book

The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896) — part 32 of 36

1 January 1896

potential differences and induction constitutes what may be called the indicator diagram of the transfonner, and shows us all that is going on inside. The quick description of these curves becomes, therefore, an important matter. Many investi- gators have devised methods for expediting this process. One effective method was described by M. A. Blondel* in 1891. M. Blondel employs a rotating contact-maker with two brushes, and the contacts are so arranged that a condenser is periodically charged at a certain moment during the complete phase of the potential and then immediately afterwards is discharged through a galvanometer. The two brushes are fixed to an arm movable about an axis co-axial with that of the revolving motor or alternator, and this brush holder is revolved by clockwork at a regular rate. Hence the galvanometer indicates a current which is varied as the brush holder rotates. If the brush holder is held at rest, the galvanometer has a series of rapid charges from the condenser sent through it, and takes a steady deflection. If the brush holder rotates, this deflection varies from moment to moment, but at any instant is pro- portional to the instantaneous potential at which the condenser is being charged. If a mirror d'Arsonval galvanometer is employed, and the image of an illuminated opening thrown on a photographic scale which is moved transversely to the motion of the spot of light, a photographic trace of the alter- nating-current curve can be obtained. By using a pair of contact-makers and two galvanometers the current and E.M.F. curves can be delineated at the same time. Such a photo- graphic record of the current and E.M.F. curve for an alternating-current arc lamp worked off a Meritens alternator is shown in Fig. 171.

A very similar arrangement has been described by Messrs. Barr, Bumie and Bodgers.f These investigators employ a revolving contact-maker of a particular kind. It is thus described by them : The shaft of the alternator or motor is fitted with a contact-making disc, and the contact brush is moved slowly and continuously through its successive angular positions. Contact is thus made each time at a slightly

See La LwnUre JSlectrtque, September 12, 1891, and September 16^ 1893 ; also see The Electrician, Vol. XXYIL, p. 603. t See T^ Electrician, September 27, 1895.

THE INDUCTION COIL AND TRANSFORMER 531

<1]fferent position of the armature. Thus the potential difference at each contact differs slightly from that at the preceding contact. This potential difference is used to charge a condenser across the terminals of which is connected either a reflecting electrometer or a high-resistance galvanometer.

The deflection of the instrument so used follows the value of the potential difference of the wave form to be determined, and accurately follows it, for the mean rate of variation of the potential differences between the terminals of the condenser is exceedmgly small in comparison with the rate of change of the electromotive force to be investigated.

Fig. 171. — Photographic Trace of CurreDt Curve I and Electromagnetic Force Curve £ of an Alternating Current Arc Lamp.

Fig. 172 shows the arrangement of the contact disc and accessories, a galvanometer being used, but for which an electrometer might be substituted. In this diagram, for the sake of clearness, the vulcanite foundation work is omitted and the brass only shown. Di is the contact disc, with knife edge and contact brush, which is rigidly fixed to the shaft of the dynamo or motor. The rings D^ and D,, and the rods and brushes Bi and B4, are mounted on a vulcanite sleeve loose

HH 2

632 TUE INDUCTION COIL AND TRANSFORMER.

upon the shaft, and are revolved slowly. The brush Bj is joined to the ring Da, with which the brush B, is in permanent connection, so that when the brush B^ makes contact with the knife edges the condenser 0 is charged to the potential difference between the terminals Ti, T,. The condenser is- throughout the whole revolution of the disc D^ discharging through the galvanometer G by way of B^, B^, B«, and the resistance B.

As the brushes Bi and B4 are moved slowly round, a suc- cession of charges passes through the galvanometer, the value of each of which is proportional to the potential of the con- denser— that is, to the potential difference of the points T^, T,. This contact apparatus, in fact, performs the operation of

Pio. 172.

charging a condenser at a definite instant during the period at the terminals Ti and T,, which are the terminals of the alternating-current drcuit under investigation, and then immediately afterwards discharges this condenser through a galvanometer. The galvanometer, therefore, gives a steady deflection which is proportional to the instantaneous potential difference between the points Ti and T, at the instant corresponding to the moment when the contact with the condenser is broken.

The rapidity with which the curves of instantaneous potential can be determined depends to a large extent upon the perfection of the insulation of the condenser and voltmeter.

THE INDUCTION COIL AND TBANSFOBMER. 533

If these leak to any sensible degree they lose charge in the intervals between the contacts, and the resulting permanent deflection is too small, and the time required for the volt- meter to take its fall steady deflection when the place of 4)ontact is changed is greatly increased. Hence it is necessary to examine this question of leakage carefully before placing implicit reliance on the voltmeter and condenser actually Qsed.

The value of the instantaneous potential may also be determined by balancing it against some point on a slide wire down which a known fall of potential is created by a battery* The arrangement known as a potentiometer consists of a uni- form fine wire stretched over a scale down which a uniform &11 of potential is created by a cell or two of a secondary battery attached to its extremities. If a sliding contact moves over this wire, we can insert between one end of the potentio- meter wire and this slider any source of electromotive force, and, by moving the slider, balance the fall of potential down any length of the slide wire against this other potential difference. If the revolving contact-maker, connected in series vnth a condenser, is placed across a proper section of a divided resistance, which resistance is across the terminals of the transformer, the contact-maker will close the circuit of the condenser at equal periodic intervals and give it a potential which depends upon the position of the contact of the contact- maker. The potential of this condenser can then be measured on the slide wire, and, knowing the value of the two sections of the divided resistance, we are able to determine the value of the instantaneous potential difference between the terminals of the transformer.

A revolving contact-maker for determining alternating- eurrent and potential curves has also been devised by Prof. Hicks.* In this instrument the same principle is adopted as in the one just described. A revolving contact-maker connects a condenser intermittently, but at definite instants in the period, to a source of alternating potential, and then in between these contacts discharges the condenser through a galvanometer. The shifting of the brush contacts varies the galvanometer deflection, but so that it is always proportional to the instan- • See The Ekctrician, Vol. XXXIV., 1695, p. 698.

634 THE INDUCTION COIL AND TRANSFORMED

taneous value of the potential charging the condenser. Manj other forms of apparatus have been described, but the principles are practically the same as those above referred to. In all cases a condenser is charged through a contact-maker, and the potential of the condenser determined by either a galvanometer or voltmeter. A few practical suggestions in connection with the construction of such contact-makers may be useful. In the first place, if a condenser and electrostatic voltmeter are used, care must be taken to see that both are very highly insulated. The use of the condenser is to act as a reservoir and supply the electrical leakage of the voltmeter. If a condenser of large capacity is employed, then the contact must be suitably prolonged, or else the condenser will not be charged completely during^ the contact. The contact springs sometimes give trouble by making imperfect contact with the disc, and too much pressute must not be applied to the brushes, or else they create a trail of metallic deposit on the insulating disc. The author has found a material called stabilit a very suitable insulating material for the construction of the insulating disc of the contact-maker, and the contact piece may be a transverse shp of steel or hard brass let into it. The contact springs are best made of steel, tempered and well cleaned at the contact surfaces. The contact-maker is best constructed by attaching a circular disc of stabilit or ebonite to the shaft of the motor or alternator and turning it up very accurately on the shafL The metal contact slip is then let into the disc and a pair of insulated springs are carried on a rocking arm which moves round an axis co-axial with that of the motor or alternator. As the disc revolves the contact slip passes under the springs, and connects them together for an instant. These springs are connected to the circuit of the voltmeter and condenser, so that when the contact is made between the springs the con- denser and voltmeter in parallel with it are connected to the alternating circuit under test for a short instant. The instant during the period when the contact is made can be varied by rocking over the arm carrying the springs.

Prof. Byan has suggested and employed a jet of salt water as a means of making an electric contact. Through this jet a steel needle passes at an assigned instant during the revolution.

THE INDUCTION COIL AND TEANSFORMEB. 535

With care and proper construction the steel spring contact- maker works very well, and is much more convenient to use than a contact in which a Hquid jet is employed.

M. Blondel has described several forms of instrument, which he calls oscillographs , for the direct representation by optical means of the form of alternating-current curves, enabling us to project on to a screen a luminous line having the form of the alternating current curve. For a description of these we must refer the reader to his Paper in the Comptes BenduSy Vol. CXVI., No. 10, March 6, 1893, p. 602, and to The Electrician, Vol. XXX., March 17, 1893, p. 671.

§ 3. Discussion of Transformer Diagrams. — The methods, some of which have been described in the previous section

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Fio. 173. — Curve of Electromotive Force of Thomson- Houston Alternator on Open Circuit.*

enable us, as it were, to look inside the transformer and observe the nature and order of the electrical operations taking place in it. We shall proceed to discuss some of the experimental results which have been thus obtained. In the first place, it must be noted that the curve of primary potential difference, or as it is generally called, the curve of primary E.M.F,,

*In Figs. 175, 174, 175, the dote represent the actual position of observations.

636 THE INDUCTION COIL AND TRANSFORMER.

depends upon the construction of the alternator producing the electromotive force, and also upon the nature of the circuit, whether inductive or non-inductive, which that alternator is sapplying. Any assumption that the curve of primary pot^tial difference is always a simple sine curve is very far from true. The form of the curve of primary electromotive force is not even a fixed and independent attribute of the alternator. The form of the E.M.F. curve of the alternator may be quite different when taken on open circuit to that which it is when taken at the terminals of the alternator when this last is loaded with an inductive or non-inductive load of transformers. In Fig. 178 is shown the curve of electro-

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Fio. 174. — Curye of Electromotive Force of Tliomson-Houston Alternator working on an Inductive Circuit.

motive force of a Thomson-Houston alternator at no load or on open circuit, and in Fig. 174 the E.M.F. curve of the same machine when actuating a load of transformers, the . secondary circuits of which are lightly loaded. It will be Been that the second curve is quite Cerent to the first, and that neither of them is even approximately a simple periodic curve. In Fig. 175 is shown the E.M.F. curve of a Mordey alternator at full load on a water resistance. It is, then, clear that no assumption must be made as to the con-

THE INDUCTION COIL AND TRANSFORMEB. 537

stancy of the form of the cnrve of eleotromotive force of any •alternator, bnt that the form of the cnrve of prunary terminal j)otential difference of the transformer nnder test must always 'be determined.

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Pig. 175. — Curve of Electromotive Force of Mordey Alternator on Water-ResUtanoe Load.

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Fio. 176.— Primary E.M.F. and Primary Current Curves of Mordey Transformer, on Open Secondary Circuit, supplied off Mordey Alternator, with .no other load.

We have, in the next place, to consider the case of the transformer when the secondary circuit is open or unloaded, and to inquire what under those circumstances is the form and

638 THE INDUCTION COIL AND TBAN8F0BMEB.

relative position of the primary terminal potential difference curve and the primary-current oarve. A number of examples of such curves are given in the diagrams on pages 587 to 541. In Figs. 176 to 188 are shown the primary-current curves and primary E.M.F. curves for transformers on open secondary circuit made by the Brush Electrical Engineering Company

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Fio. 177.— Primary E.M.F. and Primary Current Cur'e8 of Mordey Transformer, on Open Secondary Circuit, supplied off Mordey Alternator, furnishing Current alad to other transformers lightly loaded.

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Fio. 178.— Primary E.M.F. and Primary Current Curves of Thomaon- Houston IVansformer, on Open Secondary Circuit, supplied off Mordey Alternator, with no other load.

and the Thomson-Houston Company, the electromotive force being supplied by Mordey or Thomson-Houston alternators in various states of load. The Mordey-Brush transformers

THE INDUCTION COIL AND TBAN8F0BMEB. SS9 are 50 kilowatt size and the Thomson-Houston are 30 kilowatt

flize.

It will be seen that the primary current under these conditions always lags behind the curve of primary E.M.F. or primary terminal potential difference. The primary current, when the secondary circuit of the transformer is open, is called

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Fig. 179. — ^Primary E.M.F. and Primary Current Curres of Thomson- Houston Tranafonncr, on Open Secondaxy Circuit, supplied off Mordey Alternator, furnishing Current also to other Transformers lightly loaded.

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Fig. 180. — Primary E.M.F. and Primary Current Curves of Mordey Transformer, on Open Secondaiy Circuit, supplied off Thomson-Houston Alternator, with no other load.

the magnetising current of the transformer. Even if the curve of primary potential difference is nearly a true sine curve, the curve of primary current is not of a similar character, but is always more irregular. The form of the primary current curve depends not merely upon the form of

540 THE INDUCTION COIL AND TRANSFORMER.

the pximary E.M.F. curve, but upon the nature of the itoa used in the iron core and upon the structure of the trans- former generally, so that the primary-current curves of two transformers by different makers will have different forms of

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Fig. 181.— Primary E.M.F. and Primary Current Curves of Mordej Transformeri on Open Secondary Circuit, supplied off Thomson-Houston Alternator, furnishing Current also to other Transformers lightly loaded*

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Fig. 182. — Primary E.M.F. and Primary Current Curves of Thomson- Houston Transformer on Open Secondary Circuit supplied off ThomsoD- Houston Alternator with no other load.

magnetising current curve, even if worked off the same alternator. This is well shown in the curves in Pigs. 176 and 178, in which a Brush and Thomson-Houston transformer are

THE INDUCTION COIL AND TBANSFOEMEB. 641

worked off the same Mordey alternator. The ourve of primary E.M.F. is the same in each case, but the carve of primary current is of a quite different form. This is brought about by differences in the reluctance of the iron circuit producing small differences in the form of the curve of magnetic induction in the core.

By comparing Figs. 176 and 181 it will be seen that the form of the curve of primary current is also dependent upon the form of the curve of primary E.M.F., and for the same transformer the curves of current may be considerably altered by supplying it off a different alternator, or off the same

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Fio. 183. — Primary E.M.F. and Primary Current Curves of Thomaon- Houston Transformer, on Open Secondary Circuit, supplied off Thomson- Houston Alternator, furnishing Current also to other IVansformera Ughtlv loaded.

alternator in different states of load. In some alternators, such as the Mordey alternator, the armature reaction is very small and the form of the curve of electromotive force given by the machine is not very different whether the machine is worked on open circuit or on full load, on water resistance or on an inductive load. Jn the case of a machine with large armature reaction, the form of the curve of electromotive force will, under these various conditions, be greatly altered, and hence the form of the primary-current wave of trans-

542 THE INDUCTION COIL AND TRANSFORMEB.

formers on open secondary circuit connected to it will be quite different also. i

We pass on next to consider the form and position of the <3urve of secondary terminal potential difference or secondary E.M.F. when the transformer secondary circuit is open.

Fig. 184.— The Primary E.M.F. Curve (firm line) and Secondary RM.F. -Curve (dotted line) of a Thomson -Houston Tnmsformer laken off a Thomson-Houston Alternator. The Secondary Curve is drawn to a scale which makes its Maximum Ordinate equal to that of the Primary Curve, .and the Curves are seen to be identical in form.

Fio. 185. ' The same Primary and Secondary F.M.F. Curves, delineated •in Fig. 184, are here drawn with the Secondary Curve (dotted) reversed and superposed on the Primaiy Curve to show its exact ooincidenoe with the Primary Curve.

It is found that this curve of secondary electromotive force -is, under these conditions, an exact copy on a reduced scale of the curve of primary E.M.F., and that it is in exact opposition to it in phase. In Fig. 184 are shown the curves of primary and secondary terminal potential difference of a Thomson-

THE INDUCTION COIL AND TEANSFOBMEB. 643

Honston transfonner at no load. The primary terminal potential difference curve or primary E.M.F. curve is repre- sented in Fig. 184 by a firm line, and the secondary E.M.F. curve by a dotted line. The secondary curve has been drawn to such a scale that the ordinates of the secondary curve are equal to those of the primary curve. In Fig. 186 the curve of secondary E.M.F., represented by a dotted line, has been reversed and drawn over the primary to show the exact coinci- dence of the two curves.

Fio. 186.— Primary E.M.F. Curve (I), Primary Current Curve (II) and Secondary E.]iLF. Curve (III) of 10-light Westinghouse Transformer on Open Secondary Circuit

This constitutes one of the most valuable properties of the transformer, viz., that it copies varying or periodic potential difference exactly to a reduced or increased scale. Hence, if we have a pair of terminals between which there is a periodi- cally-varying potential difference having a Vmean-square value of, say, 2,000 volts, and we attach the primary circuit of a suTtably-wound transformer to these terminals, we can produce a periodically-varying potential difference of lower

544 THE INDUCTION COIL AND TRANSFORMER.

or higher value, and the curve of which is an exact copy to a reduced or increased rcale of the original. We shall see- later on that usefal applications can be made of this fact.

If the secondary circuit of the transformer is closed by a non-inductive resistance, such as incandescence lamps, then the curve of secondary terminal potential difference or secondary electromotive force undergoes a displacement and is brought forward or lags behind the curve of primary electromotive force. The reason for this is to be found in the magnetic

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Fio. 187.— Primary E.M.F. Curve (I;, Primary Current Curve (II) and Secondary E.M.F. Curve (III) of lO-light Westinghouse Tranaformer, loaded to one- tenth of full load.

leakage across the magnetic circuit which then takes place, and which will be discussed in a later section. The act of closing the secondary circuit of the transformer and produc> ing a secondary current also effects a displacement in the position of the primary-current curve. As the transformer is loaded up the primary-current curve is displaced backwards, so that the lag in phase between the primary current and primary electromotive force is decreased. At full load the

THE INDUCTION COIL AND TBAN8F0BMBR. 545

primary current and secondary electromotive force are nearly in opposition of phase. This i^*" seen to be the case by examining the series of curves in Figs. 186 to 189, which were taken by Prof. Byan from a small Westinghouse trans- former, in which magnetic leakage is not by any means absent.

We have next to consider the position of the curve of magnetic induction. The curve of induction is obtained, as already described, by integrating one or other of the

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Fio. 188.— Primary E.M.F. Curve (I), PrimaiT Current Curve (II) and Secondary E.M.F. Curve (III) of 10-Ught WeBtinghouBe Transformer loaded to half load.

curves of electromotive force. The process of obtaining a second curve, by taking as ordinates the area up to successive abscisssB of a first curve and plotting these areas as new ordinates to the limiting abscissse, is a process which always has the effect of smoothing out irregularities in the original curve, so that if the first curve is one not far removed in form from a simple sine curve the second or integration curve will be more nearly still a simple sine curve.

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646 THE INDUCTION COIL AND TRANaFORMER.

An analytical proof of this is as follows : If the ordinate y of a periodic cnrye is represented by a Fourier series, as it can always be if periodic and single valued, then y may be expressed by the series

y-Asinj»f + Bcosj)( + Osm2;7t + Dcos2jie + &c.,

where A, B, 0, &c., are constants. Hence,

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y ei«- B Anpt- A cos;? «+ --sin 2 p « - ..c-oos 2pt + &c 2» 2p

y(it=~sinpf-— cosy t+-- sin 2jpe--- cos 2pt+&c., p p 2p 2p

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Fio. 189.— Primaiy E.M.F. Curve (I), Frimaiy CurrsDt Canra (II) and Secondary E.M.F. Curre (III) of 10-light Westinghoiue Tranaformer at fuUload.

It will be seen that the result of the integration has been to effect a change of phase of all the components and to weaken the higher harmonics by diminishing the coefficients which denote their amplitudes. Hence the process of forming anew periodic curve by taking as ordinates the area of a first

THE INDUCTION COIL AND TRANSFJBMEB. 547

periodio curve up to successive absdssaB always has the effect of -wipmg out irregularities of form of the primary curve, and yielding a curve more nearly a simple sine curve. It follows, therefore, that the curve of magnetic induction is always less irregular than the curve of primary or secondary electromotive force from which it is derived. From what has been already said, it will be seen that the curve of magnetic induction in the core has its maximum value at the moment when the electromotive force curve from which it is derived has its zero value. We may, then, sum up the general facts about transformer indicator diagrams by saying that when a trans- former is at work we have—

Ist. A varying potential difference between the primary terminals which follows a certain wave form depending —

(a) On the nature of the alternator;

(5) On the state of the load of that alternator, whether full or light, inductive or non-inductive ;

{c) On the nature and construction of the transformer connected to the alternator.

No assumptions must be made as to the form of this curve, but in every case its true form at the terminals of the trans- former under test must be determined. The curve of primary electromotive force has widely different forms in the cases met with in practice.

2nd. If the transformer has its secondary circuit open, we have a primary current flowing into its primary circuit which is called the magnetising current, and which lags in phase behind the curve of primary electromotive force. As the trans- former secondary circuit is loaded up this curve of primary <nirrent is brought more into step with the primary electro- motive force under the conditions that the load on the secondary circuit is a non-inductive load.

The curve of primary current is an irregular periodic curve the form of which is affected by the form of the curve of primary electromotive force and by the nature of the trans- former, and may have very different forms as these two operating causes are changed.

8rd. We have a curve of secondary terminal potential 'difference which is in exact opposition to the curve of primary terminal potential difference when the transformer

nn2

548 THE INDUCTION COIL AND TEAN8F0BMEB.

is on open secondary drcoit, and which is an exact co^ of the curve of primary potential difference to a reduced scale* This curve of secondary potential difference may be shifted forward in phase as the transformer secondary is loaded np^ so as to come more nearly into opposition wiUi the curve of primary current.

4th. We have a curve of magnetic induction, and this- induction is not the same in different parts of the core, or the same on open secondary circuit as at full load. The form of the curve is always more nearly a simple periodic curve than is the form of the curves of primary and secondary terminal potential differ^ce.

Each of these curves being a periodic single- valued curve,, can be expressed by a Fourier series and analysed into con- stituent harmonics. Thus the ordinate ^ of the curve of primary potential difference corresponding to any instant t reckoned from the beginning of the phase can be expressed by the series

fi = El sin jp « + Fi cos ;> « + Eg sin 8 ;? t + Fj cos 3 ;> f

Ej sin 5;? « + Fj cos 6^ t + &c.

The constant or first term of the Fourier series is zero, because the curve is always symmetrical above and below the axis of time. Moreover, only the odd harmonic constituents are present, viz., the harmonics whose wave lengths are one* third, one-fifth, &c., of the fundamental wave length, and if by any form of harmonograph we mechanically resolve any of these transformer curves, we find that they can be quite adequately represented by the first three odd terms of the Fourier series — that is to say, we can build up any transformer curve by adding together the ordinates of three simple periodic curvea the wave lengths of which are in the ratio of 1:3:5, the amplitudes and relative positions being suitably chosen. The reason for the absence of the even harmonic constituents — ^viz., those whose wave lengths are ^, ^ that of the fundamental — is to be found in the peculiar symmetry of these transformer curves. On looking at any transformer curve it will be seen that it is of such a character that, if the portion below the time jixis be considered to be reversed, we should get a repetition of the same form. Thus, a curve ot electromotive force

THE INDUCTION COIL AND TEAN8F0BMEIL 649

in Fig. 190, when so treated, beoomes recHJUd into that fa Fig. 191.

On considering, then, the form of any oarve, it will be seen that the harmonic constitnents mast be such that if we move lorward 180deg. along the time axis the value of the ordinate beoomes negative but remains the same in magnitude.

If e represents the ordinate of any curve at any point corresponding to an instant t, and if p as usual is 2r n, where

— ^A Transformer Cunre showing the typical aymmetiy of aQ transformer curvet.

4000-

Fio. 191.— The samelVansformerCurye shown in Fig. 190, but with the iMoond half of the wave rectified to show the typical symmetry of the curve.

» is the frequency, then we can represent the value of e by lihe series

e^Eimnpt+Fi eoB pt + EiSia 2 pt + F^cos 2 pt

£sBin8pt + F8COs8/7t + &c.

The harmonic constituents must be such that if we put '{pt + ir) torpt the value ote becomes — «.

It is easily seen that, since sin (pt + ir)sa — dii pt and mbk {8(/>e+fr)}«:— sin8p t, &c., whereas sin {2 (pt-^ir)} '^fin 2 ptf iiie essential condition is that only the odd

660 THE INDUCTION COIL AND TRANSFORMER.

harmonies most be present, Henoe the expansion of th» ordinate of the real transformer carve can only contain th» 1st, 8rd, 5th,.&c., terms. As a matter of experience it is found that any transformer curve met with in practice can very

Fio. 192.— The Harmonio AnalvsiB of the Curve of E.M.F. of a Thomson* Houston Alternator at no Load. The thick Curve C is the Curve of E.M.F., and the Curves marked Hi, Hs, Hg, are the Harmonic Constituente with Wave LengthB in the ratio of 1, 3, 5.

Fici. 193.— The Harmonic Analysia of the Curve C of E.M.F. of ik Thomson-Houston Alternator partly loaded up on water resistance. The Harmonic Constituents of the Curve are represented by the Curvea maiWI Hi, Hi, Hg.

nearly be represented by the first three odd terms of the series, and hence any observed transformer carve can be very quickly analysed into its constituents by the arithmetical proceai explained on page 92.

By the use of mechanical harmonographs or analysers tfaif can, of course, be very easily done, and an illustration ifl

THE INDUCTION COIL AND TBAN8F0RMEB. 661

gi^n in Figs. 192, 198 and 194 of the E.M.F. curve of a Thomson-Houston alternator so analysed. The curves given in Figs. 192, 198 and 194 were analysed for the author by Mr. G. XT. Tule, with his mechanical harmonograph. It will be noticed that when the curve 0 is symmetrical, the harmonic constituents start from the same point, and have no lag relatively to one another.

Fio. 194.— The Harmonic AnalyslB of the Curve C of E.M.F. of a Thomaon-Hooaton Alternator, partly loaded up on Inductive Besistance. The Harmonic Conetituente of the Curve are represented by the Curves mariced Hi, Ht, H5, witii wave lengths in the ratio of 1, 5, 6.

§ 4. Derivation of Ounres of Power and Hysteresis. — From the curves of current, electromotive force, and induction obtained as above described we can construct two other curves which give us the variation of the total power supplied to the transformer, and the total loss in the iron core per cycle. These curves are obtained as follows : — ^Let us assume that a set of transformer curves has been taken when the trans- former is on open secondary circuit. Taking the curves of primary current and primary terminal potential difference, we mxdtiply together (as explained on page 168, §28, of Chapter III.), the corresponding ordinates of the two curves for abscissaB taken at equidistant points on the time axis, and set up a new ordinate representing the value of the product €«, where e is the primary potential difference and t the primary current at the same instant. This product set off as an ordinate defines another curve called the power curve^ and the true mean ordinate of this power curve gives us the

652 THE INDUCTION COIL AND TRAN8F0RMFR.

Provenance

Shelf: Reference library
Book: The Alternate Current Transformer Vol. 2: The Utilisation of Induced Currents (1896)

Author: J.A. Fleming
Rights: Published in 1896, before 1929, and therefore in the public domain in the United States.
Collected By: StanBot reference library