96 holes are drilled, parallel to the axis, about i^" in -diameter : in these holes are placed insulated copper bars i|-" in diameter. As fig. 86 shows, bars i, 4, 7, 10 94 — 95, 92, 89 2 — 93, go, 87 96 are connected in series, and form 3 circuits joined at Aq to the neutral wire. The other ends Aj Ag Ag are connected to the 3 terminals of the 3 circuits. A large number of tests were made on this machine at the Frankfort Exhibition. The turbine shaft, which made normally 35 revolutions per minute, was geared to the alternator spindle, which ran at 155 revolutions, by means of a spur wheel. The power of the turbine had been previously measured by a Prony ALTERNATORS 65 brake for different conditions of fall and opening of water gate, and the various values were tabulated. It was therefore only necessary to note the height of the fall, the opening of the water gate, and the height of the lower rim of the turbine wheel above the level of the race, in order to determine the power supplied to the alternator. The power given out by the alternator was absorbed by means of 3,000 incandescent lamps, divided equally between the three circuits. The three wattmeters were connected respectively across the three line wires and the centre of the star. Fig. 86 Tests were made at varying loads and the results are given in the following tables. (Tq = h.p. given to dynamo, Ti = power measured on wattmeters, Tp ■=■ power wasted, i = effective current in each dicuit, and e = effective P.D. between any line wire and the neutral return.) T« T, ■T/ I E No. ^ ; ■^ > \ ^> 1 y \ n 1 :i> iv 1 ' \ 1 1 \ > \ \ \ \ " \ A \ -?n' - > \ 1 H \ -^. \ ■v s ^ ^ >' — _ _ _ _ _ _ 2: ^ J ^_ •a t CO in 4< EfficUficy 70 ALTERNATE CURRENTS ALTERNATORS 71 The armature consists of a smooth drum of laminated iron, the coils being fixed on the periphery by means of wire bands. The Schuckert Co. as a rule only build alternators of small output of this type (up to 30 k.w.) ; but at the Buda-Pesth central station there are 100 k.w. biphase machines with external field- magnets. Fig. 93 gives the curve of commercial efficiency, and losses in the armature and field-magnets, of a triphase alternator of 80 k.w., with external field-magnet. The full curve shows the armature loss, the next above it the commercial efficiency, and the highest the losses in the field-magnets. (The ordonnates represent efficiency and watts lost in resistance, while the abscissae denote the load in kilowatts.) Siemens and Halske Alternator. — Fig. 94 represents an alternator of this type, which is intended to be driven by the engine direct. Machines driven by belt are provided with three bearings instead of two. The armature consists of a laminated iron ring, clamped by bolts between cast-iron flanges. On the inner surface of this ring there are grooves of the shape shown in fig. 13, in which the insulated bars which form the winding are placed. The field- magnet, which is also laminated, is keyed on the shaft. The alternators employed at Chemnitz, for the lighting of the town and the running of triphase motors, are driven direct by the engine. The field-magnet has 40 poles and runs at 150 revolu- tions : the frequency is, there- 20 X fore, 60 -^ = 50. The ar- mature is furnished with a sup- plementary winding, designed to give ^ E.M.F. of the main wind- ing ; this winding is used for measuring the E.M.F. and syn- chronising. Fig. 95 gives the curve of the exciting current : it will be observed that it undulates in consequence of the armature reaction. Fig. 96 gives the curve of E.M.F. of the alternator on open IVolt Fig. 95 72 ALTERNATE CURRENTS circuit ; this curve is almost symmetrical with respect to the median ordonnate. The curve of E.M.F. at full load is not symmetrical in relation to the median ordonnate, as will be seen in fig. 97. Both these curves are nearly sinusoidal : in the open circuit curve the maximum E.M.F. is a little lower, and in the full Fig. 96 Fig. 97 load curve a little higher than in a sine curve with the same effective E.M.F. Biphase Alternator of the Stanley Electric Co. — This machine, designed by Messrs. Stanley, Kelly and Chesney, of Pittsfield, yields biphase currents of 1,000 or 2,000 volts potential with a frequency of 133. The field-magnet revolves and the armature is stationary and the two armature circuits are quite separate. As will be seen on reference to fig. 98, the field-magnet is formed of a hollow cylinder of cast-steel, on the surface of which the laminated pole- ALTERNATORS 73 pieces are fixed. These pole-pieces form, as it were, two spur wheels at either end of the cylinder, leaving between them a space for the single exciting coil. This alternator resembles the Mordey Fig. 93 in that all the pole-pieces on one side of the armature are of one polarity, while those on the other side are of the opposite polarity. The armature is of ring-shape and carries on its inner surface two sets of projections, which serve as cores to the coils. Fig. 99 - A- b f 1 i Section E" F ^1:^ Section AB * Section CD vu/i/ffl////f/r/t/iii. Fig. 99 shows part of this ring developed ; separate sections are shown along the lines a b, cd, e f. Each series of armature coils corre- 74 ALTERNATE CURRENTS spends with a series of polar projections on the field-magnet. The coils are wound separately on formers and then placed in the channels in the armature surface. Fig. § 9. Parallel Rniming For a long time it was thought that only certain types of alternators could be run in parallel, but it is now agreed that it is rather a question of the engine than of the alternator. If the engines have not a uniform speed during each revolution, the alternators may run in parallel, but one machine will be taking current for an instant froni the other, or else giving current to the other, according as the respective speeds alter ; this synchronising current may be detected by placing lamps in circuit with the two alternators, or in the secondary of a transformer of which the primary is in the circuit of the alternators ; the lamps will fluctuate in brilliancy, showing that current is passing instantaneously from one machine to the other. In 1889 Mr. Mordey undertook some experiments on the synchronising of alternators of the type designed by himself. The two alternators could easily be synchronised, even though the operation was ALTERNATORS 75 effected at a moment when the machines were not in phase, and the fields were excited so as to give different E.M.Fs. The tension between the omnibus bars was then the mean between the tensions of the alternators. When steam was shut off from one of the engines the alternators did not fall out of step, but one machine supplied current to the other. When two alternators are driven by separate engines, coincidenfce of phase is maintained owing to the elasticity of the steam ; when the alternators are driven by belts from a countershaft they are kept in step by the belts slipping a litde. Alternators, driven by turbines, are very easily synchronised. The usual method of synchronising one alternator with an- other is as follows : The alternator, which is to be thrown in, is started on a resistance, and the exciting field gradually increased till the terminal E.M.F. is equal to that of the mains. The switch, putting the machine on the mains, is closed at the moment synchronism is obtained, and the resistance then gradually cut out. It is not absolutely necessary to run the alternator on a resistance ; the field may be excited so that the open circuit E.M.F. is equal to that of the mains, and the switch closed when synchronism is obtained. After closing the switch the exciting current is increased till the new machine takes its fair share of the load. Fig. loi shows one arrange- ment for determining when two alternators are in synchronism. T, and Tj are two little trans- formers, the primaries of which are connected in shunt to the terminals of the alternators or across the omnibus bars. If the secondaries s, and S2 are wound in the same directions, the lamps go out at the instant of synchronism. Instead of two trans- formers T, and Tj, one transformer, with a double primary, may be used. The acoustic apparatus, exhibited by the General Electric Co. vww^ vmaanKw -wwiVift Omnibus ban Ti, -^- Fro. 101 76 ALTERNATE CURRENTS at Chicago, consists essentially of an iron cylinder, the ends of which are closed by iron diaphragms. In front of these dia- phragms are placed two electromagnets, one of which is in the secondary circuit of the transformer connected to the terminals of the machine about to be synchronised, and the other in the secondary circuit of the transformer connected to the omnibus bars. When the machines are not in phase, the two diaphragms emit a discordant sound, but when synchronism is attained a very clear note is given out. Another arrangement consists in placing a voltmeter in the secondary circuit of a transformer with double primary. The two primary circuits are wound in opposite directions and placed respectively in the circuits of the two alternators. While the machines are not in phase, the needle indicates a certain E.M.F., but at the moment of synchronism it points to zero. Fig. At Zurich the 300 h.p alternators of the Kapp-Oerlikon type are thrown into parallel without any phase indicator by choosing the moment when the spokes of the armature are in line. Fig. 102 shows the connections of a voltmeter Vj, which serves to indicate the E.M.F. of the alternator a„ which is being started up, and fig. 103 the connections necessary for voltmeter v, to act as phase indicator : one voltmeter will suffice for both purposes if a change-over switch is arranged to make successively the connections shown in figs. 102 and 103. Hermann-Mtiller has employed at the Buda-Pesth central station the apparatus represented by figs. 104 and 105 : this apparatus enables all proper connections for synchronising to be made by the movement of one switch handle, and avoids all risk of short circuiting or any other mistake. Blocks of different size ALTERNATORS 77 are connected as shown in the diagrams, some with the terminals of the alternators, and some with the omnibus bars. A handle Fig. 104 carrying three blocks, which are insulated from one another, allows of making the necessary connections. In the position shown in fig. 104 the voltmeter indicates the E.M.F. of the Fig. 103 alternator Aj : when the handle is advanced to the position shown in fig. 105, the voltmeter shows when the machines are in phase. 78 ALTERNATE CURRENTS The other alternators a^, A3, a, are connected up in exactly the same way. In the usual method of synchronising, the exact moment when the machines are cophasal must be chosen for throwing into parallel : this requires great care and a certain amount of skill. To avoid this difficulty Mr. Kapp has designed an arrangement, by means of which a new machine may be quickly synchronised Fig. 106 without any fluctuation of the current, and which requires no special skill on the part of the operator. Fig. 106 shows the connections of this apparatus, which is in use at the Bristol central station. Li and La are the cables from the alternators, which may be joined up to the omnibus bars b b by means of the double-pole-switches I. and II. Ammeters ai and a^ and the safety fuses f are inserted in the circuit of one of the cables. Besides the main bars b b, there are two auxihary bars h h : these latter bars may be con- AL TERN A TORS 79 nected by means of plugs to any pair of alternator leads, l, Lj, &c. The Bristol switch-board was designed for five machines, but there are only two plugs, so that it is only possible to connect one alternator to the auxiliary bars at one time. One of the bars h is connected to the corresponding main bar b through the two coils A and B in series and the double-pole- switch o ; whilst the other bar H is joined up direct to the other main bar b by the same switch o. The coils a and b possess so much impedance that, with an E.M.F. double that of the alternators, they will only be traversed by a current which is a little less than the normal current of the machines : switch a and b serve to short-circuit the coils. Synchronising is effected in the following manner : Suppose the machine, of which L3 are the leads, is on the main, and that the machine with leads l, is to be thrown in. All the switches to the left of II. are open at first. The new machine is run up to speed and excited, after which the plugs s are inserted, and switch o closed. The current from the main bars b b, begins to bring the new machine into step. Switch a is then closed, and coil a cut out of circuit : this brings the new machine more nearly into phase, and on closing switch b the machines are thrown into parallel without any resistance in circuit. Switch I. is then closed, switches o, a and b opened, and plugs s removed, when all is ready for a new machine to be connected. The American General Electric Co. employs a device very similar to the above : a copper tube is pushed over the coils so as to diminish the self-induction : this tube takes the place of the switches a and b. § 10. Alternator Des^ The frequency and the speed are generally decided upon at the outset. If c represents the number of magnetic fields of like sign, we have : c N „ 60 F 60 N For drum alternators (such as the Brown, Oerlikon, Westing- house, &c.), the total number of poles is 2 c. 8o ALTERNATE CURRENTS For disc alternators with reversed fields (such as the Ferranti, Patin, Siemens), the number of poles on one side of the armature is 2 c. For alternators with fields not reversed (such as the Mordey), the number of poles on one side of the armature is c. For inductor alternators (of the Cail-Helmer or Kingdon type) the number of poles is c. For an alternator of the Thury type, the number of teeth on the bell is c. It will be necessary to take for c the whole number which is nearest the calculated value, and modify either the speed or the frequency so as to get the right E.M.F. The accompanying table will be found useful. c Number of revolutions for a frequency of 40 ■ so 60 80 100 130 I 2,400 3,000 3,600 4,800 6,000 7,800 2 1,200 1,500 1,800 2,400 3,000 3.90a 3 800 1,000 1,200 1,600 2,000 2,600 4 600 7SO 900 1,200 1,500 1.950 5 480 600 720 960 1,200 1,560 6 400 500 600 800 1,000 1,300 7 343 428 514 686 857 1,114 8 300 375 45° 600 750 975 9 266 333 400 544 666 lO 240 300 360 480 600 780 12 200 250 300 400 500 650 H 172 214 257 343 429 557 i6 150 187 225 300 375 487 i8 133 167 200 272 333 433 20 120 150 180 240 300 390 25 96 120 144 192 240 312 3° 80 100 120 160 200 260 The next proceeding is to determine the external diameter of the revolving part, according to the maximum circumferential speed permissible, and it is then possible to draw a sketch of the alternator, and find the pitch, dimensions of pole-pieces, &c. In a machine with a slight revolving armature, such as the Ferranti, a peripheral speed of 80 to 100 feet per second is safe, but ALTERNATORS 8i for a drum armature 35 to 50 feet per second is enough. When the field-magnet revolves, the peripheral speed is determined with reference to the air resistance, and is based on the speed of exist- ing alternators of the same type. It is very likely that after making the calculations given below, it will be found advisable to alter the dimensions of the alternator. The power and effective E.M.F. are not sufficient data for an alternator, as they are for a direct-current dynamo : the power of an alternator is represented by the expression p = e i cos ^, and the value of ^ depends on the self-induction of the alternator, the self-induction of the external circuit, the resistance of these circuits, the capacity of the external circuit, &c., all of which are varying quantities. If devices such as condensers or synchronous motors are placed in circuit, the lag may become zero, when cos ^ ^ i and p = E I ; in this case it is unnecessary to take into consideration the reaction of the armature. If no devices are used for avoiding the lag of the current, cos ^ may be taken as -8. The maximum induction to be used must now be decided on : if the armature contains no iron, an induction of from 6,000 to 8,000 C.G.S. units per square cm. may be adopted, but when the armature contains iron, the following values should not be exceeded, so as not to cause unnecessary loss through hysteresis. Frequency j Majdmom indacdon f Fieqnency 40 5,500 6,500 50 I 5,000 6,000 60 ; 4,500 — 5,000 70 4,300 — -4,500 80 I 4,000 — 4,300 Mayimnm induction 90 3,700 — 4,000 100 3.500 — 3,700 no 3,200 — 3,500 120 3,000 — 3,200 130 2,800 — 3,000 The minimum value of b given by this table being adopted, $ ^ s B (s ^ surfece of a coil) may be calculated. If E, be the effective E.:M.F., and e' the total E.M.F., we must have e' = e, (i -f- jj), since there is a loss of potential due to resistance of from i per cent, to 3 per cent. If no steps are taken to anniil the current lag, e' will be determined in the following manner : G 82, ALTERNATE CURRENTS Referring to fig. 14, we see that o A, o A + A A| COS .0 COS o E represents the total E.M.F. developed, o a the effective E.M.F. at the terminals, and a a, the loss of potential in the armature (a A, =>;o a). We get then oE = ^A(i±^), ^ cos ^ „, E, (l + 7/) or E ^ -^-^ — ■ — -i. cos^ Assuming the value of cos ^ to be "8, we have e' = i-25E,(i + »/). We found in § i that the value of the induced E.M.F. is given by the expression, k4>«aio~^, a being dependent on the type of alternator. For a first approximation, we may take k = 2-22, and we get E' = 2*22 * « A lO"". From this equation, we derive the value of n (number of turns of the whole armature). If b is the number of coils to be joined in series, and n^ the number of turns of one coil, we shall have J n 6ni=n, or «, = _; taking for «j the whole number next highest to the number found. If the alternator is designed for a given current, the cross- section of the armature wire will be determined so as to have a suitable current density. If the alternator must be of a given power, the value of the current will depend on (p, the angle of lag. We shall have : Ej cos (j) -8 e. In alternators with revolving armature, which contain no iron, a current density up to 3,800 ampferes per sq. in. may be adopted. When the armature contains iron, there is the additional heat due ALTERNATORS 83 ^ i i 5- 4 1 ^ ^ S ^ s 1 i i • • \ \ 54 s ^^ < ^\ •> "5 ft II \ ^^ «, ■a V. \ 1 ^ >. a ^1 M ~i V ■3 ti i IV \ 1 1^ — =« -1' a v» 1 1 "^ I 1\ Si 1 • 1 - k\ • \ lines of induction through the field-magnet cores; in a disc alternator with reversed fields i-rs to i"2 4 ; in a Mordey alternator i-i * ; and in a Schuckert or Kapp alternator i"36 *. The number of ampfere-turns necessary for exciting the alter- nator will be : 2, = Q ?, O 4 7r^ / being the length of the magnetic circuit, b the maximum induc- tion, and /J the permeability of the iron. The curves in fig. 107 give the values of , i.e. the number of ampfere-tums per cm. 47r^ ^ '^ in length of the magnetic circuit. The lowest curve gives the values for grey cast-iron, the next for mild steel, and the highest for annealed wrought-iron ; ordonnates represent induction per sq. cm., and abscissae ampfere-tums per cm. in length. Naturally we must, for different qualities of iron, draw curves of permeability in accordance with the results of tests on samples of the iron in question. ALTERNATORS 8S For the air-gap, which includes the armature in the case where the latter contains no iron, we shall have : Ampbre-turns = ^— = 796 4 _, "4" s s being the cross-section of the air-gap, and 4 the length. The subjoined table gives the values for a drum armature, as shown in fig. 108. _ Section in Magnetic induction Length of magnetic V Solid iron Ring s, 1-25* 2 X (-85) S, I^25* "2S7 k Pole-pieces s I -25* ■85 S 1-25* S 2h Air-gap . s 1-25* •85 s * T 2 la Armature Sj $ * I, ■8SS, % Fig. 108 If Q i be the total number of ampbre-tums required, the wind- ing of one pole-piece must produce a magnetising force of 2 ampfere-turns (to Q / must be added a certain number of ampfere- turns to make up for armature reaction). For a disc armature (fig. 109) the values of the induction are given in the next table : 86 ALTERNATE CURRENTS - Section in sq. cms. Magnetic induction Length of magnetic circuit Laminated iron Solid iron Rings s, I-IS* 2 X (-85)3, I'lS* 2S, 2/, Pole-pieces s •8ss I-IS* s 4 4 Air-gap . s i-iS* •8s s * 2 4 4F tr s W i N s >\__ Fig. log If Q i be the total number of ampfere-turns required, the wind- ing of one pole-piece must supply — ampfere-turns. 4 The last table gives the values for a Mordey alternator,/ being the number of poles (fig. no). - - Section in sq. cms. Magnetic induction Length of magnetic circuit Laminated iron Solid iron Arms (narrow part) . S — S k Arms (thick part) . Sj — I-I* $2 k Core Si — /x IT* h Air-gap . S — * la The winding of the core must produce q i ampere-turns. ALTERNATORS 87 If the alternator is to supply to a network, in which there are devices for getting rid of the current lag, we can at once proceed to the calculation of the field-magnet winding j otherwise it will be necessary to add to the number of ampfere-tums found those necessary to compensate for the armature reaction. If the machine is required to give an effective current \ the number of supplementary ampfere-turns will be : X4= -0156 «i i^, «i being the number of turns of an armature coil. Fig. 1 10 If the machine is to have a given power (to drive motors, for example), the effective ciurent will be : I. = - Ej COS ^ Adding x^ to q fi as calculated above, we get the total number of ampere-tums to be supplied by each field-magnet coil. After determining the number of ampere-tums, it is necessary to note whether the induction wiU exceed the values given above. As- suming that Q i ampere-tums produce an induction of — , (q i -I- X,) ampere-tums will produce an induction S Q« 88 ALTERNATE CURRENTS If the value of b, exceeds to any extent the value given in the table, it will be necessary either to increase «„ the number of turns of the armature, or else enlarge the surface of the field-magnet coils (the diameter of the revolving part cannot be altered). If the value found for Bj is considerably less than the tabular value, we can diminish n^, or even reduce the dimensions of the alternator, thus decreasing the peripheral speed of the revolving part. Generally the exciting current is taken from a circuit with a given potential difference e. We must calculate the diameter of the wire so that, when no resistance is in circuit, a sufficient current passes to excite the alternator at full load ; we must then calculate the resistance to be inserted, in order that on open circuit the exciting current may be sufficiently reduced. Let Q «' = A be the number of ampfere-turns necessary to excite one magnet coil at full load ; and let r be the resistance of the exciting circuit ; then e-=-ri. We will take an approximate value for /„ the length of a turn, assuming that the mean turn is at a distance of from "2 to "4 inch from the surface of the core. If m be the number of coils to be arranged in series, the length of wire will be given by the equation : we have r = ^-^^ — i ; a being the specific resistance, and a the i a area of cross-section. Since e = ri=''J'L±hi, t a . amPLL we get a = !. e If e is expressed in volts, /, in metres, and if a be taken as -oz, T will be expressed in sq. mm. Knowing the cross-section of the wire, we can calculate the diameter, and adding to it the thickness of insulating material, we ALTERNATORS 89 get the total diameter, «?,. Allowing a density of about 2 ampferes per sq. mm., we get i ^ 2 a. Consequently we can determine Q from the equation t Of course we shall take for Q the whole number nearest to the determined value. If k be the height of the coil in mm., the number of turns per layer, «', will be / h the number of layers, «/, will be given by the equation ««, _Q, n, -. We can, if needful, slightly increase h, without making a new calculation, for the magnetic resistance will not be sensibly increased by lengthening the core, since the latter is either of soft iron or laminated plates. We can next find the total length of wire l', and its resistance r, and from the latter calculate the loss in watts r^ P ; it will be necessary to note whether the cooling surface of the coil will be sufficient to dissipate this heat r^ P- If the field-magnet revolves the coil ought to have from 4 to 6 sq. cms. of cooling surface per watt dissipated, and if the field-magnet is stationary 8 to 1 z sq. cms. per watt. If the surface is insufficient the current density must be diminished and the calculation begun afresh. If the cooling surface exceeds the values just given, the density of current can be increased and the weight of copper diminished. From a sketch of the coil, the length of the average turn /,' and the length of the connecting wires /^ can be found. The total length of the circuit will be L = w Q /,' -1- 4'- Knowing l the total length of wire, we can calculate r and see whether; = -. If the value of /is found to be too small or too 90 ALTERNATE CURRENTS large, the calculation must be performed over again with a new value for //, the average length of a turn: We have now to determine the maximum resistance of the rheostat which is to be inserted in the circuit. On open circuit with no current lag, the induced E.M.F. must be equal to the effective E.M.F. We may assume, without great error, that the ampfere-turns are proportional to the induced E.M.F. : therefore if Q i^ be the number of ampfere-tums for no load, we shall have : q/ e' i.e. *'i=^'J' e' being the induced E.M.F. at full load. If we have «?i exciting circuits in parallel (there being m coils in each exciting circuit), the exciting current at full load for the Wj circuits must be m^ i. When the alternator is on open circuit, the total exciting cur- rent must be m-^i-^. The resistance of the parallel circuits is — , and we get at full load, r e = — niiZ ^= rt. mi If R is the resistance of the rheostat, we must have on open circuit : = ( R + — ) m^ i ; from this equation we can iind R the resistance to be given to the rheostat. If the exciting current is to be supplied by a special shunt dynamo, we must know the E.M.F. of this dynamo when the alter- nator is running with full load. We can then determine, in the manner indicated above, the resistance r of one exciting cireuit, so that the total exciting current for the m^ parallel circuits may be m^ i : and finally calculate the resistance to be inserted in the excit- ing circuit of the shunt dynamo, so that, when the alternatCM- is on ALTERNATORS 91 open circuit, the terminal E.M.F. of the shunt dynamo may be When the alternator is self-exciting, we must know the power spent in excitation (generally i per cent, to 3 per cent, of the total power), and increase the effective armature current by this amount. If the potential difference at the terminals is too great, we must transform the current before it passes through the rectifier and find the ratio of transformation, taking for the effective potential difference at the terminals of the secondary a suitable value e : we can then determine as before the section of the wire, and the resistance of the rheostat. The efficiency of the alternator may be calculated by deter- mining the various losses by friction, resistance, hysteresis and Foucault currents. The two accompanying tables will be useful in determining the losses by hysteresis and Foucault currents. To find the Foucault current loss per cubic "cm., it will be sufficient to multiply the values of -16 f*b* io~" by the square of the thickness of the lamination, expressed in tenths of nun. Values of -16 f=b- 10-" Maximum induction per sq. cm. Number of cycles per second 40 50 60 80 100 »33 2,000 •noooio •000016 •000023 •000041 •000064 •000113 2,SOO ■000016 •000025 •000036 •000064 •000100 •000177 3,000 •000023 ■000036 •000052 ■000092 •000144 •00025s 3.S0O ■000031 •000049 •000071 •000126 •000200 000350 4,000 ■000041 •000064 •000092 •000164 •000256 •000453 4.S00 •000052 •000081 •000116 •000207 •000324 ■000573 S.ooo •000064 •oooioo •000144 •000256 •000400 •000708 5,500 •000077 •OOOI2I •000174 •000310 •000696 •000856 6,000 •000092 •000142 •000207 •000369 •000576 ■001019 6,500 ■000108 •000169 •000243 •000433 •000676 ■OOII96 7,000 ■000125 •000196 •000282 •000502 •000784 ■001387 7,500 ■000144 •000225 •000324 •000576 ■000900 ■001592 8,000 ■000164 ■000256 •000369 ■000655 ■001024 ■001811 8,500 ■000185 ■000289 •000416 •000740 ■001156 •002045 9,000 ■000207 •000324 ■000467 •000829 •001296 ■002292 9,500 •000231 •000361 ■000520 •000924 ■ooiii4>i •002554 10,000 •000256 •000400 •000576 ■001024 ■001600 •002830 92 ALTERNATE CURRENTS Values of f b' •* lo-' Maximum Number of cycles per second per sq. cm. 40 50 60 80 100 133 2,000 7658 ■9563 1-1487 1-5316 1-9125 2-5439 2,500 1-0934 1-3667 I -6401 2-1868 27334 3-6354 3,000 1-4637 1-8295 2-1955 2-9274 3-6590 4-8668 3.500 1-8731 2-3414 2-8096 3-7462 4-6828 6-2282 4,000 2-3193 2-8991 3-4789 4-6386 5-7982 77116 4,500 2-8003 3-5004 4-2005 5-6006 7-0008 9-3109 S,ooo 3-3145 4-1431 4-9717 6-6290 8-2862 11-0206 5.500 3-8605 4-8256 5-7907 7-7210 9-6512 12-8361 5,000 4-4372 5-5464 66558 8-8744 11-0928 14-7535 16-7692 6,soo 5-0434 6-3042 7-5651 10-0868 12-6084 7,000 5-6783 7-0978 8-5174 11-3566 14-1956 i8-88oi 7.500 6-3410 7-9261 9-51 15 12-6820 15-8523 21-0838 8,000 7-0308 8-7885 10-5462 14-0616 17-5770 23-3774 8,500 7-7470 9-6837 11-6205 15-4940 19-3674 25-7885 9,000 8-4888 10-6114 12-7332 16-9776 21 -2228 28-2254 9.500 9-2558 11-5798 13-8837 18-5116 23-1596 30-7758 10,000 10 -0475 12-5595 15-0712 ao-0950 25-1191 33-4081 In order to find the hysteresis loss per cubic cm., the values in the latter table of fb'-^ io""^ must be multiplied by the appro- priate value of 17. M. Steinmetz has obtained values of j; for a large number of different kinds of iron, of which the following are the most im- portant : Very soft iron wire 77= '002 Very thin soft iron laminae = -0024 Thin laminsE of good iron . . . = -003 Thick laminae .....,.= '0033 Very common laminae for transformer cores . . = "004 — -0045 Mild cast steel annealed ,....= -008 Mild steel for machines = -0094 Ordinary cast steel ......= -012 Cast iron = -0162 Hardened cast steel = -025 93 CHAPTER II MOTORS Fig. Ill § I. Bevolving Fields in Practice In works on the theory, the field produced by polyphase currents traversing loops which are arranged symmetrically round a common axis are investigated, and it is demonstrated that, given a constant magnetic resis- tance, the field produced is uniform. Practically the mag- netic resistance is not constant, in consequence of hysteresis and eddy current losses, and the variation in magnetic permeability. Fig. Ill shows the arrangement of the loops to obtain a biphased field, two «ircuits being wound on the periphery of a drum : fig. 112 shows a triphased field, the three circuits being placed on the inside of a ring. It is also practicable to obtain revolving fields by means of pole-pieces : fig. 113 shows the arrangement of a biphased field. In this case the intensity of the field is not constant even Fig. 112 94 ALTERNATE CURRENTS though the magnetic resistance is uniform : it varies in the ratio of -— . or , as will be evident on determining the resultant V2 i'4i Fig. 113 Fig. 114 Li Li. r 6, d ^A^ r-'X. : ? ^-A/ Fig. us Fig. 116 field at different angles from the horizontal. In a triphased field with pole-pieces, the intensity of field is more uniform : it varies in the ratio of i : — 3 or i : i-i6. 2 MOTORS 95 Another method of obtaining revolving fields is by the use of a Gramme winding, the coils being arranged on a ring of laminated iron. Fig. 114 shows the arrangement of a biphase winding, covering the entire surface of the ring : coils i and i' are wound in opposite directions, coil 2 in the same direction as coil i, and coil 2' in the same direction as coil i'. Fig. 115 gives the plan of a Gramme winding for triphase currents with star connection, and fig. 116 the same with triangle Fig. 117 connections. In both cases the three coils are wound in the same direction. As the fields produced by Gramme windings are far from being of constant intensity, it is an advantage to increase the number of coils, for by so doing the constancy of the field is increased. Dobrowolsky, by winding each phase twice on the ring in opposite directions (fig. 117), has been able to produce, with triphase currents, a field corresponding to that obtained with six currents lagging behind one another by an angle --. He has 96 ALTERNATE CURRENTS also obtained with three currents, with a phase difference of — , 3 a revolving field corresponding to that produced by twelve cur- rents differing in phase by — , by means of combining the star 12 mounting with the triangle. Fig. ii8 gives the plan of this method of connection. Fig. iiS Haselwander has obtained a revolving field, by means of a Gramme ring, provided with a continuous winding as shown in figs. 119 and 120. It should be remarked here that in the case of a biphase current (fig. 119) it is necessary to employ two return wires, as otherwise there would be a short circuit in the ring. The Haselwander system can be used for drum windings, all the bars being connected at one of their ends by means of a ring. MOTORS 97 Ix *- • L± < ^ 3, I li < ' ■ £7 /^ <^A4 ^ J /y Y^ ^'\y\ /w* \)\ ^^ Xi ^ — ^ — li. Fig. 119 98 ALTERNATE CURRENTS Figs. 121 and 122 show a biphase drum winding arranged on the inside of a ring. In all the systems which we have examined so far, the field produced is bipolar and makes a complete revolution for every C^ ^ ^ Fig. 121 Fig. 122 period. The angular velocity is equal to the pulsation or angular speed of the current. The speed of a synchronous motor, or even that of an asynchronous motor (for in practice, as we shall Fig. 123 see, the speed of such motor is very near that of synchronism), may be a great deal too high. It becomes necessary then to produce multipolar fields, in order to reduce the speed of the motor. If the field has 2/ poles, the speed is the/"" part of the MOTORS 99 angular velocity or pulsation of the current, and the number of revolutions of the field is given by the expression n = . The field is then far from being of uniform intensity, as will be seen by determining the resultants graphically ; but, since the armature reaction tends to render it more constant, we shall not be very far wrong in assuming it uniform. Multipolar fields may be produced by a drum winding, and the motors are identical with the bar-wound polyphase alternators Fig. 124 we have described above and illustrated in figs. 67-70. A biphase field with 2/ poles is formed by 8/ bars or groups of bars : a triphase field by 12/ bars or groups of bars. Multipolar fields with pole-pieces have been investigated in the case of polyphase alternators as shown in figs. 64, 65, 66. We can also produce multipolar fields by a Gramme winding : the wire corresponding to each phase is wound so as to form 2/ coils (the field having 2/ poles), arranged symmetrically round a ring and wound alternately in opposite directions. loo ALTERNATE CURRENTS Fig. 123 gives the plan of a biphase winding producing a 6-pole field (N = ^). 3 There are six coils for each phase, i — i' — ii — 1/ — i" — i/', and 2— 2i— 2'— 2/— 2"— 2i", coils i— i,— i"— 2— 2'— 2" being wound in one direction and coils i' — i/ — i/' — 2, — 2/ — 2/' in the opposite direction. Fig. 124 gives the plan of a triphase winding, producing a revolving field with four poles, there being four coils for each phase. Fig. 125 In general, it requires 4/ coils for biphase currents, and in the case of triphase currents 6/ coils, to produce a revolving field with 2p poles. In the same way multipolar fields may be produced by the Haselwander system (continuous Gramme winding). Fig. 125 gives the plan of a biphase field with four poles, the coil being divided into eight parts. MOTORS loi § 2. History and Classification of Motors Professors Hopkinson and Gryll Adams were the first to make experiments on the transmission of energy by means of a single- phase motor. Their inability to start without special arrangements prevented their use, more especially for motors of small power, when the addition of a starting mechanism became relatively very expen- sive. A motor which could start under load without any special device, was what was required. In his celebrated experiment Arago showed that a disc would revolve under the influence of a revolving magnetic field. In June 1879 Walter Bailyread a paper at the Physical Society on a method of producing the rotation of an Arago disc by using fixed electro-magnets. The alternating currents, differing in phase by ^period, were produced by a battery and a special commutator, and the two electro -magnets were placed radially at a little distance from the disc which they caused to revolve. In 1880 M. Marcel Desprez made experiments with biphase motors : one of them, with an output of \ h.p., had a fixed field, produced by an electro-magnet between the poles of which revolved an armature which had two windings at right angles, traversed by two alternate currents, differing in phase by ;J-period. In 1884 M. Ferraris built a biphase motor, and expounded the theory of revolving magnetic fields. In 1888 M. Tesla, who was in ignorance of the work of M. Ferraris, took out a great number of patents relative to polyphase motors ; he only built biphase motors, but in one of his patents he described a triphase motor with star-winding. Then MM. Hutin and Leblanc, Wenstrom, Von Dolivo Dobrowolski, Brown, and others turned their attention to the subject, and in 1891, at the Frankfort Exhibition, the experi- ments on the transmission of energy by polyphase currents undertaken by the Allgemeine Electricitats-Gesellschaft and the Oerlikon Co. gave a great impulse to the use of polyphase currents. For some considerable time attention has been paid to I02 ALTERNATE CURRENTS asynchronous single-phase motors, which cannot, it is true, start of themselves ; however, the starting devices are very simple. In i88g Elihu Thomson exhibited one of these motors at Paris. MM. Hutin and Leblanc built one, of which they gave a description in 1891. The recent work of Brown, Dobrowolski, Kolben, Hutin, and Leblanc has rendered these motors quite practical. In order to facilitate the study of alternate current motors we shall divide them into two classes. (i.) Synchronous motors. (ii.) Asynchronous motors. Synchronous motors may be subdivided into single-phase and polyphase motors. In the case of asynchronous motors, we shall study polyphase motors first, as they came into practical importance before single- phase motors. § 3. Single-phase Synchronous Motors The motors most used are separately excited by a continuous current, but there are also small motors with a constant field, obtained by rectifying the alternating current in the magnets. Motors with Constant Field. — Any alternator will act as a motor if it is supplied with current of the right frequency. The number of revolutions per minute is given by the equation 60 F F being the frequency, and m the number of poles of the same sign. It is necessary that the motor should be run up to speed and synchronised before the load is thrown on to it. Small motors may be run up by hand to the right speed for synchronis- ing, but with large motors some starting device must be employed. For example, the motor may be employed in driving a con- tinuous current dynamo for charging cells ; in this case the alter- nating motor will be run up to speed by the continuous current dynamo taking current from the cells. MOTORS 103 Another starting device consists in placing on the motor spindle a small asynchronous single-phase motor, which will enable it to start from rest. This arrangement has been adopted by the Oerlikon Co. for a 90 h.p. motor, installed in a mill at Coire. The auxiliary asynchronous motor is of 9 h.p. When synchronism is attained, the motor drives all the machinery in the mill. In spite of the variation in the load, the motor has never fallen out of step, and the number of revolutions is absolutely constant. JO 20 30 fO so so 10 so 30 Fig. 126 The efficiency of this motor is very high ; fig. 126 gives the curves of efficiency, effective current, and power factor (the lowest curve is- that of current, the next of efficiency, and the highest of the power factor ; ordinates represent ampferes, and percentage and abscissae the load in h.p.). The power factor is true watts e i cos _ SI cos (p. apparent watts Blakesley's graphical method shows well the working condition of a synchronous motor, o A (fig. 127) represents the impressed E.M.F. at the motor terminals. If e be the maximum value of the impressed E.M.F., we have : E„ = »z o A, m being a constant. I04 ALTERNATE CURRENTS If o B represents the counter E M.F. of the motor, making an angle i\i with the impressed E.M.F. o a, we have E^ = »« o B. If we take o b' = o b, b' a will represent in magnitude and direction the resultant E.M.F., and we have : E, = »? b' a. If L is the coefficient of self-induction of the motor, r the armature resistance, and if tan = — , taking the angle b' a c = 0, and dropping from b' a perpendicular on a c, we shall have : Es = ms' c, E^ being the maximum value of the E.M.F. of self-induction ; ca will represent the effective E.M.F., which agrees in phase with the current. If I is the maximum value of the current, we have : E, mCA r r The power supplied to the motor is : p« = -^~ cos D A o. 2 Dropping the perpendicular o d from o on c a, we get : D A COS D A o = _:, DA therefore p. = ^ o a.c a.^ = ^ c a.d a. 2/- o A 2r The power wasted or transformed into heat is : i^ OT^ r — — , m'' — -Pf = r~= — 5- c A^ = — c A^ ■^ 2 2 H 2 r MOTORS los The useful power is : p„ = — ^—. — — cos (angle between c a and o b) a/2 s/ 2 moB fn c A = cos (angle between c a and o b) ^2 r n/2 = — O B'C A" sin b' o D 2r m' DC = — OB'CA • ; 2r OB' = — c A'D c (since o b = o b'). 2r We see then : (i.) The power furnished to the motor is proportional to D A-c A, (ii.) The power wasted is proportional to c a^. (iii.) The useful power is proportional to d c'C a. The efficiency therefore is : DC'CA _ DC D a-c a da' We can investigate the variation in value of these quantities, assuming that the impressed E.M.F. is given, and that the counter E.M.F. remains constant. The locus of the point d is a circle with o A for diameter, and the locus of the point b' a circle with centre o (fig. 128). To find the locus of the point c take the angle f A o = ^, and from G, the point where the circle a' cuts a o, drop the perpen- dicular G H on A F ; it is easy to prove that the circle with centre f and radius f h is the locus of the point c. It will readily iSfe, seen that the current will be a minimum when its maximum is represented by a h (i„,-„ = — a h), that is to say, when the counter E.M.F. is exactly opposed to the impressed E.M F. (J- = 180°). io6 ALTERNATE CURRENTS In 1890, at Cassel, where continuous-current dynamos are driven by synchronous motors, to which current was supplied by alternators at some distance from the town, it was noticed with Fig. 128 the same power supplied to the motor the effective armature current varied with the exciting current. As the curves in fig. 129 indicate, the armature current is a minimum for a certain value of the exciting current, and if the latter is either increased or diminished the former will be larger. These curves were plotted by Mr. Mordey from two of his motors which were supplied with a constant power. (Ordinates represent armature current, and abscissae exciting current.) Mr. Mordey found that the exciting current, which gives the minimum armature current, is almost the same at every load ; this was owing to the fact that his motors possess very little self-induction. When the self-induction is large the exciting current, which gives the minimum armature current, increases slightly with the load. If we note the angle of lag of the armature current behind the impressed E.M.F., we shall find that at first the current lags behind the E.M.F. ; as the excitation is increased the angle of lag diminishes until it reaches zero, when the armature current is a minimum ; on increasing the excitation still further the angle of MOTORS 107 lag changes its sign {i.e. the current is in advance of the E.M.F.) and increases in size with the exciting current. It is possible, therefore, by changing the excitation of a synchronous motor, to alter the phase difference of a circuit — i.e. the motor may play the part of a condenser, and in this way the capacity of a circuit may be increased since the apparent resist- ance may be diminished. The following explanation may be given of this property of a synchronous motor. It will easily be seen that the lag of the i^tl % list s e i B d 10 una If IS IB 11 IS 13 w Exciting current in umpires Fig. 129 current behind the E.M.F. will increase the intensity of the field, whereas when the phase of the current is in advance of that of the E.M.F. the tendency will be to reduce the intensity of the field. If, therefore, the exciting current of a motor is too small to produce the necessary counter E.M.F., the armature current is obliged to reinforce the field, and is therefore retarded in phase ; if, on the other hand, the motor is over-excited — i.e. so as to produce too great a counter E.M.F., the armature current must io8 ALTERNATE CURRENTS exert a demagnetising effect, and consequently is in advance in phase of the E.M.F. We can calculate sufificiently accurately the number of ampfere- turns to be added to the exciting coils, in order to annul a given retardation, from the formula of Mr. Kapp : Xj= -0156 « 01, 1^ being the angle of lag in degrees, and i the effective current, which may be found from the equation, I Ea cos = P, E^ being the effective E.M.F. at the motor terminals, and p the power. If it is required to advance the current 0° in -front of the E.M.F., we must add to the ampere-turns found above the number found from the equation : I, being given by the equation I, E^ cos 01 = p. In consequence of the report of Professor Forbes on the utilisation of the Niagara Falls, in which he gives biphase motors the preference over single-phase, a discussion was raised on the question of the transmission of energy by synchronous motors over a line possessing a certain resistance. Mr. Mordey undertook some experiments with synchronous motors of the Mordey- Victoria type, the result of which was that he found it possible to insert in the circuit a considerable resist- ance (much larger, in fact, than it would be economical to allow for transmission of energy) before the motors fell out of step. M. Boucherot, in experiments with biphase synchronous alternators which work under the same conditions as single- phase alternators, found that he could maintain synchronism when he allowed for a line loss of 40 per cent. ; beyond that figure they fell out of step. Motors with Rectified Field.— The Ganz firm builds syn- chronous motors of small power, the magnets of which are excited MOTORS 109 by the rectified armature current, taken direct from the armature, if of low tension, and if of high tension, from the secondary of a transformer. The current rectifier is the same as that used for the self- exciting Ganz alternator described above. On starting up, the magnets are not sufficiently excited to give a torque strong enough to bring the motor into synchronism. It is necessary to raise one brush of each pair and allow sparking to take place ; as soon as the motor is synchronised the brushes may be dropped again. The Ganz firm has invented for this purpose an automatic device, which consists of a governor which only allows the brushes to drop when its balls are separated to a certain extent. A committee appointed by the town of Frankfort made several experiments with a Ganz motor excited by rectified current. A motor of 25 nominal h.p. gave a commercial efficiency of from 82 per cent, to 88 per cent. It had to be started by hand, but as soon as the synchronising speed was attained (not more than one minute was required) the load was increased gradually to 40 h.p., or 60 per cent, above its nominal power. At starting the sparks were two inches in length, but they had very little eflFect on the commutator. The committee of the Frankfort Exhibition, in 1891, made experiments with three Ganz motors, of 10, i, and \ h.p., exhibited by the Helios Co., of Cologne. The power supplied to the motor was measured by means of a wattmeter, and the useful power by means of a brake. The 10 h.p. motor with six poles worked at an effective E.M.F. of 1,000 volts, and its speed was 833. The motor started automatically under no load with much sparking, and reached the speed of synchronism in \ minute, when the sparking ceased. The efficiency was about 80 per cent., but it should be remarked that the brake pulley got hot during the experiments ; consequently the temperature of the bearings was raised and the efficiency diminished. The I h.p. motor with four poles worked at an effective E.M.F. of 105 volts, and its speed was 1,250. no ALTERNATE CURRENTS In seven experiments the motor started twice of itself when fitted with the brake, which corresponded to a torque equal to • 142 1000 1600 Fig. 130 2000 Watt of the normal torque at synchronism ; and three times when the brake was loaded with -5 kilogrammes, which corresponded to '36 1000 1500 Fig. 131 imwatt of the normal torque. Fig. 130 gives the efficiency of this motor at various loads. MOTORS III The \ h.p. motor with four poles worked at an E.M.F. of 105 volts. At the maximum load, when the brake was loaded with 2327 kilogrammes, which corresponded to a power of i"o75 h.p., i.e. double the nominal power, the motor dropped out of step twice in three trials. Fig. 131 gives the efficiency of this motor at various loads. § 4. Polyphase Synchronous Motors Every polyphase alternator will act as a synchronous motor. The advantages which they possess over single-phase synchronous motors are that the motor will start of itself, and that the torque is a constant instead of being a varying quantity. As with single-phase motors, the difference of phase between the E.M.F. and the current varies with the excitation, and conse- quently synchronous polyphase motors may be used, instead of condensers, to annul the current lag. The Lahmeyer Co., of Frankfort, has applied this principle to the distribution of power by triphase current at Bockenheim, where synchronous motors are supplied with triphase currents at 600 volts. This arrangement has almost entirely done away with the current lag, and consequently the power of the generators is much in- creased. Hutin and Leblanc Motor. — In their system of transforma- tion of polyphase into direct current, MM. Hutin and Leblanc employ synchronous motors to drive the revolving commutators. The motor, when it is bipolar, has the appearance of a Man- chester dynamo : the field-magnet is provided with current by a battery of accumulators or by the dynamo. The armature is suppUed with polyphase currents, and is wound in a manner to produce a bipolar field. As very perfect synchronism must be obtained, MM. Hutin and Leblanc have adopted the following arrangement : The pole- pieces are perforated as nearly as possible to the air-gap, in order to receive copper bars, which are connected at each end to a ring, so that they form a kind of mouse-mill. As long as the motor revolves synchronously the field remains fixed in space. If there is any tendency to fall out of phase the field is displaced. 112 ALTERNATE CURRENTS so that powerful currents are induced in the bars of the mouse-mill, which prevent the motor dropping out of step. By over-exciting the motor MM. Hutin and Leblanc succeed in getting the current into phase with the E.M.F., so that when the commutator breaks the different circuits there is no sparking. Schuekert Motor. — This motor is built exactly in the same way as the alternator which we have described above (fig. 92) ; the biphase motor is provided with four rings to receive the alternate currents, and a commutator provides the current necessary for excitation. The motor cannot be excited before it has reached the speed of synchronism, otherwise it would stop. On starting up the exciting circuit is broken and biphase current sent through the ring. The motor then acts as an asynchronous motor, of which the armature is formed simply by pieces of iron. It starts by itself and soon reaches a speed sufficiently near to synchronism for it to revolve when the magnet is excited. It is necessary, then, to be able to determine the moment when synchronism is nearly attained, for if the exciting circuit is closed too soon the motor will stop. For this purpose a voltmeter is placed in shunt on the terminals of the exciting circuit. As long as the speed is not high enough the field revolves in space (with a speed equal to the difference of speed between the field and the ring) and the pole-pieces are subjected to a varying induction which causes the needle to oscillate. When the speed is high enough the field is stationary in space, and the voltmeter needle is at rest. The Schuckert firm has installed at Buda-Pesth synchronous motors, which drive continuous current dynamos for lighting the town and charging a battery of accumulators. The field-magnet is of ring shape and carries the pole-pieces on the inside. The armature is a ring with a Gramme winding, taking, by means of brushes and rings, biphase currents at a pressure of 1,800 volts. The 1 20-kilowatt motors have eight poles, and run at 400 revolu- tions per minute ; the 240-kilowatt motors have sixteen poles and run at 200 revolutions. Exciting current is furnished by the accumulators. When starting up, the dynamo acts as motor and derives current from MOTORS 113 the cells. As soon as the speed of synchronism is reached (which is determined by a voltmeter), the main switch is closed, and the motor begins to drive the dynamo. Tesla Motor. — Fig. 132 gives the plan of a synchronous bipolar Tesla motor for biphase currents. In the interior of a ring, provided with a Gramme winding, is placed an electro-magnet which is capable of rotation. The ends of the electro-magnet winding are connected to two rings on which the brushes b and b' rub. On starting, the electro-magnet winding is closed and the motor starts as an asynchronous motor, but if the resisting torque is not too strong the speed of synchronism is soon reached. The electro-magnet then makes with the iield an angle of retardation, of which the size depends on the resisting torque. If for any reason the angle of retardation increased, the winding of the armature would react so as to increase the field and in con- sequence the torque. In Tesla polyphase motors, if the number of poles of the field is 2p, the armature carries 2/ projections, each provided with a winding. The windings of the armature may be closed, but the power of the motor is a great deal increased if it is supplied with a continuous current, so that the polarity remains constant. Fig. 132 § 5. Theory of Asynchronons Motors In this section we shall attempt to give as simple as possible a theory of asynchronous motors. Let us first determine the power which must be supplied to an armature (formed of m turns, or loops arranged symmetrically round a common axis, and making an angle of — with each other) m 114 ALTERNATE CURRENTS in order that it may revolve with an angular velocity Kj in a stationary magnetic field of constant intensity. Let B^ be the intensity of the field, s, r, and / the surface, resistance, and coefiicient of self-induction of one armature turn. Suppose the armature revolving in the direction of the arrow (fig. 133), the perpendicular to loop i making an angle (k, *+a) with the field at the given instant. The loop n will make the angle : K, / + a + ^^ - ^) ■^ + 1. m 2 The flux of induction passing through this loop will be : B^ s sin f K, ^ + a + (^ ~ ^) '^ + ^^ \ m 2) = B„ s cos ('k, / + o + kLz2)jL\ V m J The E.M.F. induced in this loop will be : e„=KiB„ssin/'Ki^+ a + (f^-Hll^Y \ tn J MOTORS lit, The current will be given by the equation i„ =^iIe1 cos V- sin (k, ^ + a + (^-')" -A. r \ ml tan o being equal to — ! = — !— , putting l for 2 r r 2 The electrical power wiU be : sin ( K ^ + a + ^ '— I — — - — cos sin ( K ^ + a + ^ '— ) sin Since sin a sin ^ = ^ < cos (a — ^) — cos (a ■>r b)\ we get : i < cos — cos j 2 Ki ^ + 2 a ..,; = al!dl", +->^_,)}, The total electrical power will be the sum of the powers in the m loops. Remembering that the sum of the cosines of m angles, which form an arithmetical progression of which the common 2 TT • ratio — , IS equal to zero, we shall obtain the expression for m the total As power p_^B„2 2 r cos^ f = -Kj^COS^f I I + tan^ qi p _mBj's^ ^ 2 r _mBj's^ ^ i+- /-x . ^' Since the power is equal to the product of the torque into the angular velocity, we get for the torque the expression T = ° K, COS'' 0, ii6 ALTERNATE CURRENTS The power is expressed in ergs per second, and the torque in ergs if all the other values are expressed in C.G.S. units. It is easy to see that inversely if a uniform magnetic field revolves with a velocity Kj round an armature formed as described above, it will give rise to a torque for which we have just given the expression. Asynchronous Motors with Revolving Field. — The uniform field revolves in space with a speed k equal to the angular velocity or pulsation of the current (k = 2n- f), and the armature revolves with a speed k', so that on the whole the field revolves round the armature with a speed Kj = (k — k'). As proved above, the torque of the motor will be : ^ _ ^B„^s' ^ K — k' /•'' + (k - K')2 \? = K - K' ^?^5!l! cos'' 0. 2 r The power of the motor or the work done in the unit of time will be (since the angular velocity is k') : m b/ s^ k — k' P = K'"'°- ".r /-" + (»- k')*l2 = k' (k - K') ^Jfil" cos2 0. The current in the «'•» turn of the armature is : 4 = 'ElAIcos sin ^K, /■ + a + (^-')^ - ,i\ ^ \ m ^ ) The effective armature current, which is the same in all the turns, will be : / = 'iiJi!cos^ = (5z£)Mcosf V2/- s/2r The loss of power in consequence of the resistance of the W loops will be : ^ MOTORS 117 If only the armature loss is taken into account, the efficiency will be: p _ k' (k - k') _ k' P + p^ ~ k' (k — k') + (k — k')^ k ' The efficiency will therefore be the higher the nearer k' is to K — that is, the nearer the motor is to the speed of syn- chronism. The expressions for the torque and the power may be put in another shape. If the field-magnet possesses n turns, traversed by currents of maximum intensity i, we shall have 2 This expression is the resultant intensity of all the components of the fields produced by the turns all round the periphery of the field-magnet, taken in the direction of *„ (fig. 141). *" is the intensity of field created by a current of unit value passing through one turn of the magnet coil. b„s will be the coefficient of mutual induction of an armature and field-magnet loop when in parallel planes ; if we designate this coefficient by M, we shall have : T = (K-K')^M2cos2di2 m n^ .a K — k' , = '-^^-^ M^ r 2 8 r2 -h(k-k')''l' The currents, circulating in the armature, give rise to a field which revolves with the same speed as the main field, and is retarded behind the latter by an angle (~+f\- The intensity of this field is given by the equation : , m b' b/ = X, 2 b' being the intensity of the field created by unit current circula- ting through one loop of the armature. 1X8 ALTERNATE CURRENTS We get then (x being the maximum value of the armature current) : X = (k - k') ^"^^ cos = (k - K') ^^cos^i and b; = (k - K') ^^-^ b' cos ^ i Suppose the n loops of the field-magnet to be traversed by polyphase currents, such that the field-magnet loops make angles of - with each other, and the currents in the loops are n. retarded in phase by an angle - behind each other, the /*'' loop n will be traversed by a current of which the intensity will be : if = I sin (k / -f- -^ ^ TT y I being the maximum value of the polyphase current. The field created by the field-magnet coils makes with this loop the angle : n so that the armature field will make the angle : n 2 If s' be the surface of a loop of the field-magnet, the flux of induction will be : b/ s' sin /'k / -1- ^^Ll ,r - - - 0") = \^ n 2 V — B„' S' cos (k t +- ^~ ^ TT -fV and the induced E.M.F. : e„" = — KB/s'sin/^K^H--^-^^ JT — ^V The impressed E.M.F. at the terminals will be : e„ = E„ sin fKi+ ^-^Ll ^ 4. e V MOTORS 119 The E.M.F. of self-induction will be (if / is the coefficient of self-induction of one of the loops of the field-magnet, and if we put l' = — , l' being the resultant self-induction ol the n loops) : (•,'= — K L' I cos ( K / -t- ^ ~ TT — ^ J r' being the resistance of one loop, applying Ohm's law, we shall have : «» + «»' + «»" = r' i„ or E,sin ^K / +^^^ r + e^=z kbJ s' sin fKt+^-^ZJ. tt - 9 ^ Making in this equation f Kt + P ~ ^ ) = o, and also { K / -I--? J = -, we get two equations, from which we can determine fl and i, the two unknown quantities (e„ the maximum value of the impressed E.M.F. being known). Thus : 5, sin = K l' I — K B,' s' sin E„ cos = KB,' s' cos + r' I. Replacing b,' by the value given above and noticing that b„' s'=m, the coefficient of mutual induction of a field-magnet loop and an armature loop, situated in the same plane, we shall have ; E^, sin = [ K l' — K (k — k') '— M^ sin ^ cos ^ j I E.cose = ( k(k — k') ^-?m*cos^^ + r ji. The power supplied is 2 ? COS e = { k(k - K') ^M«COS»^ + 1 h" 120 ALTERNATE CURRENTS The total power supplied to the motor will be n times as great, since it is formed of n loops : P^ = «5iicose = I K (k - K') ^M^cosV + ^ } ^' The useful power will be : P„ = k' T = k' (k - k') '^ M^ cos« l2.. As r' will be very small, the quantity ni^ ^P■ may be neglected and the efficiency will be : k' — , as we have seen above. K Squaring and adding the two above equations, and assuming that M^ = //' (that is to say, that all the lines of force created by one turn of the field-magnet pass through a turn of the armature), we arrive at the equation : a _ y' + (k - k')^ \? 2 At starting we have : We should find the same expressions if we assumed that the field- magnet consisted of n loops, making angles of — with one n another, and traversed by polyphase currents retarded — from n loop to loop. The torque may therefore be expressed as a function of E„, the maximum value of the E.M.F. impressed on the terminals of the motor by the following equation : ^^^ ..-i ^ K — k' T = -—— M^ r K- 8 ?-V2 -1- ((k- K')^L-|- K^L'}2 And the power : P = ^ mV K' i^ - ^) E 2 MOTORS 121 The angle of lag between the E.M.F. and current in the field- magnet circuits (the cosine of which is the power factor of the motor) will be found by dividing the equation for e^ sin 6 by that for E„ cos 9 as given above. We shall have (putting k — k' = Ki) : K l' — K K, M^ sm cos 4'' tan 9 = K K, M^ COS^ + '■^ (K — K') L Ki L Since : tan i4 = ^ '— = — !— r r ■ , , tan* Ki ?-L sm COS = 1-5- = -= — - — 5— „ ^ '^ I + tan* ?) r^ + Ki^ L* and COS = therefore tan = 4 As we have very nearly ; ,, ,„ ml , nl' , mn „ 2 2 4 we get : tan 6 = YLK^ri^iJ -\- r^r' f k,* r' l'^ Asynclironoas Motor with Simple Alternating Field. — Let B„ sin K t represent the intensity of the field at a given moment, and k' the angular velocity of the armature. Suppose that the field makes at the given instant the angle k! t + a with loop i, and consequently the angle k' / + a + tt with the rfi^ m loop. The flux of induction traversing this loop will be : N = B„ s sin K / sin I k' / + « + -t | V m J 122 ALTERNATE CURRENTS or noting that : sin a sin 3 = i < cos {a — b) - cos (a ■>rb)\ N = ?^rcos |(K-K')/-a-^^T J- cos < 1 2 It is easy to see that if we suppose the armature stationary it will be just the same as if we had : (i.) a uniform field of intensity — revolving with a velocity K — k' in the direction of the arrow c (fig. 134) and making aL the given instant the angle (k — k') / — a with the perpendicular to loop i. This field will make with loop n the angle - — (k — k') / + a + TT, SO that the flux of induction traversing MOTORS 123 this loop will be : ?^ sin { !: - (K - K')/ + a + ^^ll ,r 1 = 2 12 ^ »« J 5l^C0S ((K-KO^-a-'^^llTr'l. 2 I ^ mi (ii.) A second uniform field — , making at the given instant 2 the angle (k — k') / + a with the perpendicular to loop 1 and revolving in the opposite direction to the pre- ceding field. The loop n makes at the instant t with this field the angle : (K+K')t+a + 'L+:L:iI„. 2 m The flux traversing it is : liisin l{K+K')i + a+l + 1^U.r\ = 2 L 2 m i S^icos l(K + K')^ + a + ^-=Li,r ]. 2 I mi The torque acting on the armature will be equal to the difference of the torques due to the two fields. The torque due to the first field may be expressed as : m l~\ s'r K — K ^' = 2 r^ + (k - k')'' l2 and the torque due to the second field as : K + k' T, = 2 r2-|-(K-K')2L»' The torque acting on the armature will be : T = r K — k' _ k + k' 1 124 ALTERNATE CURRENTS and the power of the motor ; r-iW^ B„''sV / K-K' _ K + K^ \ 8 Ir2 + (K-K')^L2 !r2 + (K + K')^LM" The E.M.F. acting in the «"■ loop of the field-magnet will be : dt 2 \_ \^ ' mi -sin |(k + k')^-1- a + ^^TT j1 If r is the resistance of the loop, putting . . (K—K')mi (k— -kOl j^ , .(k + k')l tan ^1 = i i — = i i—, and tan <4o = i — - — '— 2 r r r the current will be : 4= ?£_5 ["(k - k') cos sin I (k-k') t-a- ^Hl TT-^i I - (k + K') cos (^2 sin j (K-l-K')if + a + ^Zin-— (^2 J1 = ^lif i (k— k') cos 01 sin o — (k + k') cos ^j sin /3 > 1. The instantaneous value of the work lost owing to the resistance of the circuit will be : riJ = b/ s^ 4'- ["(K-KO^cos^^isin^n - 2 (k-k') (k + k') COS 01 cos 02 sin a sin /3 + (k + k')^ cos^ ^j sin* jS] , As Sin^n = 1 (l~C0S2a) sin a sin (5= I {cos (a— (5) — cos (a + (5)} ; if we sum up the values of ri^ for all the n loops, remembering that the sum of the cosines of m angles, forming an arithmetical progression of which the common difference is — , is equal to zero m ^ ' we shall have : S^4= = ^{cos*y. + cos*02}. MOTORS 125 The instantaneous value of the work lost in the armature is con- stant, and is equal to the power lost ; we have then : / (k-kQ" (k + kQ^ 1 ' 8 The efficiency, only considering the loss in the armature will be : Substituting their values for p + p^ and simplifying, we shall have finally : k' k^ 1? — k'* 1? — r^ R = K K* L* — k'^ l^ + r*' k' As r is generally very small, we may assume that r is equal to K The armature, as we have seen, is subject to the influence of two fields, one of which revolves round it in the same direction as it moves itself, with a velocity k— k', and the other which revolves in the opposite direction with a speed k+k', relative to the armature. Both fields revolve in space with a velocity k, but in opposite directions. § 6. Asyndironous Motors with Revolving Field As we have seen in the last section, if we only take into account the loss in the armature, the efficiency is given by the k' expression — ; consequently the nearer the speed, k', of the motor approaches to that of synchronism the higher the efficiency becomes. K— k'=Ki is called the ' slip,' and the ratio -, the 'coeffi- cient of slip.' In practice, we find as a rule : Kj =. '02 to '06 K K' = K — Ki = -94 to -98 K. The torque and the power are proportional to m^, the square of 126 ALTERNATE CURRENTS the coefficient of mutual induction, of an armature and a field- magnet loop in the same plane. It is important, therefore, to avoid as far as possible any leakage of the flux of induction from the field-magnet coils, by making the air-gap as short as possible. There are two methods of distribution : (i.) The effective impressed E.M.F. is constant. (ii.) The effective current in the field-magnet coils is constant. The first is the more common system in practice. Constant Impressed E.M.F. at the Motor Terminals. — The torque is represented by the equation : T = — -- M^ r 8 r^r'^^ {Kiy'LH-Ki>-L'}2 " ' If we require the value of r, which makes the torque a maximum for a given .value of k,, we get If the torque is to be a maximum at starting, we must have K V 2 L^ r'- = /2 + k2l'2' It is easy to see that if ;^ > -^ 5—-, the torque will still be a r ^ -t- K-* I,"' maximum at starting, and we shall get a curve of the shape of No. I in fig. 135. (In this figure ordinates represent the torque, and abscissae the slip or k, : the dotted perpendicular at k shows the values of the torque at starting.) If we have r^ = ^2 . j^2^^/2 ' "^^^ tangent to the curve, at the point corresponding to starting, will be horizontal as shown by curve 2. If we have r^ < ^ ,^ , the curve will have the shape indicated by No. 3. If the resistance of the armature turns is calculated to give a maximum torque, when the motor is working at full load (k' nearly MOTORS 127 equal to k), in order to increase the torque at starting, we must be able to increase r, the resistance of one armature turn or loop. As in practice the motor rotates at a speed, k', nearly equal to K, i.e. K, nearly equals zero, it will be seen that the slowing down, due to a sudden increase of the load on the motor (which dimin- ishes k' and increases k,), will cause the value of the torque to increase, and the motor does not fall out of step so long as this increase of load is not excessive ; this, therefore, is another reason for running a motor at a speed near that of synchronism. The maximum value of the currents in the field-magnet coils is given by the equation : ,2 _ - r^ + K|^L 2 y^r'»-h {K.r'L-f-KrL'}!' °" Solving this equation with respect to k,, we see that the sign of the root varies as Kj^ r' L* + K Ki r L l' — /^. When Kj = o, the root is negative. If Ki increases, the root has zero value when ^ _r^/K«L'»-t■4^- kl' Ki J , 128 ALTERNATE CURRENTS We can then construct motors for which the effective current at starting is a minimum : a value of r must be taken such that K], as determined by the above equation, is equal to k. We can also determine r so that the current at starting is equal to the current at full load, its value being a minimum for an intermediate load. In such motors the torque and power at full load are small, and the motor is very heavy in proportion to its output. In order to increase the power at full load (i.e. when Kj is small) r must be made very small : under these circumstances, we get a minimum current in the field-magnet coils for a very small value of k,, in fact so small that it cannot be reached in practice, for on account of the passive resistance k' always diflfers from K. Practically, then, in such motors the effective current in the field-magnet coils increases with Kj and is a maximum for Kj = k, i.e. at starting. It may then reach too high a value, and cause fluctuation in the distribution network. We can diminish the current at starting in two ways. (i,) By increasing r' or l' which only occur in the denominator of the expression for the value of i^ in terms of e],^ : for this purpose rheostats or self-inductive coils may be inserted in the circuit of the exciting coils. As in motors with small armature resistance, the torque is already small at starting, we thus diminish it still further (r" and l' occurring also in the denominator of the expression for the value of the torque as a function of e„), so that we may under certain conditions get too small a torque altogether. (ii.) By increasing r the armature resistance by means of a rheostat : in this case we increase the starting torque under certain conditions. We shall see further on the inconvenience of this arrangement in practice. In this case we gain the advantage of being able to vary the speed, by varying the resistance r, as will be seen on examining the formula. M. Boucherot has invented a device, which allows of a larger current in the field-magnet coils, without the line current reaching too high a value : we shall examine this arrangement in another section. MOTORS 129 The angle of lag in the field-magnet coils is given by the expression : K T^ \! tan ** = -, i— r-^, 9-7 ') K Ki r L l' + Ki^ r I.- + r'r 6 therefore decreases as k, increases. Within the practical working limits of a motor, Kj increases with the power ; therefore the lag decreases and the power factor cos increases with the load, which will readily be seen on examining the curves of different motors, given below. Constant Effective Current in Field-magnet Circuits. — In this case, which very seldom occurs in practice, we get : 8 r^ + K.^L^ If we find the values of r, which makes the torque a maximum for a given slip, k„ we get the expression : If we have then r > k, l, the torque will be a maximum at starting (curves i and 2, fig. 135) ; if r < k, l, we get curve 3 of the same figure. Within the practical working limits of the motor (k' nearly equal to k), the power and power factor will increase with k,, i.e. as k' decreases. M. G. Roux has given different curves taken from biphase motors. Fig. 136 represents in abscissae the torque expressed as pounds at the end of an arm one foot in length and in ordonnates the values of the currents. Curves a are taken from a 10 h.p. motor, and curves b from a 5 h.p. a, shows the effect produced by variations of the resistance inserted in the armature circuit on the value of the torque, the potential difference being kept constant ; Aj represents the variation of the torque as a function of the current for a variable difference of potential, the resistance being fixed in value, and of such size as to give a very powerful torque ; A3 is similar to Aj, but the resistance has been increased so as to obtain a very small torque. The torque corresponding to full load is 35 lb. x 13 inches. 136 ALTERI^ATE CURRENTS Bi, Bj, B3 are similar curves of a 5 h.p. motor of which the torque at full load is 17-5 pounds. On examination of the curves, it will be noticed that motors working under the conditions of curves A3 and B3, in order to exert at starting a torque equal to that of full load, only require a current considerably less than at full load, and that for a current of the same value the starting torque is double that at full load. 100 30 80 70 to" 1 *0 30 20 10 / r / ' 1 ^ y 1 / / ^- / / / / 'i \/ / f / / f / / i f / ^c -^ n / / / y X / / -', r ^ X y- *» / ^ * * / y ' ■y y y^ ^ f y y^ y' f^ f^ A S ,' *B 3 Full lead B Full load A. Torqtie in lb-feet 10 20 30 $0 Fig. 136 50 gT 70 80 Fig. 137 shows the variation of the power factor cos as a function of the load for two types of triphase motors. Curve A is taken from a 15 h.p. motor with four poles, working at a frequency of 50. Curve c shows what a high power factor may be obtained in a well-designed motor. At full load this reaches 90 per cent, for the 15 h.p. motor, and 94 percent, for the 10 h.p. At half load MOTORS 131 the power factor is still very high, being 84 per cent, in the case of the 15 h.p. motor, and 75 per cent, for the 5 h.p. motor b. lOf) 90 s 30 i< < 60 S N BQ ^ ,to SO ^ ti; 20 10 ..... C 1 4 ^ B / y ^ i r / / / / / 1 / }/ 1 JiiJoyvatti. 1 Z 3 4' 5 6 3 Fig. 137 8 9 10 11 \i The importance of the power factor will readily be perceived by studying the curve of current as a function of the power. In .so xn 70 y y S60 B / /* .so 1 ^.y /' Y ^ ^ ^ 20 ^X X in i lOV rsU » t i ' \ K ) . J S r 1 1 1 12 Fig. 13S fig^ 138 curve A is that of a 5 h.p., curve b of a 10 h.p., and curve c of a 15 h.p, motor. K2 132 ALTERNATE CURRENTS The field-magnets are wound so as to produce a revolving bi^ or triphase field. As, at their usual rate, the speed of these motors is almost that of synchronism (n, = n — ijN, i) varying from '02 to "05) motors of large size must be multipolar, the number of revolutions being given by the equation : 60 F / ■, Ni = N — ij N = (l — J)), F being the frequency and/ the number of pairs of poles. The armature, consisting of a drum or ring of laminated iron, is wound either ring or drum fashion, but in any case in such a manner as to obtain closed circuits (in which if necessary starting rheostats can be inserted). mniiii'iiiiiiiiiiiiiriiirMiiiimit -EEE \ Copper ring \ I Pnmiiini in jii|I|iiiit Fig. 139 Another system very often employed is due to Herr Dobrowolsky : the armature is formed of equi-distant bars, placed on the periphery of a laminated iron ring, as near as possible to the air-gap. (Fig. 139.) These bars are connected at their ends by two copper rings : the result is a mouse-mill armature of very small resistance (r resistance of one loop is equal to twice the resistance of one bar), but in this case it is not possible to insert a rheostat for starting. In small motors, the armature may be formed simply of an iron or copper cylinder : with this construction there are large Foucault current losses, and the armature currents are not confined in such a way as to flow in the direction in which their action is a MOTORS '33 maximum. The efficiency of such motors is very small, but on the other hand they are easily and cheaply constructed. The field-magnet may be stationary and the armature revolve, or vice versa. When the armature revolves and its turns are completely closed on themselves, the motor does not carry any brushes ; the starting rheostat must then be inserted in the stationary field-magnet circuits. If it is desired to insert starting resistances in the armature circuit, rings are fitted, to connect the ends of the different circuits to the starting rheostat. When the motor has reached full speed, these brushes are short circuited. When the field-mag- net revolves, the currents are conveyed by brushes rubbing on rings : it is easy in this case to in- sert starting resistances in the stationary arma- ture circuits. In large motors it is an advantage to have the field-magnet in the interior of the motor, for its volume is thereby reduced to a minimum, and the hysteresis losses are diminished. In fact, the hysteresis losses are greater per unit volume in the field-magnets than in the armature, since the current reversals in the former Copper bar » Iron bar Copper ring Fig. are more frequent than in the latter \ 2 T • K — K' In motors of large power (above 3 to 5 h.p.) starting rheostats are used, unless a special construction is adopted. In small revolving field motors, which possess neither rings or brushes, no starting rheostats are used : the armature is made of such resistance as to prevent the field-magnet current reaching a dangerous value. 134 ALTERNATE CURRENTS For this purpose, the following is an excellent method of building the armature : as shown in fig. 140, copper bars are MOTORS I3S placed on the periphery, being sunk in the iron core as usual, but the connecting rings at the two ends are of very small diameter, and are joined up to the bars by conductors of soft iron, as long as possible : these iron conductors are of sufficient section to present only a small resistance to continuous currents, but on account of the self-induction their impedance increases with the Fig. Z42 frequency. At starting, the frequency being very high, these conductors possess great impedance, whilst at full load, the frequency being small, the impedance diminishes. We shall now give some details of the different revolving field motors which are most used, classing them in alphabetical order. Brown Motor. — The Wehyer and Richemond Co., who work the Brown patents in France, build more especially biphase motors (figs. 141 and 142). The stationary field-magnet is 136 ALTERNATE CURRENTS provided with a drum winding : the armature may be in the form of a mouse-mill, or may possess (for 6-pole motors) a triphase winding terminating at three rings which communicate by means of three brushes with a triphase rheostat. In motors with a mouse-mill armature winding, M. Boucherot employs the following device (fig. 143) : across each of the circuits a self-inductive coil is placed in shunt. When these coils are wound at the factory, several eyelets a, b, c, d are soldered to the wire of the coils, so as to allow of more or less turns being put in circuit at starting according to the torque required for moving the {--E*!rti^*., Fig. 143 machinery_to be driven. As a result of experiment an eyelet is selected which allows of a sufficiently rapid start without the line current reaching a dangerous value. It may therefore happen that the line current at starting is less than the full load current, or, at least, very little greater. When the motor reaches its normal speed, the self-inductive coil is short-circuited and the motor connected direct to the net- work. In the self-inductive eoil, the effect of the self and mutual iriduetion may be such as to produce in the field-magnet coils a current considerably larger than the hne current. The greater the number of turns in shunt of the self-inductive- MOTORS 137 coil, the greater is the starting torque, but the line current is also greater. Fig. 144 gives the curves of efficiency, lag, speed and effective current in the circuits of the field-magnets of a biphase revolving field motor of 15 to 20 h.p. The number of poles is six, the frequency 40, and consequently the speed of synchronism is 60 X 40 _ N = - = 800 revolutions per minute. b s «, R| 80 Oj «D «0 0.6 «0 'm W M «0 200 20 02 20 L_ -tff^ ■ 7 \ Spt ed ■ / — A i\ / \ ^ A Y f^ y / y ^ X ^^ ^- — 4000 . 8000 12000 Watls at the Pulley Fig. 144 ISOOP Fig. 145 gives the efficiency, speed, useful and total power, as functions of the pull in kilogrammes at the periphery of a pulley 12 cm. in diameter, taken from a biphase motor with four poles of i^ h.p. The speed of synchronism is : 60 X 40 N = - = 1,200 revolutions per minute. M. Boucherot employs the following very ingenious methods 138 ALTERNATE CURRENTS of measuring the current of each phase in the field-magnet circuits, the lag and the efficiency. The current in each phase may be read on an ammeter, but on account of the great oscillations, M. Boucherot prefers the method indicated below, which allows of determining the lag at the same time. The thick wire of a wattmeter is connected to a two-way switch, which allows currents of both phases to pass through the wire : the fine wire is also connected to a two-way switch, allowing 1,1 Speed ^ ^^ ^ ^ 1^ y 06 2900 600 2 ^ X / 4« •Y > / ,^ / f i^:^ r. 1> / x \> ^ 0' 10 20 Xiloapammes Fig. 145 30 In this it to be put in shunt across the terminals of either phase, way four readings can be taken for any given load. If E„', I,, Oj are the effective E.M.F., effective current and angle of lag for one phase ; e/', I2, 62 the corresponding quantities for the other phase ; and c the constant of the wattmeter, we get : ^1 =f e/ ii cos 01 S2 = ^ E„" I2 cos 02 ^3 = ^ e/ I2 cos (e^—-\ =c e/ Ij sin 62 ^4 = (T e/' I, cos ^0,-^^ =cE/'i,sin 6,. MOTORS 139 We can easily find from these four equations (knowing e/ and e]" which are equal to one another, as also are ij and I2, 9i and ^2) the values of the effective current and the lag in each phase. The losses in the motor consist of : (i.) Ohmic losses in the field-magnet circuits, which are easily determined by measuring the hot resistance and knowing the effective current for a given load. (ii.) Losses due to armature resistance. (iii.) Losses through friction, hysteresis and eddy currents. The ohmic loss in the armature cannot be directly determined in an armature of the mouse-mill type. We have seen that if p^ is the loss in the armature, and p the power at the pulley (increased by friction losses in the bearings) we get : P _ k' _ K — K, P -I- Pj, ~ K ~ K ' K, or P< = P K — K, We can therefore determine Vp if we know p and can determine K and Ki. For the latter determination two people equally skilful take simultaneously the speeds of the motor, and of the alternator which drives it. With regard to the determination of the losses by friction, hysteresis and eddy currents in the field-magnets, it is to be noted that the induction is almost constant, whatever be the load, and that for every load this induction is equal to that which produces at no load a counter E.M.F. e — ri. If, for example, the voltage when running is 100, and the field- magnet circuits absorb 2 per cent, for a certain load, the losses due to friction, hysteresis and eddy currents at this load will be equal to the power taken by the motor when revolving at no load with (100—2) = 98 volts at the terminals. As a matter of fact this power is a little greater than the loss, since the armature revolves a Uttle faster on open circuit than with a load. This power is measured by a wattmeter. The efficiency measured in the manner we have just described is slightly smaller than is actually the case, for the reasons given 140 ALTERNATE CURRENTS above, and also because the wattmeter employed to measure the power on open circuit may indicate more than the true power on. account of the self-induction of the instrument. Measuring the efficiency by the ratio of the power absorbed in the brake to the power supplied, for a i^ h.p. motor (fig. 145), and also by the s^arate losses, M. Boucherot has obtained the follow- ing results. Load in b.p. Efficiency By the method of separate losses By the brake 0-5 i-o 2'0 3-0 •52 ' -55 •67 -67 •76 ! 76 ■75 ' -63 We see that, except for a considerable overload on the motor (double the normal power), the separate loss method gives rather smaller efficiencies than the brake method. Creusot Biphase Motors. — The stationary field-magnet (fig. 146) is similar to that of a Ganz alternator : the coils in each phase, connected in series, are wound alternatively in opposite directions, and the coils of the two phases alternate with one another. If 4 « is the total number of coils, and f the frequency, the number of revolutions at the speed of synchronism is given by the equation : 60 F The armature is formed of a ring of laminated iron, provided with grooves on its periphery. The winding consists of flat coils, of spiral form (see the Labour alternator), the outside turns embracing two teeth of the armature ring. In the first layer, there are 2 n coils (for 4 n poles) connected in series and wound alternatively in opposite directions : above this is placed the second layer of coils, exactly similar to the first, but in advance of the latter by half the interval between 2 poles. There are there- fore in all 4 n coils forming two series. MOTORS 141 Two of the ends of the wires of the two series of coils are connected together, and the common wire is joined to a collecting SSa.. ring. The two free ends of the two series of coils are connected by rings and brushes to two liquid rheostats, each of which has one terminal connected to the common wire. 142 ALTERNATE CURRENTS The liquid rheostats which are used for starting up, consist of a copper sulphate bath, into which dip vertically two metal plates which can be separated or brought into contact by means of a hand wheel. In the circuit of the wire common to the two series of coils, a little metal rheostat is inserted to vary the speed when running. The 30 h.p. motors employed at the Decize mines for working ventilators have i6 poles : as the frequency is 42, the number of revolutions at synchronism is : 60 X 42 , 4 The excitation of each pole consists normally of 1,350 ampfere- turns, and the corresponding induction in the cores is 4,500 C.G.S. units. The air-gap is -^ inch wide : the external diameter of the armature is 22 inches, and its length along the axis 12 inches. The grooves are f inch wide and i^ inch deep. The resistance of each of the series of coils, closed on themselves, is "05 ohm. The tests of these motors gave the following results : Efficiency at half load, 80 per cent. ; at full load, 88 per cent. When running with no load or with a small load, the motor started as soon as the rheostat was shifted. With a resisting torque, corresponding to the maximum power (30 or even 33 h.p.) at the normal speed, the motor started when the plates of the rheostat were an inch or so apart. At no load the speed is i per cent, less than that of synchronism, at half load 2-5 per cent., and at full load 5 to 6 per cent. At full load, at the end of a 6 hours run, the temperature did not exceed that of the atmosphere by more than 40°. The Fives-Lille Co. Motors.— The Fives-Lille Co. work in France the patents of the ' Allgemeine-Electricitats Gesellschaft,' of which Herr Dobrowolsky is the chief engineer. Small motors have a revolving armature with a mouse-mill winding and a Gramme-wound field-magnet : large motors have a stationary drum-wound armature and a revolving field-magnet. Small motors up to 3 h.p. are not provided with any starting device, but above 3 h.p. they are provided with a rheostat. MOTORS 143 The following table gives the particulars of some triphase Dobrowolsky motors. The frequency is 50 and the eflfective potential difference at the terminals 60 volts. The armature is of the mouse-mill type and there is no starting device. Normal horse power No. of revolution^ at full load No. of poles .... Slip at full load ^'. Weight in lbs. Current in j At normal load ! each phase |^^ ^^ j^^^ Power absorbed at normal load, kilowatts Commercial efficiency at full load Torque at starting in pound-feet 2,300 2 1 1,400 4 •29 •067 40 132 1-4 4 •23 ■SO . — ■71 — — I 1,375 4 •08 75 S i,39S 4 •07 207 539 20 ! 50 8 36 4-5 IS ■99 4-4 •84 37 I 187 50 8 •033 2,640 400 280 ISO 40-2 355 The temperature reached 40° to 50° for a 50 h.p. motor when running continuously. Herr Kolben, engineer of the Oerlikon Co., has made tests on a triphase motor of the ' Allgemeine-Electricitats Gesellschaft.' It was a 50 h.p. machine with 8 poles, provided with a mouse- mill armature, and supplied with current at a frequency of 50. The following are the results of the tests : "■tl-e" pulley Watts at the pulley Current in ampferes in each phase Volts between each cir- cuit and neutral wire True watts supplied to motor. Power factor Slip in % at full load Efficiency 60 42 20 44,160 30,910 14,720 318 252 ISO 125 60 60 60 60 48,300 36,800 17,700 •844 ■810 •65s 2% 1-3% ■91 •84 ■ •83 lahmeyer Motor. — The armature is stationary, and consists of a ring of thin laminated discs insulated from one another, provided with a mouse-mill winding. The revolving field-magnet is drum-wound, the turns being placed in grooves. 144 ALTERNATE CURRENTS The currents are conveyed to the circuits by means of three rings, on each of which two brushes rub. Fig. 147 shows the plan of connections of a motor at Bockenheim, working at a potential difference of 660 volts. The three line wires are con- nected to a little distribution board (one passing through an ammeter a) ; the circuits then pass through a switch and lead safety fuses, a triple-liquid rheostat r and a meter c, before being connected to the terminals of the motor. At Bockenheim, also, the Lahmeyer firm has installed revolv- ing transformers of 30 k.w. which transform triphase into con- FlG. 147 tinuous currents for lighting purposes. This transformer is an asynchronous motor, the revolving field-magnet of which is provided with a second winding connected up to a continuous current commutator, placed at the opposite end to the rings collecting the triphase currents. As fig. 148 shows, the winding is placed in very deep grooves, which are made in the periphery of the laminated iron ring which forms the field -magnet. At the bottom of the grooves is placed the field-magnet wind- ing H, which is traversed by the triphase currents ; on the top of MOTORS '45 the winding h the continuous current winding b is placed. In order to prevent, in case of a failure of the insulation, the low- tension circuits making contact with the high-tension circuits, a separators (consisting of copper-strip, insulated on both sides, and connected to the bed-plate) is placed between the two windings. The efficiency reaches 90 per cent, at full load, for the friction and hysteresis losses are a great deal less than in the case of two machines coupled together. The con- tinuous current generator works without sparking, and there is no need to shift the brushes when the load changes. Oerlikon Motors. — These motors are built with a sta- tionary field-magnet of ring- shape, wound Gramme-fashion for small powers, and drum- fashion for those of larger power. The armature is wound in either the mouse-mill or drum method (fig. 149). The Oerlikon Co. employ by preference the triphase system, and build high voltage motors. Fig. 150 gives the curves of efficiency and power factor for a 100 h.p. motor, with an i8-pole revolving field, working with a current of a frequency of 50 at a potential difference of 1,700 volts. Ordinates represent current per phase and percentage, while abscissae stand for h.p. (effective). The lowest curve is for current per phase, the next for power factor, and the highest for effi- ciency. The high-tension winding consists of wires, insulated by mica tubes, placed in grooves, in which they are held by wedges of insulating material. The armature is drum-wound with 18 poles, and the winding is divided into three parts. The speed at Fig. 148 146 ALTERNATE CURRENTS MOTORS 147 synchronism is 5_ = 333^ and the speed at full load 320 ; the slip, therefore,! is about 4 per cent. The following table gives the results of the tests of a 50 h.p. motor at a tension of about 100 volts. The number of poles was .007. 80 80 JO 60 m 30 20 10 JO 20 10 fO SO 60 W 80 30 WO 110 Fig. ISO eight per phase (speed of synchronism = 2 = 750), and 4 the armature comprised seven divisions closed on themselves. 101 3GC19 32(^8 S 28 0,3 ■^ 240,6 1, zoiis § IGOJ 1 1 — -A A |W»»p_ ^- -y / / t\,'\ S 1203 ^ f 80 2 / 01 / 1 1 1 I 11 Effective horse-power Voltage H.,at Watts at the Current ,■ in amperes between eadi ■ circuit Apparent watts True watts Power factor Slip in% Efficiency pulley pulley in each and the phase neutral wire A V A 53-8 39-600 180 93 50,220 42, TOO ■84 4% •94 46-0 33-900 158 % 45,000 37.440 ■«3 3% •90s O'O — 40 98 11,760 1,710 •I4S — Herr Kolben, engineer of the Oerlikon Co., has undertaken a series of experiments to determine the leakage of lines of force in a triphase motor — i.e. the number of lines of force which do not traverse the armature ; he thus calculated the ' factor of disper- 148 ALTERNATE CURRENTS sion,' i.e. the ratio of the flux of induction traversing the armature to the flux created in the field-magnet. The motor with a 6-pole revolving field, which was used for the tests, was of 9 h.p. The winding of the field-magnet consisted of 36 coils with seven turns each, and the winding of the armature of 90 bars placed in holes near the periphery ; these bars were so arranged as to produce six poles, and the whole number was divided into three independent closed circuits. To determine the leakage, the motor being stationary, the armature winding was replaced by an experimental winding, which passed through only 30 out of the 90 holes in the armature ; there were two wires in each hole, all the turns being in series, and a voltmeter was connected across the terminals. There were then for each phase 7 x 12 = 84 turns in the field- magnet, and 60 turns in the armature. By means of voltmeters Herr Kolben measured the E.M.F. in the field-magnet and the armature. The E.M.F. induced in the armature varied very little when its position was altered (by hand) ; the mean value found was 60-5. The E.M.F. in the field-magnet coils was 98 volts. If the flux had been the same in the field-magnet and arma- ture, the voltage would have been proportional to the turns, and if -i/ represents the voltage in the armature, we should have had : ?4 = 98 o, ^=98x60^ ^^Ijg 60 ^l-' ^ 84 ' Instead of 70 volts, Herr Kolben only got 60*5 volts ; the 'disper- sion factor ' was therefore : P, = ^=.86s. 70 There were, therefore, 135 lines of force lost by leakage for every 1,000 lines generated in the armature. This figure only holds for the conditions of the experiment — i.e. when no appreciable current is passing through the armature ; it will also be approxi- mately correct for the case in which the armature is revolving at no load, for then the armature current is of very small size. MOTORS 149 On the other hand, when the motor is loaded, the ampfere-turns of the field and the armature are much greater, the iron approaches nearer saturation, the magnetic resistance increases, and naturally the leakage also grows larger. To find the dispersion factor in this case, Herr Kolben ran the motot when provided with its ordinary armature, and placed a test coil of eight turns on one of the poles of the field as near as possible to the armature. He observed the E.M.F. in this coil for the motor revolving at no load and with full load. The fall of potential when the motor was loaded was an indication of the drop of the dispersion factor. The following table shows the results he obtained : No. of revolu- tions per minute Fre- quency of the current E.M.F. at the ter- minals Current phase E.M.F. induced in test coil Watts Disper- sion factor Arma- On a ture pole At rest At no load . At laj h.p. 980 930 so 49 49 9? 20'2 22 "3 45 '7 6o-5 26*0 24'5 36s 10,260 •86s ■865 ■815 The dispersion factor for the motor when overloaded was found by multiplying the factor at no load '865 by the ratio of the voltages of the test coil ^Al. 26"0 The efficiency of the motor overloaded to 12^ h.p. was 90 per cent., and the power factor — 10,260 3 X 98 X 457 •775- Siemens and Halske Motors The Siemens and Halske firm has built triphase motors of the type described below. It consists of a ring of laminated iron (fig. 151) on which three coils are wound ; these coils are supplied with the three currents — behind one another in phase. Inside this ring is placed a 3 Gramme ring provided with an ordinary commutator, on which rub three brushes connected to the three coils of the fixed ring. It <5o ALTERNATE CURRENTS will be seen that the inner ring is coupled in triangle fashion, and that there is developed in it a revolving field making one revolution per period, since the currents reach this ring at points which are fixed in space. In the fixed ring there is also a revolving field making one revolution per period. If the brushes are set so that thepoles of the two rings coincide with one another, the ring will not revolve. By setting them so that the two fields are not coincident radially, the rotating ring will revolve so as to bring its poles near poles of the opposite sign on the fixed ring : but it is easy to see that the commutator will assign a certain distance between the two sets of poles, which will depend on the position of the brushes. The speed of the motor A B D Fig. 151 Secti on AB I I ^ ^?g?S^ Section CD Fig. IS2 increases between certain limits with the angle of lead of the brushes, which are all carried by one rocker. Stanley Motors. — These motors are asynchronous motors with a double alternating field. They are designed to work on a secondary network at 500 volts and at a frequency of 133. As the current lag and consequently the impedance are considerable at this frequency, an. attempt has been made to reduce them by placing a condenser in shunt across each of the circuits. The condensers of the Stanley Electric Co. will stand with ease a tension of 500 volts. The field-magnet of ring-shape is formed almost exactly in the MOTORS 151 same way as the armature of the alternator made by the same company. This ring carries on its inner surface two sets of pole- pieces. (Fig. 152 shows the internal part of the magnet ring developed.) The axis of a pole-piece of one set corresponds- to the groove separating two pole-pieces of the other set. Each set, which consists of an equal number of pole-pieces, is excited by one of the two biphased currents, so that the two fields act on the armature like a revolving field. The armature is forihed of two drums of laminated iron with an interval between them, so that each one corresponds to one of the sets of pole-pieces (figs. 1153 .and 154). On the surface of the two armature drums teeth are cut out. In the hollows between these teeth, the armature winding is placed and held in position by bands. The winding forms two closed circuits in the case Fig. 153 Fig. 154 of small motors (up to 1,500 volts) ; in the case of large motors the circuits are closed through a rheostat. IJ each' ■ of 1 thai armature drums possesses 2 m poles, there are 2 M « grooves on the wurface of the armature, or 2 m consecutive groups of « wires b'ek)ngiiig '^alternatively to one or the other of the two sets, which each have therefore -m^ turns in series. In order to avoid fluctuations in the network, at the moment of starting small motors are run up to a certain speed by hand before closing the. switch. Motors of larger. power thanNi,5oo watts are started by means of rheostats. The two armature circuits, 'which have a common end, are connected to a double rheostat by means of three rings. The efficiency of motors of;. 7,50 watts is 70 per cent, that of motors of 3,500 watts 8q per cent., and that of motors of a power IS2 ALTERNATE CURRENTS above lo k.w. reaches 90 per cent. The slip at full load is high enough : it reaches 10 per cent, in small motors, and 6 per cent, in large motors. § 7. Asynchronous Motors with Simple Alternating Field. The torque is ^ _ mr^'^ b/ I K — k' K + k' 1 8 m being the number of turns on the armature ; s, r and / the surface, resistance and coefficient of self-induction of one turn respectively ; k the angular velocity of the current or 2 tt f, f being Fig. iss the frequency ; k' the angular velocity of the armature ; b„ the maximum intensity of the field ; and l = — . 2 If these values are in C.G.S. units, the torque is given in dynecentimetres or ergs. The power in ergs per second will be p = k' t. The torque is, therefore, zero at starting, and also for a value which is the nearer synchronism, the smaller ~ is. The torque is zero for a value of k' given by the equation : k'' l^ — k'^ l^ — r^ =. o. The curve of fig. 155 represents the value of the torque as a function of k'. It will be seen that it is necessary to work the MOTORS 153 motor somewhere near synchronism, for then an overload (which causes a drop in the speed) increases the torque, and the motor does not fall out of step. The efficiency increases with k' just as it does with asynchronous revolving field motors. The motor cannot start alone ; it must be run up till it reaches a speed k', higher than that which gives the maximum torque (fig. 155) ; if the torque is less than the maximum torque, the speed of the motor is accelerated until the normal speed is obtained. K k' The coefficient of slip — - is higher than in revolving field motors ; it varies from 4 to 12 per cent. As the expression for the torque is symmetrical with regard to K and k', we see that if the motor is started in one direction it will continue to turn in that direction, and this is confirmed in practice. The first asynchronous single-phase motor was exhibited by Elihu Thomson at the Universal Exhibition of 1889 ; the following description of it was written by M. Potier, chief engineer of mines, in the ' Technical Review ' of the exhibition. ' Six fixed coils, with a flat core of laminated iron, form the faces of a hexagonal prism, the edges of which are parallel to the axis, and receive the current from the generator. The spindle carries a system of six similar coils, which revolve inside the first set ; the two ends of the wire wound on these coils are connected, one to the equal segments, and the other to the unequal segments of a 6-bar commutator fixed on the spindle ; a pair of brushes rub on this commutator, one of which is joined up to one end of the fixed coil circuit, and the other to the generator, so that when they rub on the commutator the current traverses the circuit of both fixed and movable coils ; the direction of the connections is thus reversed six times per revolution in the rotating coil. If the machine is given a push with the hand, it will continue to revolve when the alternating current is switched on and its speed is accelerated. ' When the normal speed is reached (1,500 revolutions), the brushes are turned round until they make contact with two stops which short-circuit them ; the motion continues then in virtue of the reciprocal action of the current and the magnetism induced in the short-circuited coils of the rotating part. 154 ALTERNATE CURRENTS ' A special device ensures the short-circuiting- of the armature as soon as the speed reaches 1,500 revolutions. Semi-circular metallic segments, fixed on the spindle inside the commutator and held by springs, make contact with the commutator bars and close the circuit by the action of centrifugal force, when the speed reaches a certain value. ' When the machine hi&i)een started in this manner the brushes may be raised. The motor is not synchronous and continues to revolve with a less speed as the load increases, but it is not self- starting, and there is much sparking at first.' In 1 89 1 MM. Hutin and Leblanc built asynchronous motors for single-phase alternate current and gave the theory of their action. Fig. 156 Fig. IS7 Herr Brown and the Oerlikon Co. gave their attention about this time to the construction of this type of motor, and were not long in rendering them quite practical. The motor is formed of a ring-shaped field-magnet of laminated iron provided with either a Gramme, or drum winding ; it may be multipolar, and the speed is then reduced as in the. case of polyphase motors. The armature, which is generally inside, may be provided with a mouse-mill or drum winding, and may have a certain number of sub-divisions closed on themselves, producing as many poles as there are on the field-magnet, just as in the case of revolving field motors. MOTORS 155 Naturally, in order to diminish the air-gap, the wire on the inside of the field-magnet and on the outside of the armature are sunk into the iron.. Figs. 156. and 157 show a bipolar motor, with a Gramme winding on the field-iiiagnet and a mouse-mill armature. Figs. 158 and 159 show a drum-wound armature; the two opposite ends of the winding are connected by rings to the exterior circuit, in which a rheostat is inserted to vary the speed. As we have seen above, these motors are not self-starting, but when turned round a little they begin to revolve and soon reach the speed corresponding to the resisting torque. Small motors may be provided with a loose pulley and started by hand so that they may reach a speed sufficient to overcome the passive resistance ; they are then loaded by transferring the belt from the loose to the driving pulley. Fig. is8 Fig. 159 With large motors this method of starting is inapplicable, as the passive resistance is too large. Herr Brown has indicated several ways of starting in such case. The motor may be provided with a supplementary winding, placed in the intervals between the turns of the main winding ; when starting up, the current sent through this auxiliary winding is retarded in phase behind that traversing the main winding, so that a revolving field is produced which enables the motor to start from rest. As soon as the speed of synchronism is reached, the circuit of the auxiliary winding may be broken. . This auxiliary circuit may consist of conductors of small diameter. The ^retardation in phase between the currents in the two windings may. be obtained in different ways. iS6 ALTERNATE CURRENTS We may, as in fig. i6o, place in the circuit of the auxiliary winding a self-inductive coil, or, as indicated in fig. i6i, we may insert a condenser in circuit. Herr Brown uses for the purpose liquid condensers of the Stanley and Molly type. As is indicated by fig. 162, one of the windings may be arranged as a ring and the other as a drum : the self-induction in the first case is considerably larger than in the second case, whereas the resistance is smaller, and consequently the necessary lag is obtained. By these methods a powerful starting torque may be secured ; Fig. 160 Herr Brown was able to obtain in the case of a i^ h.p. motor a torque corresponding to 3 h.p. at the normal speed. Another method of starting consists in placing on the armature a winding, which is connected up to a commutator. According to the position of the brushes, the armature turns may either be put into circuit with the line current or short-circuited. When the brushes are set in the proper position, there is a very powerful starting torque. As soon as the motor gains its normal speed, the commutator may be short-circuited, either by means of a ring, which is slipped on to it, or by connecting by means of two MOTORS 157 brushes, in electrical contact with one another,two rings which are joined up to two points of the winding diametrically opposite to one another. This was the arrangement adopted by Elihu Thomson in the motor which we described above. In this case the winding of the field-magnet is simple, i.e. there is no auxiliary winding required ; but, on the other hand the armature must be provided with a- commutator, and must either be wound as a drum or ring or else like the Brush or Thom- son-Houston machines. Dr. Behn-Eschenburg, engineer to the Oerlikon Co., has designed a motor which can start by itself, and which does not require too high a current ; the speed and torque of this motor may be varied as widely as is the case with a continuous-current motor. The external armature (fig. 163) isformedofaringprovided with a continuous Gramme winding connected to a kind of commu- tator. The internal field-magnet is also a ringprovided with a Gramme winding and a commutator. The turns of both armature and field- 158 ALTERNATE CURRENTS magnet are naturally sunk in the iron on either side of the air- gap- The current is conveyed to the field-magnet through two brushes (b, Bg), which rest on the commutator ; a rheostat Rj allows of the regulation of this current. If the armature were provided simply with a continuous winding, no current would circulate, in it, as the E.M.F.'s would oppose one another. The commutator with which this ring is equipped arranges for the connection of two diametrically opposite points, Fig. 162 such as I — i', 2—2', &c., through a circuit in which a rheostat Rj is inserted ; currents then circulate in the two halves of the armature, so that a torque is produced and the field-magnet begins to revolve. The brushes Bi Bj are shifted so as to have as little sparking as possible, and, as a matter of fact, there is no more sparking than with a good continuous-current dynamo. The motor may have an internal armature and external field- magnet, but Dr. Behn-Eschenburg has stated that in this case there is a greater liability to spark. MOTORS 1S9 When the line of contact of the brushes b, and Bj of the field-magnet make with the line of contact i — i' of the armature brushes an angle between o° and 90°, there is a torque the value of which depends on the armature and field-magnet currents (which can be regulated by rheostats), and on the angle just indicated. This torque may be large enough for the motor to start under load. Under certain circumstances, the torque increases with the speed, and the brushes may then be set so that the two lines of contact are coin- cident. The regulation of the motor can be effected without using rheostats or shifting the field-magnet brushes, by simply altering the points of contact of the armature brushes. ■ There is no limit of speedy and Dr. Behn- Eschenburg has succeeded in run- ning a 6 h.p. motor -of this type with a current very httle. larger than the mag^tjsatiQn current,- the speed varying from zero to double that of synchronism. The efficiency of this motor is at least as high as that of an ordinary a^yiichrpnous: motor. If i^ apci- 12 r;epresent the cur- rents in thei field-magnet and armature respectively ; a the angle between the two lines of con- tact ; N, the number of revolutions of the motor ; n the number of revolutions when at the speed of synchronism (n = 60 f) ; p the impedance.of ^he armature circuit ; r its ohmic resistance, and / its coefficient of self-induction ; m the coefficient of mutual induction between field-magnet and armature ; r the ohmic resistance of the field-magnet circuit, and l its coefficient of self- inductioii, the torque is given by' the equation : T = J- r < 2 TT N, cos'' a -f ^ (2 ?r n)' / sin 2 a > Fig. 163. i6o ALTERNATE CURRENTS the value of ij^ being : i,* = where z^'' =/^ sin^a 4-/i^ cos' a ^ ^ 2 TT N ^i = 2!rNi. This expression shows well the relation between a, r, and r, as well as the eifect of the speed of the motor. MM. Hutin and Leblanc employ the following device for starting a single-phase asynchronous motor : Between the rotating armature and the field-magnet is placed a laminated iron ring, provided with a mouse-mill winding : this ring is loose on the spindle. At starting a push is given to this ring, which begins to revolve under the influence of the field, which rotates in the same direction as itself and soon reaches the speed of synchronism. The second revolving field, produced by the alternating field, is stationary with respect to the ring : it acts on the armature, which starts of itself, like that of a polyphase motor, and begins to turn in the opposite direction to the ring. It will be seen that the ring acts as a screen. M. Boucherot, of the Wehyer and Richemond 'firm,' has instituted tests of efficiency of single-phase asynchronous motors. He emplpyed for the purpose biphase motors of the Brown type : he only used the winding of one phase, that of the other phase serving for starting (the current in this winding was retarded in phase by means of a liquid condenser). The curves of fig. 164 give the results of tests for a motor weighing 1,144 lb., which had an output of 12 — 15 h.p. when only one phase was employed as against 17 — 20 h.p. when two phases were used. The efficiencies were obtained by the method of separate losses, and are consequently 2 or 3 per cent, too high. The same remark appUes to the figures for the little motor in the following table. Both methods were used in this case, and the difference is due to the MOTORS i6i fact that the efficiency of the armature is not exactly proportional to . COO S9 oj la SOO 60 as 120 «00 to Xii 80 200 20 n «0 - 1 1 Efficiency u V Speed / 7^ \ s^^ y 1 Sw ,A / N vri Y y "^ ^ y Wat tsai theph lUy £000 Fig. 164 6000 dOOO UOOO Load of motor Efficiency By method of sepa- rate losses By ratio of watts at pulley to watts supplied Ah.p. 1 .. 2 „ -715 .685 •56 •6s •68 •SO The curves in fig. 165 are taken from a little motor weighing 264 lbs. with an output of 1^ — 2- h.p. with one phase, and 2 "4 — 3 h.p. with two phases (the curves of fig. 145 show the working of this motor with two phases) ; the abscissae, are propor- tional to the effort in kilogrammes at the periphery of a pulley 12 cm. in diameter. M 1 62 ALTERNATE CURRENTS The following table gives the results of tests made by Ricardo Arno on a 15 h.p. motor, without contact rings, and without any device for reducing the current at starting. The motor had six poles, the normal frequency was 40, so that the speed of synchronism was ?^^ = 800. The frequency during the tests 3 was more than 40, and the E.M.F. at the terminals about 150 volts. The test was made by loading the motor by means of a brake. Number ofrevolu- tions per minute Watts at the pulley True watts Volts 1 1 Apparent watts Power factor in% Effi- ciency in% 17.595 132 150 19,800 89 876 688 157 27 4.252 16 862 574 1.173 156 27 4.303 27 49 863 1.943 2,652 15s 31 4.770 56 73 866 2,87c 3.774 157 36 5.634 67 76 868 4.136 S.I 76 156 42 6,520 79 80 863 S.08S 6,171 154 47 7,307 84 82 86z 5.652 6,732 154 51 7,792 86 84 859 6,940 7,854 152 57 8,694 90 88 858 7,728 8,823 151 64 9,634 92 88 856 9,980 11,398 149 82 12,218 93 88 851 11.385 13.923 146 102 14,943 93 82 812 11,886 15.478 143 It8 16,903 92 77 816 12,320 16,626 144 128 18,432 90 74 Herr Kolben has undertaken a series of tests to determine the dispersion or leakage factor ; he employed the same motor as for the test with triphase currents : the 36 coils of the field-magnet were all connected in series. The frequency was 50, the impressed E.M.F. 180 volts, the current 18.8 ampferes, and the power absorbed 432 watts. The E.M.F. induced in the test coil of the armature, which possessed 60 turns, was 54 volts in certain positions ; in other positions it was smaller, and in some it was zero. Tracing the curve of this E.M.F. he obtained a sine curve, and the effective E.M.F. was therefore — = 34^4. The dispersion factor was therefore 34:4 _.8_ 252 60 180 MOTORS 163 For 1,000 lines of force generated in the field-magnet, 800 passed through the armature. When the motor is loaded, the dispersion factor is smaller than when triphase currents are used. as 1800 18 300 oi UOD 12 eoo (13 (00 6 300 / J / ■ Sj, '7T~ — . / 7^ >v / / c^ / A iM. Icipd^ ' <- / / y X "^ 7 K\ / Y I- 6 12 18 Tfnn ip'fnmne.s Fig. i6s 20 The following table gives the results of tests made by Herr Kolben on a 3 h.p. Oerlikon motor at a frequency of 50. H.I).at the pulley Watts at the pulley Current in field- magnet Voltage at ter- minals \pparent watts True watts Power factor Slip % Effi- ciency % 3-6 2,650 45 lib 112 4.95° 2,440 3.776 76 ■168 4-S 70-S The two curves of fig. 166 give the results of tests made on a 2 h.p. Oerlikon motor, designed for a frequency of 42 periods. M 2 1 64 ALTERNATE CURRENTS too 90 80 30 ^ 50 I 50 30 20 10 >< ,yiods, ^: ^k\ U— "^ s, . .-^^ '■so ■prioa^- ^- °' zoo im 600 800 1000 1200 IfOO IGOO Useful power in watts Fig. i66 § 8. Motor Design The design of synchronous motors is exactly similar to that of alternators, but it should be observed that the lag of the current behind the E.M.F. tends to reinforce the field instead of diminishing it. It is impossible to design asynchronous motors straight away, for it would be necessary to determine beforehand the coefficients of self and mutual induction. We shall adopt the indirect method due to Herr Kolben, which yields very satisfactory results in practice. The field-magnet is wound either as a Gramme ring or a drum, while the armature is provided with either a mouse-mill or drum winding, closed on itself and producing as many poles as there are on the field-magnet. We must determine the dimensions of the iron core of the field-magnet and armature, the number of turns and the cross- section of the winding, and, lastly, the efficiency of the motor, the following data being given : The frequency f ; the number of phases j?i (rn being equal to i for a single-phase motor); the effective E.M.F. at the terminals e in volts ; the useful power in watts w ; the approximate number of revolutions n„ ; and the factor of slip ~ (varying from 1-5 to 6 % for a polyphase and from 4 to 10 % for a single-phase motor). MOTORS 165 Determmation of the Number of Poles and Diameter of Rotating Fart. — In fig. 167 (which gives the plan of a 4-pole single-phase motor or a biphase motor) let d be the external diameter of the armature ; x the width of the field-magnet and armature (which is the same) ; y the radial thickness of the field- magnet ring. We must first determine the number of poles of the motor according to the maximum speed admissible. We get 60 F . 60 F P N„ Na being the approximate number of revolutions when syn- as Fig. 167 chronism is reached and 2 p the number of poles of the motor. The table given in the section on alternator design may be used for this purpose, substituting/ for c. Naturally we shall take for N^ the whole number nearest the value found and deduce the exact number of revolutions at synchronising speed n,. If - is- the coefficient of slip, the number of revolutions of o the motor at full load wiU be g \ gl g If, for example, the slip is 4 % we shall have i^ 4 _ j g 100 25 1 66 ALTERNATE CURRENTS and the number of revolutions at full load will be The diameter d of the rotating part will be determined by the condition that the peripheral speed Vj does not reach a dangerous value (for a laminated iron ring Vj must be between 50 and 80 feet per second). We shall get, therefore, The diameter Dj of the stationary part must nextbe found, allow- ing as little clearance as possible/ As the conductors are usually sunk in the iron, the clearance may be reduced to -^-^ or \ of an inch, even in large motors. We can now make a sketch of the motor and determine the number, b, of coils per phase (we shall generally have b=-2p). The total number of field-magnet coils being m b, the length / of one coil, measured along the air-gap, will be I m b-=ir D^ or /= i m b in the case in which the armature rotates. In the case in which the field-magnet rotates we shall have ml) Determination of the Section of the Field-magnet Wire. — To determine i, the current per phase at full load, in an accurate manner, it would be necessary to know the current lag, but a sufficiently accurate approximation can be arrived at in the following way : it will be safe to take i, a certain per cent, larger than i„ the effective current given by the equation : ii = w 17 m e' in which w is the power in watts, 17 the efBciqncy, and e the effective E.M.F. in volts. 17 may reach -95 — "90 for a polyphase motor of large power, MOTORS 167 and "8 — "65 for a smaller motor j in the case of a monophase motor, -q varies from '9 — "6, according to the output. We have i, = ij' i, ij' being the power factor at full load, which may reach the value "95 for a single-phase motor and "90 for a polyphase. The current density /i in ampferes per square mm. may be taken between -5 and 2*5. The smaller t^ is, the greater the efficiency, but also the greater the prime cost. The section of the wire in sq. mm. will be given by the expression I s ^~. «i The diameter d^ of the wire or the section ^i of the copper ribbon will be chosen,. so as to approximate as nearly as possible to the value found by means of the above equation. The resistance of the wire in ohms per cm. of length will be given by the following expressions, which apply only to pure copper at a temperature of 60°. •00021; -0002 '' = V=^' d^ being expressed in mm. and j, in square mm. Determmation of the Section of the Field-magnet Bing and the Number of Turns of the Winding. — In consequence of hjrsteresis losses, we must not adopt an induction b greater than the values for different frequencies given in the table in the section on alternator design. The induction Bj through the air-gap may vary from 2,000 to 4,000, according to the width ; the_ narrower the air-gap the larger may be the induction in it. Fig. 16S Fig. 169 Fig. 168 shows the direction of the lines of force in the case in which the field-magnet is provided with a Gramme winding ; 1 68 ALTERNATE CURRENTS fig. 169 indicates the same thing in the case of a drum winding. It will be observed from these figures that it is quite safe to assume that the lines of force are uniformly distributed in the air- gap. Since x represents the breadth of armature or field-magnet along the axis, and y the radial thickness of the field-magnet ring, the section will be : s =■ xy, and the section of iron : Si = ^xy, 8 being a coefficient dependent on the thickness of the paper insulation between the laminse ; its value is generally "85. The total number of lines of force in the field-magnet will be : ^ ■= hxyB. The surface of a coil along the air-gap is Ix, I being the breadth of a coil : the total number of lines in the air-gap must therefore be : $j = B, I X. As there are some lines of force lost by dispersion, we must gene- rate more than ^1 lines in the coil. If a is the dispersion factor, we shall have $ = -i a a may be taken as 75, in accordance with Herr Kolben's experi- mental determination. We shall have therefore a8a;vB = B] I x,ox y= — r / ~J. a 8 B Replacing I by its value as found above, viz. ^^ we shall have mb ttDiB, a.hmb'B' Taking a. = 75, and 8 = '85 we get ;' = 4-92^J. mi V MOTORS 169 In determining x we must endeavour to minimise the losses in the field-magnet, viz. losses due to hysteresis, eddy currents, and copper resistance. We can calculate the loss w, through hysteresis and eddy currents per cubic cm. by the aid of the tables given at the end of Chapter I. The hysteresis and eddy current loss for one coil will be ap- proximately : /, :=^ X y Iw^. The equation giving the number of turns n per coil is . _ \/2 ElO* . 2irFn whence n/2 E 10* « =: -^^ : 27rF* but we know that $ = 8 xy b, therefore >/2 E 10* I A n = :^ 5 . - = -, 2 irF bjC B X X A being a constant, since jy is known. In the case of a Gramme winding the length of a turn is ap- proximately 2(x + y) ; the total length of the winding will be then ' X X A, and Ag being two constants. In the case of a drum winding, the length of a turn is 2 (jj -|- /), so that the total length of wire for one coil will be given by an expression of the form a^ -| — ^. X The resistance of the wire being p per cm. in length, and the effective current i, the loss by resistance in watts will be The total loss of power in one coil will be Pi +/2 =&xy iwi -f- p ^A, + ^^ i2. I70 ALTERNATE CURRENTS i.e. it takes the form a'" a' a: + a" + — . X The value of x, which renders the loss a minimum, will be given by the equation a' -ti"x-^ = o A.'x^-tJ" =o Having thus determined x, we can calculate the values of *, and *, whence we can deduce the value of n. As a result of tests on a great number of motors, Herr Kolben has determined a constant which allows of the direct calculation of n, the number of turns of one field coil. This constant c is the ratio of the number of ampfere-turns per cm. of the development of the circumference, on which are made the holes in which the field-magnet bars are inserted ; to the diameter of the armature mb\n \n c = TTDi / For 40 to 60 periods and an induction of 2,000-3,000 in the air- gap, the value of c is between 100 and 150. This is, of course, only a rough approximation, and must be used in a judicious manner. The number of turns of the winding of one coil is given by the equation n\=. cl ttd, c n = — L-. I mb Having determined n, x will be given by the equation a X ■=-. n We can determine x by the first method, deduce from it the value of n, and then see whether the value of c falls within the limits of Herr Kolben's method. Sometimes, especially with motors having a large number of field-magnet coils, in order not to have too complicated a winding, it becomes necessary to reduce n and increase x, i.e. to sacrifice a little of the efficiency. MOTORS 171 We shall adopt for n the whole number next highest to the value found, and shall then be able to make a complete sketch of the field-magnet. It is easy to see that motors which have a large number of field-magnet coils, will possess an armature of reduced section, and will consequently be light ; on the other hand, the number of turns on the field-magnet will be large. Calculation of the Armature. — The motor must give a useful power of w watts with a coefficient of slip -, so that the number g of turns is 60 F / i> as we saw above. The winding of the armature is divided into u parts closed on themselves, each part comprising v conductors in series. If r, is the resistance of one conductor (including the terminal connections), the resistance of one of the u parts of the winding will be The average velocity per second of a conductor is ttD, N V. ■ ^ (-a 60 Dj being the average diameter of the winding. Each conductor has. a length x, and traverses a field of inten- sity B,, with a velocity — ; the E.M.F. induced is therefore e, = — ^ volts, and the E.M.F. induced in the v conductors of one of .the u parts of the winding is : _Z'JCV2Bi The total loss of power in the copper will be : 172 ALTERNATE CURRENTS We have seen above that the efficiency, when only taking k' account of the armature loss, is proportional to — . We have then ■ w K^ . w + OJ, K ' and since : we shall get : K o>l_ K -K' _ " V gJ g I . , K — K ( I — 1 g) g therefore : Substituting the value for Ej in this equation : • ^ x^ux^^^-B.^ g — I . »« is the total number «, of conductors placed on the periphery of the armature ; we have therefore : ^ ^ j^i^x'Va'Bi^ _ g-i I0'*«Rl ' g^ Solving for Ri, the resistance of one of the u parts of the winding, we have : _VfC^JV2^^ g— I The current circulating through the armature conductors will be : I _ El _ vxv^-Bi Rl 10* Ri^' or, replacing Rj by its value, and noting that w» = «, ^iVj^Bi^— i" MOTORS 173 We can now calculate the section of the winding and see whether the current density is too high. These equations are applicable to all armatures, and for the case of a mouse-mill armature we have »= i, « = «, and r, is the resistance to be given to one bar. In these expressions Vj is expressed in cm., w and 0)1 in watts, Ri in ohms, Ej in volts, and Bi in C.G.S. units. Determination of the Magnetisation and Full Load Currents. — The effective current, when the motor is running light, may be found in the same way as for a transformer. If /(, a and 4 (fig. 170) are the average lengths of the magnetic circuits ; b', b/, Bj' the r'oots of the mean squares of the induc- tion (which we may call the effective induction) respectively in the field-magnet, the air-gap and the armature core ; /i, and /iij the values of the magnetic permeability in the iield-magnet and armature respectively (these may be determined from the mag- netisation curves) ; the total number of ampere-turns of the field for each phase, of a motor with b coils per phase, running light, will be : i'«'=i5.^/'2aBi'-^iL-(-J^Y and the effective current when running light will be : ■8 ,5 ^2 a b/ + il -f ^ Fig. 170 This expression shows that the effective current in the field- magnet increases with b, i.e. the number of poles ; if the speed remains constant, it will also increase with the frequency, for the principal factor, viz. the air resistance, remains constant for given dimensions of the motor (it is proportional to the air-gap, which remains constant). 174 ALTERNATE CURRENTS The effective current when the motor is running light will differ very little from the simple magnetisation current, for the power in watts a>', which must be supplied to the motor to over- come passive resistances, losies in the copper, &c., is very small. ■■■=:- is the effective current necessary to overcome the passive re- sistances, &c. The effective current when the motor is running idle will be : i2' = v/i'2+i,'« and I2' will be very nearly equal to i'. If, when the motor is finished, it is observed that \^ is greatly different from i', we must conclude that the design is bad. Currents are induced in the armature in the wrong direction ; these currents do not tend to increase the torque, and simply cause a loss of energy. In such case the slip, even when running idle, will be very large. Currents of this nature cannot be avoided in single-phase motors. The effective current at full load may be determined in the following manner : We may safely assume that the effective magnetisation current at full load is i' (although in consequence of the diminution of induction in the iron, it may be a little less). The effective current necessary to yield the required power may be expressed as follows as a function of the useful power, w, and the power wasted, w-^ : j„_ w + W| The total current, being the resultant of the magnetisation current and the power current (which differ in phase by 90°), will be given by the expression I = ^Y^~+7^. We can now verify the section of the wire as found above and the power wasted due to its resistance. MOTORS 175 Calculation of the Efficiency. — The different losses may be determined as follows : (i.) Hysteresis and eddy current losses. We can calculate these losses per cubic cm. for the field- magnet from the tables at the end of Chapter I. The total loss may then be found. The same losses in the armature may be determined by assuming that the maximum induction is Bj and the frequency -. g (ii.) Loss in copper resistance of the field. This loss will be : 0) 1= m I* R, I being the effective current per phase at full load and r the total resistance of the field circuit per phase. (iii.) Loss in copper resistance of the armature. This is given as above by the expression = u R ^ (iv.) Losses by friction and air resistance. These must be determined by comparison with an existing motor. § 9. Influence of the Shape of the E.M.F. Curve of the Generator on the Efficiency of a Motor In 1894, as a result of laboratory tests, Professor Duncan, at a meeting of the American Institution of Electrical Engineers, called attention to the influence of the current curve of an alter- nator on the working of a motor. The OerUkon Co. undertook experiments with a great number of motors. The conclusion arrived at from these experiments is that the working of a well-constructed motor, either at starting, when running idle or when fully loaded, is practically unaffected by the method of construction of the alternator and the shape of the current curve. For example, a single-phase asynchronous Oerlikon motor of 10 h.p., working at an E.M.F. of 220 volts, was under the same conditions driven — 176 ALTERNATE CURRENTS (i.) By an alternator of the Kapp type, the current curve of which is almost sinusoidal ; (ii.) By an Oerlikon alternator, the armature turns of which were sunk in the iron, and of which the current curve is given in fig. 91 supra. The following results were obtained : Working with a Kapp alternator of 50 h.p., 14 poles, 430 revolutions per minute, 2,000 volts and a 20 k.w. transformer : Useful Power Revolutions E.M.F. Current Watts Supplied H.P. Watts 8-3 ii-o 12-2 Starti 1,840 6,100 8,100 9,000 ng light i,S8o I.S7S 1,560 1,520 215 215 210 210 210 33 33-S 60 60 70 45 1,100 2,930 7,600 9,800 11,100 Working with an Oerlikon alternator of 100 h.p., 12 poles, 500 revolutions, 2,700 volts and a 15 k.w.' transformer : Useful Power E M F Current Watts Supplied H.P. Watts 1,520 215 33 1,106 3-1 2,300 — 212 34 3.400 8-3 6,100 1,500 220 45 7,400 9-8 7,200 1.494 220 48 8,800 II-8 8,700 1,480 205 70 10,800 Starting light 200 45 — : . It will be seen from these results that the form of the curve of the alternator has practically no influence on the motor. The influence of the motor on the shape of the curve of the generator is, on the other hand, a great deal more important, and may, in certain cases, exert a dangerous effect. Under certain circumstances, a generator, of which the curve, when running light, or when loaded with non-inductive resistances, is very nearly a sine curve, may give a very capricious curve, as shown in fig. 171. The curves of this figure have been taken from a triphase MOTORS 177 alternator of old-fashioned type, with an armature wound with bars placed in holes. Curve II., taken with no load, is very nearly sinusoidal. When the alternator, driven by a turbine, actuated an asynchronous motor of 200 h.p., which drove the transmission shafting of a factory, in conjunction with a steam engine provided with a good governor and powerful flywheel, Curve III. was obtained. The dotted curve is a true sine curve. In addition to increasing the losses in the iron of the generator, transformer and motor, due to the double fluctuations of the current, the increase of the maximum E.M.F. has two serious consequences. (i.) The insulation of the installation is in danger. (ii.) The self-induction of the hne and the factor of impedance are greatly increased, and consequently, at the same time, the loss of potential on the line due to the apparent resistance. The curve in such circumstances would be just as irregular even if the alternator gave with no load a true sine curve. N 178 ALTERNATE CURRENTS CHAPTER III TRANSFORMERS AND CONDENSERS § I. General Properties of Transformers Dr. Hopkinson has investigated this subject by an indirect method, in which the number of turns wound on the transformer coils enters into the calculations. Supposing the permeability of the core constant, if E. represents the magnetic resistance of the iron circuit, we have E=S- I indicating the lengths of the different parts of the magnetic circuit, s their sections, and /^ their permeability (supposed constant). Dr. Hopkinson supposes the magnetic induction in the core to vary in a simple periodic manner, so that if * denotes the induction at a given moment, and *„ the maximum value of this induction, we have * = *„ sin K ^ where k = ^, t being the time of a complete period, and t the time at which the instantaneous value is taken. On the other hand, if i^ and 4 represent the instantaneous values of the primary and secondary currents, we have : 4ir(«, iy + n.^i^ = ib'B>, = *„sin K/E. Let us put ti = ij sin (k ^ — <^,) ?j = ij sin (k ^ — .^2), TRANSFORMERS AND CONDENSERS 179 I, and I2 representing the maximum values of the primary and secondary currents, <^i and 4>i the respective retardations behind the induction. The total induction through the secondary circuit at a given moment is $2' = «2 * ; the induced E.M.F. acting in this circuit, which is equal to the impressed E.M.F., is then _ ^$2' _ _ ^ = — K «2 *o cos K t. If Lj is the coefficient of self-induction of the external part of the secondary circuit, and r^ the resistance of the secondary coil, we have (i) K «2 *o cos K/ + K L2 ij cos (k / — (/ij) + r^ ij (sin k / — ^2) = o. On the other hand, the expression 4 IT («, «■ 1 + «2 ''2) = B, *o sin K / gives 47r«, «, (2)11 sin(K/' — ^1) = ~ sinK^ — _? I2 sin (k ^ — *2), 4 71* ^j n-^ If L, and ^1 represent the coefficient of self-induction (of the external circuit) and the resistance of the primary coil, and if c„ = E„ sin (k / — B), e„ and £„ being the instantaneous and maximum values of the impressed E.M.F., when ?i = I, sin(K^ — <^,), then the E.M.F. 's acting in this circuit will be «a-L^= -KLiI,COS(Kif- <^,), N 3 i8o ALTERNATE CURRENTS and the E.M.F. due to the variation of the induction through the core will be : e,' = — K «, *„ cos K t. We shall have therefore on the whole : (3) E„sin(K/— &) = r^ I, sin(K^— 9),) + kLj i, (cosK/— 1^^ + K«, $„COSK/. In the case in which l, and Lj, the coefficients of self-induction of the external circuits, are small enough to be neglected the equations become (1) K«2*.C0SK/+ >'2l2Sin(K/— ^2) = o. (2) I, sin(KZ'— 0i)= ^sinK^ ^i2sin(K/ — ^j)- (3) E^ sin (k /■ — fl) = ^1 1, sin (k / — ^1) + k «i *„ cos k t. These three equations are sufiScient to solve all transformer problems. Making successively k^=o and k^= - inequation (i), we shall have ^2l2Sin^2 = K«2*o /•a I2 cos ^2 = o. Squaring both equations and adding, we shall have whence I2 = ^^ *» ; tan 1^2 = °° ; ^2 = - • r^ 2 Making K/=oand k ^ = - successively in equation (2), we get — ij sin ^, = _? I2 sin ^^, or substituting from (i) I, sin,^,= -!^3''*^ TRANSFORMERS AND CONDENSERS I8i and ii cos <^i = i- — — I2 cos <^2 47r«i since cos <^2 = <>. Squaring both equations and adding, we have Dividing one equation by the other, we have tan d, -_ kV4^^i _ _ i^^K^. ?-2 «i R ^^2* Making Kt=o and k / = - successively in equation (3), we 2 have — E, sin 6 = — r, I, sin 0i + k «i *„ E„ cos ^ = y, I, cos <^i. Squaring and adding the two equations, we get e/ = r^^ii^ + k''«i**„^ — 2K?'i «i*<,Ii sin ^p Substituting, we have p 2_ J „ a 16 ^' k' ^2^ + J^a" R' , k2« 2 , 2Kr,«,i^2K«2l . j ^ l67r''K''«2^yi'' + yiV2''RHl67r^K''i>giV2^ + 327r^K^«l''i^2V|»-2 ^ 2 l6 7r2«iV22 16 IT* «j^ ^2"* _ 16 7r'K^(yi ^a" + y-a ^i")' + n" »-2'' R' 16 TT* «i^ ^2^ " Dividing one of the above equations by the other, we have tane = K^l !»-, I, sin <^, — K «i *„ '■a «, ' '^''' >-, I cos <^i 4 7r «, _ 4 7rKf«,i'«2M R l^ ^J" 1 82 ALTERNATE CURRENTS As tan..^, = ^-JLJt^ and tan ^ = 4^^ f^ + ^) we see that Q is greater than ^i ; that is to say, the current lags behind the impressed E.M.F. in phase. If ^ is the angle of lag of the current behind the E.M.F. we have 4 •n- K «i^ r^ B tan i/r = tan (^ - <^,) = i6 -TrS k2 n^ [r^ «i2 + ri n^) + ^i r^ R' K 6' Applying Blakesley's graphical method, if oa (fig. 172) repre- I sents the direction of the magnetic in- duction, OB making the angle ^1 with OA will represent the direction of the current in the primary coil, and oc making the angle 6 with oa will repre- sent the direction of the impressed E.M.F. Let us take ob = « ij, we shall have ba = OB sin <^, = w I, sin ^1 ^=. Wl. * CD ?--«, (as we found above from equation 2). OA = OB cos (1)1 = m R Thus ob2 = oa2 + AB^ = m^li^ 4'7r«j Fig. 172 =. m^i whence K^ V w iGtt^ 1 1** • ■={ r^ n^ L |$! The current in the primary circuit is therefore the resultant of two currents differing in phase by -. 2 If we put 1/= — *-*„ and ii" = * >■, «i 47r«i TRANSFORMERS AND CONDENSERS 183 we have but The current i/, which is proportional to I2, may be called the working current, and the current i/', which is proportional to the flux of induction, may be called the magnetisation current. Since the current in the secondary is retarded by an angle - behind the flux, as we have seen from equation (1) above, we 2 can represent it in direction by ob'. ob' = BA = w -? I2 I2 = — L ob'. m n^ The maximum value of the E.M.F. induced by the flux in the primary circuit is (as we have seen above) k «, *„, and it has the same direction as o b', making o k' = »« k «i *„ »2 K «, ^-o «, BA ratl,^ m K n^ «2 for *„ = — — ' — r- (see equation for b a above). mYin^ ' ok' will represent in magnitude and direction the E.M.F. induced in the primary. The maximum effective E.M.F. is r^ i,. Taking OL = ;/z^i I, = ^1 OB o L will represent in magnitude and direction the effective E.M.F. which is the resultant of the impressed E.M.F. and the induced E.M.F. Taking o k = o k' and completing the parallelogram, o m will represent in magnitude and direction the impressed E.M.F. We shall have therefore o M = »« E.. 1 84 ALTERNATE CURRENTS It is easy to verify that m o n = by substituting for the lengths in the equation tan m o n = ML + LN ON , the values they represent. In practice it is also necessary to take account of hysteresis and eddy current losses. If / is the loss in the iron of a trans- former, for the value of o corresponding to a given load (we shall see further on that *„ varies with the load) the maximum current ii'" of the same phase as the impressed E.M.F. necessary to compensate for this loss will be given by the equation E„Ii =/orii"'=i£. Fig. 173 In the diagram (fig. 173) let us take QVi=-m\-l" ; drawing B E equal and parallel to o d, o e will represent in magnitude and in phase the total current in the primary, and we shall have : OE = mi-^. The effect of the losses by hys- teresis and eddy currents is there- fore to increase the current in the primary in the ratio of o e : o b and to diminish the lag between the E.M.F. and current for The power expended in the primary of a transformer is the mean value of e^ i\ , e^ being the instantaneous value of the im- pressed E.M.F. Now e^ = E^ sin (k / — ^) and ?i = i, sin (k / — <^,). There- fore gg t\ = e^ I, sin (k ^ — 6) (sin k ^ — ^1) = E^ii {sin'' K/ cos ^ cos <^, — sin k / cos k ^ (sin 6cos<^i + cos^sini^i) + cos'' K/sin^sin<^i}. Now the mean value of sin k fcos k /is o and the mean value of sin^ K /and cos^ k / is L TRANSFORMERS AND CONDENSERS 185 Thus the mean value of «„ « 1 is ^(e„Ii cos^cos^i + E^ii sin ^ sin (jij) = 4 (''1 h^ cos^ ^1 + ''1 ii^ sin^ i^j — K K, $„ I sin <^,) or, taking into account the hysteresis and eddy current losses, we shall have as the mean value of the power in the primary r^, the resistance of the secondary, varies inversely as the load, for the resistance of the secondary winding is small and may be neglected. When the secondary circuit is open we get ^2 = 00 : I] = o. If the impressed E.M.F. is constant we have $2 = ■!.6i:^ni^r^ 16 ir^ K^ (?-, n^ + ^2 n^^Y + r^^ r^ "B? It is easy to see that $„ increases when r^ increases, that is as the load decreases. On open circuit we have *2_ leir^KSwi^ + z-iaRa since the value of r, n^ may be neglected. The intensity of the magnetisation current is given by the equation It increases with R, the magnetic resistance of the transformer, and diminishes when k increases — i.e. with the frequency— for $„ diminishes when the frequency increases. It increases also with r, r^ -&?, which is always the case in practice. The lag in the primary increases therefore when R increases. This effect is still further enhanced by the leakage of induction which increases with R. The increase of the lag involves supplementary losses in the whole primary network (if no steps are taken to annul the lag), for in order to transmit the same power it is necessary to increase the effective current, and consequently the line losses. If no account is taken of hysteresis and eddy current losses the efficiency varies inversely as R. Influence of the Resistance of the Primary Circuit. — The loss in heat increases naturally with r-^. Further, if r, exceeds a certain value the transformer may cease to be self-regulating, for we can no longer neglect the term r^ n^ in the equation for the difference of potential at the terminals of the secondary. Influence of the Frequency.— The equation — ^^' ^° =$. 192 ALTERNATE CURRENTS shows that «i and $„ decrease with the increase of frequency — i.e. for a given maximum induction the section of the transformer is inversely proportional to the frequency, and consequently the volume will be inversely proportional to rf. The decrease in the dimensions cannot be carried very far, for it is not practicable to adopt as large a magnetic induction B, for a high-frequency transformer as for a transformer of lower frequency. Nevertheless, a high-frequency transformer will be con- siderably smaller (for a given power), and will cost less than a low-frequency. Effect of the Dispersion of the Magnetic Indnction. — Up to this point we have assumed that all the lines of force traverse the primary and secondary circuits. As a matter of fact, it is impossible to realise this condition completely in practi lines lost by dispersi The number of ce, and there are always a certain number of on. nes of force traversing one turn varies in the same circuit. However, let us suppose that all the turns of one circuit are *o traversed by the same flux. We can then divide the total flux into three parts (fig. 17 s) : (i.) One part of intensity *„ traver- sing both circuits. This is the useful ^"^- '75 flux, which we have taken into account in all the above calculations. Its instantaneous value is *„ sin k t. (ii.) A part of maximum density *, traversing only the primary circuit. This flux is in phase with the primary current. Its instantaneous value is *, sin (k ^ — <^i). (iiL) A part of maximum density *2 traversing only the se- condary circuit. This flux is in phase with the secondary current, and its instantaneous value is $2 (k ^ — ^2)- The instantaneous value of the E.M.F. induced in the primary by the flux $] is — K «, *, cos (k / — ^,), and that induced in the secondary by the flux 4>2 : — K «2 *2 cos (k / — ^2)- TRANSFORMERS AND CONDENSERS 193 It is easy to see that these fluxes play the part of self-induction, and that they will have the same effect, supposing that the flux in the transformer is *„ and that in the primary is inserted a self- induction of value Li = «, *!, and in the secondary a self-induc- tion of the value Lj = «2 *2- The dispersion of the induction has therefore the effect of increasing the lag between the E.M.F. and current in both the primary and secondary coils. Dispersion naturally increases : i. With the resistance of the magnetic circuit. 2. With the value of the maximum induction. If Li and L2 are the coefficients of self-induction of the primary and secondary of a transformer, and m the coefficient of mutual induction, then : Without dispersion : Li L2 = M. With dispersion : M = Vl, Lj (i — l/f). The efficiency is : R = I — Consequently the efficiency decreases with m. Influence of the Joints of the Magnetic Circuit. — Accord- ing to the experiments of Messrs. Ewing and Low, the influence of the joints in the inagnetic circuit is very large in a closed circuit transformer, but, on the other hand, it is negligible as soon as the circuit possesses an air-gap of any size. In the following table the influence of ihe joints corresponding to layers of air is given : Induction | Layer of air in mm. Induction Layer of air in mm. 4,000 6,000 8,000 2-6 3-0 3-1 10,000 12,000 14,000 3-1 3-S 3-7 Professor Ewing considers that this resistance is not due to the thickness of the joint, but attributes it, according to his theory, to the discontinuity of the reaction of the elemental magnets. 194 ALTERNATE CURRENTS Influence of the Variation of the Permeability of the Core. — The variation of the permeabiUty of the core has the effect of modifying the curve of the secondary current. As the secondary reacts on the primary, the curve of primary current is also modified. In modern transformers, in which the maximum induction is small, this effect is more noticeable than in the old- fashioned type of transformer. § 2. Classification of Transformers and Considerations on the Magnetic Circuit The iron core of the transformer is surrounded as closely as possible (in order to reduce the length of the turns, and conse- quently the c^ R losses) by the primary and secondary circuits, only excepting the spaces necessary for insulation. The turns of the two circuits are as near as possible to one another, in view of the great difference of tension between the two circuits. The turns of the two coils may be alternated, or the primary circuit may surround the secondary. In all cases the whole of the primary and secondary turns form what may be called the copper ring. Transformers may be divided into two great classes : (i ) Those with open magnetic circuit.- (ii.) Those with closed magnetic circuit. In transformers with open magnetic circuit the copper ring surrounds an iron cylinder of almost the same length as itself, and the magnetic circuit is completed through the air. In transformers with closed magnetic circuit the iron takes the form of a ring. Closed transformers may be formed of : I. A ring of iron and a ring of copper. {a) The ring of copper completely surrounding the ring of iron (fig. I go). yb) The ring of iron completely surrounding the ring of copper (fig. 191). TRANSFORMERS AND CONDENSERS 195 (c) The ring of copper partially surrounding the ring of iron (fig. 176). II. A ring of iron and two rings of copper (fig. 177). III. A ring of copper and two rings of iron (fig. 178). B A' B' Fig. 176 Fig. 177 Fig. 178 We may also have several transformers combined into one, or a transformer with multiple circuits. Transformers with closed magnetic circuit may therefore be divided into : (a) Transformers with simple magnetic circuit. {V) Transformers with multiple magnetic circuits. When the core is of circular section, the length of the turns which surround it is a minimum for a given surface. When the core is formed of iron wire it may easily be of circular section, but when it is made of insulated laminated plates, as is the case with modern transformers, it is an advantage to make all the laminae- of the same dimensions, i.e. to give it a rectangular shape. In this case, the length of a turn is a mini- >•- SCt^ mum, when the section is square. In transformers of the Westinghouse.type, the coil surrounding the core has the shape indicated by figure 179. If x is the breadth of the core and m X its height, we have w *^ = s •= a constant. The length of a turn is (2 to + b-) x. 196 ALTERNATE CURRENTS We want, therefore, to find the value of m which renders a minimum the expression : (2 »i + Ttf X^ = -S —^ S=(4OT + 4?r+— IS we shall have — lA wr"^ = o 4 2 We have seen above that for the core surrounded by the ring of copper, there is a section for which at a given load the total losses in the iron and copper are a minimum. If the load for which it is required that the total losses should be a minimum diminishes, it is easily seen that the section of the core must diminish, it being of course assumed that the maximum induction in the iron remains constant. In the parts of a transformer which are not surrounded by copper, the hysteresis and eddy current losses may be diminished by increasing the section which has the effect of diminishing the maximum induction. Thus, for example, in the parts a b and a' b' of the transformei shown in fig. 177, it will be an advantage to make the section as large as possible (without unduly increasing the prime cost). In fact, it is possible to increase the section without increasing the length, i.e. the volume is proportional to s. As b is inversely proportional to s T b = — j the loss by hysteresis and eddy currents per cubic cm. will be of the form : a b_ si-6 "•" s» ■ The total loss will be of the form : i^'5"^ s' It will diminish in proportion as s increases. When the volume of iron not surrounded by copper increases more quickly than <-he section, there is then a section which gives TRANSFORMERS AND CONDENSERS 197 !i ma * eofB ""f ^- 1 V P \ \ 1 / ^^V6 / N k V Y ^1, / ' K K '\N k. \ A k 1 r.o . -« -.N I \ Y / \ -^-^ 1 \ / Y , V 1? /^ \ %N i_ ^ K s 70 id »v^ L / ^ — -< S^'"' \ / > k H Fig. 185 Looking at fig. 186 we see that the secondary E.M.F. is retarded more than 180° behind the primary E.M.F. ; the reason is that the leakage of the lines of force increases with the load. ^. '.^0 •V -N — ^'t ? loag \ 1 ^ > — , s, / '> Kn ■h / 500 \ / /] 1 s 1 s V 1 \v / \ \v \ / / ^ w / , a - 20 i. 1 \ / L-s^- -i 30 10 A ^- z / / \ 1 j 1 %\. 60 eo / V e u J s -^ 30, no y \ \ s 1 / ^ \ \ \ <- ^ i ,1 1 Fig. 186 204 ALTERNATE CURRENTS The power absorbed on open circuit is 39-6 watts ; the losses in the copper being 2*58 watts (the effective magnetising current was nearly an ampfere), and the losses by hysteresis, &c., about 37*o2 watts. The curves shown in fig. 187 are the values of the efficiency, the primary current, and the fall of potential at the terminals of the secondary as functions of the load. The efficiency at two-thirds of the load reached 96-6 per cent. The eflScient of the transformer considered by itself is there- fore excellent, but as the magnetising current is very large the line losses are increased and may more than balance the saving in the transformer. Si con idat JTJ E.h /.^ ■• ■' "■" ' 100 I ^ 30^ Em ciencv ■ Y 80^ / 70' > so; so' ... 10: so! ri" o,r. ^c* ^^ ■" zo: F To? --" 'dCO son 5flO ItJ IICO 250 fua eoo 800 ■m tm uo 600 600 30p0 ZflO 400 600 800 Waits in secondary Fig. 187 Experiments with Condensers. — For the purpose of these experiments, six condensers of the Stanley Electric Company, which were capable of resisting a difference of potential of 500 volts, were connected as a shunt to the primary. These con- densers had a capacity of 15 microfarads. By arranging them in parallel or in series it was possible to obtain capacities between •25 and 2-25 microfarads without the potential difference at the terminals exceeding 500 volts. The capacity which would bring the line current into phase TRANSFORMERS AND CONDENSERS 205 with the E.M.F. was calculated to be about one microfarad, and this calculation was borne out by the experiments. The con- densers were arranged in different manners until a minimum line current was obtained ; the minimum was reached when the con- densers were three in series and two in parallel, and with this disposition the capacity was about one microfarad, viz. : 2x1-5 3 These experiments were made, the first on open circuit, the second at a load of fifteen lamps, and the third at a load of forty- five lamps. The results are given in the following table : Load Primary Current (without condensers) Line Current (with condensers) 15 lamps (1,012 w) 45 „ (2,740 '^) •95 1-24 3-07 ■187 ■867 2730 We thus see that the line current is five times as small as it would be were no condensers used. — LEUQ s ■/ i 2 ^ ,^/1 1000 N / .p^ \ L5 ^ s ( ^ >/■ ao LO /' V V /\ ^&/ r V k N ) ^ — s V 1A ,^ \ cii,-,v .../ k. 1^ ^ r s 1 > X /A ^ ^ t Z 1 b i / S k \ Y N ^ A k ^ / S( X* k / -"<, ■W !L> / ■"- / I \ / '' K, y — Fig. Figs. 188 and 189 give the various curves for no load and for a load of forty-five lamps. 206 ALTERNATE CUMBNTS The line current is the algebraic sum of the primary current and the condenser current ; if the currents were exactly sinusoidal it would be exactly in phase with the E.M.F. As we see from fig. 187, this can be realised in practice. In fig. 188 the line current is very irregular ; it has a higher frequency than the E.M.F., which arises from the fact that it is the algebraic sum of two currents which are not absolutely sinusoidal. These experi- ments confirm the results of theory, i.e. that in the case in which the line resistance is sufficiently great, there is no advantage in employing open circuit transformers, for then the line losses' due to the larger current may reach a higher value than the economy effected in the transformer itself, unless steps are taken to annul the lag. liOO 'i I --> ^ r i .1 ifia \ / ^ y h % ; V y s \ A L^ 500 2 Y > k / f \ tl 4 , iV/ s // / x; ^/^ '^ V \l 1 k ^ ^ / f.\. r\, 40 / 2 V \ \ A L % Ss ill EO . y A\^ S /j / \ /I / ^ ' F !^.P- ^\ \J\ 'jj ■~ \ 1 Fig. 189 II. Transformers with Closed Magnetic Circuit. — (a) Transformers with Simple Magnetic Circuit. — Brown Trans- former. — This transformer is of the simple magnetic circuit type. The primary and secondary are wound concentrically on a straight core, and the magnetic circuit is completed by a bundle of laminated plates in the shape of I 1, the two ends of which abut on the ends of the core of the coils. The joints are scraped true, and, in order that the magnetic joint may be as perfect as TRANSFORMERS AND CONDENSERS 207 possible, the two parts of the iron circuit are held tightly together by means of a screw. The windings of all transformers are preferably baked in oil. For high tension the windings are immersed in an insulating oil, and are baked in the oil so as to expel all moisture. The following data relate to a 20,000 watts transformer : Load Efficiency Load Efficiency 20,000 15,000 10,000 5,000 •967 •96 •95 •91 4,000 3,000 2,000 1,000 •88 ■86 ■80 ■69 Ganz Transformer (Zipemowski Dery & Blathy). — The old type of Ganz transformer had the shapes indicated by figs. 190 and 191. In the first transformer the core was formed of a ring of iron wires, the primary windings a and the secondary windings b (fig. 190) being placed alternately on the ring-shaped core. I Fig. 190 In the second transformer the secondary formed one ring ; it was surrounded by the primary, and the whole was enveloped by a winding of soft iron wire, wound on the ring formed by the primary and secondary (fig. 191). 208 ALTERNATE CURRENTS At the present time the Ganz firm builds its transformers after the type of fig. 190, but the core is formed of insulated iron laminae. These laminae are in the shape of a flat ring, and when assembled form a ring of rectangular section. The discs are held by radial cheeks (fig. 192) ofi — i shape. The primary is wound all round the ring, and covered by the secondary coil. The cheeks at top and bottom are fixed to iron discs ; on the top disc the terminals and fuses are placed. In 1890 a committee, ap- pointed by the City of Frankfort, stated that at full load the effi- ciency reached 95 to 96 % ; at \ load, 93 to 94 % ; i load, 90 % ; and at ^ load, 80 %. The curve in fig. 193 gives the efficiency at various loads and the fall of potential at the terminals of the secondary, as functions of the load for a i\ k.w. transformer. The ' Institut dlectrotechnique f^d^ral Suisse ' tested a 4 k.w. 5^=^^p^' Fig. 192 Fall of potential 100 ■ ^ no AO ^ 111 / Rn / fin / %0 ' to 1000 zaiio 3000 tcoo 5000 eooo 7000 aooo 9000 toooo uooo Secondary load in watts Fig. 193 Ganz transformer, of which the primary was designed for a tension of 9ooz»., and the secondary for a tension of 100 v., in order to TRANSFORMERS AND CONDENSERS 209 determine the increase in the iron losses due to an increase in the tension. The results of the tests are given in the following table : Frequency 40 40 ' 40 40 40 40 40 40 40 Primary tension E, (in volts) . Losses in iron p (in watts) . . , El*'" . 300 23"' 53° 400 36-5 539 500 53"4 531 600 70-6 543 700 gz'2 537 800 ii6'9 523 900 140-8 532 1,000 166-5 535 1,100 195 535 We observe that we shall not be far wrong in assuming the product e/'^'p is constant. Labour Transformer. — The magnetic circuit of this trans- former, which is built by the ' Eclairage electrique ' Co., is formed of^ laminated plates, insulated from one another, and having the shape indicated by fig. 194. The circuit is completed by a cylinder of laminated plates, which is driven into the gap left in the horseshoe ; straps with Fig. 194 bolts through them are so arranged as to compress the iron and, thus diminish the magnetic resistance. As fig. 194 shows, the laminated plates are not all of the same width, in order that spaces or channels may be left for the purpose of ventilation. The charcoal iron laminae, about jJ-j^inch in thickness, are. insulated from one another by shellac paper. p 3IO ALTERNATE CURRENTS The two coils are wound separately on formers of hard, dry wood, impregnated at a high temperature with some insulating material such as gum-lac or bitumen. The distance between the outside primary coil and the secondary coil, as well as the distance between the latter and the core, is dependent on the tension at which the transformer is to work. Fig. 19s The wires are insulated by silk and by ribbons soaked in an insulating liquid, which hardens on the application of heat. The whole transformer is clamped between cast-iron plates and is placed on wooden rails (fig. 195). When the tension in the primary reaches a certain value, the transformer is placed in a case, which is filled with an insulating material which melts on the application of heat. A window closed by a shutter, which is held by two screws, allows of observing the height of the liquid without taking off the cover. TRANSFORMERS AND CONDENSERS 211 As the curve in fig. 196 shows, the efficient of these transfor- mers is excellent even at light load. 36^ 90 80 1)0 50 GO Usefiil load in per cent. Fig. Z96 100 Full laod. lowrie-Hall Transformer.— This transformer consists of two bundles of rectangular plates, insulated by paper. On each of these bundles is wound first a primary coil and then a secondary above. The bundles of iron plates are longer than the coils, and the two ends are bent over and the plates interlocked as shown in fig. 197. The whole is then placed in a cast-iron case so that the two bundles are strongly compressed with a view to decreasing the magnetic resistance. The two secondary coils, as well as the two primary, are connected in series. The terminals and safety fuses are placed in 212 ALTERNATE CURRENTS porcelain boxes in the cast-iron case. These transformers are used by the House to House Co. at the West Brompton Central Station. Fig. 197 {p) Transformers with Double Magnetic Circnit.— Cail- Helmer Transformer.— This transformer has magnetic circuits of variable resistance. Rectangular laminated plates with a hole punched out of the centre as shown in fig. 198, are built up with Vertical section. Fig. 199 paper between and clamped firmly between two cast-iron plates s s (fig. 159) connected by bolts. TRANSFORMERS AND CONDENSERS 213 The primary coil B, as well as the two halves of the secondary coils which surround it, is arranged as shown in the figures in such a way as to produce two magnetic fluxes, the mean paths of which are indicated by dotted lines. In the central circular aperture is inserted a cylinder of laminated discs, threaded on a bolt t. This cylinder is provided with two cavities and is capable of revolving round its own axis. When the cy Under occupies the position indicated in fig. 198, the magnetic resistance is a minimum. When it is turned through an angle of 90°, the magnetic resistance becomes a maximum. Since in the formula 2 16 17^ ^i' s 16 ,r2 K^ «,« + n' R' ' ' the magnetic resistance B, occurs in the denominator, *„ diminishes when R increases. As *„ decreases the losses by hysteresis and eddy currents also grow less. We may, therefore, with such a transformer, increase the magnetic resistance when the load decreases, and in consequence diminish the importance of the hysteresis and eddy current losses. It is also possible, by increasing the magnetic resistance at light load, to render the secondary E.M.F. absolutely constant for any load ; this will be understood on reference to the formula giving the value of the terminal secondary E.M.F. The following data relate to a Cail-Helmer transformer of 10 k.w. output, for a primary tension of 2,000 v., and a secondary of 1 10 v., at a frequency of 60. Section of the iron excluding the central cylinder ..... Length of the magnetic circuit Maximum magnetic induction (C.G.S.) Total weight of iron No. of turns on the primary coil . Current density per sq. in. (primary coil) No. of turns on the secondary coil Current density per sq. in. (secondary coil) Ferranti Transformer. — The primary and secondary are wound on a bundle of insulated laminated plates, interleaved with one another as shown in fig. 200. 40 sq. in 35 in- S.630 458 lb. 545 800* 3° i.opo*^ 214 ALTERNATE CURRENTS In the Ferranti system the sub-station transformers lower the voltage from 10,000 to 2,400, and other transformers placed in the customers' houses lower it again from 2,400 to 100 or 50. The 150 h.p. transformers, designed to lowerthe tension from 9,600 to 2,400 — i.e. having a ratio of transformation of 4 to i, are built in the following manner. There are three coils, of which the middle is the primary, and the two others form the secon- dary. Each of these coils consists of copper ribbon elements, the turns being insulated, as in the alternator coils, by strips of vulcanised fibre. SgggggSSgSSSSSS^ gSSS%SSSSgS!SgSSSS0 Fig. 200 k. ■--> 1 *. 1 i .' 1 1 il »" — i '' r ^ m I '(■^ -^ m Fig. 201 Fig. TRANSFORMERS AND CONDENSERS 2IS The primary and secondary coils are separated by plates of ebonite, with considerable intervals between for the purpose of the circulation of air or oil. The different iron plates which form the magnetic circuits are separated from one another by spaces of half an inch for ventila- tion or oil circulation. Mordey Transformer. — The Mordey transformer is of the same kind as the Thomson-Houston and the Westinghouse, which we shall study further on. This kind of transformer is formed, as shown by figs. 201 and 202, of two coils, which are placed either side by side (fig. 201) or on the top of one another (fig. 202). These coils, of elongated shape, are enveloped by a hollow rectangular prism of insulated a \t' f' A V K- V. 9' d. 1 1 L b' c D Fig. 203 E ■ F e e K 8 H laminated iron plates, arranged in such a way as to form a double magnetic circuit. The difierence between the various trans- formers of this type lies in the manner in which the rectangular pieces are cut out of the laminated plates. In the Mordey transformer, the secondary coil is wound on a thin former of dry wood impregnated with ozokerit, and the primary is wound on the top of it. The transformer is built in the following manner. First, a rectangular plate a b c d (fig. 203), with a piece abed cut out, is threaded on the coil : the magnetic circuit is completed by placing inside the coil, at e'fg'K a rectangular plate efgh which has been removed from the plate efgh. Paper insulation is then put on, and above that, at Aa' ef adh' b' c, a plate of the same 2l6 ALTERNATE CURRENTS shape, obtained by dividing what remains of the plate e r G h along the line ik. The magnetic circuits are completed by placing on a' d e' b' the part abed which was removed from the first plate abcd. This process is repeated till the whole magnetic circuit is complete. The whole is then clamped firmly by end plates of cast iron held together by screws. The terminals and safety fuses are fixed on a porcelain block in a cavity of the cast-iron envelope. The Committee of the Frankfort Exhibition, under the presi- dency of Professor Weber, of Zurich, tested two Mordey trans- formers, built by Kremenzky, Mayer & Co., of Vienna. They were of 316 k.w. output; the primary tension was 2,000 w., and the secondary 100, whilst the frequency was 100. The curve of the primary E.M.F. shows the effective tension at which current must be supplied in order that the secondary E.M.F. may remain constant. The following table gives the value of the cosines of the angles of lag between the primary current and E.M.F. — i.e. the power factor. It will be observed that even at light load the cosine is nearly 1 —i.e. the lag is negligible. First Series of Tests Second Series of Tests Load Cosi(«' Load Cosi^i' watts 6,302 5.329 4.327 3.370 2.437 1.485 994 528 •999 I -000 I -000 I -001 I-OOI •997 ■980 ■975 watts 6,261 5.299 4.352 3.457 2,438 1,488 1,008 531 •997 I -000 ■998 i-ooo ■992 •987 •98s •945 The load of the secondary circuit consisted of incandescent lamps — i.e. there was practically no self-induction. Oerlikon Transformer.— The core of the transformer is formed of a bundle of insulated laminated plates, of the shape indicated by the transverse section in fig. 204. The secondary coil is wound on a former, enveloping the straight core, and the primary TRANSFORMERS AND CONDENSERS 217 surrounds the secondary. The two magnetic circuits are closed by means of plates of 1 — 1 shape at top and bottom, as the longi- tudinal section indicates. The curve, fig. 205, transformer. Fig. 204 gives the efficiency of a 2 k.w. Oerlikon SS ' - — ■ 96 ^ — = 98 ^. ai) ^ -* 3? 1 RS y -* 91 5 no / 7S 75 / in / fiS / 60 i 61. 1 ss ... sn »s to 36 i so t 85 ■IQ IR 10 ~" 6 "~ ~ 1 1 1 1000 150c 2000 'W^iiz Fig. 20S ' 2i8 ALTERNATE CURRENTS The Committee of the Frankfort Exhibition conducted tests of an Oerlikon transformer of 7-5 k.w. output, the primary tension being 2,000 v., and the secondary 100 v. This transformer, which was built for a frequency of 50 ~, could only be tested at a frequency of 100, which naturally altered the conditions of working. The curves (fig. 206) give the efficiency, the losses in the iron and copper, as well as the tension which must be impressed on the terminals of the primary to obtain at any load a constant E.M.F. of 100 V. at the terminals of the secondary. With regard to the efficiency, it may be remarked that the losses in the iron diminish as the frequency increases ; this result is borne out by the tests made on an Oerlikon transformer of 3 k.w. output by the Institut dlectrotechnique fdd^ral of Zurich, which are given below : Frequency . 27-5 32-5 37-5 42-5 47-5 52-5 sr^ Iron losses . ■ 777 72*2 66-6 6i-8 58-0 567 55-0 The efficiency of the transformer at a frequency of 50 would be therefore slightly lower than that shown on the curve. On the other hand, at the normal frequency the variation of the primary tension necessary to maintain a constant secondary E.M.F. is a little less than that given by the curve. In fact, if Ej' is the tension at the terminals of the secondary on open circuit, and E2" the tension at a given load, we have Eo — Eq' 1/ ; I f^l\^ I 2 TT F (l, L, — M'') . . 1 ^2 being the resistance of the whole of the secondary circuit, corresponding to the given load ; r^' the resistance of the secondarycoil ; l, and Lj the coefficients of self-induction of the primary and secondary circuits ; and m the coefficient of mutual induction. When the frequency increases the first two terms do not alter, but the third increases, since it contains r and sin <^i, for we have tan <^, = i^^iL^', andK=2,rF. TRANSFORMERS AND CONDENSERS 219 The loss of power in the iron (fig. 206) increases rapidly with the load. This arises from the fact that the transformer tested -"OX fs -£i y" ,' / .,i'?>-" f vr r • 1-* 4-U <^ r- ^l-ryi^-i 4« *0' J' .. *t ■* ■'.■' .*c •1 JJ ^ /° >1 cot vYl [^ i""':^ r" _^ -n 1 Ho tea If ISO 110 «0 100 to Sun im ««« Sm eno }oio im ICo^ Fig. 206 was provided with a case of iron which was not laminated, so that when the load increased the leakage through this case also increased. Modern Oerlikon transformers are not provided with this iron case. The following table gives the value of the cosines of the angles of lag between the primary current and E.M.F. at different loads : First Series of Tests Second Series of Tests Load in watts Cosi^' Load in watts Cosv)«' 7,241 6,307 5.30s 4,376 3.429 2,454 1,497 535 •997 I -002 ■996 I-OOI •996 •992 ■999 •984 7.329 6,328 5,344 4.402 3.405 2,472 1,50s 534 ■997 ■996 I-OOO i-ooo I-OOI 1-003 ■996 ■980 Thomson-Honston Transformer. — The general shape of this transformer is given in fig. 201. In the first types the iron plates had the shape of a double T (fig. 207); A.Bj'e' pic CD gone k; the two coils were wound 220 ALTERNATE CURRENTS in the spaces v v, and the magnetic circuits were completed By the two pieces efg h and // k I, also formed of laminated plates: A B e- s i s' v' 7 V V, ,y K F '■ a" d Fig. 207 At the present time the plates are in the shape of an E (%• 208) ; the coils are placed in the spaces v v, and' the magnetic circuits are completed by the two pieces abed and efgh. The Thomson-Houston Co. have also built transformers for constant current in the secondary ; the secondary coil is suspended on a rocking lever above the primary. When the induction varies A. < 1^ b e s c c d 3 iL v V 1 ■ 1 « X. D c Fig. 208 Fig. 2og the secondary coil is displaced in relation to the primary, so that the secondary current remains constant. TRANSFORMERS AND CONDENSERS 221 Westinghouse Transformer. — This transformer also is of the type indicated by fig. 201. Fig. 209 shows the method of form- ing the magnetic circuits ; the stampings are cut along the lines a b and c d, and the pieces removed. The coils are then placed on the central part of the e, and the pieces which were removed are replaced, so as to complete the magnetic circuits. As a rule no paper is placed between successive stampings, as the rust insulates them sufficiently. The whole transformer is then clamped firmly by means of bolts between two cast-iron frames placed at the ends of the iron stampings. Fig, Messrs. Ryan and Meritt have traced by the method of instan- taneous contacts, curves showing the working of a Westinghouse ALTERNATE CURRENTS transformer at different loads, ing dimensions (fig. 202) : a = 4'6 inches c=t6 „ This transformer had the follow- d=- 2> inches ^ =- i'2 inch The volume of iron was 132 cubic inches, the principal section of the magnetic circuit 10 square inches, and the average length T2 inches. Fig. : The number of turns of the primary circuit was 675, and that of the secondary 35 ; the resistance of the primary circuit was 2 1 '8 ohms, and that of the secondary "04 ohm. The curves (figs. 210, 211 and 212) show the working of the transformer (i) on open circuit ; (2) with a load of one lamp ; (3) with a load of ten 6 c.p. lamps. TRANSFORMERS AND CONDENSERS 223 The efficiency, the various losses, the tension in the secondary, &c., are given in the following table ; the primary tension was Load Volts in Secondary Watts Efficiency Losses Hysteresis Circuits " | Primary Secondary Primary Secondary Open circuit I lamp . 5 lamps . 10 lamps . 52 -3 52-3 50-I 47-1 96'I ISQI 388-6 607-9 64-3 300-9 525-0 64-3 77-S 86-6 9S7 93 9 83-1 697 ■4 •9 3-3 8-7 ■9 1-3 4-S The retardation of the secondary E.M.F. behind the primary Fig. 212 E.M.F. which will be observed in fig. 212 (10 lamps on secondary) arises from magnetic leakage. The losses through hysteresis and eddy currents decrease rapidly with the load, as we have seen above (hysteresis and eddy current losses). 224 ALTERNATE CURRENTS (c) Transformers with multiple Magnetic Circuits.— Schuckert Transformer. — These transformers are formed by a ring consisting of thin iron strip wound spirally, consecutive turns being insulated with paper. On the upper surface there are 4, 6, or 8 radial grooves, separated by wedge-shaped projections, and every other projection carries a primary and secondary coil on the top of each other, as shown in fig. 213. Fig. 213 The upper faces of the projections are turned up, and a flat ring of spirally wound iron strip is placed on the top, being held firmly by means of bolts. The Committee of the Frankfort Exhibition conducted tests of a Schuckert transformer of 10 k.w. output ; the primary tension was 2,500 v., the secondary 139 v., and the frequency 50. The transformer consisted of four divisions, each of which had 435 primary and 24 secondary turns. The weight of the copper was respectively 13-6 and 17-4 lb. The ring carrying the teeth weighed 264 lb., and the cover 170 lb. The Committee could not test the transformer under its normal working conditions - they had to adopt a frequency of 100 ; and as they could not reach a tension of 2,500 v. (at this pressure the TRANSFORMERS AND CONDENSERS 225 transformer was intended to have two primary windings in series and all the secondary windings in series), they connected all the primary windings in parallel at a tension of 1,600 v. (or about 30 % more than the normal ^-%°-''), and left the secondary windings in series. The curves (fig. 214) give the results of the tests. The curve of the primary E.M.F. shows the tension which must be impressed on the terminals of the primary in order that the secondary E.M.F. may remain constant (about 176 ».). The Committee also investigated the effect of an increase of the primary tension and frequency on the efficiency of the transformer. /i!sii saea ^st Jtio 8t YTi u^ u-i irt N p t^Qp roroN « r^tN.cp Op « W M M irjioii-im ^ V ^ ^ 4 P P r « 00 00 00 00 C4 N op op ininvp vp CO CO CO CO to irjirim HI pN p N inminin "1 \0 «0 \0 VO VO VO \0 VO CO COCO CO « es w N '-"i VO Tj-mm vpop tN.r^ vb VO »o \b roco CO CO Vpvp M P CO rom"^ , O O O O M HI M HI vovo VO VO CO CO CO CO CO CO CO CO MVO OOO rN.vo r^vo Losses in the cables inh.p. VO VO vO vO pco ro CO « N M N t-^ tV. tN. t^ M M HI ll N W M N CO CO CO CO ^■i O^ O* On O* CO CO CO CO W MOO ON IN c»» VO m HI M W l-l CO CO CO CO Tl- ^ ^ ^ Effi- ciency of dynamo ON ON ON OS On CK On 0\ Op Op Op Op VO VO VO VO u^imrjin Op op op op ^^ IH M M M M HH M tH t^t^W HI t^ t>. ON ON IH HI Ht HI t-l HI l-l HI VO VO VO VO 1 ONvb b b « t^ wop b On b ON M M HI M p HI HI ON b b b On ossa p o M M M l-( ^-3 AhHhHhH hH HH »-H hH hH HH Jin t^ hH I— 1 hH h- ( l-l l-l l-l l-l t-( l-l hH l-l TRANSFORMERS AND CONDENSERS 231 (a) EfBciency of the Transformers of the Allgemeine Electricitats-Gesellsehaft. — The high-tension circuits of the two transformers were connected to one another. The low-tension circuits of one were connected to the alternator, and in the low- tension circuits of the other were inserted the three watt meters and some incandescent lamps. The power t,' suppUed to the first transformer was calculated by means of the power t„ supplied to the dynamo and the known efficiency of the dynamo. This gave t,. Deducting from t, the power lost in the cables between the dynamo and transformer, the value of t,' or the power supplied to the transformers is obtained. T3, the power supplied by the second transformer, was obtained by means of watt meter. The efficiency R] R2 of the two transformers combined was T ~. It was assumed that r, = Rj ; i.e. that the two transformers had the same efficiency. The above table gives the results of four series of tests : ii represents the mean value of the current in the three dynamo circuits, e, the mean p.d. between a dynamo circuit and the common return wire, and E2 between a circuit of the second transformer and the return wire. The following table gives a summary of the results of the large table, and also gives the loss, Pj, in the second transformer calculated from the efficiencies : Power supplied to first transfonner, t/ Power supplied by Efficiency second transformer, T3 T, 1 T,' Losses in second transformer, 'a 136-76 104-36 7336 48-69 126-18 96-04 66-92 43-62 -961 •959 •955 •947 S-12 4-II 3-iS 2-49 In order to be able to apply these results to the calculation of the efficiency of the OerUkon transformer it is necessary to consider the different losses in the transformer. We have p, = p.- -1- p. 232 ALTERNATE CURRENTS p„ the iron losses, are almost constant at given frequency ; v„ the copper losses in the two windings, vary with the load. The Committee assumed after discussion that the following equation was true : p, = 2'26 + •000185X3^. The following table, calculated by means of this equation, gives the efficiencies at various loads : Power absorbed, T, Losses Efficiency Power absorbed, t. Losses Efficiency 40 2-56 ■940 100 4-1 1 •960 SO 272 ■948 no 4-50 •961 60 2-92 •954 120 4-92 ■961 70 316 •957 130 S-39 •960 80 3-44 •9S9 140 5-89 •960 90 377 •960 ISO 6-43 •959 The normal power is about 140 h.p. (100 k.w.), and the effici- ency is then -960. The maximum efficiency for which the iron and copper losses are equal is about •961. {b) Determination of the Efficiency of the Oerlikon Trans- former. — No. I transformer of the first experiment was replaced by the Oerlikon transformer, and a second series of tests, similar to the first, were made. R, is the total efficiency, r„ that of the transformer of the Allgemeine Gesellschaft, and r„ that of the Oerlikon transformer, which was obtained from the equation R„ = ^ TRANSFORMERS 'AND CONDENSERS 233 ^ in 1^ vo ro rn hH M 00 ^^ 00 HI «° in in m m Tl- Th y^ ON OS 9^ ON ON On ON ON ON On n n vo vo M M *& •o >o ^O vo ■«!h X y^ ON ON ON pN On On On OS m vO m vo -^ II « t."|H" t^ \o 00 m vn ro t^ vo 00 vo « K II 00 00 m in 0» ON ON op Op (X> 00 ■S s ^ IUI& ■* 00 m \o w W vo m HI N p p W w M r-^ « ■ m ■* m jO-'2 \o vo vo vo vo vo mm m -* ■* ^ Losses in trans- formers h.p. t^ on 00 r^ •^ p p t-t « ^ On o» hH M M 00 00 VO vn ^ *~* '"' M ro n cr> vo ^ 1^ r^ 00 0> 00 m r-^ M m N 00 00 00 in in in m m in m HI N N « ON On On On vo vD vo -* ^ ■^ »^ IT) (-1 "^ On en N ON i-i in NO h":? '^h ■«i- ^ m Ti- '^ m -^ IH ■-, !> -trt in m in in m -ut \ri m m i2 •^ ^ ■^ in t^ tN. i^ w ■^ in MO t^ r-* 1^ vo vo vo in vo ro r^ > m m in in in in mm m in 3 -* ■* " Q. in m a \o vo '^ ■* ■^ mm M w < 00 00 On, -^00 On ON iri -d- ■* 0^ 00 ■•d- -"i- i^ tN. t^ t;. r^ m in ^ m vo On On On m in On a\ On W OD op op op w ■= P w N ^ ro ON « h'i' 00 00 00 in m ! ja in in in w M M *" ft -si M in On on m °p r* 9P b ON b b^ p W'S' m in ■^■ m -^ in Tj- m ^ M M IH M IH »-( HI ^^ ^•^ & & > 55 »— 1 234 ALTERNATE CURRENTS The total loss in the Oerlikon transformer was capable of being represented by the equation P* = 3'6 + '0001075 t/, Tj being the power supplied by the transformer. The following table, calculated from this equation, gives the efficiency of the Oerlikon transformer at various loads : Ta Efficiency Ta Efficiency Ta Efficiency so ■913 no •949 170 •957 60 ■923 IZO ■951 i8g •957 70 •932 130 •9S3 190 •957 80 •938 140 •9S4 200 •957 90 ■943 ISO •9SS 210 •957 100 ■946 160 •956 220 •957 § 6. Transformer Testing It is first necessary to ascertain whether the different circuits are capable of withstanding the required tension. For this purpose the ordinary insulation tests are of very little use. The trans- former must be run, for at least one hour, at a potential difference two or three times the normal value — (i) Between the primary and secondary ; (2) between the secondary and the core. The transformer must also be tested for rise of temperature at full load and on open circuit. The transformer is run either at full load or on open circuit till the temperatures shown by ther- mometers placed at different points remain stationary ; the temperature should not exceed 600°. If the temperature when running on open circuit is high, the reason is that either the magnetisation current is too large, or that the magnetic circuit is badly arranged. Care must be taken to observe whether the variation of tension at the terminals of the secondary exceeds the limits admissible for a transformer ; in no case should the difference of potential on open circuit differ from that at full load by more than 5 %. The next point to be determined is the efficiency at different loads, as well as the loss on open circuit. The efficiencies may easily be deduced from the curves TRANSFORMERS AND CONDENSERS .235 obtained by the method of instantaneous contacts given in Chapter VII. Or we may employ the calorimetric method of testing. The transformer is placed in a calorimeter, and worked at the required load until the temperature of the water issuing from the apparatus is stationary. If W2, expressed in watts, is the power in the secondary, p the weight of the water in grammes passing per second through the calorimeter, t the temperature of the water on entering the calorimeter, and t' the temperature on leaving, the efficiency is expressed by the equation : V- 4-2^(/-^) + Wj In these tests the resistance in the secondary circuit is always arranged so as to be non-inductive, either by means of incan- descent lamps, or by means of two conductors stretched out in such a way that the current in one is opposite in directio'n to that in the other, or by means of a double-wound coil. The power in the secondary can then be easily determined by means of a dyna- mometer and voltmeter, or a wattmeter. The power in the primary circuit is more difficult to ascertain, in consequence of the lag between the E.M.F. and current. We shall investigate the various methods in Chapter VII. § 7. Transformer Design The data are generally : (i.) E„ the effective E.M.F. at the terminals of the primary coil (in volts). (ii.) Ej, the effective E.M.F. at the terminals of the secondary (in volts). (iii.) The power in watts in the secondary, w. (iv.) The load, — , for which the total losses in the copper and m iron must be a minimum. (v.) The frequency. We first determine the sections of the primary and secondary turns from the maximum current density admissible. The 236 ALTERNATE CURRENTS density usually varies from 330 .amperes to 1,300 ampferes per sq. in. (The lower the density, the better is the efficiency, as well as the automatic regulation.) As at full load the lag is practically nothing, we shall have : w 1) being the efficiency at full load, which may vary from -90 to -97, according to the power. We shall have also : — ^ E2 If /, is the current density allowed, the sections in sq. in, of the conductors will be : _ I, _ I2 Si — -:-, S2 — J-. We can thus find the sections, and choose the wire or strip the section of which approximates most nearly to the value found. In the case of the section of secondary thus calculated being too large, it will be necessary to form the winding by means of several coils placed in parallel, so as to avoid Foucault currents in the copper. The resistance per unit length of the wire can easily be found from tables when the section is known. The next proceeding is to make a sketch of the transformer, proportioning all the dimensions to one unknown quantity. For example, in the case of a Ganz transformer (fig. 219) we shall determine by comparison with an existing transformer the dis- tance /, of the average turn of the secondary from the core, the distance 4 of the average turn of the primary from that of the secondary, and the distance 4 of the average turn of the primary from the axis. It is important to diminish 4 as much as possible, for the volume of the core depends on it. The total volume of the core will be : v = IT (x -f 2/1 + 24 + 24) m x^. TRANSFORMERS AND CONDENSERS 237 The volume v, of the iron will be = 8 v 8 varies with the thickness of the lamination and the paper insulation : it may be generally taken as -85. ^*Zi,*|2ij*_*i» U -•¥'i?-i^-*\ Fig. Z19 Fig. 220 For a transformer of the Labour type (fig. 220) we will take, as before, the lengths /i, 4, 4, by comparison with an existing trans- former. The total volume of the cores, in which there is an induc- tion B, will be : Vi =: 2mnx?. The volume of the end-plates, in which there is an induction .-, will be : V2 = 2 (jc -|- /, -f- /j 4- 4) mp x'^. 238 ALTERNATE CURRENTS Of course it will be necessary to multiply Vj and Vj by 8 in order to get the volume of iron. For a transformer of the Westinghouse t)^e (fig. 221) we shall refer all the dimensions to one unknown x, and we shall have : Volume of iron (induction b), v, = 8 »z 01?. Volume of iron of the rest of the magnetic circuits (induction — ), V2 = 2 8/ (2/ + 2« + o+i)»?^. The maximum induc- 2/ tion, B, being chosen according to the frequency from the table at the end of Chapter I., we If — jc i - ->i can calculate the loss m watts per c.c. of iron for t--x<. 1 »----- -J a the values b, - and B of Fig. 221 / 2p the maximum induction. The total loss by hys- teresis and Foucault cur- rents in the transformer will be expressed by an equation of the form p^^ as^ + bx^. The average length, l, and L2, of a turn in each case is determined as a function of x. For the ring transformer (fig. 220) we shall have : Li ^ 2 (»? + i)je + 8/,. L2 ^ 2 (w + i) a: + 8 (/[ + 4). For the Labour type we shall have the same equation. For the Westinghouse type (fig. 221), the two coils being placed side by side and being rectangular, we shall have : L[ = L2 = 2{m + 2 n + i) X. If the coils are rounded at the ends, we. shall have : L| = L2 = {2 w + TT (i + n)}x. TRANSFORMERS AND CONDENSERS 239 We shall have, then, as a rule : Lj = a' X -\- b' La = a" X + b". The total length of the wire of the primary will be n^ l,, that of the secondary «2 ^2- If Pi is the resistance per unit length of the primary, and pa that of the secondary, we shall have as the total resistances Rj and R2 of primary and secondary : Rj ^ «, Li p] = w, (a! X + ^') pi Rj = «2 L2 P2 = «2 («" X + 3") P2 But we have : — ^ — + a, ^2 E2 a being the ratio of transformation. The transformer must be so designed that the total losses at the power — are a minimum : thus we shall have : m -I w , / _ w 17' m E,' m E2' rf being a coefficient having reference both to the efficiency and the lag ; the value of r)' must be taken less than that oi-q. If m is great 1; must be small, for the lag increases as the load diminishes. We can determine 17' approximately from the curves of effi- ciency and the values of the lag in a similar transformer. The losses in consequence of the resistance of the conductors will be : p,' = n,{a'x + b')p,{i,'f p^ = ^{a"x + b")p,{i^f. The total losses in the copper will therefore be expressed by an equation of the form : /2 = «i(a"'^ + ^"')- 240 ALTERNATE CURRENTS On the other hand, the general formula for transformers is : (J)„ = B s = L^_. We have (figs. 219, 220, and 221) : We get, therefore : 2 IT 'S "zo m x' x" The total loss of power in the iron and copper may then be ex- pressed as : a.x^ + byx-' +- -+-i- X x' This expression is a maximum for a value of x given by the equation : 3 fl, ^^ + 2 ^1 a: — Ci x~ ''■ — 2 (f ] x~^ = o 3 fl, ^* + 2 b^x!^ — c-^x — 2d^-=^ o. This latter equation may be solved by successive approximations or by constructing a curve. We shall then be able to completely design the transformer, and see whether there is space enough for the turns and insulating material. If there is not enough or too much space, the calcula- tion may be gone through afresh with new data. We can afterwards examine whether there would be any ad- vantage in choosing a maximum induction different from that adopted. We may assume, for example, a maximum induction a little higher, and see whether in this case the sum of the iron and copper losses is greater or less. If it is greater we may assume a maximum induction less than that chosen in the first place, and examine the effect of this change. TRANSFORl^ERS AND CONDENSERS 241 We shall thus succeed in reducing to a minimum the loss at a given load. We may afterwards, by means of the equations given, calculate the efficiency at various loads, the magnetisation current, the lags, and verify the value adopted for ly . It is well to note whether the cooling surface is sufficient, so that the temperature of the iron and copper may not reach a dangerous value. We can assume a surface of 4 sq. cm. per watt transformed into heat. § 8. Condensers A condenser is usually formed of a series of metal plates, separated by a solid or liquid insu- lator, which is called the dielectric. As fig. 222 shows, alternate plates are connected in parallel. If m is the total number of plates {m is always an odd number), k the specific capacity of the insulator, s the useful surface of a plate in sq. cms., e the thickness in cms., c the capa- city, we have : Fig. K ^ ?J- electrostatic units : 47re ^= K {m — i)s I 47r« 9'IO'' C.G.S. units ; = k(^ ^ — L_ farads ; ^Tre 9*10 = K (^i^lil/ -L- = 884 K (^Zli)i 4 ire Q'lo" microfarads. 242 ALTERNATE CURRENTS Condensers may be arranged in parallel as shown in fig. 223. In this case, if c is the capacity of one of the n condensers, the capacity of the whole is n c, and each one of them is subject to the total tension. If they are arranged (as in fig. 224) in series, the capacity of the whole is -, and each one of them is subject to the «th part of the total tension. We may also join a certain number in parallel, and then join these groups in series. Fig. 2Z4 For example, with four con- Fig. "^ densers of i -5 microfarads we can obtain : (i) A capacity of 4 X 1-5 = 6 mf. — all in parallel. (2) 3 X 1-5 = 4-5 mf.— 3 in parallel. (3) 2 X i'5 = 3 mf. — 2 in parallel. (4) I -5 mf. with one alone. (S) ■75 mf. — 2 in series. (6) ■50 mf. — 3 in series. (7) •375 mf. — 4 in series. MM. Hutin and Leblanc undertook a complete series of experi- ments with condensers. In some for moderate tensions (up to 2,500 volts) they used parafiSned paper as insulator ; in others leaves of ebonite. _ The first kind were manufactured by M. Labour, with paper of mediocre quality and ordinary paraffin warmed to about 70° C. Their capacity, measured by the ordinary methods, gave a specific inductive capacity (k) of about 8. The residual charge was almost a quarter of the original charge. If the capacity was measured by the method of alternating currents (Chapter VII.), the value of k was found to be about one-third smaller than by the ordinary method. TRANSFORMERS AND CONDENSERS 243 These condensers, when subjected continuously to a difference of potential (alternating) between 1,500 and 2,000 volts, quickly got warm, and the paraffin melted. They began to hum, and, if the experiment was not stopped, they were soon destroyed. They then tried special paper and paraffin, but this made no sensible difference. They attributed the phenomena observed to the presence in the cells of the paper of drops of water, and traces of sulphuric acid left in the paraffin after refining. That is to say, they found that the dielectric was rendered useless by the presence of conducting spheres. This explains the high specific inductive capacity and the warming when working. ^ By warming the paper several hours at the temperature of the dissociation of paraffin, the constitution of the paper is destroyed and the traces of sulphuric acid eliminated. The paper came out of the paraffin completely changed in appearance : it had increased in thickness, and all trace of fibres had disappeared. By employing this paper as dielectric the specific inductive capacity is reduced to 2 '56, the residual charge is negligible, and the condenser no longer gets warm. This method of preparing paper is, on the other hand, very expensive ; there is a large quantity of paraffin decomposed, and, as the leaves stick to one another, they must be warmed in order to separate them, so that the process is difficult, and results in a great increase in the price of the workmanship. The first condensers, which were considered defective, were subjected to a difference of potential of 4,000 volts for a con- siderable period. After some time these condensers no longer heated, and the specific inductive capacity of the dielectric fell to 2-56 ; i.e. the condensers improved vastly. The effect of the action of heat for several hours was, therefore, the same as the continued electrical displacement which went on among the conducting par- ticles enclosed in the paper. It is possible, therefore, to obtain excellent results with paraffin paper, if the condensers are formed by an alternating current in the manner above indicated. When first put in service they must be watched carefully, and cut out as soon as they begin to get sensibly warm. MM. Hutin and Leblanc give the following practical rule : 244 ALTERNATE CURRENTS A condenser working noiselessly is perfectly safe ; as soon as it com- mences to hum it is in danger. The formation of a condenser with paraffin dielectric shows that the action of alternating currents, contrary to that in the case of continuous currents, improves the insulator rather than weakens it. The explanation of this fact is as follows : " Under the action of a constant difference of potential all the conducting molecules enclosed in a dielectric set themselves once for all, like the ions and cathions of an electrolyte. These molecules tend to move towards one angther, which they can only do by breaking a way through the dielectric, and thus altering its composition. " Under the action of an alternating difference of potential there is electrical displacement in the interior of the mass itself. Now we have never been able to send an alternating current, even of very small size, through a Uquid without showing traces of libera- tion of gases. Is it not logical to assume that the same action occurs in the case of these conducting particles, and thus the gaseous products are never completely recombined ? It could not be otherwise, for there is no transformation of which the efficiency is equal to r. " We thus have an explanation of the fact that all imperfectly conducting substances, which only transmit current like an electro- lyte, that a dielectric may contain, will be destroyed by the action of an alternating difference of potential before the mass of the dielectric has been changed by the action of these molecules on one another." By employing ebonite as dielectric, the capacity'measured by the ordinary method, or by the use of alternating currents, is the same, and the condenser does not get warm. MM. Hutin and Leblanc stuck the leaves of foil on the ebonite plates by means of Chatterton compound. The ebonite sheets were laid on a warm plate, when they softened and became quite pUant ; the foil was applied by means of an ordinary flat- iron. The thinnest ebonite plates ('2 mm. in thickness) were not perforated by a potential difference of ii,ooo volts, which was the highest the experimenters could reach. TRANSFORMERS AND CONDENSERS 245 Celluloid gave excellent results, but its great inflammability (a spark is sufficient to set it on fire) prevents it being used com- mercially. The variety of celluloid known as American linen gave the best results, but as they found ebonite very clieap they gave it the preference. When the tension at the terminals of the condenser is raised to any extent, a crackling noise is heard, and at the same time there is a smell of ozone. MM. Hutin and Leblanc attribute this fact to lateral discharges, due to the higher harmonies of the current. This noise may be suppressed by in- creasing the distance of the edges of the foil from those of the dielectric. When the tension exceeds 10,000 volts this distance must be at least two inches. MM. Hutin and Leblanc tried glass as dielectric, but when it is subjected to rather high tension it breaks up into small pieces and ruins the condenser. It is also possible to employ oil as an insulator ; but then it is necessary to separate the plates by a certain interval, so that the oil may circulate between them. The specific inductive capacity of oil varies with the temperature within wide limits. MM. Stanley and Molly have built liquid condensers (fig. 225) formed in the following way : Cones of sheet-iron are placed in a case, one on the top of another, and separated by insulating pieces ; the case is then filled with a solution of bicarbonate of soda. It is the polarisation capacity which is made use of, the apparatus being simply a liquid bath with multiple electrodes ; thus the condenser can only act for a moment, and its capacity varies. MM. Brown and Boucherot used condensers of this type to obtain the lag necessary to start asynchronous single-phase motors. The Stanley Electric Company of the U.S.A. builds condensers Fig. 225 246 ALTERNATE CURRENTS which will stand a difference of potential of 500 volts, using sheets of foil separated by waxed paper. M. Bedell, in his experiments with the hedgehog transformer, used the condensers of this company. The I'S microfarad condenser consisted of two parts each of •75 mf connected in parallel. Each of these parts consisted of sixty-five sheets of foil ■0018 cm. in thickness. The waxed paper was "0113 cm. in thickness; the useful part of the plates was 26-67 f^tiis. long and 20*32 cms. broad. From the specific capacity of the insulator we have : e 10'" e lo^" 75 X "0113 X 10'" K = 884 (»? — i)i 884 X 64 X 2667 X 20-32' M. Bedell employed in his experiments six condensers of i"5 mf. As the tension was about 1,000 v., and as the condensers would not stand more than 500 v., it was necessary to arrange at least two in series ; he could obtain a capacity of from -^ = •25 2 ^ The commercial condensers of Swinburne are formed of leaves of foil, separated by several layers of thin paper. The whole is then placed in a case fiill of oil, and warmed to expel the moisture. A vacuum is then produced in the case to extract the air, and it is hermetically sealed. There are always in a condenser, beside losses due to leakage, bad insulation, &c., a loss due to the dielectric itself The power supplied is always greater than the power delivered, on account of a kind of hysteresis analogous to magnetic hysteresis. Curve fig. 226 was obtained by M. Bedell. The abscissae represent the instantaneous values of the E.M.F., and the or- donnates the corresponding charge, ^ = J ii^f- It will be seen that the curve is similar to that for magnetic hysteresis ; the surface enclosed is proportional to the loss of power. TRANSFORMERS AND CONDENSERS 247 With a current of a frequency of 140 the loss was 4-4 watts, corresponding to an efficiency of 96-9 per cent. 1 " oue IJ *f5^ fl OOiO 0009. nm OOOJ 0006 0006 00041 :s ^ T rag ^ X Uo p ^^ ^ 15 ^ r 000! OOflJJ ^ J^ Si 10 8 10 7 10 e 6 )0 * 3 ]0 2 10 u K 0000 10 2 13 3 10 * 10 e 10 6 10 5 10 80 9 10 ^ ^ 0002 II ^ y 0001 IS / ^ i^ 0000 i i^ ^ 53 = oooe "1 ^ y 0010 17 0' 1 _,„ 00i8 !1 Fig. 226 Condensers may be of large capacity and work by means of transformers on a low-tension circuit, or of small capacity and work in the high-tension circuit. In the two cases the energy stored may be the same — ?>. the condenser may produce the same effect. It is difficult at the present time to give the preference to either system from the point of view of the prime cost, as con- densers are employed very little commercially. 248 ALTERNATE CURRENTS CHAPTER IV DIRECT TRANSFORMATION OF A CURRENT OF ONE SYSTEM INTO THAT OF ANOTHER § I. Comparison of the Different Systems from the Point of View of the Conductors The loss in the line wires, in relation to the loss in the case of a single-phase current, due to the same maximum E.M.F. at the generator, for an equal weight of metal used is : loo % for "biphase currents with separate return wires. 73 % for biphase currents with common return wires. 25 % for triphase currents with the double-star method of connection. 75 % for triphase currents with the double-triangle method of connection. 25 % for triphase currents with the star-and-triangle method of connection. 75 % for triphase currents with the triangle-and-star method of connection. In the case of single-phase current the maximum tension between the two conductors is equal to the maximum tension of the generator, but in the case of polyphase currents the difference of potential between two conductors may be considerably greater than the E.M.F. of the generator. Suppose that e is the greatest allowable difference of potential between any two conductors (in the case of single-phase current E will be the E.M.F. of the generator) : (i) In the case of biphase current with separate return wires the maximum allowable E.M.F. of the generator will be v/ 2 DIRECT TRANSFORMATION OF CURRENTS 249 Consequently, for the same power transmitted the Hne losses will be double those for single-phase current. (2) In the case of biphase currents with common return wires the maximum allowable E.M.F. of the generator will be —-=. V 2 Consequently, for the same power the line loss will be i -46 times that for single-phase current. (3) In the case oitriphase currents with star method of connection E the greatest permissible E.M.F. of the generator is — ^ . Con- sequently the line loss will be 75% of that with single-phase current. (4) In the case of triphase currents with triangle method of con- nection, the greatest allowable E.M.F. of the generator is — . 3 Consequently the line loss will be 675 times as great as for single- phase current. Summing up, if we compare the weight of the conductors for the same loss of power in the line with the weight in the case of single-phase current, we have as the weight of conductors (the weight for the conductors in the case of single-phase currents being 100) : I. Employing the same tension at the generator — For biphase currents with two return wires, 100. For biphase currents with one return wire, 73. For triphase currents with triangle mounting, 75. For triphase currents with star mounting, 25. II. Employing the same difference of potential in sepa?-ate circuits — For biphase currents with two return wires, 100. For biphase currents with one return wire, 146. For triphase currents with triangle mounting, 225. For triphase currents with star mounting, 25. III. Employing the same difference of potential between any iivo conductors — For biphase currents with two return wires, 200. 2 so ALTERNATE CURRENTS For biphase currents with one return wire, 146. For triphase currents with triangle mounting, 675. For triphase currents with star mounting, 75. § 2. Transforming of Currents The transforming from one system to another may always be effected by using a motor which drives a generator producing the required currents. If necessary, the motor and generator windings may be superposed on the same armature. In the following section we shall describe special devices for effecting a direct transfor- mation. We shall be able by means of these devices to transform — (i.) Continuous into single-phase alternat ecurrent, and vice versa ; (ii.) Continuous into polyphase currents, and vice versa ; (iii.) Single-phase current into polyphase currents ; (iv.) Triphase currents into biphase, and vice versa. §3. Transformation of Continuous Current into Single- pliase Alternate Current, and vice-versa The Solignac Periodiser. — As a shunt to the primaries of two transformers, t, and Tj, connected in series, are placed resistances ^ij ''21 ''sj &c- (fig- 227), of which the ends are joined by means of brushes by and b^ to the revolving commutators a, and Aj, which are fixed on the same spindle. The metal part of these commu- tators (shaded in the figure) are joined up to the dynamo d by means of the brushes Bi and Bj. If the two commutators are in the position shown in the figure, and it is easy to see that the current coming from the dynamo D will pass directly through a 3i Bi c, on reaching c the whole of the current will pass through the primary of Tj, since the brushes ^2 are insulated ; while practically no current will traverse the primary of t„ which has considerable impedance. When the commutators have turned through a certain angle the first brush, b^, will touch the insulating material, and the current at a will be divided between the primary of t, and the cir- cuit a B, c, which has a resistance r,. At this moment the bottom DIRECT TRANSFORMATION OF CURRENTS 251 brush b^ of the commutator Aj will be upon the metal portion, and the current at c will be divided between the primary of Tj and the circuit c b^ B2 d. CL + \ rj b^ ''it h k Fig. 227 It will be seen, therefore, that as the commutators revolve, the current in the primary of x, increases in proportion as the current in the primary of Xj decreases. This will be the case till all the brushes bi are on the insulated portion, and then the total current will pass through the primary of Xj, whilst the primary of Xj is short-circuited owing to all the brushes ^2 being on the metal portion of the commutator. After this the current in the primary of X, will diminish, whilst that in the primary of X2 will increase. By placing the primary circuit current reversers ij and ij, which alter the connections each time that the current passes through 252 ALTERNATE CURRENTS the yalije o, the secondaries are traversed by alternate currents. The theoretical curves for these currents are represented in fig. 228, one as a full line, and the other dotted. M. Hospitalier has conducted tests of the efficiency of this machine, and has obtained the results in the table below. The powers p„, Pi, Pj in this table are expressed in arbitrary units ; the total power was almost 14 k.w. In these tests no account was taken of the power necessary to rotate the commutators. To sum up : in this system the ampere turns of the transformer are varied by altering the value of the current, whilst in the Hutin and Leblanc system the ampk'e turns are varied by altering the number of turns. Number of the experi- ment Power supplied to the machine, Power delivered by the machine, p, Efficiency Pi Power delivered by the transformer, Ta Efficiency of the whole Speed of the commutators I 2 3 Average I4S 141 142 142 '6 131 133 133 •93 ■93 •936 ■932 114 114 113-6 78 •80 ■805 796 f 1,120 /1. 130 11,170 J 600 I 620 The reversing transformer of Felix Lucas, engineer-in-chief of bridges and highways, allows of giving to the alternate current a frequency which only depends on the number of revolutions. Two copper discs, a and b (fig. 229), insulated from each other, are fixed on one spindle. Each of these discs has a cylindrical boss (see section), and is divided up into a certain number of metallic sectors of equal width, separated by intervals of the same width. The two discs, placed face to face and insulated by ebonite, are arranged so that the sectors of one DIRECT TRANSFORMATION OF CURRENTS 253 correspond to the intervals of the other. The ebonite piece which insulates the two discs carries projections which fill up the intervals between the sectors ; this ebonite piece also insulates the bosses from the spindle. The whole forms a large disc with copper bosses on either side ; when rotated the periphery presents a regular alternation of copper and ebonite bars on either side of the ebonite in the centre. Fig. 229 gives the plan of connections. The two discs are there represented as detached from one another and in the same plane. Each disc carries fifteen copper sectors and fifteen ebonite sectors, the ebonite being represented by the shaded part. Fig. 229 On the periphery two brushes, m n and P Q, rub ; these brushes are connected as shown in the figure. The continuous current, supplied by a dynamo or battery of accumulators s, is conveyed to the metalbosses of a and b by two brushes, which are joined respectively to the positive and negative poles. In the position shown in the figure, as the brushes M and Q are joined to s, while brumes n and p are insulated, a current traverses the external circuit in the direction of a b. When the discs have advanced one division (^^ of ^ revolution) the case is reversed : P and N are joined up to s, whilst m and q are insulated, so that the external circuit is traversed by a current in the direction b a. It will therefore be seen that on rotating the disc an alternating current is sent through the external circuit. If n is the number of revolutions per minute of the dist, n the number of copper sectors, the frequency of the current will be n n. It is necessary that the bearing surface of the brushes on the disc should be 254 ALTERNATE CURRENTS small, so as to only make contact with two brushes at a time, for when the four brushes are in contact with the copper sectors at the same time the current generator is short-circuited. By modifying the arrangement, as is shown in fig. 230, the brushes may have a larger bearing surface. Fig. 230 The copper sectors correspond to an angle of — , and the 3« The brushes have an angular in the figure n = 10, = 6° ), and 3« / ebonite sectors to an angle of ^~. . 2,n bearing surface of — (in the figure « = 10, ^^^^ = 6" 1, and are 3« \ 3' arranged so that when m is in the middle of an ebonite sector N and p are in the middle of a copper sector, and Q in the middle of an ebonite sector. The short-circuits are then instantaneous, and take place when one of the edges of each brush corresponds to the line of separation of a copper and an ebonite sector ; this occurs simultaneously for all four brushes. Fig. 231 The alternating current thus produced is not sinusoidal theoretically (that is to say, supposing the short- circuiting is DIRECT TRANSFORMATION OF CURRENTS 255 instantaneous, and neglecting the influence of self-induction) : it is represented by the curve in fig. 231. The effective current and the mean E.M.F. are equal to those of the continuous current from which it is derived. By adding 2 m pairs of twin brushes, retarded behind each other by - th period, it is possible to produce m currents retarded ~th period behind one another, i.e. polyphase currents may be generated. The triphase system is particularly interesting ; it is easy to see that if the centres of the stars are joined to the ends of the circuits an alternating current of the same nature traverses the wire which joins them ; this current, however, although it has the Fig. 232 same value as each of the partial currents, has three times as many periods. (In the case of true sinusoidal currents there is no current in this wire.) We thus obtain easily a three-fold frequency, which is of importance in certain cases. The curve of current is shown in fig. 232. M. Felix Lucas has had built by the Sautter-Harld firm two transformers, one after the pattern of fig. 229, with fifteen copper sectors, and the other after the pattern of fig. 230 with ten. In the first transformer the brushes were arranged in a special manner. The double brush was composed of a copper cylinder, one inch in diameter, which rolled on the periphery of the discs. Each of the two parts m and p of the cylinder was insulated from the other, and both were a little greater in breadth than the disc. This double brush rotated in contact with the discs, and the current from either half was collected by gauze brushes. 256 ALTERNATE CURRENTS Each of the two transformers could be driven by a little Gramme motor, running at 2,000 revolutions per minute. The frequency of the current from the first transformer was : 2000 X IS -"60 = 5°°- Of the second : 2000 X 10 6^ = 333- M. Liicas states that the continuity and invariability ,of the current taken from the generator were almost perfect, when either single-phase or polyphase currents were being- produced. In the case of polyphase currents the theory of the three-fold frequency of the current in the wire joining the centres of the stars was confirmed practically. By sending the alternating current from either of the trans- formers through the primary of a Ruhm-Korff coil (the trembler being fixed), an alternating current of the same frequency but of higher tension was produced, by means of which a Geissler tube could easily be incandesced even when only one of the terminals was connected to one end of the tube. The transformer with metallic sectors equal to the ebonite sectors allows, for the same diameter and speed, of a greater frequency than the other type. The two discs may be simply insulated from one another by air without interposing any ebonite ; they may consist of a metallic wheel, the periphery of which is notched and the spaces filled up with insulating material. M. Lucas makes the following calculation. Suppose the discs are 40 inches in diameter — i.e. 125 inches in circumference, and have 314 teeth about \ inch in width. If the discs revolved at a speed of 32 revolutions per second, the frequency would be 10,000. By giving each disc a breadth of 4 inches, 50 amperes could be collected by one system of twin brushes (M. Lucas states that 5 amperes per -4 inch in width may be collected with- out sparking if the brushes are carefully set) ; but as it would be possible to employ simultaneously twenty systems of twin brushes connected in parallel, 1,000 amperes at a frequency of 10,000 could be collected. DIRECT TRANSFORMATION OF CURRENTS lyj Apparatus of M. Follak for Transforming; Singl«-phase Alternate into Direct Current.— The alternating current is used to charge a battery of accumulators, and the direct current is taken from these. The apparatus consists of a commutator, fixed on the spindle of a little synchronous motor. This commutator is provided with as many bars as the motor has poles. In fig. 233 the motor has eight poles and the commutator eight bars. Bars i, 2, 3, 4 are connected to one another and to one of the poles of the battery of accumulators ; the other four bars, 5, 6, 7, 8, are connected to the other pole. Two pairs of brushes, c d and ef, make contact respectively with two consecutive bars of the commutator ; the pair of brushes c d are connected to one end of the alternating circuit, and brushes efto the other end. .A f^ / V \ •^ a.' (-•• g" tV \ 1 V \ «? 0; d ;4 ' ^ Fig. 234 As the commutator has as many bars as the motor has poles, it will be evident that a rectified current will flow through r and s. If the bars were separated by a very small space, or if the brushes were set in such a way as to make the time very short during which the contacts were broken, a rectified current would be produced" with curve as shown by the upper part of fig. 234. If the E.M.F. of the battery is represented by the straight line a h, it will be seen that if the circuit was kept closed all the time the battery would -discharge s 258 ALTERNATE CURRENTS into the alternating circuit during the intervals a' d, d' h', &c. To remedy this defect, the commutator bars are separated from one another by a certain interval, and it is only necessary to move the brushes in order to regulate the time during which the alternate circuit is open. This time is determined practically by shifting the brushes until there is no sparking, for at the right moment the two E.M.F.'s must be equal. When the E.M.F. curve is sinusoidal, it will be noticed that the times during which the circuit is open are relatively large, and that the E.M.F. varies very much during the time that the circuit is closed (from c' c to g' g), which has a bad effect on the life of the accumulators. M. Pollak has overcome this difficulty by altering the shape of the curve of the alternator, by sending the current through a transformer the core of which is almost saturated. In this way a curve, represented by the lower part of fig. 234, is obtained ; the intervals during which the circuit is open are shorter, and the variation in E.M.F. while the circuit is closed is much less than in the case of a sine curve. With this type of curve it may "happen that the part d\ o^ may not he equal to the part o^ h\ : it is for this reason that the brushes are duplicated, so as to permit of exact regulation of the intervals of open circuit. In the apparatus that M. Pollak used for his experiment, the commutator, of ring shape, had eight segments and eight pairs of brushes : brushes such as d and / were shifted simultaneously by a common rocker. A Siemens alternator supplied current to the motor, which ran at 300 revolutions. The rectified current was taken from the secondary of a little transformer with saturated core (the ratio of transformation being i), and the primary was traversed by the current from the alternator. The battery of accumulators consisted of 24 cells, and had a capacity of 500 ampere hours. A reversing switch arranged for the changing of the connections, so that the E.M.F. of the recti- fied current should be in opposition to that of the cells : the direc- tion of the E.M.F. was determined by means of incandescent lamps. In the primary circuit of the transformers there were 62 volts and 50 ampferes, and in the charging circuit there were 60 volts and 40 amperes. The synchronous motor absorbed 100 watts. DIRECT TRANSFORMATION OF CURRENTS 259 § 4. Transformation of Continuous into Polyphase Currents and Vice-versa Hutin and Leblanc's Transformer.— The first trial of this transformer took place between La Chapelle and Epinay. At the w tension generator "1 Sick view of I tnotot Liiu No. 1 to Efitiay Line No. 2 to Epinay Line No. 3 to Efinay Fig. 23s generating station at La Chapelle, a continuous current machine was installed, giving 100 amperes at 160 volts. The transformer for converting the continuous current into polyphase currents S2 26o ALTERNATE CURRENTS was formed as shown diagrammatically by fig. 235 and in per- spective by fig. 236. A little synchronous motor (represented for greater simplicity in the figure as being bipolar) carries on its spindle a commutator A, with as many segments as there are primary .coils on each of the cores of the polyphase transformer (in the figure there are six). As for a moderate frequency the synchronous motor, if bipolar, would have too great a speed, a multipolar motor is generally used ; if this motor has 2.p poles, the commutator has np bars,- n being the number of primary coils on each core. The motor spindle also carries six insulated rings, each of which is connected to one of the commutator bars (or to/ bars in the case in which the motor has 2p poles). The motor is excited by current from the continuous generator. When the motor revolves at n revolutions per minute the circuits of the- DIRECT TRANSFORMATION OF CURRENTS 261 secondary coils (connected in star fashion) are traversed by currents differing in phase by — and with a frequency f =/ — , 3 "O if the motor has 2/ poles. The variation of the currents in the secondary coils of the transformer is effected by the device of varying the number of turns of the primary coils. It will be seen from the figure that the six coils on each core of the transformer are of sizes varying according to the sine law. As these coils are successively con- nected to the generator of continuous current by means of the six rings and the commutator a, the induction in the core will be such as to produce a sinusoidal current in the secondary coil of the transformer. The three series of primary coils on the three cores of the transformer are arranged in such position as to produce a retardation of — in the respective secondary coils. 3 The receiving apparatus at the Epinay station is arranged in an exactly similar manner, the current taken from the commutator being used to charge accumulators. The exciting currents of the two synchronous motors are so regulated as to annul the current lag, both in the six primary circuits at La Chapelle and the six secondary circuits at Epinay ; consequently the commutators do not spark. At the Epinay station the transformer is used to charge a battery of 64 cells with 9 plates. This battery lights 60 incan- descent lamps of 10 c.p. The frequency is about 55 ; it was intended to use a frequency of from 80 to 100, but with the apparatus used maximum effi- ciency was obtained for a frequency of 55. The tension in the line, with respect to earth, varied from 4,300 to 4,975, the maximum current being i'96 ampferes. In February 1894 the tests given in the accompanying table were made. The power supplied and delivered was measured by Aron meters, carefully calibrated. The efficiency increased with the power and reached 85*6 %. If the engine had been large enough to give the full output of the generator the efficiency would have been higher. 262 ALTERNATE CURRENTS Dura- tion of test Volts and current of the generator at La Chapelle Kilowatts supplied by La Cfhapelle Kilowatts received at Epinay Efficiency (rough) Efficiency excitation included Voits Current h. 2 3 2 3 3 2 2 2 4 3 2 2 i6o 170 IS5 200 150 180 160 15s 200 iSS 198 170 16S 52 52 47 60 54 54 67 60 60 57 I 50 16-4 26-9 r6-s 28-3 13-9 9-8 19-6 15-37 33-5 TS 28-3 26-8 24-2 12-8 22-3 127 23-6 11-8 8-1 17 127 30 lO-OI 24-07 23-3 ig-S % 80 82 79 82-3 85 81 -s 867 84 89 87 847 ^5 81 % 75-4 79 74-1 8o-6 8o-5 76-3 82-4 8o-6 85-2 79-6 83-1 82 78-5 The excitation of the motor at La Chapelle absorbed '085 k.w. and that of the motor at Epinay -236 k.w. The rough efficiencies are the ratio of the kilowatts in low-tension direct current at Epinay to the kilowatts in low-tension direct current at La Chapelle. The net efficiency is equal to the above mjnus the excitation of the Leblanc motors at La Chapelle and Epinay. The E.M.F. on the line varied from 4,800 to 5,500, and the current from '8 to i'5 ampere. The distance through which the power was transmitted was about five miles. § 5. Transformation of Single-phase Currents into Foljrphase There are several ways of transforming single-phase into poly- phase currents. (i.) By means of two shunted circuits. In the Tesla system, the time constants of the two circuits are very different in con- sequence of the different self-induction of the two circuits. In the Hutin and Leblanc system, the retardation of the current in one circuit behind that in the other is obtained by the use of condensers. (ii.) In the Ferraris system, the single-phase current traverses one circuit while the other has an induced current in it. (iii.) The single-phase current may be sent through the primary DIRECT TRANSFORMATION OF CURRENTS 263 of a transfonner with two secondaries which furnish biphased currents. Fig. 237 264 ALTERNATE CURRENTS (iv.) By means of a condenser transformer. The apparatus of M. Ddsird Korda allows of the transforma- tion of single into triphase currents. It consists essentially of a transformer with three cores Tj, Tj, Tj (fig. 237) and of a coil with a variable coefficient of self-induction. The circuit of the single-phase current is divided at a and b, and the two branches have the same resistance r. Suppose that in the branch (2) we place a coil, the coefficient of self-induction of which fulfils the condition : KL ,— , „ — = V •J = tan 60°. R "^ The instantaneous value of the current in branch (i) being : E /, =— sin Y^t, R that of the current in branch (2) will be : «2 = -7==== sin (k ^ - 0) = ^ sin (k i? - 60°). 2 R ^ ' By winding branch (2) n times on the core Tj, and branch (i) - times on the core Tj in the opposite direction, we shall get two magnetic fluxes. That of the core t, will be represented by the expression : *i = $0 sin K t, and that of the core Tj by : *2 = — *o sin (k ^ — 60°) = *„ sin (k / — 240°). By winding on the third core T3, the branch (2) n times, and the branch (i) _ times, but in the opposite direction to the windings on Ti and Xj, the flux in the core of T3 may be represented by the expression : *3 = — *i - *2 = * {sin (k ^ — 60°) — sin k i\ — % sin (k / — 1 20°). DIRECT TRANSFORMATION OF CURRENTS 265 We have therefore three fluxes of the same maximum intensity, retarded behind one another by one third of a period. By pro- viding each of the cores with a secondary coil, we can collect triphase currents. One end of each secondary coil may be joined at o, which will be the centre of the star. If o is connected to the symmetrical point o' or to Earth (o' being in that case also connected to Earth), so long as the condition ~ = ^/ 3 is fulfilled no current will circulate in this wire. As long as this transformer works at full load transformation takes place in the usual way, and the retardations are theoretically correct ; but as soon as the load diminishes such is no longer the case, and the lags are far different to the theoretical quantities. § 6. Transformation of Triphase into Biphase Currents and vice-versa The apparatus effecting this transformation is due to Mr. Scott, who described it at a meeting of the National Electric Light Association of Washington. A B C 0.s^ tumsi'-^n^'""'^ saaaaaaaaa/ 71' turns D) 1 Ti turns Wwyvvw /vwwwwi n turns E F Fig. 238 Fig. 238 indicates the principle of this apparatus, which is formed of two transformers t and t'. The three circuits are connected in star fashion, the point o forming the centre ; in the circuits d e and f g two currents circulate differing in phase by an angle _ . 2 266 ALTERNATE CURRENTS The, flux in the transformer x' may be expressed by the equation : «>'=*,sin I^K^+i^y The transformer t having "577 « turns for each of the currents, instead of n turns as in t', the flux may be represented as : $ = -577 $„ i sin [k / + ^ J — sin K ^ I = X sin ( K / + <^) X sin ^ = -577 $„sin— = -5 $„ 3 X cos <^ = -577 *„ (cos ?-^ — I J = — -865 "t, X' = [(-5)' + (-ses)^) ^? = ^J" X = $ tan d being expressed in cm. and - being the frequency per second. d" d' d' i-oooo 720 1-3180 2,880 2-3937 20 i-oooo 980 I -4920 S.I 20 3-0956 80 I-OOOI 1,280 1-6778 8,000 3-7490 180 I -0258 1,620 1-8628 18,000 5-5732 320 I -0805 2,000 2-0430 32,000 7-3250 Soo I -1747 2,420 2-2190 DISTRIBUTION MAINS 269 It will be sufficient, therefore, in order to find the effective resistance of a given wire, to calculate the value of the product — and take the corresponding value from the table (interpolating if necessary). If the specific resistance of a metal other than copper is less than I "597 C.G.S. units, and if its magnetic permeability is equal to I (which excludes iron, steel and nickel), the factor — must be multiplied by— 5zZ, s being the specific resistance of the metal in C.G.S. units. When the factor — exceeds 32,000 the effective resistance may be determined sufficiently accurately by calculating the resistance of a solid conductor equal to that of a tubular conductor of the same external diameter as the original conductor, of which the thickness is : 6-38 n/t cm. § 2. Influence of Heat and Cold The ohmic resistance of the copper increases with the tempe- rature. For average temperatures, we can assume that if r is the resistance at ^ the resistance Rj at ^1° is : R, = R: (1-00388) '■-'■ The following table gives the coefficient of the increase in resistance of copper for temperatures increasing by 5° at a step. A wire of pure annealed copper i mm. in diameter and i m. in length has a resistance of "02034 ohm at 0° C. (Matthiessen). DiflFerence Difference Difference of CoefGcient of Coefficient of Coefficient temperature temperature temperature s I -0196 35 I -1453 65 1-2863 10 I -0395 , 40 1-1636 70 I-3114 IS 1-0598 ! 45 1-1904 75 1-3371 20 I -0806 50 I -2137 80 1-3663 25 I-I0I7 55 1-2374 30 1-1232 60 I •2616- 270 ALTERNATE CURRENTS The copper usually employed for electrical conductors has a conductivity of 98 per cent, of that tested by Matthiessen, so that the resistance at 0° of a wire of i mm. diam. and i metre in length is : 100 , r = •02034 — ^ "02075 ohm. 98 The resistance at 0° of a wire d mm. in diam. and i metre in length will be : -02075 d" and that of a wire of s (mm.)^ section (- — = s ) ■01629 The resistance at 0° of a wire / metres in length is R ■■ '02075 / '01629 , d^ s At 27° the resistance is : •o|2^^;oi8 d^ s In practice we generally take as the values of r : ^22 '018 for conductors, and for wires on the coils of apparatus : ■02; , '02 It must be remembered when applying these formulae, that r is expressed in ohms, / in metres, d in mm., and s in (mm.)^. The sections of different conductors are determined, as we shall see further on, either from the point of view of economic working, or so as not to exceed a certain line loss. When the section of the conductor is thus determined, it is necessary to verify that it is not too small, i.e. that the resistance is not too high ; otherwise the metal might reach too high a temperature, DISTRIBUTION MAINS . 271 which would have the double disadvantage of increasing the resistance of the conductor considerably and diminishing that of the insulator. In fact the power lost in consequence of the resistance r of a conductor is r i^, i being the effective current ; this work is transformed into heat, and, unless the wire is cooled, it would not take long to melt it with a very small current. Cooling takes place by conduction, radiation, and convection. As the loss of heat by cooling increases with the temperature of a body, it is evident that a conductor traversed by a given current and placed under given conditions will, at the end of a certain time, reach a fixed temperature. In order that the insulator may not deteriorate, this tempera- ture must not exceed a certain limit. The Committee of the Institution of Electrical Engineers has formulated the following practical rule : ' The temperature of a conductor traversed by a current double that of the normal value should not exceed 65° C As the rise of temperature varies very nearly in proportion to the square of the effective current, and as we can assume the temperature of the air to be 25° C , this rule practically allows in the conductor a rise of temperature of 10° when traversed by the normal current. It is, then, of importance to be able to determine beforehand the temperature of a conductor under given conditions ; unfor- tunately there is a want of practical data, the only conclusive experiments being those undertaken by Kennelly in 1889, which dealt with the cooling — (i.) Of insulated conductors placed in wood casing. (ii.) Bare wires inside houses. (iii.) Bare wires in the open air. The insulated conductors in wood casing cooled to a certain extent by conduction ; when the casing is sufficiently warm radiation and convection also occur. Kennelly found that the rise of temperature varies very nearly proportionately to the square of the current for a given wire, and that for a given rise of temperature the square of the current varies in the same proportion as the cube of the diameter of the wire. 272 ALTERNATE CURRENTS Kennelly has given the following formula for a wire of d mm. in diameter, traversed by a current of i ampere so as to fulfil the rule of the Electrical Engineers. d=-n^l/^ ^ = -052313 I = 4-375 n/^- We have seen above that the copper usually employed has at the temperature of 35° C. (25° + 10°) a resistance r = - °1^ per metre. If we introduce R into the formula, we have : rf3 = -0523l2R — --, 0238 or d^ 2'2 Ri^, a formula which may be used in the case in which the" effective resistance of the metal would be different from that of the copper generally used either on account of its specific resistance or in consequence of the use of alternating currents. In the case in which the conductor is a bare cable, d repre- sents the external diameter in mm. and R the resistance per metre length. The external surface of the cable is per metre : Sj = 1000 IT d. We shall then have from the preceding formula : Sj = 1000 TT 2 '2 Ri^ ^ 6912 RI^, Sj being expressed in sq. mm. If s/ is the external surface of the conductor per metre length in sq. cm. we have : S/ = 69 '12 RI^, R being the effective resistance per metre. R i^ represents the number of watts lost per metre ; the external surface must therefore be 69'i2 sq. cm. per watt transformed into heat. There are no experiments with reference to the cooling of DISTRIBUTION MAINS 273 underground cables, which takes place by conduction and convection. If the cable is concentric, r i^ represents the loss in both lead and return conductor. Let us take a Ferranti concentric cable, which we shall describe further on. It is composed of two tubular conductors of copper, one inside the other, with insulation between. The cable for a current of 250 ampferes (eflfective) has a resistance of 2 ohms per kilometre (lead and return) or -0002 per metre ; the power lost in heat is then : Ri2 = -0002 X 250^ = i2'5 watts. The external diameter of the cable is 49 mm., thus d = 49, which gives a surface of 100 x tt x 4'9 = i"S29 (cm.)^ per metre run. The external surface is therefore -i-5 = 122 sq. cm. 12-5 If we adopt the same value for all underground cables we must have : Sj= 12200 R i^, s, being expressed in sq. mm. As s, = 1000 ir dwe must have : d> 3-88 Rl2. Bare wires inside houses cool by radiation and convection. Kennelly found that for an excess of temperature of a wire of 10° or 1 5° above the atmosphere, the diameter of the wire must satisfy the condition : Ri2= -0175 (f/+ ■175/', / being the diflFerence of temperature, d the diameter in mm., r the effective resistance per metre in ohms, and i the effective value of the current in ampferes. For bare wires in the open air we must have : ri^ = -1175 (// +-175^. If the conductor is formed of several strands we cannot take as the total section the section of the whole, which is greater than that of the wires which form it. T 274 ALTERNATE CURRENTS Each wire, in consequence of the twist, is longer than it would be if stretched taut. The length of the wire, according to the method of stranding, varies from 1-05 to i'28 metre per metre length of the cable. If ^ is the resistance per metre of one of the n wires forming the cable, the resistance of the cable will be : ^ _ y(i-o5toi-28.) n The ohmic resistance of the cable is greater than that of a straight wire, having for section n times the section of one wire, but the effective resistance will generally be less, as we have seen, than that of the corresponding single wire of equal section. § 3. Influence of Capacity and Self-induction The equations relative to capacity uniformly distributed along a cable are very complicated, and unsuitable for ordinary purposes. We shall therefore assume that in practice the capacity is concen- trated at certain points. In armed cables with one conductor we may suppose" the capacity replaced by a condenser inserted in the circuit. Practi- cally no current circulates in cables with one conductor (lead and return) when the circuit is broken at one end. When the circuit is closed the capacity comes into play, and may annul the effects of self-induction in the alternators and transformers or produce a rise of potential. Concentric cables may be compared to a circuit as a shunt to which is connected a condenser of capacity c equal to the total capacity between the inner and outer conductors of the cable. If R is the effective resistance of the cable, l the coefficient of self-induction of the generating portion of the circuit, d the total capacity of the cable between outer conductor and the arming, r and / the effective resistance and coefficient of self-induction of the portion of the circuit in which the power transmitted by the cable is utilised, we have, representing by i the maximum current circulating in the cable : DISTRIBUTION MAINS 275 The intensity x of the current circulating in the receiving apparatus will be, according to the values of k, c, r, and /, smaller or large'r than that of the current in the cable. The capacity in farads per cm. length of the cable is given by the equation : 18 X 10" X log,, Kl, r\ Ti and r^ being respectively, in a cable with one conductor, the interior radius of the arming and the external radius of the conductor. In a concentric cable, to get the capacity between the inner and outer conductors we must take for r2 the interior radius of the outer conductor, and for r^ the exterior radius of the inner conductor. The capacity in farads is 100 k/ k/ 18x10" log„ tL2 18 X io9 log,.-?' I being the length of the cable in metres. As log. — = 2"3 log — we have : c = farads 4i"40 X 10^ log ^ — m.f. 41 -40 X 10' log-'' K is the specific inductive capacity of the insulator ; this coefficient is often different from that obtained for a continuous current. MM. Salford and Halmann give the following values for k in the case of an alternating current : 276 ALTERNATE CURRENTS Petroleum (Brook's system) K = I"6 Caoutchouc K = 3'7 Solid paraffin = 2-0 Cotton soaked in paraffin in a vacuum = 2-0 Cotton soaked in boiling paraffin = 2-0 Artificial gutta-percha (Gwin) . = 4-2 Glass = 4-6 Ferranti cables for 250 amp. have an inner conductor 8 inches in diameter (external), and an outer conductor of 2 inches internal diameter; their capacity is "31 m.f. per mile. The specific inductive capacity of the insulator, which is waxed paper, may be found from the formula given above. We have : 41 '4 X 10' log — ^ K- ^^ log ^ = log ^^ = '356 ^ ?onn K / ^ .^ ■^ y x'' 's ^ // / / r f Fig. 242 The first experiments were made to determine the sparking distance in air. The tension was measured at the terminals of the transformer : one of the electrodes was fixed in a horizontal position, and the other was capable of being moved horizontally by means of a screw, which indicated the hundredth part of a mm. The electrodes were brought together until sparking appeared. Each experiment was made three times, and the electrodes were polished each time. Fig. 242 shows the curves which were the result of these experiments. < Curve I was obtained with a fixed electrode formed by a disc 100 mm. in diameter, with rounded edges, and a movable electrode 288 ALTERNATE CURRENTS formed of a hemisphere lo mm. in diameter. The temperature was about i6° C. Curve 2 was obtained with the two electrodes formed of brass discs, the fixed one loo mm. in diameter and the movable one 37 mm., with rounded edges. The temperature was i4'7S° C. Curve 3 was obtained with the same fixed electrode, the movable electrode consisting of a steel point making an angle of 6o°, the section of which was an equilateral triangle of 5 mm. side. The point was polished after the production of €ach spark, but the sparks did not always pass to the point. The temperature was 12° C. These experiments were repeated with a frequency of 80 periods, and very little difference was found ; although, from theoretical considerations, it might have been expected that the sparking distance would vary directly with the frequency. The effect of capacity was determined by connecting one or more insulated wires to the transformer circuit in parallel with the micrometer circuit. The sparking distance is stated to have decreased with the capacity. With the discs they found, with a tension of 10,000 volts, the sparking distance to be : Without capacity, 4-5 mm. ; with a capacity of -113 m.f., 4'i7 mm. ; and with a capacity of "28 m.f., 2,'9\ mm. With the point and spherical surface they found the sparking distance to be : Without capacity, 4-5 mm. ; with a capacity of -14 m.f., 4'o8 mm. ; with a capacity of •28 m.f., 4-06 mm. With the point and disc they found the sparking distance to be : Without capacity, 578 mm. ; and with a capacity of -14 m.f, 4'83 mm. The voltage measured by the electrostatic voltmeter is the effective voltage. As it is certain that the sparking distance depends on the maximum voltage, to obtain the true voltage the figures given must be multiplied by v/2. The figures may then be applied to continuous currents ; in fact, these results are practically identical with those obtained by Warren de la Rue in 1878. DISTRIBUTION MAINS 289 Experiments were also made at Siemens's works on different insulating materials, the voltage being measured by an electro- static voltmeter, and, in the case of very high tensions, with a Kelvin voltmeter balance. Fig. 243 shows the curves obtained with various substances. Curve I has been obtained with several thicknesses of indu- rated calico firmly pressed between the disc and sphere electrodes. The ends of the curves show the points at which rupture occurred. Curve 2 is taken from concentric cables, of which the insula- tion was obtained by means of a fibrous indurated material ; the terminals of the transformer were connected to the two conductors. Molls / / / 8, / / "l / -- '" } 2, -^ j y^ 1 italhxaatcai Fig. 243 Curve 3 is taken from concentric cables insulated with rubber. Curve 4 shows the sparking distance through celluloid, which was placed in the form of sheets between the two disc electrodes of the micrometer. M. Steinmetz has made experiments on the sparking distance at different tensions, using as generator a Westinghouse alternator giving 50 volts and 1 5 ampferes. The secondary of the transformer was determined by means of a few turns of wire wound on the secondary circuit and connected to an electro-dynamometer. All the experiments were made at a frequency of 150, and each time the tension was gradually increased by means of the excitation of the alternator till rupture occurred. To find the maximum difference of potential, it is necessary to know what kind of current-curve was used. M. Steinmetz u 290 ALTERNATE CURRENTS assumed that it was sinusoidal ; consequently it is necessary to multiply the effective tension by \/ 2. M. Steinmetz used as electrodes discs of metal 5 cm. in diameter; the solid dielectrics were clamped between these discs, which were considerably less in diameter than the insulating material, so as to avoid brush discharges as far as possible. In the case of liquids the electrodes were completely im- mersed. The formulae below show the results obtained. The distances, d, are expressed in thousandths of a cm., and the potential differences (maxima), v, in kilovolts. Mica ^= ■24e' + -0145 w^ between 800 and 16,500 volts. Vulcanised fibre d=- 7"66» + 2-3»'', between 8,000 and 22,000 volts. Paraffined paper d= ^v, between 6,900 and 24,800 volts. Melted paraffin d = 1 2 -4 w, between 3,900 and 27,000 volts. Boiled oil J r^ + TS? \?, as is well known. When l and r are once known it is only necessary to find the value of the root for the different speeds of the alternator which is supplying the current in order to determine the apparent resistance in each case. The other measurements which are most frequently made in practice are — (i.) Measurement of effective potential difference. (ii.) Measurement of effective current. (iii.) Measurement of power. (iv.) Measurement of instantaneous values of an alternate current and tracing the current curve. (v.) Measurement of phase difference. (vi.) Measurement of self-induction. MEASUREMENT OF ALTERNATE CURRENTS 355 (vii.) Determination of the quality of iron, (viii.) Measurement of the efficiency of alternate current apparatus. § I. Measurement of Effective Potential Difference Electromotive force may be measured by means of sensitive electrometers ; the optical method by which a spot of light is deflected by means of a concave mirror fixed to the movable part of the electrometer is generally employed. We sha,ll not enter into a description of electrometers, but shall only indicate their use in the kind of measurement we have to deal with. For these measurements the armature and needle are arranged on the idiostatic method. To understand this arrangement we must recall to mind that every electrometer consists of two groups of quadrants or armatures and of a movable needle. In the application of the idiostatic method to continuous currents one of the groups of quadrants is charged to a potential Vi, and the other, which is preferably connected to the movable needle, to a potential Vj. Under these circumstances the deflection obtained must .satisfy the equation S = K (Vi - VJ)^ K being the constant of the apparatus. We see, then, that the difference of potential is proportional to the square root of the deflection I ; consequently, when using the electrometer with alternate currents, the average difference of potential will be proportional to this quantity n/T. Now, as we have the equation E, = n/ (e"'')„, E, being the effective E.M.F. and (e^)^ the average square, it follows that Ee=v/^S, 3S6 ALTERNATE CURRENTS « and therefore an electrometer calibrated for continuous currents will also be correct for continuous currents. The chief difference between the electrometer^ used com- mercially and those, employed in the laboratory consists in the ■ method of suspending the moving part. For laboratory work, where great care is taken of the. instru- ments, very fine wire, or even silk thread, may be used for suspen- sion j this gives the apparatus great sensibility, but also great delicacy, which prevents rapid measurements being made. In commercial electrometers it is still possible to use wire suspension (the wire being stronger), but pivoted bearings or knife-edges are generally preferred, so as to allow electrostatic voltmeters to be made of the same shape as the voltmeters usually employed for continuous current. Lord Kelvin has designed a special voltmeter, which he call^ multicellular. There are a large number of quadrants, so as to increase the couple which causes the deflection of the needle. This type of instrument allows of obtaining a large deflection with loo volts and upwards when a thick wire suspension is used ; but or very accurate measurements and for special circuits it would be interesting to know whether these instruments do not cause a perturbation in the circuit by the introduction of the appreciable capacity of the quadrants. The second category of industrial voltmeters are those in which the deflection is produced by the warming of a wire owing to the current traversing it : these may be called thermal volt-, meters. This instrument is generally composed of two distinct parts — first, the part which expands under- the action of the heat generated ; and secondly, a non-inductive resistance, to give the instrument the necessary resistance. As, in accordance with Joule's law, the heat generated is pro- portional to the square of the current, the deflections of the instrument are proportional to the square of the current, which is produced by the square of the difference of potential at the terminals With alternating currents it is evident that the deflection wi'l be proportional to the mean square of the difference of potential. Therefore the efective potential difference will be proportional to MEASUREMENT OF ALTERNATE CURRENTS 357 the square root of the deflections, and the instrument may be calibrated with a continuous current. Industrial instruments of this type give sufficiently accurate indications, but they have the disadvantage of being cumbersome, for the wire, the expansion of which is measured, must be of a certain length, so that the external dimensions of the instruments must be of considerable size. The last category consists of soft iron voltmeters, which are much used industrially. Just as with continuous currents, these instruments require that the iron which they contain should be saturated by the smallest current passing through the instrument, and they must be calibrated for a definite frequency, so as to render constant the perturbation due' to self-induction. Instruments based on this principle should not be considered exact ; they only give approximate indications. It is imperative to split the metal bobbin which holds the winding, so as to eliminate the intense Foucault currents which would otherwise result. § 2. Measurement of the Current There are two ways of doing this, (i) We can measure the potential difference at the ends of a resistance (without self- induction), the value of which is known, by means of a volt- meter (by preference an electrometer), the capacity of which will have no influence on the value of the current circulating through the resistance ; this perturbation need not be feared, as the capacity of ordinary electrometers is very small. Under these circumstances, the potential difference at the terminals of the resistance being in phase with the current, we can write, in accord- ance with Ohm's law : potential difference current = *- ■. • resistance (2) We can use an electro-dynamometer, the best known type of which is the Siemens. The first method needs no explanation ; in practice it is a 358 ALTERNATE CURRENTS great advantage in the case of heavy currents, which would require a large and costly electro-dynamometer. The second method is more rapid and is more generally used. The electro-dynamometer is perhaps the most accurate industrial instrument, and unless it is subject to external influences always remains the same. The principle of the dynamometer- is to utilise the repulsion which is exerted. on one another by two circuits, one fixed and the other movable, traversed by currents in opposite directions ; the torque is balanced by a spiral spring, the angular torsion of which, necessary to bring the movable coil to zero on the scale, is a measure of the current. The angle through which the spring is twisted is proportional to the square of the current which traverses the two circuits of the instrument in the case of a continuous current. Consequently, in the case of an alternate current, the deflection of the spring is proportional to the mean of the squares of the instantaneous values of the current— that is to say, is proportional to the square of the effective current. It is sufficient to calibrate the instrument with a continuous current of known value ; in this way the constant K of the instrument is determined, and for -any deflection 5 we have : effective current = k N/g7 The electro-dynamometer, although it requires delicate hande ling, is yet a very accurate instrument, more especially on account of the small tension of the spiral spring. Its principle has been applied by Lord Kelvin to a series of industrial instruments which allow for the different types of the measurement of from i centi -ampere to 10,000 amperes. These instruments have received the name of balances and are much employed in England : they are very accurate. All types of electro-dynamometers possess too small a number of tui-ns for any perturbation to be caused by self-induction in any circuit in which they are inserted : they are, therefore, most valuable for alternate current measurements. The approximate measurement of alternate currents may be effected by means of the industrial instruments called ammeters^ with a soft iron needle, like the voltmeters mentioned above : the MEASUREMENT OF ALTERNATE CURRENTS 359 conditions of working and the disadvantages are the same as in the case of the voltmeter. It should be observed that the self- induction of these instruments is so small as not to cause any perturbation in the circuit in which they are inserted : further, contrary to what obtained in the case of soft iron voltmeters, this self-induction cannot modify the current passing when the fre- quency changes. § 3. Measurement of the Power The power of an alternate current of instantaneous value i an^ E.M.F. e is given by the equation w = e . /, or v^m = (effective E.M.F.) x (effective current) x cos <^ for the power during a complete period. Consequently the power can be measured by means of separate voltmeters and ammeters only when ^, the angle of lag, is known. To measure the power by one instrument of a practical character recourse must be had to the wattmeter, which is a direct descendant of the electro-dynamometer. One of the circuits, consisting of a few turns of thick wire, is traversed by the total current to be measured ; the other circuit, formed of a very fine wire, with as little self-induction as possible, is put in shunt across the points between which the potential difference exists which causes the current to circulate. If then the self-induction is zero the small current circulating in this fine wire coil will be equal to the quotient of the difference of potential by the resistance of the wire : consequently this current is proportional to this potential difference and in pfiase with it. As a result, the deflection of the wattmeter being proportional to the product of the currents circulating in the two circuits, the permanent deflection will be proportional to - ^ ei dt, T Jo which when integrated gives E (effective) x i (effective) x cos ^.. 36o ALTERNATE CURRENTS The wattmeter will, therefore, give by a single reading the value of the power, provided that there is no perturbation due to self-induction of either of the circuits, or to the mutual induction of one circuit on the other. But as a general rule this is not the case, and wattmeters can only be used with the same frequency as that for which they are calibrated. The value of the power as a function of the deflection is given by the expression Ty _ I + K'Ci' ^ deflection, M I + K^ Ci Ca in which r^ is the resistance of the fine wire circuit, m a constant, K = — , Ci and C2 the time constants of the fine wire and thick T wire circuits respectively. This expression, which Dr. Fleming calls the correction factor of the wattmeter, can only be constant when Cj = o, /.«. when the fine wire circuit has no self-induction, or when Cj = C2, i.e. when ■the two circuits have the same time constants. In these two cases the correction factor becomes ^J, and the M readings are accurate whatever be the frequency ; but these con- ditions imply that the wattmeter causes no perturbation in the circuit in which it is inserted, for C2 is not zero, i.e. the thick wire circuit must possess some self-induction : this is contrary to what obtains in practice, for every effort is made to make C2 = o, which reduces the ccwrection factor to the expression ^ (i -)- k2 c,2). The value of this expression will be more nearly constant the nearer Cj = o. The ideal values, therefore, are Ci = C2 = o. The extreme sensibility of instruments based on the principle of the electro-dynamometer allows of this condition being very nearly fulfilled, for it is sufficient to place a few turns on the fine MEASUREMENT OF ALTERNATE CURRENTS 561 wire coil, which is movable, and form the rest of the fine wire circuit of a resistance r^ wound non-inductively and having no part in the electro-dynamic action which causes the deflection. Just as in the case of dynamometers, no metallic masses must be used in their construction, as they may falsify the measure- ments, owing to the Foucault currents produced in them. § 4. Measurement of Instantaneous Current Values and Tracing of Current Curves All methods of tracing current curves are derived more or less from the method of instantaneous contact, invented by Joubert in 1881 ; possibly the electro- chemical methods of M, Paul Janet may be an exception. Joubert's method consists in measuring the current during an indefinitely short time, corresponding exactly to the same point in each phase ; the instantaneous impulses, which are thus com- municated a great number of times per second, produce in the measuring instrument a permanent deflection, the value of which varies with the instant at which the measurement is made. His apparatus is arranged as follows : On a prolongation of the alternator spindle a little commutator is arranged, with a double contact, consisting, firstly, of a pointed wire fixed radially, against which a fixed brush rubs during a fraction of a second. This pointed wire communicates with a metal ring, which forms the other part of the commutator and on which a brush rubs constantly. If it is desired to measure the instantaneous potential differ- ence between the two terminals of the alternator, an electrometer is arranged which is connected directly to one of the alternator terminals and to the other alternator terminal through the com- mutator we have just described. In this way a permanent deflec- tion is obtained on the electrometer, which will give the instanta- neous value corresponding to the point of the phase at« which instantaneous contact is made by means of the point and brush. To completely study a periodic current a series of measure- ments must be made, corresponding to a complete phase, by giving 362 ALTERNATE CURRENTS the fixed brush smalj angular displacements in the same direction round the axis of rotation. Each measurement corresponds to a new point in the phase, very near the last one ; using a suitable scale the results can be plotted as ordonnates on a sheet of paper, the distance between the ordonnates being proportional to the angular displacement of the fixed brush. When the ends of these ordonnates are joined the current curve is obtained. This graphical method is the only one which allows of study- ing the working of any alternate current apparatus, for it shows at once all the special features of such apparatus, and the working can be seen at a glance, just as in the case of a steam-engine indicator diagram. Any deformations at any one part of the curve are easily discovered in this way. This method of Joubert has, however, the disadvantage of obliging the operator to take a. series of measurements ; it would be infinitely preferable to obtain automatically a continuous tracing of the curve : M. Blondel has effected this by the aid of photography. The deflections of the measuring instrument are shown by the displacement of a luminous ray which, after reflec- tion from the concave mirror of the electrometer or galvanometer, falls on a sheet of sensitive paper rolled round a drum. Clock- work works both this drum and the instantaneous contact brush, so that the two movements are proportional. The image of the luminous point is impressed on the sensitive paper, and traces on it a curve which represents the variation of the alternating current. This method of tracing a current curve is very ingenious, but not suited for industrial requirements ; however, in practice there is no need to make such delicate measurements, and in a labora- tory the method presents no difficulties. M. Blondel, instead of employing a sensitive electrometer, prefers to use an ordinary condenser charged by the instantaneous contact and discharged by another instantaneous contact into an aperiodic galvanometer of the Deprez-D'Arsonval type. To avoid the vibration of the movable brush at the moment at which it impinges against the point, M. Blondel prefers tg sink MEASUREMENT OF ALTERNATE CURRENTS 365 the point in an insulating disc, the surface of which is carefully turned up ; the brush bears on this disc and is not jerked at the moment it makes contact. There is another very simple method of obtaining instantaneous contacts. It consists in replacing the brush by a small jet of conducting Uquid, flowing in a direction normal to the fixis of rotation of the commutator. The contact pomt is replaced by a very thin well-mounted knife-edge, placed in a radial plane, which cuts the liquid jet without any splashing. Acidulated water may be employed as the liquid. With this arrangement the liquid jet can only be displaced by a relatively small angle about its higher vertical position, so as not to introduce any error due to the curve which the liquid jet would follow when it did not flow in a position near the vertical. All the methods we have just examined are fairly convenient when near the alternator producing the current ; but this condition cannot always be realised. We may then proceed in the manner Dr. Fleming has indi- cated ; he mounts the commutator on the spindle of a small . synchronous motor, which is specially built to absorb very little energy, to produce at the same time very little perturbation in the phase difference of current and E.M.F., and, finally, to revolve as nearly as possible absolutely in synchronism with the alternator. Dr. Fleming states that these conditions can be realised quite sufficiently in practice. In this manner a study may be made of the current curves at various points of the network. § 5. Measurement of Phase Difference This is a measurement very seldom made, and it has no practical importance except when it is desired to ascertain the working of an installation or special piece of apparatus. For example, in the study of an alternator or transformer it is useful and even indispensable to know the lag of the current in the primary and secondary circuits. But when such investigations are undertaken it is imperative to trace the curves, and under these circumstances it is unnecessary to measure separately the 364 ALTERNATE CURRENTS phase difference, for this quantity can be determined from the curves. In order to measure the difference of phase between two isolated currents, of which the instantaneous values at the same moment are z'l and i^, the following method of procedure may be pursued : If the two currents differ in phase by an angle ^ they may be written as /, = ii sin K t. 4 = I2 sin (k t — <^). Take three electro-dynamometers, two of which are in circuit with the two currents respectively, whilst the third is in circuit with both currents at once, one circulating through the fixed and the other through the movable circuit. We shall have as the three deflections of the dynamometers S, = ll! 8j = ^ 83 = '-li2cos.^, 2 -whence we get cos d> = — -^ - v/8,«2 This method is not true in general, because it assumes that the- currents follow the sine law, which is far from being invariably the case. To measure the phase difference between two currents with curve of any shape whatever there is no exact method except the plan of measuring the lag from the curves traced experimentally. § 6. Measurement of Self-induction The determination of the self-induction is, as we have seen, of the highest importance in alternate current investigations, but it is a very difficult and delicate operation : it is only in the case of circuits of constant permeability, i.e. containing no iron, that the measure- ment is quite accurate. For circuits of variable permeability recourse must be had to methods which only give an approximate idea of the self-induction. MEASUREMENT OF ALTERNATE CURRENTS 365 :Z3X To measure accurately the self-induction of constant permea- bility circuits Ayrton and Perry have invented two methods. First Method of Ayrton and Perry. — The coil to be tested is placed at l (fig. 285) in a Wheatstone bridge. There is a commutator c, driven with a uniform rotating motion, and which at every revolution — {a) Breaks and makes the circuit of a short-circuiting resistance across the terminals of the galvanometer. {b) Opens and closes the battery circuit. According to the lead of the brushes, the interval between these two actions may be varied. In taking the measurements the following plans are followed : (i.) The bridge is adjusted for per- manent current ; then, the switch being put in motion, resistance is taken out of the branch d c till there is no deflec- tion of the galvanometer. (ii.) Equilibrium being obtained for permanent current the balance is upset by removing a certain resistance p from the branch c d. The commuta- tor is then started, and its speed in- creased till there is no deflection. The speed of the commutator is measured, and from the number of revolutions is deduced^ the time, T, which has elapsed between the making of the circuit and the short-circuiting of the galvanometer. Under these conditions the coefficient of self-induction is L =T(0. Instead of measuring T on the commutator it is preferable to determine it electrically by means of a coil of known self- induction. The accuracy of the method increases with the number of revolutions up to a certain limit. Second Method of Ayrton and Perry. -In this method a bridge a b c d is used, formed of two branches «, b, without any Fig. 285 366 ALTERNATE CURRENTS self-induction ; one branch R, in which is inserted a pair of coils, which can be shifted into different angular positions relative to one another, so as to vary X, the self-induction of the pair ; and the fourth branch having in circuit the coil whose gelf-inductioii is to be measured. A galvanometer is joined to points b and d, and a battery to points a and c. First equilibrium for permanent current is established by means of a sliding resistance. Then interrupted currents are sent through the bridge by opening and closing the battery key, and the equilibrium obtained in this case by altering A, When equilibrium is obtained we have L _ fl whence I — '^ X The sensibility of this method is the greater the larger the number of interruptions per second of the battery current. For this purpose Ayrton and Perry have designed a little commutator, which opens and closes the battery circuit periodically, and at the same time closes the galvanometer circuit and then short-circuits it. The instantaneous currents are always sent in the same direction through the galvanometer, and the deflections thus made are steady. The bridge connections to the commutators are, of course, in this case not as shown in fig. 285; A similar method may be used for a circuit of variable permeability with more or less exactness, but it is evident that, as the self-induction varies with the value of the current, it would be necessary to employ the heavy currents, for which these circuits are designed, and which would not be suitable for a laboratory instrument. Practically Joubert's method may be employed, as it give? an idea of the self-induction under working conditions. This is how it works : In series with the apparatus to be tested is placed a non-iriductive resistance, such as a series of incandescent lamps or an electrolytic bath. Let r be the resistance of the apparatus under test, and r' the resistance in series. Suppose we send a current I through it, and measure by means of an electrometer the MEASUREMENT OF ALTERNATE CURRENTS 367 •potential differences e and e' at the terminals of the resistances R and r'. Under these circumstances the effective current is expressed as e' _ e whence ' = ^\/(^')^(^-^' It is evident that there is no need to measure e and e' abso- lutely. It is sufficient to take the ratio of the deflections of the electrometer. This method has the fault of being based on the supposition that the current is sinusoidal ; but even when this is not the case it gives an approximate value. § 7. Determination of the Quality, of Iron As regards alternate currents, there is very little need to pay attention to Foucault current losses ; in fact, with the plates which are generally used, about ~- mm. in diameter, Foucault currents are negligible. The great source of energy loss is hysteresis : it alone is sufficient to always keep a load on the station even when no lamps are burning. As a consequence it is important to deter- mine the quality of iron from this point of view when, for example, it is desired to build a transformer. It does not follow that the permeability of any iron should be neglected, but as high per- meability and small hysteresis are not always found in the same specimen, any sample of iron must be submitted to two kinds of te^ts to be able to judge of its quality. For continuous current apparatus, such as dynamos, per- meability is the chief requisite, for the variations in polarity are not sufficiently frequent to cause any appreciable hysteresis loss. We shall first describe the measurement of the permeability. Measurement of the Permeability. — In manufacturing works the most simple method is that due to Dr. Silvanus P. Thomp- son. His permeameter consists of a massive soft iron frame a 368 ALTERNATE CURRENTS (fig. 286), in which a hole a is bored for the insertion of a rod cd of the iron to be tested. This rod is surrounded by a coil a d which produces the necessary magnetomotive force. By means of a spring balance r, or a scale pan loaded with weights (the apparatus in this case being turned upside down), the attraction at the point d is measured : instead of overcoming the adhesion by - a very small increase of the mechanical effort it is better to diminish the current a little, since this does not shake the apparatus. The force p which overcomes the attraction is given by the equa- tion ; p = Stt X 981' p being expressed in grammes, and s being the section of the rod in sq. cm.s. The permea- bility ju is : „ — ^8p TT X 981 H'S Fig =85 ^^ ^^ know that H = 4 TT « / X io~', /x is easily found. This method, although not very exact, may be very useful in workshops where comparisons rather than exact measurements are wanted. The fault of this method is that there must be joints which always diminish the permeability of the whole circuit. In the present case the joint has a very small surface, and requires in consequence very careful adjustment. For more accurate measurements it is better to determine the permeability ft. from magnetisation curves traced, like those of Professor Ewing, through axomplete cycle. If we take a solenoid which is very long in proportion to its diameter and insert in it as core a sample of iron in the form of a rod, we can by means of a ballistic galvanometer measure the total flux O traversing the rod. If the section is s, the flux per unit of surface will be b = - ; and as we know the field h = — , / being the length of the MEASUREMENT OF ALTERNATE CURRENTS 369 solenoid, we get /* = -. Frequently the sample is in the form of a ring entirely covered with the primary winding, the secondary being placed at any part of the ring. In any case the shape of the sample must be such that the intensity of the field h due to the exciting solenoid is constant over a large portion. In the case of a short cylinder the field at any point is partly due to the field of the solenoid and partly to the poles at either end of the cylinder. It is necessary, then, to employ a long solenoid and cylindrical iron rod, which should be at least 40 times the diameter in length. Under these circumstances the field is almost constant. The same result is arrived at by employing a sample of ring form, for there are no poles to influence the field. When it is desired to determine a series of values of b and h so as to construct a curve of hysteresis, the primary current must not be interrupted : it must be suddenly increased several times in succession, and the deflection measured each time on the baUistic galvanometer in the se- condary. Each point in the curve is the resultant of all the preceding impulses of the galvanometer, starting from the specific induction corresponding to H = o. Every error, therefore, affects all the points of the curve. f>g- =87 The method due to Evershed and Vignoles seems to us the most accurate. On a ring formed of the iron to be tested are placed three windings (fig. 287) : the first or secondary winding s is connected to the ballistic galvanometer g ; the other two or primary windings are used to produce the magnetising force. One of them is traversed by a constant current, —n, which pro- duces an induction corresponding to the lower point of a hysteresis curve of Ewing. The second winding is traversed by a variably current, producing a magnetising force opposite to that of the first coil, and which can vary from o to -|-2« : it is evident, there- fore, that the ampere turns acting on the iron will be equal to the resulUnt of the ampere turns due to the two coils, and the iron will B B 370 ALTERNATE CURRENTS be submitted to a magnetising force varying from — « to + « ampere turns. To make a test the constant current is first started in the first winding ; and in the second sufficient resistance is inserted, so that when the circuit is closed the algebraic sum of the ampere . turns gives the desired value of the magnetising force. The deflection of the galvanometer is noted, and the resistance then diminished, so as to get the maximum positive value — ^viz. — « + 2«=+« ampfere turns. The second circuit is then broken and the ampere turns return to their maximum negative value — «. This course is pursued for each point on the curve. In practice the two primary windings are superposed. This method is very convenient : all error may be avoided by recommencing the test, and, as the galvanometer deflection is larger than in the preceding method, greater accuracy is obtained. The descending curve is obtained by reversing the currents. As it is sometimes inconvenient to construct a ring, Dr. Hopkinson's apparatus (fig. 288) may be preferred. A rod is Fig. 288 prepared of such dimensions as to fit accurately into the holes ac,bd'vi\ the soft iron frame a b, the joints being so large as to be of negligible magnetic resistance in comparison with the rod. The primary windings are divided into two coils ed; and the secondary winding consists of a Kttle coil a e placed at the middle of the rod. Measurement of the Hysteresis.— The hysteresis varies from one to three times its value not only in the same batch of iron, but even in one plate : bending, or torsion, or any other opera- tion which affects the molecular structure, may cause the hysteresis to vary. The measurement of the hysteresis by the tracing of the complete curve obtained by the ballistic method is an operation which can only be carried out in a laboratory. MEASUREMENT OF ALTERNATE CURRENTS 371 In Ewing's method a small bundle of plates, cut in the shape of a long rectangle, can be driven by hand with a rapid rotating motion round an axis. This small bundle revolves between the poles of a magnet of c shape, which is mounted on knife-edges on an axis which is a prolongation of the axis of rotation of the plates. A pointer fixed on the magnet indicates the angular displacement. During rotation the power absorbed by the reversals of polarity as a result of the hysteresis exerts an effort on the magnet and brings it into a new position, making a certain angle with its original position. The torque on the magnet is evidently inde- pendent of the speed, and consequently when the latter has reached a certain value in relation to the time of one oscillation the deflection of the magnet becomes permanent, whatever the increase of speed. If, however, the speed becomes too high induced currents may falsify the readings, and consequently a dash pot is provided to deaden the oscillation. The sensibility is regulated, as in a balance, by raising or lowering a little mass of metal by means of a screw. The deflections are very nearly proportional to the hysteresis ; the large air-gap ensures the constant magnetic resistance of the circuit, so that the field is practically constant, whatever class of iron is being tested. The induction in the bundle of plates is usually 4,000 C.G.S. units, and to vary this the number of plates must be changed. Every instrument is accompanied by calibrated specimens and tables giving all necessary data. § 8. Measurement of EfB.ciency (i) Alternators. — The direct method in which a transmission dynamometer is employed is the most exact The prime mover is connected to the alternator by a transmission dynamometer showing the power supplied. The output is measured by a watt- meter, and the ratio of the two quantities gives the efficiency. The power used in excitation must be taken into account. If a transmission dynamometer is not available the indicated h.p. of the engine must be measured, and also the brake h.p. by means of a Prony brake, so as to know the efficiency of the prime mover. 371 ALTERNATE CURRENTS The alternator may be driven by a continuous or alternating motor of known efficiency, if there is one of sufficient power at disposal. If sufficient power is not at hand to give the full output of the alternator the methods due to Mordey, Ayrton, Sumpner, and Blondel may be used, as they require practically no power, but, on the other hand, are liable to inaccuracy. (2) Motors. — The measurement in this case is just the same as for alternators : the power supplied is measured by a watt- , meter, and the mechanical power by a Prony or absorption brake. The same indirect methods may also be employed as in the case of alternators. (3) Transformers. — The secondary circuit is connected to a non-inductive circuit, such as incandescent lamps. The power supplied to the primary is measured by a wattrheter, and that yielded by the secondary by means of an ammeter and volt- meter. Other methods are the Mordey calorimetric method, the Ayrton and Sumpner 3-voltmeter method, and the Sumpner method. To estimate the loss on open circuit the power supplied to the primary when the secondary is open is measured on a watt- meter ; this gives the hysteresis and eddy current losses as well as the c^'r loss in the primary. To determine the c*r losses at full load in both windings the secondary is short-circuited through an ammeter, and the current raised to its normal value by raising the potential of the primary, which then reaches its normal value. Under these circumstances the losses in the core become negligible, and the power supplied to the primary is almost equal to the c'^r losses in the two windings. INDEX ALL Allgemeine Electricitats-Gesell- SCHAFT : Alternator, 60 Motor, 142 Transformer, 231 Alternators : Caii-Helmer (single-phase), 21 Ganz (single-phase), 26 Elwell-Parker (single-phase), 25 Gramme (single-phase), 29 Mordey (single-phase), 30 Patin (single-phase), 32 ■ Ferranti (single- phase), 34 Kapp (single-phase), 37 Labour (single-phase), 38 Siemens (single-phase), 41 Thomson-Houston (single-phase), Wesfinghouse (single-phase) ^ 43 Cail-Helmer (inductor), 46 Kingdon (inductor), 48 Thury (inductor), 51 Brown (polyphase), 58 Fives-Lille (polyphase), 60 Forbes (polyphase), 60 Oerlikon (polyphase), 63 Schuckert (polyphase), 67 Siemens & Halske (polyphase), 71 Stanley Electric (polyphase), 7a Alternator Design, 79 Armature Reaction, 14 Armed Cables, Loss of energy in, 281 Laid direct in earth, 302 Asynchronous Motors ; Theory of, 113 With simple alternating field, 121 With revolving field, 125 Brown, 135, 154 Behn-Eschenburg, 157 Creusot, 140 Dobrowolsky, 132 CLA Asynchronous Motors : Fives-Lille. Allgemeine Electrici- tats-Gesellschaft, 142 Hutin & Leblanc, 154 Lahmeyer, 143 Oerlikon, 145, 154 Siemens & Halske, 149 Stanley, 150 Behn-Eschenburg, Dr., Motor, 157 Berthoud & Borel Cables, 293, 298 Biphase System, 248 Bitite, 291 Bockenheim (revolvingtransformer), 144 Boucherot, M. Motor (polyphase), 136 Tests of single-phase asynchronous motors, 160 Distribution with condensers, 336 Brook's System of Mains, 302 Brown Alternator, 58 Motor (polyphase), 135, 154 CAStES, Classification of, 290 Siemens, 294 Norwich Insulated Wire Com- pany, 294 Patterson, 295 Felten & Guiileaume, 295 Ferranti, 295 Cables, ' armed, loss of energy in, 281 Cail-Helmer Alternator, 21, 46 Callender- Webber Mains, 301 Capacity of Cables, influence of, 274 Cardew, device for protecting secondary circuits, 312 Choking coils, 351 Classification of Transformers, 194 Claude, Safety Shunts lo Cables, jio 374 INDEX MAT Condensers, experiments with, 241 Hutin & Leblanc, 242 Stanley & Molly, 245 Distribution with, 336 Creusot, Biphase Motors, 140 Current curves, 361 Current, measurement of, 357 D'Arsonval, accidents, 307 Design of alternators, 79 motors, 164 transformers, 235 Dimensions of coils and pole-pieces, i Dispersion factor, 147, 162 Dispersion of magnetic induction, effect of, 192 Disruptive discharges, 287 Distribution, methods of, 318 Westinghouse System, 319 Thomson - Houston Sys- tem, 319 Elihu Thomson System, 320 with Condensers System, 336 with Polyphase Currents, 337 Mixed System, 342 Dobrowolsky winding,-95 motor, 132 Dorsett System of Mains, 301 Drake & Gorham, apparatus for pro- tection of Secondary Circuits, 312 Dynamometer, electro, 358 Efficiency of Alternators, 18 measurement of, 371 E.M.F., measurement of, 355 Elwell-Parker Alternator, 25 Epinay, 259 Ewing, measurement of Hysteresis, 371 Felten & Guilleaume Cables, 295 Ferranti, Alternator, 34 Transformer, 213 Cables, capacity of, 276 Cables, 295, 299 Weighted cut-outs, 313 Fuse (safety), 354 Fields, revolving, 93 Fives- Lille Company Alternator, 60 Motor, 142 Fleming, Dr., Capacity of Cables, 276 Forbes Alternator, 60 Frequency Alternators, 12, 316 Transformers, 191, 316 Fuses, safety, 353 Ganz Alternator, 26 Transformer, 206 System of E.M.F. regulation, 332 System of switches, 348 Gramme Alternator, 29 Winding of motors, 98 Gutta-percha, 291 Haselwandee, winding of motors, 96 Hedgehog Transformer, 201 Hermann-MuUer synchronising appa- ratus, 76 Hopkinson, choking coil, 351 Permeameter, 370 Hospitaller, tests of Solignac Perio- diser, 252 House wiring, 304 Hutin & Leblanc Motor, in, ii;4 Condenser, 242 Transformer of con- tinuous into poly- phase currents, 259 Hysteresis, measurement of, 370 India-rubber, 291 Inductor Alternators, 45 Instantaneous Current Values, 361 Institution of Electrical Engineers, temperature of wires, 271 Insulation of Conductors, 284 Interior Conduit Company, 306 Iron, 367 Johnston, system of mains, 300 Joints in Magnetic Circuit, 193 Joubert, current curves, 361 Kapp Alternator, 37 Synchronising Apparatus, 78 Kelvin Multicellular Voltmeter, 356 Kennelly, temperature of wires, 271 Kingdon Alternator, 48 Kolben Dispersion Factor, 147, 163 Korda, M. Desir^, 264 Labour Alternator, 38 Transformer jsingle-phase),209 (triphase), 228 La Chapelle, 259 Lahmeyer Motor, 143 Lauffen-Frankfort Transformers, 228 Loss of energy in armed cables, 281 Lowrie-Hall Transformer, 211 Regulation of E.M.F., 329 Lucas Reversing Transformer, 252 Mains, underground, 296 Mathews Fusing Tables, 353 INDEX 37.5 Measurement of Alternate Currents, 354 Effective E.M.F., 355 Current, 357 Power, 359 Instantaneous Current Values, 361 Phase difference, 363 Self-induction, 364 Quality of iron, 367 Efficiency, 371 -Mordey, Efficiency of Alternators, 18 Alternator, 30 V curve for Motors, 107 Transformer, 215 Protection of Secondary Cir- cuits, 311 Safety-fuse, 35a Motors, single-phase synchronous, 102 Ganz, with rectified field, 108 Polyphase synchronous, m Hutin & Leblanc, in Schuckert, iia Tesla, 113 Asynchronous, theory of, 113 Dobrowolsky, 133 Brown, 135 CreusOt, 140 Fives-Lille (AUgemeine E!ec- trJcitats-Gesellschaft), 142 Lahmeyer, 143 Oerlikon, 145 Siemens & Halske, 149 Stanley Electric, 150 Asynchronous, with simple alternating field, 152 Hutin & Leblanc, 154 Brown, 154 Oerlikon, 154 Behn-Eschenburg, 157 Motor Design, 164 MuUer Stage Regulator, 346 Multiple Circuit Transformers, 234 Norwich Insulated Wire Co., 294 Oerlikon Alternator, 63 Motors, 14s Transformer, ai6 Parallel running, 74 Patin Alternator, 3a Patterson Cables, 395 Periodiser Solignac, 250 Permeability, variation of, 194 measurement of, 367 Perry, Ayrton & Secohmmeter, 365 Phase difference^ measurement of, 363 Pitch, I SYN Pollak's Transformer, Alternate current to Direct, 257 Polyphase Alternators, S3 Synchronous Motors, in Asynchronous Motors, 132, "3 Potential, regulation of, 295 Precaution, measures of, 307 Preece, W. H., fusing tables, 352 Reaction, armature, 14 Regulation of Potential, 325 Lowrie-Hall System, 329 Ganz, 332 Regulator, house, 345 stage, 345 Resistance, effective, of circular con- ductors, 268 Resistance, affected by temperature, 269 Revolving fields, 93 Revolving Fields Asynchronous Mot tors, theory of, 116 Roux, G., Curves of Triphase Motors, 129 Schuckert Alternator, polyphae, 41 Motor, 112 Transformer, 224 biphase, 228 Scott Transformer of Biphase into Tri- phase Current, 2S5 Secondary Circuits, protection of, 311 devices, 343 Self-induction Alternators, 9 Cables, 274 Measurement of, 364 Shock, treatment of persons suffering from, 314 Siemens Alternator, 41 Siemens & Halske Alternator, 71 Motor, 149 Siemens Cables, 294 Single-phase Synchronous Motors, 102 Asynchronous Motors, 152 Solignac Periodiser, 250 Sparking distance, 287 Stage Regulator, 345 Stanley Electric Co. A.lternator, 7^ Motor, 150 Stanley & Molly Condenser, 245 Steinmetz, sparking distance, aflp Swinburne Hedgehog Transformer, 201 Transformer cut-out device, 344 Switches, Ganz Central Station, 348 Westinghouse, 349 Synchronising, 74 Hermann-MuUer apparatus,. 7S Kapp apparatus, 78 376 INDEX Temperature, effect on nsistance, 269 Tesia Motor, 113 Shunted Circuits, 262 Thomson-Houston Alternator, 42 Transformer, 219 Device for secondary circuits, 312 Direct distribution, 319 Thomson, Elihu, three-wire distribu- tion, 320 Thompson, Silvanus P., Permeameter, 367 Thury Inductor Alternator, 51 Tracing Current Curves, 361 Transformer testing, 234 design, 235 Reversing, Felix Lucas, 252 Single-phase into direct, 257 pirect into polyphase, Hutin & Leblanc, 259 Single-phase into tri- phase, Korda, 364 Biphase into triphase, 265 Transformers : General properties of, 178 Classification of, 194 Methods of using, 198 Description of, 200 Swinburne Hedgehog, 201 Closed circuit, £>6 Brown, 206 Ganz, 207 Id. 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