DIRECT AND ALTERNATING CURRENT TESTING > BY FREDERICK BEDELL, PH.D. n PROFESSOR OF APPLIED ELECTRICITY IN CORNELL UNIVERSITY ASSISTED BY CLARENCE A. PIERCE, PH.D. SECOA^D IMPRESSION Of THE UNIVERSITY OF NEW YORK D. VAN NOSTRAND COMPANY 23 MURRAY AND 27 WARREN STREETS LONDON : CONSTABLE & CO., LTD. 1909 Copyright, 1909 By FREDERICK BEDELL All rights reserved Printed September, 1909 Reprinted November. 1909. PRESS OF LANCASTER. PA. PREFACE. This manual consists of a series of tests on direct and alter- nating current apparatus, selected with reference to their practical usefulness and instructive value. While the book has been pre- pared primarily for students, it is hoped that it may prove helpful to others. The presentation is in the form of a laboratory manual; the author, however, has not restricted himself to a mere statement of instructions for conducting tests but has directed the reader's attention to the principles that underlie the various experiments and to the significance of the results. Ex- perience has shown that theory is more readily grasped when it is thus combined with its application and that the application is more intelligently made when its broader bearings are understood. The material has been systematically arranged and it is believed that the book may be found useful for reference or as a text, aside from its use in testing. From the text proper are excluded specialized tests and those that are of limited application or require unusual testing facili- ties, such tests being described in the appendices to the several experiments. These appendices thus permit a fuller discussion of some of the details of the tests and various modifications than could be included to advantage in the text proper. The tests in general are those that can be performed in" any college laboratory. No attempt has been made to make the work exhaustive or complete ; on the contrary every effort has been made to eliminate matter of secondary importance and that which is of questionable technical or pedagogical value. The aim has been to arrange an introductory series of experi- ments of a comprehensive nature, so that in a reasonable time and with a reasonable amount of effort the student may acquire vi PREFACE. the power to proceed to problems requiring a continually increas- ing initiative and originality. Although standardized tests afford the quickest way for obtaining certain desired results and, in th case of a student, for obtaining a knowledge of testing methods, the ability to conduct such tests with full instructions given is soon acquired. Beyond this point the exclusive use of standard- ized tests should be avoided. Standards in electricity serve best as new points of departure. The student who is to become more than the " ordinary slide-rule engineer " or " mental mechanic " will have sufficient intellectual curiosity to desire more than any standardized tests can give him and should be encouraged in every way to seek new results and to devise ways and means for obtain- ing them with the facilities at hand. To attempt to formulate such work would at once deprive it of its freshness. The student may well be referred to the current technical press and to the transactions of the engineering societies for suggestions as to subject matter for further study and also as to methods to be adopted. With reference to prepared blanks and forms, the writer be- lieves that their use can be, and often is, carried too far, leading perhaps to good technical but not to good pedagogical results. In a certain sense the one who prepares the forms and lays out the work is the one who really performs the experiment, the tabu- lators of data being assistants who, for commercial work, require only a common school education. Progress undoubtedly results from the development of indi- vidualism and if room for such development is to be given in a college course specifically in a college laboratory course the more or less standardized instruction must needs be reduced so as not to fill the entire available time. The natural tendency has been quite the reverse. Two decades ago, the study of electrical engineering meant, practically, the study of direct currents, there being little else. Laboratory courses were developed in which the whole available time was well filled with test after test upon PREFACE. vii direct current generators and motors. The transformer and alternator were then added, with extensive time-consuming tests, with the apparent assumption that the full development of alter- nating currents was reached. In succeeding years came the gen- eral development of polyphase currents, the rotary converter, in- duction motor, etc., these subjects being added to a crowded course by a process of compression rather than judicious elimina- tion. The student was given more than he could possibly assimi- late. As types of machines have multiplied, it would take years to perform all the permutations and combinations of tests on all the different types. But is this necessary for a student? Why not develop a student's powers by a few typical experiments on a few typical kinds of apparatus? With this end in view the writer has made selection from ma- terial which has long been collecting in the form of typewritten outlines. These have been in a process of continual evolution, frequently rewritten and used by many classes. By a process of elimination and survival, experiments consisting of a large amount of mechanical data-taking and tabulation and a relatively small amount of technical content have been dropped in favor of those experiments which have proved most effective in student de- velopment. Various demands upon the writer's time prevented his preparing for the press a book on testing a number of years ago and the present appearance of the book is due in no small way to the valuable assistance of Dr. Pierce. Meanwhile several admirable manuals have appeared, which differ, however, in aims or scope from the present work. The author hopes to find leisure, in the near future, to make good some of the omissions of the present volume and to include in a later edition additional chapters on alternating current motors and converters. The present work is self-contained and requires only such pre- liminary courses in physical and electrical measurements as are usually given in colleges. The book may be used to advantage in conjunction with standard texts on electrical engineering, as those viii PREFACE. by Franklin and Esty, S. P. Thompson, and Samuel Sheldon, or with an introductory text such as that by H. H. Norris. The experiments given in the book may be supplemented by others of an elementary, intermediate or advanced nature, as circumstances may require. The division of experiments into parts and sections will be found to add materially to the flexibility of the book. The author desires to express his appreciation of the initial instruction and inspiration of Professor H. J. Ryan and of the continuous cooperation for many years of Professor G. S. Moler. He wishes also to express his indebtedness to many who have been associated with him in laboratory instruction, in particular to Dr. A. S. McAllister, as many references in the present text bear evi- dence. He likewise desires to express his appreciation of the spirit of cooperation shown by Professors H. H. Norris and V. Karapetoff and other engineering colleagues. The author is in- debted, furthermore, to various professors and students, who have used and corrected this book in proof during the last year and to a number of engineers who have looked over the proof sheets and have made valuable suggestions. For all shortcomings the author alone is responsible. ITHACA, N. Y., July i, 1909. CONTENTS. CHAPTER I. DIRECT CURRENT GENERATORS. PAGE. EXPERIMENT i-A. Generator Study and Characteristics of a Series Generator i EXPERIMENT i-B. Characteristics of a Compound Generator. . 13 CHAPTER IT. DIRECT CURRENT MOTORS. EXPERIMENT 2-A. Operation and Speed Characteristics of a Direct Current Motor (Shunt, Compound and Differential). 27 EXPERIMENT 2-B. Efficiency of a Direct Current Motor (or Generator) by the Measurement of Losses 41 CHAPTER III. SYNCHRONOUS ALTERNATORS. EXPERIMENT 3~A. Alternator Characteristics 62 EXPERIMENT 3~B. Predetermination of Alternator Character- istics 73 CHAPTER IV. SINGLE-PHASE CURRENTS. EXPERIMENT 4-A. Study of Series and Parallel Circuits Con- taining Resistance and Reactance 102 EXPERIMENT 4-B. Circle Diagram for a Circuit with Resistance and Reactance 123 x CONTENTS. PAGE. CHAPTER V. TRANSFORMERS. EXPERIMENT 5-A. Preliminary Study and Operation of a Transformer 128 EXPERIMENT 5~B. Transformer Test by the Method of Losses. 150 EXPERIMENT 5~C. Circle Diagram for a Constant Potential Transformer 179 CHAPTER VI. POLYPHASE CURRENTS. EXPERIMENT 6-A. A General Study of Polyphase Currents.... 196 EXPERIMENT 6-B. Measurement of Power and Power Factor in Polyphase Circuits 222 CHAPTER VII. PHASE CHANGERS, POTENTIAL REGULATORS, ETC. EXPERIMENT 7~A. Polyphase Transformation 241 EXPERIMENT 7-6. Induction Regulators 250 w \>*' * UNIVERSltV OF ILIFORj CHAPTER I. DIRECT CURRENT GENERATORS. EXPERIMENT i-A. Generator Study and Characteristics of a Series* Generator. PART I. GENERATOR STUDY. I. Faraday discovered (1831) that when a conductor cuts lines of force an electromotive force is generated in the conductor proportional to the rate at which lines are cut, and all dynamos (or generators as they are now commonly called) operate on this principle. To generate an electromotive force, it is essential there- fore to have a conductor (or several conductors combined by various winding schemes) forming the armature as one member; and to have lines of force or magnetic flux set up by field mag- nets which form the second member. For operation it is neces- sary also to have a source of mechanical powerf by which either one of these members can be given a motion with respect to the other. A generator may havej a stationary field and revolving armature; or, a revolving field and stationary armature, desig- nated as the revolving field type. Although the latter is useful for large alternators, serious objections to it have been found in direct current machines, for with the commutator stationary, the brushes must revolve, which leads to difficulties in construc- tion and operation. It is the custom, therefore, to build all * Where a series generator is not available, this study may be taken without experimental work or in connection with Part I. of Exp. i-B. f Power is required to overcome friction and other losses, and to over- come a counter torque ( 1-3, Exp. 2-A) which varies with the load. t Outside of this classification is the inductor alternator which has a stationary armature, a stationary field winding and a revolving inductor of iron; its study should be taken up later under alternators. 2 i 2 DIRECT CURRENT GENERATORS. [Exp. direct current generators and motors with a stationary field and revolving armature. 2. The student should consult any of many excellent treatises for a detailed discussion of different types of generators and if possible should note one or two machines in the laboratory or elsewhere which are examples of each important type. Machines noted should illustrate the following terms, some of which are briefly explained in later paragraphs: Stationary field, revolving field, bipolar, multipolar, separately-excited, self-excited, series wound, shunt wound, compound wound, magneto-generator, open and closed coil armature, drum armature, Gramme (or ring) armature. Only the general structure of the various machines need be noted. Observe particularly the magnetic circuit of each machine and the disposition of the field winding. Keep in mind that magnetic flux is proportional to magnetomotive force (field ampere-turns) divided by the reluctance of the complete magnetic circuit, i. e., the sum of the reluctance of each part (air gap, core, etc.). As the reluctance of any part of a magnetic circuit is equal to the length divided by the product of the cross-section and per- meability, it is obvious that an unnecessarily long magnetic circuit should be avoided, a fact neglected in some early machines. 3. In a bipolar generator, one pole is north and the other south; in a multipolar generator (with 4, 6, 8, etc., poles) the poles are alternately north and south. Each armature conductor accordingly passes first underneath a north and then underneath a south pole and has induced in it an electromotive force first in one direction* and then in the *(3a). An exception is the so-called unipolar, homopolar or acyclic dynamo, which has a unidirectional electromotive force generated in the armature conductor; it accordingly delivers direct current to the line with- out commutation. Faraday's disk dynamo (one of the earliest dynamos) was of this type. For years it was the dream of zealous electricians to make this type of machine practicable, but it was considered only as an in- teresting freak, for at ordinary speeds the voltage generated is too low i-A] SERIES GENERATOR. 3 other, i. e., an alternating electromotive force. The simplest form of generator is therefore the alternator, the current being taken from the armature to the line without any commutation. If the armature is stationary, the alternating current from the armature is taken directly to the line ; if the armature is revolving, the armature windings are connected to collector rings (or slip rings) from which the current is taken to the line by means of brushes. In a direct-current generator the armature windings are con- nected* to the several segments or bars of a commutator, from which the current is taken by brushes to the line. The alter- nating electromotive force generated in each coil is thus corn- mutated, or reversed in its connection to the line, at or near the time of zero value of the electromotive force of the coil. The electromotive force in each coil increases from zero to a maximum and back to zero, and at any instant the electromotive forces in the various individual coils have different values rang- ing from zero to a maximum, according to the positions of the coils. The sum of these coil-voltages, as impressed upon the line as terminal voltage, is however practically constant. for most purposes. But changed conditions have made it a practical and important machine (i) driven at high speed by the steam turbine, or (2) driven at moderate speed to generate large currents at low voltage for elec- trochemical work. Dynamos of this class are not included in this study. For further information, see " Acyclic Homopolar Dynamos," by Noeg- gerath, A. I. E. E., Jan., 1905 ; also, Standard Handbook, or Franklin and Esty's Electrical Engineering. For description of some structural im- provements, see pp. 560 and 574, Electrical World, Sept. 12, 1908. * (3b). The details of armature windings will not be here discussed; they are amply treated in many text and handbooks. In almost all machines a closed coil winding is used. (The Brush and T-H arc dynamos and a few special machines use open coil winding.) In a closed winding, the armature coils are connected in series and the ends closed. There are two ways of connecting the coils in series: wave winding and lap winding. In the wave or series winding there are always two brushes and two paths for the current from brush to brush, irrespective of the number of poles. In the lap or parallel winding, generally used in large generators, there are as many paths (and brushes) as poles. The two schemes are essentially the same in a bipolar machine. 4 DIRECT CURRENT GENERATORS. [Exp. 4. Field magnets are usually* energized by direct current passed through the field windings ; permanent magnets being used only in small machines, called magneto-generators, used for bell- ringers, etc. A generator is separately-excited or self-excited according to whether the current for the field is supplied by an outside source or by the machine itself. Alternators are sepa- rately excited; direct current generators are usually self -excited. 5. A direct current machine (either generator or motor) may be: (i) Series wound, with the field winding of coarse wire in series with the armature and carrying the whole armature current ; (2) Shunt wound, with a field winding of fine wire in shunt with the armature and carrying only a small part of the whole current ; (3) Compound wound, with two field windings, the principal one in shunt and an auxiliary one in series with the armature. The compound generator is in most general use, being best suited for all kinds of constant potential service, both power and lighting; the shunt generator performs similar service but not so well. The characteristics of these machines will be studied fully in Exp. i-B. The series generator is of interest because: (i) It is one of the earliest types and of historical importance; (2) It is the simplest type and illustrates in a simple manner the principles which underlie all dynamo-electric machinery, both generators and motors; (3) In a compound wound "generator or motor, the series winding is an important factor in the regulation of poten- tial or speed. In itself the series generator is of relatively small importance, because neither current or voltage stay constant; it is used only in some forms of arc light machines with regulating devices for constant current. In direct current motors, all three types of winding are em- ployed : series wound motors for variable speed service in traction, crane work, etc.; shunt and compound wound (including differ- *The induction generator, to be studied in a later experiment, does not come under this classification. i-A] SERIES GENERATOR. 5 ential wound) motors for more or less constant speed service (Exp. 2-A). PART II. CHARACTERISTICS OF A SERIES GENERATOR. The characteristic curves to be obtained are: the magnetisa- tion curve, with the machine separately excited; the external series characteristic, with the machine self excited; and the total characteristic, which is computed. 6. Magnetization Curve. This curve shows the armature voltage (on open circuit) corresponding to different field currents when the generator is separately excited from an outside source, as in Fig. I. No load is put upon the machine. Means for vary- ing the field current must be provided ; see Appendix, 14. 7. Data. Readings are taken of field current, ar- ^ ^ A mature voltage and speed ; the first reading is taken with field current zero, showing the voltage due to ... , . rp, FIG. i. Connections for magnetization residual magnetism. Ine , . , curve, separately excited. field current is then in- creased by steps from zero to the maximum* rating of the machine, the readings taken at each step giving the " ascending " curve. The descending curve is then obtained by decreasing the field current by steps again to zero. In Fig. 3, only the ascend- ing curve is shown ; see also Fig. 2, of Exp. i-B. To obtain a smooth curve, the field current must be increased or decreased continuously; there will be a break in the curve if a step is taken backwards or if the field circuit is broken during *(?a). Current Density. For field windings an allowable current density is 800-1,000 amp. per sq. in. (1,600-1,275 circ. mils per amp.) ; for armatures, 2,000-3,000 amp. per sq. in. (640-425 c. mils per amp.). For a short time these limits can be much exceeded. The sectional area of a wire in circular mils is the square of its diameter in thousandths of an inch. 6 DIRECT CURRENT GENERATORS. [Exp. a run. This is true of all characteristics or other curves involv- ing the saturation of iron. 8. Brush Position. During the run the brushes are kept in one position; if for any reason they are changed, the amount should be noted. For a generator the best position is the position of least sparking and of maximum voltage, which locates the brushes on the " diameter " or " line " of commutation. Under load this line is shifted forward from its position at no load, on account of field distortion caused by armature reaction,* and the brushes are accordingly advanced a little to avoid sparking. As it is desirable to keep the brushes in the same position in taking all the curves, with load or without load, it is well to give the brushes at no load a little lead, but not enough to cause much sparking. 9. Speed Correction. If the speed varied during the run, the values of voltage as read are to be corrected to the values they would be at some assumed constant speed. Since, for any given field current, voltage variesf directly with speed, this correction is simply made by direct proportion ; each voltmeter reading is *(8a). Armature Reactions. Armature current has a demagnetising effect and a cross-magnetising effect, the two effects together being called armature reaction, as discussed in various text books. The demagnetizing effect due to back ampere-turns weakens the field; the cross-magnetizing effect due to cross ampere-turns distorts the field (weakening it on one side and strengthening it on the other) and shifts forward the line of commutation. In many early machines this made it necessary to shift the brushes forward or back with change of load to avoid sparking; in modern machines the armature reactions are not sufficient to make this necessary and the brushes are kept in one position at all loads. If a very accurate determination of the neutral position of the brushes is desired, it can be found by a voltmeter connected to two sliding points which are the exact width of a commutator bar apart. The neutral posi- tion is the position of zero voltage between adjacent commutator bars, and this is shown by the voltmeter. t (Qa). If the speed can be varied at will, this can be verified for one field excitation. A peripheral speed of 3,000 feet per minute is permissible with the ordinary drum or ring armature. i-A] SERIES GENERATOR. multiplied by the assumed constant speed and divided by the observed speed. 10. Curve. After the speed correction is applied, the magne- tization curve is plotted as in Fig. 3. The abscissae of this curve, field amperes, are proportional to field ampere-turns or magneto- motive force; the ordinates, volts generated at constant speed, are (by Faraday's principle, I ) proportional to magnetic flux. The curve, therefore, is a magnetization curve (showing the relation between magnetic flux and magnetomotive force) for the magnetic circuit of the generator, which is an iron circuit with an air gap. The bend in the curve indicates the saturation of the iron. ii. External* Series Characteristic. This characteristic, which is the operating or load characteristic of the machine, shows the variation in terminal voltage for different cur- rents, when the machine is self excited and the exter- nal resistance is varied. The armature, field and external circuit are in series, as in Fig. 2; read- ings are taken of current, voltage and speed, for an ascending curve as in Fig. 3. The descending curve may be taken if desired. For any point on the curve, the resistance of the external cir- cuit is R E -^ 7, or the tangent of the angle between the /-axis and a line drawn from the point to the origin. Below the knee of the curve, it will be seen that a small change in the external resistance will make a large change in current and voltage. * ( ua.) In any characteristic the term "external" indicates that the values of current and voltage external to the machine are plotted; the term " total " indicates that the total generated armature current and voltage are the quantities used. FIELD ARMATURE FIG. 2. Connections for series character- istic, self excited. 8 DIRECT CURRENT GENERATORS. [Exp. If the speed varied during the run, the external characteristic should be corrected* for speed as before (9). The watts output, for any point on the external characteristic is given by the product of current and voltage, and may be plotted as a curve. 12. If the field coil is connected so that the current from the armature flows through it in the wrong direction, so as to demagnetize instead of building up the residual magnetism, the machine will not " pick up." For one direction of rotation, the proper connection of the field will be found to be independent of the direction of the residual magnetism. Note the effect of pre- vious magnetization (from an outside source) first in one and then in the other direction, and the effect in each case of revers- ing the field connections. 13. Total Series Characteristic. The total characteristic is derived from the series characteristic, so as to show the total generated electromotive force instead of the terminal brush voltage. Resistance Data. The only additional data needed are the volt- age drops through the field and armature for different currents ; this is plotted as a curve (Fig. 3) which is practically a straightt line. With the armature stationary, current from an outside source is passed through the field or armature (separately) ; the current is measured and the difference of potential at the termi- nals. The ratio E -=- 7 gives the resistance. This is called meas- *(iib). This correction is applied to the external characteristic and not to the total characteristic for convenience. Inasmuch as it is the generated electromotive force which is proportional to speed, to be accurate the correction should be applied to the total and not to the external char- acteristic. t ( T 3a). This would be a straight line if the resistance were constant. The resistance varies with temperature; see Appendix, 15. The armature resistance also varies with current since it includes the resistance of brushes and brush contact, which depends upon current density. The hot resistance is to be measured after the machine has run awhile, and is to be considered constant. i-A] SERIES GENERATOR. ^ACTERISTIC tiring resistance by "fall of potential" method; see Appendix, 17- Curve. By adding to the external characteristic the RI drop for field and armature, we have the generated voltage or total characteristic Fig. 3. Interpretation. The total characteristic falls below the magne- tization curve on account of armature reaction, that is, the de- magnetizing effect of the armature current which weakens the field and hence reduces the gen- erated voltage ; for, in taking the magnetization curve, there was no armature current and hence no armature reac- tion. The external char- acteristic falls below the total series characteris- tic, on account of resist- ance drop. The magnetization curve would be higher than the total character- FIG. 3. AMPERES Characteristics of generator. istic for all currents, if in taking it the brushes were given no lead, that is were in the position of maximum volt- age. Giving the brushes a lead lowers the magnetization curve so that for small values of the current it may fall below the total characteristic. 10 DIRECT CURRENT GENERATORS. [Exp. APPENDIX I. MISCELLANEOUS NOTES. 14. Current and Voltage Adjustment. For currents of small values, when a wide range of adjustment is desired, a series resist- ance (Fig. i) is frequently inadequate and it is better to shunt off current from a resistance R, as in Fig. 4. I FIG. FIG. 5. Methods for adjusting voltage or current. By adjusting the slider p, the voltage delivered to the apparatus under test can be given any desired value from zero up to the value of the supply voltage. A modification which is sometimes conveni- ent employs two resistances, B and C, Fig. 5. The adjustment is made by short circuiting or cutting out more or less of one resistance or the other, but not of both. The full amount of one resistance should always be in circuit. 15. Temperature Corrections. The conductivity of copper varies with temperature, according to the law given below. Resistance values to be significant should therefore be for some specified tem- perature; known for one temperature they can be computed for any other. Temperature rise can be computed from increase in resist- ance. In all cases where accuracy of numerical results is important, as in commercial tests for efficiency, regulation, etc., definite tempera- ture conditions should be obtained ; for this the detailed recommenda- tions of the A. I. E. E. Standardization Rules should be consulted. To meet standard requirements, a run of several hours is commonly required. In practice work this is not necessary, it being usually sufficient to specify resistances as cold when taken at the beginning and hot when taken at the close of the test. Let R t be the resistance of a copper conductor at a temperature i-A] SERIES GENERATOR. n t C. At a higher temperature the resistance will be greater and experiment shows that the increase in resistance will be in direct proportion to the temperature rise. At a temperature (t -\- 6} C. the resistance is accordingly The temperature coefficient a (per degree C.) depends upon the initial temperature t (degrees C), or the temperature for which the resistance is taken as 100 per cent., and has for copper the following values :* t o 6 12 18 25 32 40 48 a .0042 .0041 .0040 .0039 .0038 .0037 .0036 .0035 From the formula given above, if the resistance is known for one temperature, the resistance can be computed for any other tempera- ture or for any temperature rise. 16. From this formula we can also compute the temperature rise 6, above the initial temperature t, corresponding to a known increase in resistance. By transformation the formula becomes The temperature rise above an initial temperature t is accordingly equal to the per cent, increase in resistance divided by a. 17. Fall of Potential Method for Measuring Resistance. This method is based upon the fact that the fall of potential through a resistance R carrying a current / is E = RI (Ohm's Law). The resistance R v/hich is to be determined may be the resistance of any conductor whatever (transformer coil, field winding, armature, etc.) which will carry a measurable current without undue heating and is not itself a source of electromotive force. An armature, there- fore, must be stationary while its resistance is being measured by this method. Connect the unknown resistance to a source of direct current through a regulating resistance, Fig. 6 (see also 14), so that the current will not unduly heat the resistance or exceed the range of instruments. Take readings of the two instruments simultaneously, * A. I. E. E. Standardization Rules ; also, A. E. Kennelly, Electrical World, June 30, 1906. 12 DIRECT CURRENT GENERATORS. [Exp. and without delay so as to minimize the effect of heating. The re- sistance R is equal to E-+-L Fig. 6 shows the usual arrangement of apparatus, in case the volt- meter current is but a small part of the total current. The voltmeter leads should be connected di- rectl y to the resistance to be measured (not including un- necessary connectors, etc.) or should be pressed firmly against its terminals. The resistance of an armature winding is taken by pressing FIG. 6. Measurement of resistance by , r ,, r . . i- . the voltmeter leads against fall-of-potential method. the proper bars 180 or 90 apart; if resistance of brushes and connections is to be included, the voltmeter is connected outside of these connections. In case the ammeter current is very small, so that the voltmeter current is a considerable part of the total current, the voltmeter should be connected outside the ammeter so as to measure the combined drop of potential through the ammeter and unknown resistance. With the voltmeter connected either way, an error is introduced which may often be neglected but can be corrected for when par- ticular accuracy is desired. 18. The voltmeter should always be disconnected before the cir- cuit is made or broken, or any sudden change is made in the current, to avoid damage to the instrument. If the resistance being measured is highly inductive, not only the instrument but also the insulation of the apparatus under test may be damaged by suddenly breaking the current through it on account of the high electromotive force induced by the sudden collapse of the magnetic field. This may be avoided by gradually reducing the current before breaking the circuit. 19. The value of an unknown resistance can be found in terms of a known resistance placed in series with it by comparing the drops in potential around the two resistances, the current in each having the same value. i-B] COMPOUND GENERATOR. 13 EXPERIMENT i-B. Characteristics of a Compound* Generator. i. Introductory. A compound generator is made for the purpose of delivering current at constant potential either at the terminals of the machine or at some distant receiving point on the line. In the former case the machine is flat compounded, the ideal being the same terminal voltage at full load as at no load, giving, a practically horizontal voltage characteristic. In the latter case the machine is over compounded, giving a terminal voltage which rises from no load to full load to compensate for line drop, so that at the receiving end of the line the voltage will be constant at all loads. Constant potential service is used both for power and for lighting. Constant delivered voltage is essential in lighting for steadiness of illumination and in power for constant speed. 2. For such service, the series generator is not at all adapted, its voltage being exceedingly low at no load and, for a certain range, increasing greatly with load. 3. A shunt generator almost meets the conditions, generating a voltage which is nearly constant but decreasing slightly with load (Figs. 4 and 6). Obviously by increasing the field excita- tion (field ampere-turns) when the machine is loaded, the voltage can be increased to the desired value ; this is true, however, only in case the iron is not saturated and it is accordingly possible for the increase in field ampere-turns to produce a corresponding in- crease in the magnetic flux. (Compare Fig. 2.) In a shunt machine this increase in field excitation (fan be obtained by an increase in field current produced either by an attendant who adjusts the field rheostat or by an automaticf regulator. * (ia). This experiment can be applied to a Shunt generator by omit- ting 20-25. t ( 3a). Tirrell Regulator. Many older forms of regulators, which oper- ated by varying field resistance, are superseded by the Tirrell Regulator. This regulator operates through a relay as follows: (i) When the volt- age is too low, it momentarily short circuits the field rheostat, causing the H DIRECT CURRENT GENERATORS. [Exp. 4. In a compound generator, the necessary increase of field excitation with load is simply ancf effectively obtained by means of an auxiliary series winding. Since the current in the series winding is the load current, the magnetizing action of the series winding (that is its ampere-turns or magnetomotive force) in- creases in direct proportion to the load. This increases the mag- netic flux and hence the generated voltage by an amount depend- ent upon the degree of saturation of the iron. Looked at in another way, a shunt winding (which alone gives a falling characteristic) and a series winding (which alone gives a rising characteristic) are combined so as to give the desired .flat compounding or a certain degree of over-compounding. As the shunt winding -alone gives very nearly the desired charac- teristic, the shunt is the principal winding, the series winding being supplementary and of relatively few ampere-turns. The characteristic curves for a shunt or compound generator may be classed as no-load characteristics, and load characteristics. PART I. NO-LOAD CHARACTERISTIC. 5. There is one no-load characteristic, the saturation curve, which shows the saturation of the iron, for different field exci- tations ; for this the generator is usually self-excited but may be separately excited when so desired. 6. (a) No-load Saturation Curve.* This curve shows the terminal voltage for different values of field current. 7. Data. The machine is connected as a self-excited shunt voltage to rise; (2) when the voltage is too high, it momentarily removes the short circuit, causing the voltage to fall. The voltage would be much too high or too low, if the short circuit were permanently made or broken. The short circuit is, however, rapidly made and broken and of a varying duration, a nearly constant voltage being thus secured. It may be applied directly to a generator (D.C. or A.C.) or to its exciter. It may be used advantageously in connection with a compound winding, and may be arranged so as to cause the voltage to rise with load in the same manner as in an over compounded generator. *Also called excitation characteristic, or internal shunt characteristic. i-B] COMPOUND GENERATOR. RHEOSTAT FIG. i. Connections for no- load saturation curve. generator, Fig. i, and is driven without load at constant speed. Readings are taken of field current, terminal voltage and speed. The field current is varied by adjust- ing the field rheostat by steps from its position of maximum to minimum re- sistance. This gives the ascending- curve ; the resistance is then increased again to its maximum for the descend- ing curve. If the rheostat, with re- sistance all in, does not sufficiently reduce the field current, a second rheostat may be placed in series with it. The machine " builds up " from its residual magnetism as does the series generator ; if the field winding is connected to the armature in the wrong direction, the machine will not lick up but will tend to be- come demagnetized. Should the direction of rotation be reversed, the field connection should be reversed. 8. Curves. Voltage read- ings are corrected by propor- tion for any variation in speed (9, Exp. i-A), and the curves plotted as in Fig. 2. 9. Interpretation of Curves. The curves in Fig. 2 show the saturation of the iron and are much the same as the characteristic of a series dynamo. The current through the armature is small, being only a few per cent, of full-load current ; the resistance drop through the armature may accordingly be neglected and the meas- ured terminal voltage be taken as (practically) equal to the total 2 3 FIELD AMPERES FIG. 2. No-load saturation curve. 16 DIRECT CURRENT GENERATORS. fExp. generated voltage. Likewise, the armature current is so small that armature reactions are negligible, and the curve is practically the same as a separately-excited magnetization curve. There is no necessity, therefore, for taking curves both self- and sepa- rately-excited. By separately exciting a generator, it is pos- sible to obtain a higher magnetization and consequently a higher generated voltage than can be obtained by self-excitation. In design work and in manufacturing tests, the saturation curve is commonly plotted with field ampere-turns, instead of amperes, as abscissse. However plotted, the abscissae are proportional to magneto-motive force and the ordinates to magnetic flux.* 10. Saturation Factor and Percentage of Saturation. There are two ways for expressing! numerically the amount of satura- tion for any point P on the working part of the curve. ( I ) The saturation factor, f, is the ratio of a small percentage increase in field excitation to the corresponding percentage increase in volt- age thereby produced. (2) The percentage of saturation, p, is the ratio OA -f- OB, when in Fig. 2 a tangent to the curve at P is extended to A. Compute these two for some one point on the curve, corre- * (9 a )- Magnetic Units. For electrical quantities there are three sys- tems of units in use the C.G.S. electromagnetic, the C.G.S. electro- static and the practical or volt-ohm-ampere system. For magnetic quanti- ties there is only one system of units in use, the C.G.S. electromagnetic system; magnetic units of the practical system would be of inconvenient size, they have no names and are never used. The unit of magnetic flux is the maxwell, which is one C.G.S. line of force. The unit of flux density is the gauss, which is one maxwell per square centimeter. The unit of magnetomotive force is the gilbert, which is (10-^-45) ampere-turn. The unit of reluctance is the oersted, which is a reluctance through which a magnetomotive force of one gilbert pro- duces a flux of one maxwell. The maxwell and the gauss are author- ized by International Electrical Congress, but not the gilbert and the oersted. Analogous to Ohm's Law (current = electromotive force -f- resistance), we have the corresponding law for the magnetic circuit : flux (maxwells) = magnetomotive force (gilberts) -l- reluctance (oersteds). f A. I. E. E. Standardization Rules, 57, 58. i-B] COMPOUND GENERATOR. 17 spending say to normal voltage, and check by the relation P = i - 1//- These terms are useful because they make possible an exact numerical statement of the degree of saturation of a machine, under working conditions, without the reproduction of a satura- tion curve. For a more complete study, compute p and / for different points and plot. PART II. LOAD CHARACTERISTICS. II. The usual load characteristics are the shunt, compound and armature characteristics. In taking the shunt and compound characteristics, the machine is left to itself with the field rheostat in one position during the run, the curve showing the variation in terminal voltage with load. In taking the armature characteristic the field rheostat is con- stantly adjusted; the curve shows the variation in excitation necessary to maintain a constant terminal voltage at different loads. The differential and series characteristics are not commercial characteristics but are included to show more fully the operation of the series winding. (For full-load saturation curve, see 33.) 12. (b) Shunt Character- istic. This is the working characteristic of the machine when operated at normal speed as a shunt-wound gen- erator and shows the varia- tion in terminal voltage with FIG. 3. Connections for shunt cnarac- load (Curve A, Fig. 4). teristic> 13. Data. The connec- tions are shown in Fig. 3. Readings are taken of terminal voltage, field current, line current and speed. No speed correction is made, there being none which is simple and accurate. The field rheostat is set in one position and no change is made in it during the run. 3 iS DIRECT CURRENT GENERATORS. [XP: 14. The setting of the rheostat for commercial testing ( 21 a) is made for normal voltage at full load. For the purposes of this experiment, it is usually preferable to set the rheostat for normal voltage (or for any selected value of voltage) at no load; in this case the shunt, compound and differential curves, Fig. 6, all start from the same no load voltage. The load current is then increased from no load up to about 25. per cent, overload and then decreased, if so desired, back to no load. The return curve will fall a little below, on account of hysteresis. Data are also to be taken for a characteristic starting at no load with a voltage below normal ( 18). Armature resistance is measured by the fall-of-potential method, ( 17, Exp. i-A). 20 40 60 80 100 120 140 160 AMPERES FIG. 4. Shunt characteristics. 15. Curves. The armature RI drop is plotted as Curve D in Fig. 4. For the external shunt characteristic (Curve A, Fig., 4), plot observed line current as abscissae and observed terminal voltage as ordinates. i-B] COMPOUND GENERATOR. 19 For the total shunt characteristic (Curve B), plot total arma- ture current* (line current plus field current) as abscissae, and total generated voltage (terminal voltage plus armature RI drop) as ordinates. 1 6. Interpretation (Armature Reactions and Regulation}. An ideal characteristic would be the straight horizontal line, Curve C, indicating a constant voltage at all loads. As a matter of fact the terminal voltage (Curve A) decreases with load. There are, at constant speed,f three causes for this : ( i ) armature resistance drop, (2) armature reactions which reduce the magnetic flux and (3) decreased field excitation as the voltage decreases. The difference between Curves A and B shows the effect of (i) resistance drop; the difference between B and C shows the effect of (2) armature reaction and (3) decreased excitation, and of (4) if speed varies. The difference between B and C will show the effect of arma- ture reactions (2) alone^l if a run is made at constant excitation and constant speed, thus eliminating (3) and (4). This is the practical method for determining armature reactions. The ma- chine may be self excited or (preferably) separately excited. 17. The regulation of the generator is shown by the drop in Curve A. To express regulation numerically as a per cent., the rated voltage at full load is taken as 100 per cent. In a commercial test, therefore, the curve is taken by beginning at full load at rated voltage (100 per cent.) and proceeding to open circuit. The regulation|| is the per cent, variation from normal *The difference between line and armature currents is so small that for many practical purposes the distinction between them can be neglected. t (i6a). Should the generator slow down under load, as when driven by an induction motor, this would constitute a fourth cause (4). $ ( i6b). Included, as a part of armature reaction, is the effect of local self-induction of the armature conductors, when traversed by the arma- ture current which (in any one conductor) is rapidly reversing in direc- tion. II A. I. E. E. Standardization Rules 187, ct seq. 20 DIRECT CURRENT GENERATORS. [Exp. full-load voltage (in this case the per cent, increase) in going from full load to no load. 1 8. Characteristics taken with Low Field Excitation. On short circuit a shunt generator has no field excitation and the short-circuit current (depending on residual magnetism) is com- monly less than normal full-load current. The current, however, is much greater before short circuit is reached. On account of this excessive current, the complete characteristic curve cannot be obtained with the field rheostat in its normal .setting. To show the form of the complete shunt characteristic, set the field rheostat for a no-load voltage much below normal, and take Curve E (Fig. 4) from open circuit to short circuit, and Curve F returning from short circuit to open circuit. The form of these curves should be interpreted. 19. With a weak field, armature reactions cause the terminal voltage to fall off with load more rapidly than with a strong field. This is seen by com- paring Curves E and F with Curve A. The effect of armature reactions is least when the iron is highly saturated, for then any decrease in magneto- motive force (due to arma- ture ampere-turns) does not cause a corresponding decrease in magnetic flux. (Compare Fig. 2.) It follows, therefore, that a shunt generator gives the best regulation when worked above the knee of the saturation curve. It will be found ( 22) that this is not so for a compound generator. 20. (c) Compound Characteristic. The connections for taking the compound characteristic, Fig. 5, are the same as for the shunt characteristic, Fig. 3, with the addition of the series FIG. 5. Connections for compound char- acteristic. i-B] COMPOUND GENERATOR. 21 field winding which is in series* with the armature. The same readings of terminal voltage, field current, line current and speed are taken as for the shunt characteristic and no speedf correc- tions are made. 130 ( ||M f|1 , nr rnvercornpo"^^_ 1 - 120 , **" 110, ^g&s-m *-""" F/at -Z>poun ded 100 ^"- -* 90 ^^""Vw *"***"""'**--< ^^^ /\ """^^^^ 80 ^^j^ ^^x^^ 70 ^ .1 ^ 60 V = 50 \ ^ 40 ^^9 30 r ^^ 20 / . SEgJl^. - 1 10 , , ^ ~-r I i t i i , i ^"T i i. i i i i i i i l } 20 40 60 80 100 120 140 160 180 200 AMPERES FIG. 6. Series, shunt, compound and differential characteristics. 21. In Fig. 6 are plotted shunt, compound and differential characteristics, beginning with the same no-load voltage.J The compound characteristic cannot be made a perfectly straight line from no load to full load. What can be done is to have the terminal, voltage at full load the same as the no-load * ( 2oa). Short Shunt and Long Shunt. The connection shown in Fig. 5 is short shunt; it would be long shunt if the shunt field were con- nected to the line terminals ac, instead of to the armature terminals ab. Both methods of connection are used commercially, the difference between them being slight. f (2ob). A generator is compounded for the particular speed at which it is to operate. When it is to be driven by an induction motor, it may be compounded so as to take into account the slip of the motor, i. e., its slowing down under load. $ (2ia). In commercial testing, the compound and shunt characteristics would be taken with the same normal voltage at full load ( 14). The differential characteristic would not be taken. DIRECT CURRENT GENERATORS. [Exp. voltage (flat compounding) or a definite percentage higher (over compounding). In either case the regulation is the maximum percentage deviation from the ideal straight line at any part of the characteristic, rated full-load voltage being taken as 100 per cent. (See 17, and Standardization Rules.) 22. If the field magnets of a compound generator are highly saturated, the increase in field ampere-turns with load due to the series winding cannot cause a corresponding increase in the mag- netic flux and there will be considerable deviation from the ideal straight line characteristic. A compound generator accordingly gives better regulation when the iron is below saturation, which is opposite to the conclusion reached for the shunt generator ( 19). In a compound generator there is less cause for sparking and shifting of brushes than in a shunt generator, on account of the strengthening of the field by the series winding under load. For fluctuating loads, as railway service, the compound generator is accordingly superior and generally used. Obviously, on account of the series winding, it is much worse to overload or short circuit a compound than a shunt generator. 23. Shunt for Adjusting Compounding. If the characteristic of a compound generator rises more than is desired, there are too many series ampere-turns. These can be reduced without changing the number of turns by reducing the current which flows through them. This is done by a shunt resistance in paral- lel with the series winding. A generator is usually given more series turns than are necessary, the desired amount of compound- ing being obtained by adjusting the shunt resistance. This is much easier than changing the number of series turns and makes it possible to change the amount of compounding at any time, even after the machine is in use. 24. (d) Differential Characteristic. The connections for this are the same as for the compound characteristic (Fig. 5) except that the series field winding is reversed so as to be in i-B] COMPOUND GENERATOR. opposition to the shunt winding. The effect of the series wind- ing is now to decrease (instead of increase) the magnetization of the iron, as the armature current increases, causing the volt- age to fall off with load more rapidly than with the shunt field alone. As there is no demand for this, generators with differ- ential winding are not used. (In a motor, Exp. 2-A, a differ- ential winding is useful in giving constant speed). 25. (e) Series Characteristic. This characteristic shows the effect of the series winding alone, with the shunt winding not connected. The procedure is the same as in testing a series generator, the connections being as in Fig. 2, Exp. i-A. 10000 8000 6000 4000 2000 CONSTANT SPEED CONSTANT TERMINAL VOLTAGE -7,900 40 80 120 160 ARMATURE, AMPERES 200 FIG. 7. Armature characteristic or field compounding curve, showing that at full load 2,200 more ampere-turns are needed than at no load for constant terminal voltage. 26. (/) Armature Characteristic. This curve is used in de- termining the proper number of series turns for compounding a generator ; and is therefore frequently called a field compounding curve* It shows, Fig. 7, the variation in field excitation * This has also been called an " excitation characteristic," a name which is ambiguous since it may be taken to mean the saturation curve, 6. 24 DIRECT CURRENT GENERATORS. [Exp. (amperes or ampere-turns*) necessary at different loads to main- tain a constant voltage at the terminals of a shunt generator driven at constant speed.f The connections are shown in Fig. 3, readings being taken of field current, line current, terminal voltage and speed. Separate excitation may be used when a higher excitation is wanted than can be obtained by self-excita- tion. The load current is increased from no load to about 25 per cent, overload. At each load, before readings are taken, the voltage is brought to the desired constant^ value by adjusting the field rheostat. 27. The rise in the armature characteristic shows the in- crease in ampere-turns of excitation needed to compensate for loss in voltage due to resistance drop, armature reactions, etc. (16). If in service the machine is to be operated as a shunt gene- rator, this increase in excitation can be obtained by adjusting the field rheostat as was done in obtaining this curve. If, however, the machine is to be operated as a compound gen- erator, this increase in excitation is to be obtained by the ampere- turns of the series winding. 28. Determination of Proper Number of Series Turns. We know from the armature characteristic the additional ampere- turns of excitation which must be provided at full load to pro- duce the desired terminal voltage. We know also the amperes (load current) which will flow through these turns at full load. The necessary number of turns is accordingly readily found by dividing ampere-turns by amperes. Thus in Fig. 7, we note that *To plot in ampere-turns, the number of turns in the shunt field must be known ; see Appendix I. The number of turns multiplied by field current gives the number of field ampere-turns. t (26a). In case the generator is to be normally driven by an induc- tion motor, with speed decreasing with load, it should be so operated in taking the armature characteristic. (See i6a, 2ob.) $ (26b). The curve may be taken for a voltage which increases with load; such a curve would show the series ampere-turns to be added for over-compounding. i-B] COMPOUND GENERATOR. 25 for full load (200 amperes) there are needed 2200 more ampere- turns excitation than at no load. The series winding will be traversed by the current of 200 amperes, and must accordingly have ii turns in order to make the required 2,200 ampere-turns. If the armature characteristic were a straight line, the series turns calculated as above would be the same for all loads and the generator could be compounded so as to have perfect regulation and give an exactly constant voltage at all loads. But the armature characteristic always curves, bending more after saturation is reached. The series turns are, therefore, calcu- lated for one definite load (full load) ; for other loads the com- pounding will be only approximately correct (21). The armature characteristic and hence the proper number of series turns for correct compounding, will differ for different speeds and terminal voltage, an interesting subject for further investigation. APPENDIX I. MISCELLANEOUS NOTES. 29. Determining the Number of Shunt Turns. The number of shunt turns on a generator can be more or less accurately deter- mined, if the machine has a series winding or a temporary auxiliary winding with a known number of turns. With the machine separately excited, take an ascending no-load saturation curve, using the shunt field winding of unknown turns; take a second similar curve, using the series or auxiliary field wind- ing of known turns. A comparison of the two curves shows that the shunt winding requires a much smaller -current than does the auxiliary winding to give the same generated armature voltage. De- termine this ratio of currents for equal terminal voltage (found for several voltages and averaged) and suppose it to be 1 : 40. The shunt turns are then 40 times as many as the auxiliary turns, the ampere-turns for equal terminal voltage being the same. If for example the auxiliary turns are 10, the shunt turns are accordingly 400. 30. The number of turns in two field windings can be compared 26 ' DIRECT CURRENT GENERATORS. [Exp. by the use of a ballistic galvanometer (or voltmeter or ammeter used as a ballistic galvanometer) ; the chief advantage of the method is that it does not require facilities for running the machine. With the armature stationary and the galvanometer connected to the ter- minals of one field, break a certain armature current and note the throw of the galvanometer. Repeat, breaking the same armature current with the galvanometer connected to the other field. The ratio of galvanometer throws gives the desired ratio of field turns. It is best to take a series of readings and average the results. 31. An estimate of the number of turns in a coil can be made from its measured resistance, size of wire and mean length of turn. This can be used as a check, but the method is commonly only approximate on account of the uncertainty of the data. 32. To Compound a Generator by Testing with Added Turns. The proper number of series turns required to compound a generator can be ascertained by trial by means of temporary auxiliary turns. With the generator running at full load, pass current from an inde- pendent source through these auxiliary turns and adjust this current until the terminal voltage of the generator has the desired full-load voltage. This current (say 220 amperes), multiplied by the number of auxiliary turns (say 10) through which it flows, shows that 2,200 extra ampere-turns are needed at full load. If the full-load current is 200 amperes, the generator would accordingly require n series turns. 33. Full-load Saturation Curve. For obtaining this curve, the field excitation is varied and the load adjusted at each reading, so that the external current remains constant at its full-load value. Field currents are plotted as abscissae and terminal voltages as ordi- nates. Such a curve is to be taken later (Exp. 3~A) on an alter- nator; it may accordingly be omitted, in the present experiment, if time is limited. CHAPTER II. DIRECT CURRENT MOTORS. EXPERIMENT 2-A. Operation and Speed Characteristics of a Direct Current Motor, (Shunt, Compound and Differential). PART I. INTRODUCTORY. i. Generators and Motors Compared. Structurally a direct current generator and a direct current motor are alike,* the essential elements being the field and the armature. The same machine may accordingly be operated either as a generator or as a motor. Operating as a generator, the machine is supplied with me- chanical power which causes the armature to rotate against a counterf or opposing torque; this rotation of the armature gen- erates an electromotive force which causes current to flow and electrical power to be delivered to the receiving circuit. Operating as a motor, the machine is supplied with electrical power which causes current to flow in the armature against a counterf or opposing electromotive force; this current creates a torque which causes the armature to rotate and mechanical power to be delivered to the shaft or pulley. *(ia). Since generators are built in much larger sizes than motors, one generator being capable of supplying power for many motors, there may be a difference in design due to size. Moderate size machines, gene- rators or motors, are built with few poles, four being common in small motors. On the other hand, very large machines that is generators are built with many poles. In all direct current machines, generators or motors it is common practice to use a stationary field and a revolving armature ( i, Exp. i-A). f ( ib). There is no counter torque in a generator until current flows in the armature; there is no counter electromotive force in a motor until there is rotation of the armature. 28 DIRECT CURRENT MOTORS. [Exr. It is seen that the operation, either as a generator or as a motor, involves (i) the generation of an electromotive force and (2) the creation of a torque, both of which depend upon funda- mental laws of electromagnetism. 2. Generation of Electromotive Force. An electromotive force is generated in a generator or in a motor due to the cutting of lines of force, this electromotive force being proportional to the rate at which the lines of force or flux are cut, as already discussed in I, Exp. i-A. In a generator this electromotive force causes (or tends to cause) a current to flow; in a motor, it is a counter electromotive force and opposes the flow of current. 3. Creation of Torque. A torque is created in a generator or motor due to the forces acting upon a conductor carrying current in a magnetic field. In a motor this torque causes (or tends to cause) a rotation of the armature with respect to the field ; in a generator, it is a counter torque and opposes the rota- tion of the armature. The creation of torque depends upon the following funda- mental principle : When a conductor carrying current is located in a magnetic field, it is acted upon by a .force that tends to move the conductor in a direction at right angles to itself and to the magnetic flux, the force being proportional* to the current and to the flux density. This force creates a torque, that is a turning moment or couple equalf to the product of the force and the length of the * (3a). In C.G.S. units this force is equal to the product of the cur- rent, flux density, length of conductor and sine of the angle between the conductor and direction of flux. This sine is unity when the conductor and flux are at right angles, as in most electrical machinery. When there are a number of conductors, each conductor is subject -to this force; the total torque of a motor is therefore proportional to the total number of armature conductors. t (3b). Torque may be expressed as pounds at one foot radius, pound- feet, kilogram-meters, etc. Power is proportional to the product of torque 2-A] SPEED CHARACTERISTICS. 29 radius or lever arm to which the force is applied. It accordingly follows that: torque is proportional to armature current and to the flux density of the field; this is irrespective of whether the armature is rotating* or not. A reversal of either the current or the flux alone reverses the direction of the torque. Of the total torque, part is used in overcoming friction, wind- age and core loss ; the remainder is useful torque and is available at the pulley. 4. Automatic Increase of Current with Load. The counter- electromotive force E' is always a few per cent, less than the sup- ply voltage E. The difference is due to the resistance drop in the motor armature, including brushes, brush contact and con- nections, and the series field (if any) ; that is E' = E-RI. (i) and speed; thus, if R.P.M. is revolutions per minute and T is torque in pound-feet 33,000 If power is known, torque may be found by dividing power by speed. In pound-feet, torque is 33,000 H.P. 27T A R.P.M. ' When power is in watts, it is frequently convenient to express torque in synchronous watts "; thus, "R.P.M.* (One synchronous watt = 7.04 pound-feet.) (One pound-foot = 0.142 synchronous watt.) Torque is also expressed in "watts at 1,000 R.P.M."; thus, *(3c). Torque with the armature at rest (static torque) can be de- termined for various field currents and for various armature currents by means of a lever arm attached to the armature and a spring balance or platform scales. 3 DIRECT CURRENT MOTORS. [Exp. Within the usual range of operation, this RI drop for a com- mercial motor is only a few per cent, of the total line voltage. Good design does not permit more, inasmuch as the output and efficiency are decreased by the same percentage. The current which flows in the armature is seen to be If under running conditions the current / is not sufficient to give the motor enough torque (which is proportional to current and flux) to do its work at the speed at which it is running, the motor will begin to slow down, thus decreasing the counter- electromotive force E' (which is proportional to speed and flux). As E f decreases / increases, until the torque is sufficient to meet the demands upon the motor. The current accordingly increases automatically with the load, and this increase can be continued until the safe* limit, determined by heating, is reached. On the other hand, if the current I is more than is needed to give the torque required for the load at a certain running speed, the surplus torque will cause the armature to accelerate, thus increasing E' and decreasing / to a value which gives the proper torque for the load and speed. It will be seen that a small change in E' is sufficient to cause a large change in / and therefore in the torque. As an example, suppose E' = 100, E= 104; if an increase in speed causes E' to increase 2 per cent., that is to 102, the current / will be reduced 50 per cent. 5. Relations between Speed, Flux and Counter-electromo- tive Force. Counter-electromotive force is proportional to speed (S) and flux () ; that is E'cc+S. (3) Hence, speed varies directly as the counter-electromotive force and inversely with the flux ; that is * A motor is usually rated so that it can be run for several hours at 25 per cent, over its rated load. 2-A] SPEED CHARACTERISTICS. 31 E' 5oc ^r; (4) id or, E- Rf * (5) This is the speed equation for a motor. It is seen that if is reduced the speed will increase. The equation shows the defi- nite numerical relations of the quantities involved. Hozv an increase in speed is brought about by a decrease in flux is made more clear in 7. 6. Speed of a Shunt Motor. A shunt motor with constant supply voltage has a constant field current and therefore a con- stant flux. It accordingly follows that the speed is nearly con- stant. The RI drop causes it to decrease with load (compare equation 5) ; this is partially offset, however, by the effect of armature reactions, as seen later (8). 7. It is seen from equation (5) that the speed may be in- creased or decreased by weakening or strengthening the field. The process is explained as follows: When the field is weakened the counter-electromotive force is reduced ; this permits more current to flow in the armature, thus giving greater torque* and speed. The speed accordingly in- creases until E' has increased so as to limit the current (and hence the torque) to a value which will give no further accel- eration. The cause for increase of speed is surplus torque. 8. Armature Reactions and Brush Position. If the brushes are given a backward lead (which is usual in motors running in one direction, in order to obtain better commutation) the field is * (7^). As an example, suppose the field is weakened so that the flux is reduced 2 per cent, and E' the same amount ; and suppose the armature current increases 50 per cent. Torque is proportional to flux and armature current and in this assumed case is increased 47 per cent. ; for .98 x 1.50 - 1-47. 3 2 DIRECT CURRENT MOTORS. [Exp. weakened by the demagnetizing effect of armature reactions (8a, Exp. i-A). This causes the flux to decrease with load, so that the speed does not decrease as much as it would with the brushes in the neutral position. On account of armature reac- tions, therefore, the speed regulation of a motor is better; the voltage regulation of a generator is worse ( 16, Exp. I B). The proper brush position for best commutation is the posi- tion which gives minimum speed. 9. If the backward lead of the brushes is increased, the speed of the motor under load can be increased until it equals or ex- ceeds the speed at no load. Such a control of speed by brush adjustment is not practicable, however, on account of bad com- mutation and destructive sparking; the brushes should be given the position of best commutation. A small variation of speed can be made, if desired, by shifting the brushes, provided it is not enough to cause much sparking. 10. Speed Control. From equation (5) it is seen that the speed of a motor can be varied : by changing the impressed volt- age, E; by varying resistance, R (series controller) ; or, by vary- ing flux, (j>. Each of these methods is in use for operating variable speed motors. (a) Varying line voltage. Several line voltages can be ob- tained by using a number of line wires. Such a system is called a multiple-voltage system. (b) Varying resistance. The series controller is in common use with series motors ; it is used occasionally with shunt motors of small size. (c) Varying flux. This can be accomplished either by a change in excitation (magnetomotive force) or a change in reluctance; for flux magnetomotive force -f- reluctance. ( i ) Speed control by varying excitation is obtained in a shunt motor by a rheostat in series with the field (7) ; in a series motor, by an adjustable resistance in parallel with the field. 2-A] SPEED CHARACTERISTICS. (The possible method of control by brush-shifting, 8, is not used.) (2) Speed control by varying reluctance is obtained in certain shunt motors by varying the air-gap. A limit to speed control by a variation in flux (by varying either excitation or reluctance) is reached on account of arma- ture reactions ; a considerable reduction in flux causes bad com- mutation. For varying the speed through a wide range, there- fore, these methods can only be used if the effects of armature reactions are overcome. This Was first SatisfaC- Constant Potential Supply torily accomplished by the compensated winding of Prof. H. J. Ryan, which was placed in slots in the pole faces. This compensa- tion is now generally ac- complished by the more easily constructed inter- poles or commutating 'poles of the inter pole motor. o RHEOSTAT /^~^( SHUNT FIELD S N. / rj r- / inffitftfWtf >> / A y STARTING BOX FIG. i. Connections for operating shunt motor. PART II. OPERATION. 11. Shunt Motor. If the motor is compound, cut the series coil out of the circuit. Connect the sup- ply lines to the main terminals of the motor and complete the connections, as in Fig. I. Note the queries, 15. To start the motor, have all the starting box resistance in cir- cuit and all the field rheostat out of circuit; make sure that the field circuit is complete. The circuits should be so arranged that closing the supply circuit will excite the field (which takes 4 34 DIRECT CURRENT MOTORS. [Exp. an appreciable time) before* the armature circuit is closed. The armature circuit is then closed and this is commonly done by the starting box lever. Bring the motor, unloaded, up to speed by cutting the starting box resistance slowly^ out of circuit until the whole resistance is cut out. Note the ammeter during the process and the in- crease of speed as indicated by the hum of the motor. The starting box should be kept in circuit only during starting, for (except in special cases) it is not designed for continuous operation. If the motor does not now run at normal speed, the speed can be increased by gradually varying the field current by means of the field rheostat. Do not reduce the field current too much, nor under any circumstances break the field circuit,^ or the motor will run at a dangerous speed. Note the speed at no load for several excitations ; also, when facilities permit, for several supply voltages. (For example, operate a no-volt motor with 55 volts on armature and on field; with 55 volts on armature and no volts on field; but not with no volts on armature and 55 volts on field.) 12. Stopping. Motors are commonly stopped by opening the supply switch and not by first opening the armature circuit. * ( na). If the starting box were made with sufficiently high resistance, so as to properly limit the current irrespective of counter-electromotive force, the armature circuit could be closed simultaneously with the field. This, however, is not usual practice. t (nb). Starting boxes are sometimes made so that it is impossible to manipulate them too rapidly. The " multiple-switch " motor starter, used particularly in starting large motors, has a number of switches, thrown successively by hand; these give good contact for large currents and re- quire time for cutting out the successive sections of the resistance. $ ( nc). Automatic Release. This danger is commonly guarded against by a solenoid on the starting box which releases the lever and allows it to spring back to the starting position when there is no current in the field circuit. This also acts as a " no-voltage " release, giving protection against damage which might occur were the current supply cut off and put on again with the starting box resistance all out. 2-A] SPEED CHARACTERISTICS. 35 There is then no sudden discharge of field magnetism and con- sequent liability to damage ; for, as the armature slows down it generates a gradually decreasing electromotive force which main- tains the field excitation so that it too decreases gradually. (If there is an automatic release on the starting box, it opens the armature and field circuits after the field excitation has decreased to a low value.) The effects of induced electromotive force caused by sudden field discharge can be reduced by absorbing its energy in a high resistance shunt in parallel with the field circuit, or in a short- circuited secondary circuit around the field core. A brass field- spool will act in this way. Throwing power suddenly off the line, by opening the supply switch, may cause fluctuations in line voltage, particularly in case of large motors under load. To avoid this, before the sup- ply switch is opened, the starting resistance may first be gradu- ally introduced into the armature circuit, which, however, is not to be opened ; then the supply switch is opened. 13. Compound Motor. In a compound* motor, the series winding strengthens the field as the armature current increases. On starting or under heavy load (i. e., at times when the arma- ture current is large) the motor is accordingly given a very strong field and therefore has for a given armature current a greater torque than it would have with the shuntf winding only. * ( I3a). To tell whether a series winding is connected "compound " or "differentially," throw off the belt and start the motor (for a moment) with the series coil only. If the motor tends to start in the same direction as it does with the shunt coil, the winding is " compound " or "cumula- tive;" if in the reverse direction, the winding is "differential." t(i3b). This means a greater torque than it would have with the same shunt winding only. The motor could be given a different shunt winding which would give as strong a field and as great a torque as is obtained by means of the compound winding. Such a shunt winding, however, would give the strong field at all times; whereas the compound winding gives the strong field only at particular times, i. e., at starting and under load. 3 6 DIRECT CURRENT MOTORS. [Exp. Under load the compound winding, by strengthening the field, causes the motor to slow down. For certain kinds of service as in operating rolling mills, cranes, elevators, etc. this is desir- able in that the motor can work at great overload without the excessive demand for power which would be made by a constant speed motor. As compared with a shunt motor, it works under load at greater torque and less speed, and can stand a greater overload. In this respect it is similar to the series motor (see 18). It differs from the series motor in that at light load there is still a certain strength of field due to the shunt winding, and the speed, therefore, cannot exceed a certain value, whereas a series motor will attain a dangerous speed if the load is thrown off. Under some operating conditions the compound motor can accordingly be used where neither the shunt nor the series motor would be suitable. If slowing down with load is not wanted and a constant speed is desired at all loads, together with a large torque at starting, the series winding is used during starting only and is then cut out or short-circuited. 14. Differential Motor. Since a differential winding weak- ens the field as the load increases, such a winding makes possible a speed which increases with load. This is practically not desir- able. In some cases, however, it is desirable to have the same speed at full load as at no load and to use a series winding just sufficient to overcome the tendency which a shunt motor has to slow down with load. If the series turns are too many for this, their effect can be cut down by a shunt of proper resistance con- nected in parallel with the series winding. The starting torque of a differential motor is poor, particularly under load, inasmuch as the large starting current in the differ- ential winding greatly weakens the field. For this reason, when a differential winding is used, it is usually cut out of circuit or short-circuited during starting. 2-A] SPEED CHARACTERISTICS. 37 If there are many series turns and no shunt is used, the cur- rent taken by a differential motor may become excessive as the load increases, thus weakening the field so that the motor races, or even reversing the field so that the motor suddenly reverses. 15. Queries. For increasing the speed, is the field current increased or decreased? Why? What is the use of the starting box? In starting, why do you not close the field and armature circuits simultaneously? Why is the starting box connected in series with the armature and not in series with the line? Why is a strong field needed for starting? Does this become of more or of less importance when starting under load? Would an added series winding be an advantage or a disadvantage in starting? Why would it be dangerous to break the field circuit? What is the effect of shifting the brushes? What is the proper position for the brushes? What is effect of interchanging positive and negative supply lines? What changes in connections are necessary to reverse the direction of rotation of the armature? (Be careful not to run more than a moment in the reverse direction, if the brushes would thus be damaged.) PART III. SPEED CHARACTERISTICS. 1 6. Shunt, Compound and Differential Motor. It is the pur- pose of the experiment to determine the variation of speed with load for the same motor connected in three ways, shunt, com- pound and differential ; the line voltage is constant throughout the three runs. The brushes should be in one position during all the runs (8), or the amount of any change noted. With the motor connected as a shunt machine, Fig. I, adjust the field current by means of the field rheostat so that the motor runs, on no load, at the speed for which it is designed, and keep the field current constant at this value during the run. For the other two runs, compound and differential, adjust the field cur- rent for this same no-load speed* and keep the field current constant during each run. * ( i6a). Starting with the same no-load speed, and making runs from no load to full load, gives the three speed characteristics of Fig. 2 coincid- ing at no load ; this is the best procedure for instruction purposes. In commercial testing, the field should be adjusted so that the motor runs at rated speed at full load. The curve is then taken from full load to no load ; the maximum per cent, variation in speed from its full load value is the per cent, speed regulation. (Standardization Rules, 195.) DIRECT CURRENT MOTORS. [Exp. Vary* the load on the motor by steps between no load and 25 per cent, overload, reading line voltage, field current, armaturef current (or else line current) and speed, for each step. Make runs with the motor connected shunt, compound and differential. With current as abscissae (either line current or armature current) and speed as ordinates, plot speed characteristics for the three runs as in Fig. 2. 1100 1000 900 800 700 Q 600 UJ iu500 ft 400 300 200 100 mcFERENTjAL, 04 8 12 16 20 24 28 32 36 40 ARMATURE CURRENT FIG. 2. Speed characteristics of a motor, shunt, compound and differential. 17. It is instructive to take runs as a differential motor with different resistances in shunt with the series coil ; also, to take the various runs (shunt, compound and differential) with the field excitation above and below saturation. * (i6b). This may be done by means of a brake, a blower, a belted generator or other convenient load ; if a generator is used, its output may be absorbed in resistance or pumped back into the line (26, Exp. 2-B). f (i6c). If the armature current is measured, the field current is added to give the line current; if the line current is measured, the field current is subtracted to give the armature current. 2-A] SPEED CHARACTERISTICS. 39 APPENDIX I. SERIES MOTOR. 18. Operation. A series* motor is distinctly a variable speed motor. Its characteristics are shown in Fig. 3. The speed increases rapidly as the load is decreased, becoming dangerouslyf great if the load is removed or reduced too much. The series motor, therefore, cannot be run at no load and normal voltage; it can be run at no load with a series resistance in circuit. The series motor, be- sides being used for trac- " tion,:}: is used for hoists, etc. For such service it is well adapted. The im- portant characteristic is that by slowing down under heavy load, it can increase its torque with- out requiring a corresponding increase in power ; for torque = power -r- speed ( 3b). If the speed did not decrease with load, it is seen that the power would have to be greatly increased to give the same torque. This would require a much larger motor. * ( i8a). For the purpose of comparison with the shunt, compound and differential motor, the characteristics of the series motor are here described, although its test is not usually to be included as a part of the present experiment. When the test is made, it is well to combine it with efficiency measurements, 33, Exp. 2-B. t(i8b). In the laboratory, be prepared to shut down quickly if ex- cessive speed is reached. With a belted load, there is danger of the belt flying off; with a brake, there is danger of an unintentional sudden de- crease in load. $(i8c). In traction, the controller is usually so arranged that two motors can be connected in series or in parallel with each other for speed control, thus giving each motor half or full voltage. The series resistance is likewise used for control and for starting. In starting, the resistance and both motors are all in series. AMPERES FIG. 3. Characteristics of a series operated at constant voltage. motor, 4 DIRECT CURRENT MOTORS. [Exp. 19. Torque. Since torque varies as flux X current, the torque would vary as / 2 , if flux were proportional to current. For small currents below saturation this is more or less true. For large currents after saturation the flux is practically constant and the torque directly proportional to /. The torque curve, Fig. 3, is there- fore at first more or less parabolic and then becomes a straight line. 20. Speed. From equation (5) it is seen that speed varies in- versely with flux. For small currents, if we consider RI negligible and flux proportional to current, speed varies as 1/7; the speed curve (Fig. 3) would then be an hyperbola. For larger currents satura- tion is reached, the flux becomes practically constant and the speed more nearly constant. On account of RI drop, speed continues to gradually decrease as current increases, even after saturation is reached. Series motors are sometimes overwound, that is, wound so that saturation (and hence more constant speed) is soon reached. 21. Test. The load is varied between an overload (determined by maximum safe current) and an underload (determined by maxi- mum safe speed). The line voltage is constant; a series resistance is used for starting and may be used for adjusting voltage. Any method for loading can be used. If a shunt generator is used as a load, its output may be absorbed in resistance or pumped back into the line. (See 26, Exp. 2-B.) The pumping back method has been modified by A. S. McAllister, so as to form a convenient method for determining the torque of any kind of motor, direct or alternating (Standard Handbook, 3-239 and 8^-151; McAllister's Alternating Current Motors, p. 185). 2-B] EFFICIENCY. 4 1 EXPERIMENT 2-B. Efficiency of a Direct Current Motor* (or Generator) by the Measurement of Losses. I. Introductory. Efficiency is the ratio of output to input. The obvious and direct method for determining the efficiency of a motor is, therefore, to measure the outputf and the input and take their ratio. An indirect method, known as the method of losses or stray power method, avoids the measurement of output. In this method the losses are measured and the output obtained by subtracting the losses from the input ; the efficiency is then determined. This method of losses possesses several advantages over meth- ods that involve the measurement of output. The motor output is in some cases a troublesome quantity to measure, especially if accuracy is essential ; but, even with the same degree of accuracy in the measurement of output and of losses, the efficiency cannot be as accurately determined^ from the former as from the latter. *With the appendices, this experiment covers the main features of the usual methods for determining the efficiency of any machine, direct or alternating. The main experiment is explicit for determining the efficiency of a shunt motor, and it is suggested that the student, without reference to the Appendices, first performs this main experiment. The Appendices should then be read and, if desired, a second experiment made (either now or later) under some of the special conditions which are there treated. t(ia). Direct Measurement of Output. The output of a motor can be determined directly by electrical measurement (using for a load a calibrated generator, 24), or by mechanical measurement (measuring torque by means of a Prony brake, Brackett cradle dynamometer, etc.). Power can be readily computed when torque and speed are known (3b, Exp. 2-A). There are various forms of absorption and transmission dynamometers conveniently arranged for the direct measurement of power. For description of Prony brake, see Flather's Dynamometers and the Measurement of Power and the usual hand and text books ; also Electric Journal, I., 419. For the cradle dynamometer, see Nichols' Laboratory Manual, Vol. II., and elsewhere. $(ib). Let us suppose that the error in measuring the input, output or losses is one per cent., due to inaccuracies in the instruments or in 4 2 DIRECT CURRENT MOTORS. [Exp. t A further advantage of this method is that a load run is not an essential, as will be seen later, and hence may be omitted. Conditions often arise, as in testing large machines, when a load test is impossible and this advantage then becomes important. It is always best, however,. to make the load run when this can be done. The method of losses is general and can be applied for deter- mining the losses, and hence the efficiency, of a shunt, compound, differential or series wound motor or generator. In the follow- ing paragraphs the directions are full and explicit for testing a shunt-wound motor. Modifications are outlined in the Ap- pendices for applying the method to other types of motors and generators. 2. For testing any machine two runs are made : a load run to ascertain working conditions, and a no-load run (or runs) to determine losses under these same conditions. In making the no-load run for losses the machine can be driven electrically as a motor or mechanically as a generator. The for- mer method is used in this experiment ( 7) ; the latter method is described in 21 of Appendix I. The resistance* of the armature is to be found by the fall of potential method both before and after the load run, in order that it may be determined both cold and hot (see 17, Exp. i-A). Since this includes the resistance of the brushes and of brush contact, which varies with current, to be exact it would be necessary to measure the armature resistance for each load their reading. Assume the true output to be 95 when the true input is 100. The output, as measured, might vary from 94.05 to 95.95 and the input, from 99 to 101 ; hence the efficiency, determined from output, might vary from 93.1 to 96.9 per cent. On the other hand with the same percentage error in their determination, the measured losses might vary from 4.95 to 5.05 and the measured input from 99 to 101 ; hence the efficiency, determined from losses, could only vary from 94.9 per cent, to 95.1 per cent. * In measuring armature resistance the voltmeter is to be connected to the same points as in the load run. 2-B] EFFICIENCY. 43 current. No account will be taken of a possible difference be- tween the contact resistance with machine running and that measured with armature stationary. 3. Load Run (Shunt Motor). This run is made* to ascer- tain the working conditions for which tbe losses are to be deter- mined, that is, to ascertain the load current and hot resistances for calculating copper losses and to ascertain the normal speed and excitation for which the iron and friction losses are to be determined in the no-load run. (The load run is a repetition of the run made in Exp. 2-A for obtaining speed characteristics.) 4. Connect the motor to the supply lines, the voltage of which should remain practically constant during the run. (See Fig. i of Exp. 2-A.) Adjust the field current by means of the field rheostat so that the motor runs at its rated full-loadf speed (or the speed for which its efficiency is desired) and keep the field current constant at this value during the run. Care in keeping the field current constant will increase the accuracy of the results ; it is not sufficient to leave the rheostat in one posi- tion and assume the field current constant because it is very nearly so. * (3a). Omission of Load Run. It will be seen that the load run is not essential and that the method may be employed even when the load run is impossible. Whenever it is possible, however, the load run should be taken, since it serves to get the machine " down to its bearings," that is, down to its working condition of friction as well as of temperature. When the load run is omitted, cold resistances are measured and hot resistances determined by suitable temperature corrections or assumptions. Values of field current and speed are determined for no load; values are assumed for full load which it is believed will most nearly represent the operating conditions for which the efficiency is to be obtained. In a motor, for example, we may assume a constant excitation and a constant speed, or a speed which is say 5 per cent, lower at full -load, etc. In n generator we may assume a constant speed and a constant excitation, or an excitation which is a certain amount lower (shunt generator) or higher (compound generator) at full load. t(4a). For commercial testing the speed should be adjusted to its rated value at full load; in laboratory practice the adjustment, when de- sired, may be made at no load. 44 DIRECT CURRENT MOTORS. [Exp. 5. Beginning at about 25 per cent, overload, as estimated from the input, vary the load by steps from overload to no load or vice versa; at each step measure the line voltage, armature cur- rent,* field current and speed. 6. The motor may be loaded in any manner that is convenient. A brake may be used for this, but it is frequently more con- venient to load with a generator and to absorbf the output of the generator by suitable resistances. 7. No-load Run (Shunt Motor) ; Machine Driven Electric- ally 4 For a shunt machine one|| no-load run is made; the machine is operated as a motor at the same constant excitation as in the load run. The object is to determine the losses for different speeds at this constant excitation. Before taking read- ings the motor should be run awhile so as to attain its normal working condition of lubrication, temperature, etc. With the motor running unloaded, adjust the field current to the same value as during the load run and hold constant at this value during the no-load run. By varying the electromotive force impressed on the armature terminals, vary the speed of the motor by steps so as to cover as wide a range of speed as pos- sible; this will give more accurate results than if only the speed range of the load run is covered. At each step measure the * See i6c, Exp. 2-A. flf a direct current generator of suitable voltage is used, the current from the generator may be " pumped back " into the motor supply line (26). $ (7a). This run can be made with the machine driven mechanically (21) instead of electrically. || (7b). Although a run at only one excitation is necessary for de- termining the efficiency of a shunt motor, runs at other excitations are recommended. These additional runs may be taken by the two voltage method (7d). They are necessary if hysteresis loss is to be separated (Appendix I.) or if flux density is variable (Appendix III.). If a run is wanted at a very high saturation, a higher voltage may be supplied to the field than the rated voltage supplied to the armature. 2-B] EFFICIENCY. 45 Constant Potential Supply electromotive force impressed on the armature terminals, arma- ture current,* field current and speed. By using two resistances, B and C, arranged as in Fig. I, the electromotive force impressed on the armature may be varied by short circuiting more or less of B or of C. A single series resistance B may suffice, but the adjustment in many cases can be better made with two. An independent genera- tor can be used as a supply to obtain variable voltages for the armature circuit, or the \\ /^~~X SHUNT FIELD X X ' * j j-nnRnnsTOP ( A /~- STARTING BOX FIG. i. Connection for no-load run as a shunt motor for determining losses. two voltagesf of a three- wire system. 8. Results. The losses of the motor include: (1) Copper losses of field and armature; (2) Iron losses of armature; (3) Friction and Windage, or air resistance. Losses (2) and (3) are rotation losses and are independent of load. * (7c). For the no load run the armature current is small; if a low reading ammeter is used, it should be short-circuited at starting to avoid damage by the initial rush of starting current. t(7d). Two-voltage Method. For instruction purposes a complete series of armature voltages and corresponding speeds is desirable. Where two supply voltages (as no and 220 volts on a 3-wire system) are avail- able, accurate results may be obtained by a two-voltage method, by taking 8 or 10 readings and averaging first with say 220 and then with no volts impressed on the armature of a 220 volt motor. These points, accurately determined, are sufficient for working up results by the straight line method of Fig. 2, in which they are represented by black dots p and q. By this method the trouble of adjusting armature voltage is avoided. 4 6 DIRECT CURRENT MOTORS. [Exp. 9. Copper Losses. The copper losses for any circuit can be computed, if the current and resistance through which it flows are known, being equal to RP where R is resistance and / is cur- rent. The armature copper loss is thus computed ; it is a vari- able loss, changing with load. The field copper loss is a constant loss and does not vary with load. It also can be computed by the formula RP, or more con- veniently from the formula El, the product of current in the field circuit and voltage supplied at its terminals. (The formula El cannot be thus used unless copper loss is the only expenditure of energy; it cannot be used for determining copper loss of an armature or other circuit in which there is a back electromotive force.) In a self-excited machine, in which a field rheostat is used under normal operation, the loss in the rheostat is to be included in the field circuit loss. 10. Iron Losses. The iron losses are losses due to hysteresis and eddy currents ;* they are independent of load, but vary with the speed and with the flux density in the armature. At con- stant speed, hysteresis loss (within the usual working range) varies approximately as the 1.6 power of the flux density; eddy currents as the square of the flux density. At constant flux density, hysteresis loss varies directly with the speed and eddy currents with the square of the speed. If the field current of the motor is held constant, the flux density in the armature will be practically constant for all loads. It will be modified under loadf to a small extent by armature reaction, the effect of which will be neglected. Hence in a shunt motor run with constant * This includes eddy currents in the pole pieces and in armature copper as well as in armature iron. t ( loa). Load Losses. Losses which occur under load in addition to copper losses and to the no-load iron, friction and windage losses are termed load losses. Any loss due to field distortion constitutes such a loss. Load loses are usually neglected as small or are estimated. See Standardization Rules 114-7. 2 _B] EFFICIENCY. 47 field current, the iron losses are independent of load and depend upon speed alone. ii. Friction and Windage. The friction and windage losses are also independent of load and depend alone upon speed, being (for all practical purposes) directly proportional* to speed. Friction includes frictions of brushes as well as of bearings. 12. Rotation Losses W (Combined Iron Losses, Friction and Windage). In the no-load run the power supplied to the armature (product of armature voltage and current) gives the rotation losses plus a small armature copper loss. This copper loss is subtracted (or neglected as small) to get the rotation losses. These losses are sometimes termed stray power.\ The combined rotation losses W , thus determined at no load, will be present at all loads and will have the same value for the same speed and excitation. If the speed of the motor is very nearly constant, the W losses will be correspondingly constant. Rotation losses are commonly classed among the constant losses,! inasmuch as they are independent of load and the variation due to any small change of speed is small. For determining efficiency there is no necessity for ascertain- ing the separate losses due to hysteresis, eddy currents, friction and windage, their combined value W being sufficient. 13. A curve should be plotted showing the rotation losses W for constant field current at different speeds. To plot this curve accurately, it is best|| to first plot for various speeds the *(na). Windage increases more rapidly than the first power of the speed ; but windage loss is comparatively small and does not, at usual speeds, materially affect the law of variation of the combined friction and windage losses. t The term stray power applies to any loss except copper loss. $(i2a). The no-load losses are the rotation losses plus the copper loss of the field circuit (and the practically negligible copper loss of the armature) ; the no-load losses are therefore termed "constant." II ( I 3 a )- This is advantageous because a straight line can be drawn more accurately than a curved one, when the observed data are few or irregular; two accurate points are sufficient, but three are better as a 4 8 DIRECT CURRENT MOTORS. [Exp. values of W -=- speed, which will give the straight line ac in Fig". 2. At very low speeds, there may be a deviation from a straight line, due possibly to errors in assumptions as to friction, etc., at these speeds. This, however, does not affect the accuracy of the construction; the straight part of the curve is to be ex- tended back to a. Ut s o cc a SPEED (R.R M.) FIG. 2. Variation of rotation losses W (iron losses, friction and windage) with speed, at constant field excitation. The torque dc to overcome rotation losses is composed of db to overcome friction, windage and hysteresis and be, to overcome eddy current loss. After plotting this line for W -r- speed, pick off values from it and multiply by speed, thus getting as many* points as desired for plotting the W curve. For fuller treatment, see Appendix I. 14. Efficiency. For any load (corresponding to readings in the load run, or assumed), the input is equal to the product of line current and voltage. The losses are : the (variable) RP loss in the armature for the particular armature current 7; the (constant) copper loss of check. It is always desirable to plot the results of any experiment, if possible, as a straight line, arc of circle, or as some curve whose law is known. The arc of a circle is much used in alternating current testing. * Obtained in this way, more points may be used in plotting IV o than the number of observations. 2-B] EFFICIENCY. 49 the field; and the (almost constant) rotation loss W , obtained from the curve in Fig. 2 for the particular speed and excitation. The output is found by subtracting these losses from the in- put; the efficiency is output divided by input. 15. Curves should be plotted with power output (or more simply with armature current) as abscissae, showing separate and total losses, input, output, efficiency, total current and speed ; also useful torque (watts output -f- speed) ; see Fig. 3. Compare the curves of Fig. 3 with the curves for a transformer, Fig. 4, Exp. 5~A, and Fig. 8, Exp. 5-6. Field RI 2 Los9 POWER OUTPUT FIG. 3. Losses and efficiency of a shunt motor. Maximum efficiency occurs when the variable loss (armature RI 2 ) equals the constant losses; see 28. It is seen that efficiency at light loads is low; this is true of both generators and motors. For this reason several generators are commonly run in parallel in a central station ; as the load on the station decreases, the generators are cut out one at a time, so that the remaining generators will be more or less fully loaded and will run nearer the point of maximum efficiency. 5 DIRECT CURRENT MOTORS. [Exp. APPENDIX I. INTERPRETATION OF METHOD; AND SEPARATION OF LOSSES. 1 6. Interpretation* of Figure 2. For constant flux density (con- stant field excitation in a shunt machine), the losses due to 'hystere- sis, friction and windage are proportional to speed ( 10, n) and may be expressed as AS, where A is some constant and 6* is speed. Eddy current loss being proportional to the square of the speed may be expressed as BS Z , in which B is some constant. The total rota- tion loss is accordingly the sum which is the equation of the W Q curve in Fig. 2. Dividing by S, we have the torque to overcome rotation losses which is the equation of the straight linef ac in Fig. 2. (See 3b, Exp. 2- A.) Extending this line back to zero speed at a and draw- ing the horizontal ab, we have be the torque to overcome eddy cur- rent loss (proportional to speed) and db the torque to overcome hys- teresis, friction and windage (independent of speed). These state- ments and the statements made in the following paragraphs, hold true throughout the range of speeds for which W -^-S is a straight line, which is much more than the working range of the machine. 17. Determination of Watts Eddy Current Loss. For any speed, *(i6a). The principle of the graphical method which is here used was brought out by R. H. Housman and by G. Kapp, independently, in 1891 (London Electrician, Vol. XXVI., pp. 699 and 700) ; each made use of a straight line relation for plotting data obtained by running a motor at constant excitation and varying armature voltage. The details, as here given, have been modified by the writer with a view to making the method simpler and more useful. The original papers are excellent, but their method has been made unnecessarily cumbersome by writers who have followed them. Earlier, Mordey had used equations similar to those of 16 for analytical separation of losses. t(i6b). Since, at constant excitation, armature voltage (or more strictly counter-electromotive force) is proportional to speed, the Wo curve can be drawn with E' as abscissae instead of speed. We then divide by E' (instead of S} and get the straight line ac, the ordinates of which (Wa -:-') are amperes. 2-B] EFFICIENCY. 51 (multiplying be by S, gives watts eddy current loss; multiplying db by 5 gives watts loss in hysteresis, friction and windage. If the eddy current loss were zero, ac would coincide with the horizontal line ab; the first equation in 16 would become W = AS, showing that W would be proportional to speed and the W curve in Fig. 2 would become a straight line. 1 8. A Convenient Approximation. Since the eddy current loss is commonly only a small part of the total rotation losses, for small changes in speed it is nearly correct and often very convenient to say the rotation losses IV are directly proportional to speed. 19. Further Separation of Losses. Hysteresis loss can be ap- proximately separated from friction and windage by additional runs at other field excitations. Friction and windage can not be separated from each other by any simple means and hence are considered together. There are various graphical and analytical methods for separating losses, all based on the following facts : friction and windage losses vary as first power of speed and are independent of flux density; eddy current loss varies as square of speed and square of flux density ; hysteresis loss varies as first power of speed and 1.6 power of flux density. At any one speed, armature voltage is taken as a measure of flux density. In any of these methods it is necessary to make some assumption or approximation ; for this rea- son the graphical methods are superior. (In the graphical method given below the approximation consists in obtaining Oa by extra- polation to zero excitation.) The analytical methods will not be taken up here; they consist in obtaining several equations (based upon the above relations) and eliminating between them after substituting numerical values obtaine'd from observation of W at various speeds and flux densities. 20. Graphical Method. Various graphical methods for separat- ing losses differ chiefly in detail; the following procedure (either a or b) is suggested: (a) Make a series of no-load runs, as already described, at vari- ous field excitations, extending these to as low a field excitation as possible. Plot results as in Fig. 2, obtaining a series of curves (straight lines) ac with intercepts Oa^ Oa 2 , Oa 3 , etc., corresponding to various field currents. It is desired to find a value for an inter- cept Oa for the supposed case of zero field current, for which of 52 DIRECT CURRENT MOTORS. [Exp. course no run can be made. To obtain this, plot a curve showing Oa lt Oa 2 , Oa 3 , etc., for various field currents and continue the curve back to zero field current so as to get a value for Oa by extra- polation. (b) It will be found by experience that the value of Oa found by a run at a very low field excitation will differ but little from the desired value Oa for zero excitation; that is, the iron losses at very low excitation are negligible. Instead of a series of no-load runs and extrapolation, one no-load run is taken at as low an excitation as possible ; the value Oa obtained from this run is taken as the value of Oo which would be obtained at zero excitation. Referring to Fig. 2, Oa obtained by either procedure just described is the torque to overcome friction and windage, for at zero excitation there is no hysteresis loss. To obtain watts loss in friction and windage at any speed, multiply Oa by S; this is independent of excitation. To obtain watts loss in hysteresis at any speed for some particular excitation, multiply a a (for that excitation) by S. 21. Determination and Separation of Losses; Machine Driven Mechanically by an Auxiliary Driving Motor. This method, with the machine driven mechanically, is not limited to testing direct current machines; it can be used in testing alternators, synchronous motors, etc. By this method separate values are found for the iron losses and for the mechanical losses; that is, for hysteresis and eddy currents combined and for friction and windage combined. The preceding method, with the machine driven electrically (7), gave directly the eddy current loss and the combined hysteresis, fric- tion and windage (17). Each method has its advantages; in the one hysteresis is combined with eddy current, in the other with fric- tion and windage. The procedure is as follows: (i) The machine to be tested is sepa- rately excited and is driven as a generator* on no load at normal speed and excitation by means of a shunt motor ; compare 25. The motor input is measured. (2) The generator field circuit is broken and motor input again measured; the diminutionf in motor input * The armature winding is idle; this test therefore can be made for finding iron loss and friction of a machine with armature unwound. t(2ia). This assumes that the motor losses remain constant. The small change in armature RI~ loss will usually be negligible; if not 2-B] EFFICIENCY. 53 gives the iron losses (hysteresis and eddy current) of the generator. (3) The brushes of the generator are lifted, the diminution in motor input giving brush friction. (4) The belt is next thrown off, the diminution in motor input now giving the generator journal friction, windage and the belt loss. The iron losses may be found for various excitations at normal speed. These losses should be determined for an increasing excita- tion ; the losses with a decreasing excitation would be more. For obtaining iron losses alone, this method with the machine driven mechanically is better than the method (7) with the ma- chine driven electrically; for it gives iron losses directly, separate from friction, and it is not necessary to go through any separation of losses as in 20. This avoids error due to extrapolation and makes no assumption that friction and windage are directly propor- tional to speed. On account of belt tension, journal friction will be more than in the no-load test with the belt off (7). Belt losses are also included with friction and windage. This may sometimes be desirable, since it is the usual condition of operation. In a test of the motor per se, these losses ought not to be included, but they cannot be simply sepa- rated ( 24a). If the loss found by lifting the brushes is more when the machine is excited than when not excited, the brushes are not in the neutral position, thus causing additional loss by current circulating through an armature coil and brush. If it is desired to separate the iron losses into components, hyster- esis loss and eddy current loss, runs are made with varying speed and a constant excitation for each run. For each run plot iron-loss -=- 5" as a straight line, similar to ac in Fig. 2.- For any speed, the product be X S gives watts eddy current loss for the particular ex- citation ; db X $" gives watts hysteresis loss. negligible, it should be taken into account. Belt loss cancels out and does not enter into the determination of iron losses or brush loss. 54 DIRECT CURRENT MOTORS. [Exp. APPENDIX II. MISCELLANEOUS NOTES. 22. Efficiency of a Generator. To find the efficiency of a machine as a generator, a load run is made as a generator to ascertain the working conditions of speed, excitation and voltage. A no-load run as a motor is then made under these same conditions. The load run should be made whenever possible, but it can be omitted ( 3a). In the load run, the field rheostat may be kept in one position ( 12, Exp. i-B) or changed so as to maintain the desired terminal voltage (26, Exp. i-B), according to what may be taken as the working conditions of the machine. Commercially the latter is more usual. For a compound generator, see 31. 23. Efficiency of a Motor Generator.* A load run is to be made when possible and measurements made of the various currents and voltages for both motor and generator. (See 3a.) A no-load run is to be made if possible with the generator uncoupled; this deter- mines the motor losses. Next make a run with the generator coupled but not excited, the increase in losses over the no-load run showing the friction and windage of the generator. Follow this with a run in which the generator has its proper excitation, the increase in losses over the preceding run showing the iron losses of the gen- erator after copper losses have been taken into account. This last run gives the combined rotation losses for both machines. The cop- per losses are computed and added to these to get the total losses; knowing these, the efficiencies are readily computed for the two machines, combined and separately. As in the case of a generator or motor, due care is to be taken in all the no-load runs to have the proper speed and flux density in both machines. If the flux density in either machine was not constant in all the runs (as would be the case in a compound or differential machine), take note of Appendix III. The test may be made by reversing the set, that is, running the generator as a motor ; this makes it possible to determine the friction and windage of the motor separate from iron losses. 24. Calibrated Generator for Measuring Motor Output. The out- * The details of this test can be modified according to circumstance; see 21. 2-B] EFFICIENCY. 55 put of a motor can be determined if for a load it drives a shunt gen- erator whose losses are known; it is best to have the generator separately excited. The motor output is equal to the power taken to drive the genera- tor, that is, to the measured generator output (El} plus generator losses. The losses are the copper losses and the rotation losses picked from curves (as in Fig. 2) for the particular speed and exci- tation ; to this should be added the belt losses,* a small but uncer- tain quantity. If the generator is separately excited, no account need be taken of field copper loss. 25. Calibrated Motor for Measuring Power to Drive a Generator. The power used in driving a generator can be determined if it be driven by a shunt motor whose losses are known. The power taken to drive the generator is equal to the motor input (El for the arma- ture) less armature RI 2 , less W 9 for the particular speed and exci- tation, less belt loss (24a). 26. Return of Power to Line by "Loading Back." If a direct current generator of suitable voltage is used as a load for a direct current motor, the current from the generator may be " pumped back" into the motor supply line (or into any other supply line). Used as a method of loading, it saves power, avoids the necessity of providing load resistances for the generator and introduces little complication. The variation in load put upon the motor in driving the generator is obtained by varying the generator field current. First let us sup- pose that this is adjusted until the generator generates a voltage equal to the line voltage. When connected to the line (the positive terminal to the positive line), the generator will now neither give nor receive current, that is, will neither give power to nor receive power from the line. (At a lower excitation, it will receive power as a motor.) If the field current of the generator is now increased, it will generate a voltage higher than that of the line and will supply power to the line. This power can be increased by a further increase * (243). Belt Losses. Cotterill (Applied Mechanics, p. 365) says: "In ordinary belting this loss is small, not exceeding 2 per cent." The belt, on account of its tension, also increases the journal friction of both motor and generator. 5 6 DIRECT CURRENT MOTORS. [Exp. in excitation, thus increasing the load on the driving motor as desired. When the loading back method is thus used simply as a loading method and not as a testing method (27), no measurements are made on the generator; measurements are made on the motor the same as though the generator were loaded with resistances. Since one machine takes power as a motor and the other returns it as a generator, the net power taken from the supply line is only that which is required to supply the losses in the two machines. 27. Opposition Method for Testing Two Similar Machines. If two similar machines are operated as in the preceding paragraph and measurements are taken on both, they can be tested by Kapp's* opposition method and their combined losses determined. There are various other opposition methods for accomplishing the same object; in each of these two similar machines are run, one as motor and the other as generator under load conditions. The two machines are connected both electrically and mechanically, so that power circulates between them and the only outside power taken is that necessary to supply the combined losses. These losses may be all supplied by the line (Kapp's method) or either partly or wholly by an auxiliary motor or by an auxiliary booster, giving rise to the various methodsf of Hopkinson, Potier, Hutchinson and Blondel. Although opposition methods are economical of power, they are not economical of time or apparatus; they are accordingly limited to testing pairs of large machines which could not be tested under load conditions in any other way. Temperature runs, regulation and efficiency tests are made in this way. Kapp's method is the simplest, but (on account of the different field excitation of the two machines) theoretically is not so accurate as some of the other methods. 28. Point of Maximum Efficiency. Consider that a machine has a certain constant loss (W 9 -\- field copper loss) and a variable loss (armature RI 2 ) which varies as the square of the load current / and *This method and a modification by Prof. W. L. Puffer is fully de- scribed in Foster's Electrical Engineering Pocketbook; see also 273. t(27a). For full description and complete references, see Swenson and Frankenfield's Testing of Electromagnetic Machinery; see also R. E. Workman, Electric Journal, Vol. L, 1904, pp. 244, 289, 363; Karapetoff's Exp. Elect. Eng.i and various text and handbooks. 2-B] EFFICIENCY. 57 hence as the square of El (the line voltage E being constant). These are shown in Fig. 4, in which the curve for total losses is a parabola. At any point P on the total loss curve, the loss PA, expressed as a percentage of El, is PA -- OA, which is the tangent of the angle POA. It is clear that this percentage loss is a minimum (and the efficiency a maximum) for the point P' where the line OP' is tangent to the total loss curve. But at this point P', we have A'B' = B'P'. (From the prop- erties of a parabola, Od is bisected at c.) Hence: For any apparatus hav- ing a constant loss and a variable loss proportional to load current, maximum efficiency occurs at such a load that the constant loss and variable loss are equal. The same result can be shown analytically by obtaining an expression for efficiency, differentiat- ing and equating to zero (See Franklin and Esty's Electrical Engi- neering, L, 137). This is true for any apparatus; thus, in a transformer, the effi- ciency is a maximum when the copper loss and constant core loss are equal. Within limits the designer may make the efficiency a maxi- mum at the particular load he desires, giving due consideration to expense and to the uses to which the apparatus is to be put. APPENDIX III. , MODIFICATION FOR VARYING FLUX DENSITIES. 29. In the foregoing tests, the load run was made with constant field excitation, and hence at constant flux density; the no-load run was made at this same constant flux density. In cases where the flux density varies during the load run (due to a variation in the shunt field current or due to the action of the series field coil in a compound, differential or series wound machine), three (or more) no-load runs should be made at three different flux densities. A El FIG. 4. Total losses repre- sented by a parabola ; P' is point of maximum efficiency. DIRECT CURRENT MOTORS. [Exp. FIG. 5. for different The following is suggested as a method for conducting the test. 30. Varying Excitation, Shunt Machine. First let us consider the case of a shunt machine, in which the excitation varied during the load run. Make three no-load runs at three excitations covering the range of excitations used in the load run. From these no-load runs, after plotting W --S, plot three curves (A, B, C in Fig. 5) showing W for different speeds as before. To get W 9 for a particular speed, erect a perpendicular in Fig. 5, corresponding to that speed. This perpendicular intersects the three curves A, B, C, giv- ing (for a particular speed) the values of IV for different field currents. For each speed a derived curve may now be plotted giving W^ for different field currents. 31. Compound Generator. In testing a compound gen- erator, first make a load run to ascertain the equivalent shunt excitation and then make no-load runs as a shunt motor. Load Run. Make a load run as a compound generator, and note the values of terminal voltage and speed at three (or more) differ- ent loads ; in each case ascertain the equivalent shunt excitation, i. e., the field current which would give the same terminal voltage (and hence the same flux density) with the machine run as a shunt* gen- erator at the same speed. No-load Runs. Knowing this equivalent shunt excitation, make the three corresponding no-load runs as a shunt motor at constant excitation, in each run using one of the three equivalent shunt field currents just determined. *(3!a). This equivalent shunt excitation may be determined after each reading: without stopping the machine, the series winding should be first short circuited and then opened ; or, the machine may be stopped and started again. Instead of this the equivalent excitation can be found from a separate shunt run (like an armature characteristic 26, Exp. i-B) in which is determined the field current which will give for each load the same terminal voltage as in tfie compound run. SPEED Rotation losses excitations. 2-B] EFFICIENCY. 59 Results. Results are worked up as in the preceding paragraph. Curves are plotted as in Fig. 5 and derived curves found showing the variation of W^ with field current for any speed. Such a derived curve is plotted for each speed observed in the load run. 32. Compound or Differential Motor. A load run is first made to find the equivalent shunt excitation ; no-load runs are then made as a shunt motor. Load Run. Make a load run as a compound or differential m'otor, and note the speed at three (or more) different loads so chosen as to cover the speed variation of the run. In each case ascertain the equivalent shunt excitation, i. e., the field current which would give the same speed* (and hence the same flux density) with the machine run as a shunt motor, the load and the line voltage being the same as before. No-load Runs. Knowing this equivalent shunt excitation, make the three corresponding no-load runs as a shunt motor at constant excitation, each run using one of the three equivalent shunt field currents just determined. Results. The results are worked up as in the preceding para- graphs. From the three no-load runs three curves are plotted, as in Fig. 5, showing W \ for varying speed at different excitations. From these curves a derived curve may be plotted showing the varia- tion of W with field excitation for any speed. Such a derived curve is plotted for each speed observed in the load run, and from it the value of W 9 obtained for the corresponding excitation. *(32a). The equivalent shunt excitation may be determined after each reading by cutting out the series coil as in 3ia. The adjustment to a definite speed is, however, difficult without some particularly sensitive tachometer. To avoid this adjustment, proceed as follows : Determine say five shunt speed characteristics, that is make five runs at different constant shunt excitations, determining speed for different loads. For each excitation plot speed as ordinates and armature current as abscissae. By interpolating between these curves, we can find the shunt excitation that gives a particular speed for a particular armature current. This will give the equivalent shunt excitation corresponding to any speed and armature current found in the load run as a differential or com- pound motor. Knowing the equivalent shunt excitation, the correspond- ing no-load runs are made. 60 DIRECT CURRENT MOTORS. [Exp. 33. Series Motor. A series motor may be tested for losses in substantially the same manner as a. shunt motor. So far as losses are concerned, a series motor is like a shunt motor in that the losses are the copper losses, which can be computed, and the rotation losses W which depend only upon speed and excitation. In a series motor, however, speed and excitation vary greatly with load. Load Run. A load run as a series motor is taken to obtain speed and current for different loads; see Appendix L, Exp. 2-A. (If the no-load run is to be taken as in 36, the load run is not a necessity.) 34. No-load Runs for Obtaining Rotation Losses; General Pro- cedure. No-load runs may then be made at different constant exci- tations and W^ found for different speeds by varying the armature voltage and measuring armature input in the usual manner. Read- ings are taken of field current, armature current and armature volt- age. (The procedure is sometimes to take runs with constant arma- ture voltage and varying excitation.) Any convenient means may be employed for obtaining the proper constant excitation and the desired armature voltage; the armature and field can best be sup- plied separately and not in series (see also 37). Curves are plotted for each excitation, as in Fig. 5, showing W 9 for different speeds. Instead of speeds, armature voltage is commonly plotted as abscissae. 35. No-load Run for Obtaining Rotation Losses; Special Pro- cedure. No-load runs, taken as in 34, gives curves (Fig. 5) which tell the complete story, giving rotation losses for different speeds and field currents. As a matter of fact such complete information is often unnecessary; for, with constant potential supply, a series motor has a definite counter-electromotive force and a definite speed for any particular current (see Fig. 3 of Exp. 2-A). It is necessary, therefore, to get the rotation losses with each field current for the one corresponding speed only, this speed being obtained by supplying the armature with the proper voltage. 36. This proper voltage to supply the armature could be found by trial (being adjusted until the speed in the no-load run for a par- ticular field current is the same as in the load run for the same current). It is easier, however, to compute this voltage without making a load run. We know that in any run (load or no load) speed is proportional to counter-electromotive force for the same excitation. For a par- 2-B] EFFICIENCY. 61 ticular field current / we will, therefore, have the same speed in the no-load run as in an assumed load run with current I, if in the no- load run the counter-electromotive force (which in this case is the impressed* armature voltage) is equal to the counter-electromotive force of the assumed load run. But for the load run we can com- pute the counter-electromotive force, E r = E RI, for any assumed load current /. (Here E is the rated or assumed constant line volt- age for which the losses are desired; R is the hot resistance of the armature and field, including brushes, etc.) Hence this is the proper voltage to supply the armature in the no-load run when the field current is /. In testing a series motor by this method the field is excited with current I, which is given successive values, and the armature is sup- plied with the corresponding proper voltage, E RI. (Or the armature can be given successive voltages and / adjusted to cor- respond.) 37. A convenient method sometimes used for adjusting field cur- rent and armature voltage to their proper corresponding values is to connect the field and armature in series as a series motor with one regulating resistance in series with the line and one in shunt with the armature. For the first reading the series resistance is adjusted; after that, adjusting the shunt resistance alone will tend to cause the field current and armature voltage to assume automat- ically their correct relative values. (For this condition the series resistance is made equal to the armature resistance.) For modified ways of conducting the test, see R. E. Workman, Electric Journal, L, 169. 38. No-load Run for Friction. When the field current is very small, hysteresis and eddy current losses are S> small that W gives practically the friction and windage loss; compare paragraph (&), 20. A run at low field excitation can be made as in 34. This run, however, can most conveniently be made with the field and armature in series, the motor being run as a series motor on no load at a low voltage. The voltage and the speed are controlled by a series resistance; no shunt resistance is used. At no load the cur- rent through the field is so small that iron losses in the armature are negligible. * The copper drop due to armature resistance at no load can be neglected or a small correction made. CHAPTER III. SYNCHRONOUS ALTERNATORS. EXPERIMENT 3-A. Alternator Characteristics.* i Introductory. Alternating current generators are usually synchronous. Any machine generator, motor or converter is said to be synchronous when the current which it delivers or receives has a frequency proportional to the speed of the ma- chine; otherwise it is asynchronousf or non-synchronous. In a synchronous machine, the current or electromotive force has one half-wave or alternation first positive and then nega- tive for each pole passed by a given armature conductor. A cycle is a complete wave of two alternations. In a synchronous machine, there is, therefore, one cycle for each pair of poles passed; the frequency (cycles per second) is, accordingly, equal to the speed (in revolutions per second) multiplied by the num- ber of pairs of poles. To deliver current with a frequency of 60 cycles per second (7,200 alternations per minute), a bipolar alternator would have to be driven at 60 revolutions per second, or at 3,600 revolutions per minute; a 4-pole machine, at 1,800 revolutions per minute, etc. Alternators are commonly made multipolar, and usually with manyj poles, so as to avoid excessive speed. * The curves used to illustrate this experiment and Exp. 3-B all relate to the same machine. t ( ia). The induction motor and the induction generator are asyn- chronous. An induction motor must run below synchronous speed, i. e., there must be a certain slip, in order to produce power. An induction generator, on the other hand, must be driven above synchronous speed in order to generate an electromotive force. $ ( ib). The high speed of the steam turbine has made possible, in fact has made necessary, large alternators with only few poles ; for example, a bipolar 10,000 K. W. turbo-alternator, 1,500 revolutions per minute, is men- 62 3-A1 CHARACTERISTICS. 63 2. Types of Alternators. Synchronous alternators are of the following three types (compare Part I., Exp. i-A) ; 1. Alternators having a revolving armature and stationary field, used only for small machines. 2. Alternators having a revolving field and stationary arma- ture, the most common type. 3. Inductor alternators, having a stationary armature and sta- tionary field, the revolving part or inductor consisting only of iron. The first type corresponds to the nearly universal type of direct current generator; there is, however, no commutator and alternating current is delivered from the armature winding to the line by means of collector (or slip) rings and brushes. In the second and third types, the armature is stationary and current is delivered directly to the line without collector rings. The con- tinuity in insulation, thus made possible, is an important ad- vantage in high potential machines. In revolving field alterna- tors, the field current is introduced through slip rings. Each type is made in several forms which may be studied by reference to standard works,* or better by examination of actual machines. The form most desirable depends upon conditions of operation, character and speed of prime-mover, etc. In some cases, it is desirable to make the moving mass as small as possi- ble ; in other cases as in direct-connected engine-driven genera- tors a certain fly-wheel effect is advantageous. Alternators of the second type usually have an internal revolving field, a con- spicuous exception being the umbrella form of external revolving field in the vertical-shaft alternators at Niagara. In the old Mordey and Brush form of machine, the stationary armature coils were in a vertical plane between the two parts of the revolv- tioned in Electric Journal, p. 550, October, 1908. The steam turbine has thus modified both alternating and direct current generators (3a, Exp. i-A). * See also " The Mechanical Construction of Revolving-field Alterna- tors," by D. B. Rushmore, Transactions A. I. E. E., Vol. XXIII., p. 253. 64 SYNCHRONOUS ALTERNATORS. [Exp. ing field. The inductor alternator, although possessing obvious mechanical advantages, is handicapped by large magnetic leakage and consequent poor regulation unless built in an expensive manner with much material. 3. Choice of Frequency. In the early, applications of alter- nating current, when power transmission was not developed and current was used for lighting only, the common frequencies in America were 125 and 133^ cycles per second, and these fre- quencies were satisfactory for the service. The efficiency of a transformer increases with the frequency (Exp. 5-B), and from this consideration even a higher frequency would be desirable; but as frequency is increased, we have greater inductive drop and poorer regulation in generator, line and transformer. The rotary converter, introduced in the early nineties, required a lower frequency. The highest frequency at which it can operate is practically 60 cycles, and 25 cycles is better. With its advent, the higher frequencies were abandoned ; 25 and 60 cycles became standard, the former for power alone, and the latter for lighting and (usually) for combined power and lighting. The induction motor has its best* operation within this same range. Below 25 cycles, or thereabouts, the flicker of incandescent lamps of the usual types becomes prohibitive. On account of the high speed of the steam turbine, it is not adapted for driving generators below 25 cycles. The series alternating current motor, which is more economical the lower the frequency, is prac- tically the only apparatus for which a frequency lower than 25 cycles is desirable. As the art progresses, it is possible that some new application may be developed which will demand a frequency much higher or lower than the frequencies now recog- nized as standard. * (3a). In a discussion on the choice of frequency, A. I. E. E., Vol. XXVI., p. 1400, June, 1907, Dr. Steinmetz stated that the most efficient frequency for the induction motor is 40 cycles, the best frequency for small motors being higher and for large motors lower. He also states that, for converters, 25 cycles is better than either a higher or lower frequency. 3-AJ CHARACTERISTICS. 65 4. Characteristics. Four characteristics are to be taken: One no-load characteristic the no-load saturation curve. Three load characteristics the external characteristic, the full- load saturation curve, and the armature characteristic. These characteristics are similar to the corresponding char- acteristics of a direct current generator, Exp. i-B. 5. No-load Saturation Curve.* This curve shows the ter- minal voltage for different values of field current, the machine being driven at constant speedf without load. The connections are shown in Fig. i. Data are taken in the same way as for the no-load + saturation curve of a direct current generator (5-10, Exp. i-B) ; the alternator, however, is necessarily II" L . ^ , , ., . Mwm-LJ separately excited. RHEOSTAT The field current can be varied! by FlG * ' Connections for n - load saturation curve. a field rheostat in series, as in Fig. i (with a second rheostat in series with it to give greater range, if necessary) ; or by an arrangement of resistances as in Figs. 4 and 5, of Exp. i-A. Voltage readings are corrected by proportion for any varia- tion of speed, and plotted as in Fig. 2. Descending, as well as ascending, values may be plotted when desired. The saturation factor and per cent, saturation are determined as in Fig. 2, of Exp. i-B. 6. External Characteristic. This curve- shows the variation in terminal voltage with load. The alternator is driven at nor- * (5a). If the alternator is motor-driven, it is commercial practice to determine its core loss and friction at the same time that the no-load saturation curve is taken. See 15. f (5b). Speed and frequency are proportional; with a good frequency meter at hand, it may be more convenient to observe frequency than speed. If the speed can be varied, note that voltage is proportional to speed. $(5c). As in all such curves, the variation should be made continu- ously and no back steps should be taken ( 7, Exp. i-A). 6 66 SYNCHRONOUS ALTERNATORS. [Exp. 900 mal speed and excitation, readings being taken of speed and field current to see that they are constant. The connections are shown in Fig. 3. The characteristic is to be obtained for unity* power factor, a non-inductive variable resistance being used for a load. Read- ings are taken of termi- nal voltage and external current from o to 25 per cent, overload. In commercial testing, the excitation is adjusted for normal voltage at full load. Fig. 4 shows the characteristic of a 25 K.W. alternator in which the voltage in- creases from 575 at full load to 627 at no load a regulation of 9 per 8 9 10 11 12 13 u is 16 cent. (See 14, 17, Exp. i-B.) It is de- Sirabl tO hae ** ^' o l 234567 FIELD AMPERES FIG. 2. Saturation curve at no load, and at full load (43.4 amperes at unity power factor). Field ampere-turns equal field amperes multi- plied by number of field turns, 464. All curves in Exps. 3-A and 3-B relate to A . , -, i tne same 25-kilowatt alternator. ulation as close as possible, i. ., with the ,, -11 smallest possible vana- tion in the voltage from no load to full load. Since with non-inductive load the power factor is unity, the power output is found by taking the product of terminal voltage and external current. 7. The causes for the decrease in terminal voltage with load are impedance drop in the armature (due to its resistance and inductance) and armature reactions, discussed more fully in the * For other power factors, see 13 ; take data as in 14. Also see Fig. 7, Exp. 3-B. 3-A] CHARACTERISTICS. 67 next experiment. Compare also 16, Exp. i-B. As in the case of a shunt generator (19, Exp. I B), when the iron is highly saturated, the demagnetizing effect of armature reaction is the least and the regulation the best. + 8. The external character- t;||;S> istic, Fig. 4, is practically an 5<3J> ellipse.* At one end of the - RHEOSTAT _i characteristic (near Open cir- FIG. 3. Connections for loading an cuit), an alternator tends to alternator, regulate for constant voltage; at the present day, this is the usual working part of the characteristic. At the other end' (near short circuit), an alternator tends to regulate for constant current. The earliest alter- nators were constructed for such operation. Constant current alternators are used (less now than formerly) for series arc lighting. For this service an alternator should have high armature reaction so as to limit the current on short circuit to the desired value; a reac- tance external to the arma- ture will serve equally well. 20 40 60 80 100 ARMATURE AMPERES FIG. 4. External characteristic of an alternator at unity power factor. (The dotted parts of these curves were cal- culated according to Exp. 3~B.) 9. Full-load Saturation Curve. The machine is run at constant speed so as to give its normal full-loadf current at different field excitations. The connections are as in Fig. 3. To obtain the curve for unity power factor, a non-inductive resistance * See discussion of Fig. 7, Exp. 3-6. t (9a). Curves taken at intermediate loads (one fourth, one half and three fourths full load) would lie between the no-load and full-load 68 SYNCHRONOUS ALTERNATORS. [EXF. is used as load; with constant armature current, readings are taken of terminal voltage for different field currents, and plotted as in Fig. 2. For the first reading, adjust the field rheostat to its maximum resistance;* with field circuit open, reduce the load resistance to zero (i. e., short-circuit the armature through the ammeter) ; close the field circuit and adjust the field rheostat until the de- sired value of armature current is obtained. For each succeed- ing reading, increase the load resistance by a small step and re- adjust the field rheostat until the desired value of armature current is again obtained, taking care that the increase or de- crease in excitation is continuous. 10. In Fig. 2, the excitation data are as follows: Excitation. Volts. Amperes. Ampere Turns. No Load. Full Lead. 6.66 7-33 3090 3401 575 627 525 575 A comparison of the no-load and full-load saturation curves, Fig. 2, shows the following : At constant excitation, the difference in the ordinates of the two curves (their distance apart vertically) shows the difference in terminal voltage of the alternator at no load and at full load. At constant terminal voltage, the difference in the abscissae of the two curves (their distance apart horizontally) shows the difference in excitation (magnetomotive force) required at no load and full load in order to maintain the voltage constant. At constant excitation, a voltage of 575 at full load increases to 627 when the load is thrown off, giving a regulation of 9 per curves of Fig. 2. To take these is unnecessary, unless some special object is in view. For inductive load, the full-load saturation curve will be lower than with non-inductive load (as shown in Fig. I, Exp. 3-B, for zero power factor). For different power factors, see 13, and take data as in 14. * This resistance should be sufficient to reduce the field current to but a small fraction of its normal value. 3-A] CHARACTERISTICS. 69 TERMINAL VOLTAGE, 575 T3 3 4000 3000 2000 1000 cent., the same as already obtained from the external character- istic, Fig. 4. For constant terminal voltage of 575, the excitation must be increased from 6.66 amperes at no load to 7.33 amperes, at full load. This will be found to check approximately with the arma- ture characteristic, Fig. 5 ; an exact check can not be expected. Fig. 2 shows that, as we go above saturation, there is 10 less difference between the no-load and full-load voltages, UJ *. e., the regulation is better [ (7). 11. Armature Character- c istic or Field Compounding Curve. This curve is taken for an alternator* in the same way as for a direct current generator (26, Exp. i-B). The curve in Fig. 5, taken for a constant terminal volt- age of 575 at unity power factor, shows that in going from no load to full load (43.4 amperes) the excitation is increased from 6.6 to 7.25 amperes. This checks with the increase 6.66 to 7.33 amperes in Fig. 2. Armature characteristics for lower power factors than unity will rise more rapidly ( 13). * ( na). Composite Winding. Although an alternator can not be com- pounded by a series winding carrying the line or armature current, as in the case of a direct current generator (since the field winding requires a direct current and the line or armature current is alternating), the result can be accomplished by rectifying part of the alternating current and passing it through what is called an auxiliary field winding. Such an alternator is said to be composite wound. The alternating current to be rectified is commonly derived from the secondary of a transformer, through the primary of which flows the line or armature current; for the core of this transformer the armature frame or spider is used. The 20 40 60 80 ARMATURE AMPERES FIG. 5. Armature characteristic, or field compounding curve ; unity power factor ; speed constant. 7 SYNCHRONOUS ALTERNATORS. [Exp. APPENDIX I. MISCELLANEOUS NOTES. 12. Tests on Polyphase Generators. The tests described above may be made on polyphase generators in the same manner as on single-phase machines. The polyphase generator when loaded should ordinarily be given a balanced load, i. e., one that is divided equally between the several circuits. Tests may also be made by loading down one phase only and taking measurements on the unloaded as well as the loaded phases. In plotting curves, plot voltage and current per phase (the more usual way) ; or, line voltage and equivalent single-phase current. See Exp. 6-A, particularly 28-30. 13. Power Factors Less than Unity. The characteristics of an alternator under load vary with the power factor of the load. With a power factor less than unity and current lagging, the regulation will be poorer, the full-load saturation curve will be lower, the exter- nal characteristic lower and the armature characteristic higher than at unity power factor. The reverse is true when the current is lead- ing (instead of lagging), as it may be when there is capacity in the line or in the load, or when the load consists in part of over-excited synchronous motors or converters. These facts may be fully shown by calculation (Exp. 3~B), or by a complete series of runs made with loads of different* power factors. If such runs are to be made, it will be more profitable to make them after Exp. 3-6. At present, it will suffice to illustrate these facts by a few readings only, as in the next paragraph. 14. Tests to Compare Effects of Inductive and Non-inductive Loads. The difference between inductive and non-inductive loads composite winding is not, however, being extensively used, for it can not give constant voltage under all conditions e. g., varying power factor and the rectifying commutator is liable to spark. The Tirrell regulator (3a, Exp. i-B), applied to the exciter of an alternator, can maintain constant voltage under all conditions of load. * ( I3a). This will require special facilities for adjusting power factor; for an inductive load, this can be done by means of an adjustable resist- ance and adjustable reactance in parallel. Runs should be made at one high power factor, one medium, and one as low as can be obtained. 3-A] CHARACTERISTICS. 71 can be illustrated by the following tests, or by modifications which may be devised by the experimenter. 1. Load the alternator on inductive load, using for this any one particular load which can be conveniently obtained. An induction motor can be used for a load, as in commercial practice; but a choke coil will serve fully as well. With the same speed and excitation as were used in taking the external characteristic on non-inductive load, Fig. 4, take readings* of load current and terminal voltage with the inductive load. These readings are plotted,f in Fig. 4, as the point p, which is one point on a characteristic for low power factor. (For more complete curves, see Fig. 7, Exp. 3~B.) Throw off the load and ( at the same speed and excitation) read the no-load voltage; the per cent, increase in voltage when the load is thrown off gives the per cent, regulation. 2. With the same speed and excitation, repeat with a non-inductive load, so adjusted as to obtain the same load current as in i. Note the terminal voltage under load, the no-load voltage when the load is thrown off, calculate the regulation and compare with the regulation in i. 3. With the same speed and terminal voltage as were used for obtaining the armature characteristic on non-inductive load, Fig. 5, note the increase in field current required with inductive load to maintain constant terminal voltage and plot the point q, Fig. 5. 4. Repeat with a non-inductive load (adjusted for the same load current) and compare results. 15. Efficiency. If the alternator is driven by a direct current motor, the friction and core loss are conveniently determined by the method of 21, Exp. 2-B. If the driving motor is alternating, a wattmeter is used to measure its input, the increase in motor input * ( 143). If a wattmeter reading is also taken, the power factor can be found by dividing the reading of the wattmeter by the product of current and voltage. t ( I4b). Since the same value of exciting current may at different times give different amounts of magnetization (as in the case of the ascending and descending curves), the point p thus located and the point q as located later may not be exact in their positions, as compared with the characteristics previously taken. They will, however, serve to illus- trate the effects in question. 7-2 SYNCHRONOUS ALTERNATORS. [Exp. giving the friction and core loss of the alternator any changes in motor losses being corrected for, if necessary. The copper losses of field and armature are calculated from resist- ance measurements, and the efficiency so determined. If the armature has large, solid conductors, the loss in them will be greater with alternating than with direct current, this additional loss being a load loss. Load losses are losses which occur under load in addition to the losses already accounted for, i. e., in addition to core loss, RI 2 , friction and windage. There is no simple and accurate method for determining load losses in alternators. The A. I. E. E. Standardization Rules (116-7) gi ye a method for estimating these losses by assuming them to be in the absence of more accurate infor- mation equal to one third of the short-circuit core loss. 3-B1 PREDETERMINATION. 73 EXPERIMENT 3-B. Predetermination of Alternator Charac- teristics.* i. Introductory. It is desirable to be able to predetermine the performance of any machine without loading, and this is particularly true of alternators; for, in the case of large ma- chines, the regulation can not be conveniently found in any other way. There are two simple methods for predetermining the per- formance of an alternator approximately, the electromotive force method and the magnetomotive force method. Although other more complex methods are proposed for the more exact determination, no one method has been found which is generally accepted and gives correct results in all cases. It is well to first thoroughly study the electromotive force method, on account of the insight it gives into the general performance of the alterna- tor and into other methods of dealing with the subject. The magnetomotive force method should then follow; after which, other methods (essentially modifications of these two) can be made a special study by those who desire to pursue the subject further. (See Appendices I. and II.) 2. There are primarily two causes for the change in termi- nal voltage of an alternator with load : 1. The effect of armature resistance, which is small and defi- nite ; this causes a drop in electromotive force which is in phase with the armature current and is equal to R I. 2. The effect of the flux set up by the armature current, a much larger and less definite effect, discussed in the next para- graph. 3. All the flux set up by the armature current encircles the *To be preceded by Exp. 4-A. See 9 for a statement of data to be taken. For a short experiment, take 1-18 and 26-30, plotting curves for unity power factor only. The curves used to illustrate this experi- ment and Exp. 3-A all relate to the same machine. 74 SYNCHRONOUS ALTERNATORS. [Exp. armature conductors. There are, however, different paths which the flux may follow, causing different inductive effects. 4. (a) True Armature Reaction. By one path, flux set up by the armature conductors passes into the pole pieces and through the magnetic circuit of the field magnets (Fig. 10), linking with the windings of the field coils. This flux has a demagnetizing effect, weakening* the field by a certain mag- netomotive force produced by the ampere-turns of the armature. This flux through the field magnets is maintained by successive armature conductors; in a single-phase alternator it is pulsating, but in a polyphase alternator, due to the combined effect of the armature currents in the different phases, it is constant both in position and in magnitude. 5. (b) Local Armature Reactance. By a different path, flux set up by the armature current encircles the armature con- ductors without entering the pole-pieces; this flux (the fine lines in Fig. 9) is entirely in the armature, or partly in the armature and partly in the air gap. The flux surrounding any particular conductor varies periodically and produces a reactance electro- motive forc.e or reactance drop, XI, in quadrature with the arma- ture current and proportional to it, as in any alternating cur- rent circuit. 6. By another and somewhat similar path, flux encircles the armature conductors by entering into and returning from the poles without linking with the windings of the field circuit; this flux is shown by heavy lines, Fig. 9. This is cross-magnetising flux and distorts the field ; it does not weaken the field except incidentally to a small extent by saturating the pole pieces. This cross-magnetization is alternating with respect to the armature conductor, as in (b) ; with respect to the pole pieces, it is con- stant in a polyphase and pulsating in a single-phase alternator, as in (a). It may be treated separately; or with (a) or (b). I * The field is weakened by a lagging current, but strengthened by a leading current, 46-8. 3-B] PREDETERMINATION. 75 7. It is thus seen that there are two somewhat different effects produced by the armature current: the first (a) is a magnetomotive force, which reduces the field flux and so reduces the generated voltage; the second (b) is an electromotive force, which is subtracted from the generated electromotive force (in the proper phase) so as to give a lower terminal voltage. These two effects operate simultaneously to lower the terminal voltage, the relative amounts of the two varying according to details of design, saturations, air-gap, shape of slots, etc. To take full and accurate account of the two effects treating one as a magnetomotive force and the other as an electromotive force is difficult* and will not be undertaken here. 8. We may, however, instead of treating the two effects separately, treat them combined, following either one of two methods : (a) The magnetomotive force or ampere-turn method, which assumes that all the effect is magnetomotive force ; or, (b) The electromotive force or reactance method, which as- sumes that all the effect is electromotive force. If the saturation curve were a straight line, the two methods would be identical ;f for, magnetomotive force would produce a proportional electromotive force. With the saturation curve, however, not a straight line, a given increase or decrease in mag- netomotive force will cause a less than proportional change in electromotive force. Hence, if we consider that all the effect of armature flux is a magnetomotive force, we will have a less drop in terminal voltage than if we consider that all the effect is an electromotive force. The magnetomotive force method is, accordingly, opti- mistic (Behrend) and gives the generator a better regulation * See Appendix II. fThis would be true if the details of the two methods were in all respects the same. Differences in the details of the two methods, as usually applied, cause differences in the results, even though the saturation curve is straight. 7 6 SYNCHRONOUS ALTERNATORS. [Exp. than it actually has ; the electromotive force method, on the other hand, is pessimistic, giving the generator a poorer regula- tion than the actual. The two methods, therefore, give the limits between which is the true performance of the machine. 9. Data. For either method, the data required are obtained from the following two* runs, which are made without loading the generator : 1. An open-circuit run, giving the open-circuit voltage EQ, for different field currents, i. e., the no-load saturation curve, obtained as in 5, Exp. 3~A. See Curve (i), Fig. i. To save labor in the many subsequent calculations, it is customary to use only the ascending curve. 2. A short-circuit run, giving the short-circuit current Is, for different field currents, called also a synchronous impedance test, as described in the next paragraph. See Curve (2), Fig. i. These data enable us to ascertain the synchronous impedance of the armature and hence to compute the volts impedance drop for the electromotive force method ; they also enable us to ascer- tain the magnetomotive force required to overcome the mag- netizing effect of the armature, for the magnetomotive force method. The hot armature resistancef is to be found by the fall-of-po- tential method. 10. Test for Short-circuit Current and Synchronous Impe- dance. With the armature short-circuited through an ammeter,J * (Qa). Two such runs are common in testing many kinds of appa- ratus ; note, for example, the open-circuit and short-circuit tests for trans- formers, Exp. 5-B. t(Qb). On account of eddy currents, the resistance will be greater for alternating currents than the value found by direct current. This is of importance as affecting efficiency ( 15, Exp. 3-A), but is of little con- sequence so far as regulation is concerned, for RI drop has only a small effect at high power factors and is negligible at low power factors, as will be seen later. ( loa). The ammeter leads should be short and heavy; for, by the 3-B] PREDETERMINATION. 77 10 11 12 13 14 15 18 FIELD AMPERES FIG. i. No-load saturation curve (i) and short-circuit current (2 and 3) for different field excitations. Also full-load saturation curves (4, 5, and 6) for zero power factor, current lagging. the short-circuit current is found for different values of field current. The ammeter should have a range of about three times full-load current. The speed should be normal, but special care in maintaining constant speed is not necessary.* methods of computations used later, any drop in them is included in the impedance drop of the armature. * ( lob). If facilities for varying the speed are provided, with constant excitation vary the speed through wide range and note the practical absence of change in the short-circuit current. Note, however, that the open-circuit voltage is proportional to speed. How are these facts explained? 7 8 SYNCHRONOUS ALTERNATORS. [Exp. Beginning with the field weakly excited, increase the field cur- rent by steps so that the short-circuit armature current (/s) is increased from, say, J normal to ij or 2 times* normal full-load current. At each step read field and armature currents and plot as in Curves 2 and 3 of Fig. i. In the short-circuit test, we may have either the field or the armature under normal full-load working conditions, but not both at the same time. ii. The curve for short-circuit current, will (as in Fig. i) be a straight line through a wide working range, and may be extended as a straight linef beyond the observed data. The ultimate bending of the curve depends upon the relative satura- tions of various parts of the magnetic circuit, armature, teeth, poles, etc. Fig. i shows that normal excitation, OH = 7.33 amperes, gives a short-circuit current of 116 amperes. (Normal excita- tion is the excitation giving rated voltage, 575, at full load, unity power factor; for this machine see Figs. 6 and 7 the corre- sponding no-load voltage is found to be 627.) * ( loc). By taking the run quickly, even higher values of current can be reached. Running an alternator on short circuit, as described, affords the best means for drying armature insulation. An alternator in shipment may have been unduly exposed to weather or have been allowed to stand in a damp place. The insulation readily takes up moisture and is much impaired thereby. In such a case, as soon as the alternator is installed it should be run for one day with the armature short-circuited, the field excitation being so low that the normal armature current flows; there is no high voltage to break down the insulation. The armature is thus baked and the insulation restored. This precaution, particularly in the case of high voltage machines, may avoid a break-down of insulation upon starting up. t ( na). Extrapolation as a straight line (2) gives (after saturation is reached) a diminishing value for synchronous impedances Z = Eo -f- Is, as used later. It thus favo'rs the machine by giving a smaller impedance drop; in the electromotive force method this is justifiable because it par- tially offsets the pessimistic tendency of that method. This justification is empirical. Curve (3) has been extrapolated by assuming Eo -r- Is to be constant. 3-B] PREDETERMINATION. 79 An excitation, OG = 2.6 amperes, is required to cause normal full-load current (43.4 amp.) on short circuit. The corresponding impedance voltage is 2 = 234, for on short circuit the whole generated voltage is used in overcoming the internal or armature impedance. 12 Synchronous Impedance. On short circuit, the whole generated voltage is equal to the internal impedance drop in the armature. Impedance is equal to impedance drop divided by current; hence, the synchronous impedance of the armature i. e., its impedance when running at synchronous speed is equal 40 60 80 100 120 140 AMPERES ON SHORT CIRCUIT: I a FIG. 2. Impedance, reactance, and resistance drop. (All the curves in Exps. 3-A and 3-6 relate to the same machine.) to the generated voltage EQ, divided by the short-circuit current Is. For any field current, the values of EQ and Is are obtained from curves (i) and (2), Fig. i ; the corresponding synchronous impedance, Z = Eo-+-Is, should be plotted as a curve (not shown). It will be found nearly constant \ for a wide range, diminishing, however, for high values of field current. 13. In Fig. 2, the curve marked impedance drop is plotted by . So SYNCHRONOUS ALTERNATORS. [Exp. taking, from Fig. i, corresponding values for and 7 S . Eventually there is a tendency for the curve to bend, although in this instance there is none within the range for which Fig. 2 is drawn. The ratio of any ordinate to the corresponding abscissa gives the value of the synchronous impedance; thus, in Fig. 2, the impedance drop is 234 volts for a full-load current of 43.4 amperes, and the impedance is, therefore, 234^-43.4 = 5.4 ohms. The normal full-load voltage of this machine is 575 ; the impedance drop is, accordingly, 40.7 per cent. This is called* the impedance ratio. An open-circuit voltage of 627 is seen to give a short-circuit current of 116 amperes, as already seen in Fig. i. 14. Resistance drop is plotted as a straight line, Fig. 2. The resistance, found by the fall-of -potential method, is 0.17 ohms; the resistance drop, for 43.4 amperes, is 0.17 X 434 = 7-4 volts. 15. The reactance drop is Ex V-E?- E R 2 ', or, for 43.4 amperes, reactance drop = V 2 34 2 74* = 2 33-9 volts. Usu- ally, as in this case, resistance is small so that there is little differ- ence between the values of synchronous impedance and synchro- nous reactance. It is common, therefore, not to calculate the value of reactance drop, but to use the value of impedance drop in its place. Synchronous reactance is proportional to speed ; hence, syn- chronous impedance is practically proportional to speed. Synchronous impedance and synchronous reactance are ficti- tious quantities, comprising not only the real impedance and re- actance of the armature, but also including the effect of arma- ture reactions. It is instructive to compare the curves of Fig. 2 with similar curves for a transformer ; see Fig. 7, Exp. 5 B. 1 6. Electromotive Force Method. Aside from its usefulness in predetermining the performance of alternators, this method serves as an excellent illustration of the use of vector diagrams * Standardization Rule, 208. 3-B] PREDETERMINATION. 81 in solving alternating current problems ; it is a practical applica- tion* of the elementary principles discussed in detail in Exps. 4-A and 4-B. The electromotive force method is general, apply- ing to all classes of alternating current problems, transmission lines ( 56), transformers (Exp. 5-C), etc. For this reason the method will be treated in considerable de- tail. ^ ft}7 8 17. Unity Pozver Fac- ^^ fc J_ O Z=43.4 ' T =575 B*C tor. With a non-inductive 7 load, the power factor of ^ the load is Unity; the CUr- FlG - 3 ' E1 ^rom 0t ive force diagram, at unity power factor ; current in phase with rent which flows is, accord- terminal voltage. ingly, in phase with the ter- minal voltage. This is shown in Fig. 3, in which the terminal voltage ET, is in phase with the current I. The armature resis- tance drop, E R = RI f is in the direction of in phase with the current / ; the reactance drop, Ex = XI, is in quadrature with 7. The total generated electromotive force EQ, is accordingly the vector sum of the following three electromotive forces: ET de- livered to the load ; RI to overcomef armature resistance and XI to overcome armature reactance. * ( i6a). This application illustrates the way that general principles can be put to practical purposes ; the application was first made indepen- dently, and more or less simultaneously, by ^various engineers. The writer used the method in numerical problems to illustrate the elementary principles of Bedell and Crehore's Alternating Currents in the early nine- ties soon after the issue of that book, and applied it a little later to laboratory data. The data and some of the curves here given are taken from a laboratory outline prepared by the writer for student use and printed in the Sibley Journal, 1897-8, p. 215. t(i7a). The arrows show the direction of the vectors in the sense that EC and CA are electromotive forces to overcome resistance and reactance, respectively; in the reverse sense, CB and AC are the electro- motive forces produced by resistance and reactance. 7 82 SYNCHRONOUS ALTERNATORS. [Exp. 18. Knowing the values of resistance drop RI, and reactance drop XI, we may have either of two problems to solve : (a) Given the terminal voltage ET, to determine the open- circuit voltage EQ; or, ,i (b) Given the open-circuit voltage EQ, to determine the termi- nal voltage ET. The following examples will make clear the solution of either problem. (a) Given 7 = 575; #7 = 7.4; XI = 233.9. Required to find EQ. Lay off to scale the values of ET, RI and XI, as in Fig. 3 ; by construction EQ is found to be 627. Designating the total in- phase voltage by Ep, and the quadrature voltage by EQ; we have, by computation, Eo = = V ( 575 + 74) 2 + 233^ = 62 ?' The regulation is 9 per cent., EQ being 9 per cent, greater than ET. (b) Given = 627; ^7 = 7.4; XI 233.9. Required to find ET. Lay off RI and XI to scale, as in Fig. 3. From A as a center and radius EQ = 627, strike an arc cutting at O the line OB, drawn as a continuation of BC. By this construction, ET is found to be 575 ; by computation E^ = Vo 2 (Xiy RI = V627 2 233.9* 74 = 575. At unity power factor, it is seen that the terminal voltage is always less than the generated or no-load voltage. 19. Power Factor Less than Unity, Current Lagging. With an inductive load, the power factor of the load is less than unity and the current, accordingly, lags behind the terminal electro- motive force. This is shown in Fig. 4 in which the current / lags behind the terminal electromotive force ET by an angle = 30, the power factor of the load, in this case, being cos 30 = 0.866. 3-B] PREDETERMINATION. Fig. 4 is drawn by first constructing to scale the triangle ABC, with two sides equal to RI and XI, respectively, and then laying Cos 6 = 1 Cos - 0.5* - Cos 0-0 FIG. 4. Electromotive force diagram, at power factor 0.866 ; current lagging 30 behind terminal voltage. off OB at an angle with BC, so that cos 6 equals the power factor of the load. (a) Given Er = 575, we find by construction = 726; or, by computation cos RI)* + ( T sin 6 + XI) = V(575 X -866 + 7. 4 ) 2 + (575 X .5 + 233-9)"* = The regulation is 26.3 per cent. With inductive load, the regulation is always poorer than with non-inductive load. The clotted quadrant indicates the locus of the point O for different power factors. (b) Given EQ and power factor; required the terminal voltage ET. Lay off a line in the direction BO making the proper angle 6. S 4 SYNCHRONOUS ALTERNATORS. [Exp. Strike an arc from A as a center, with a radius EQ, cutting the line OB at O, thus giving* OB = E T . 20. Power Factor Less than Unity, Current in Advance. This case is shown in Fig. 5. The triangle ABC is drawn as be- fore, and OB is laid off making an angle 6 with BC, so that cos equals the power factor of the load. The current I, for this case, is 30 in advance of ET- (a) Given 7 = 575, we find by construction = 508; or, by computation, cos sin XI) = V(575 X .866 + 74) 2 + (575 X .5 233-9) 2 = 58. The regulation is 12 per cent. Cos-0_ Cos 0-1 (b) Given ; the terminal voltage ET is found, as before, by striking an arc from A as a center, with a ra- dius EQ, cutting the line OB at 0. For a leading current, 3 the terminal voltage is CN ^ always greater than for a lagging current or for unity power factor, and g may even be equal to or Electromotive force diagram, at greater than the no-load FIG. 5. power factor 0.866 ; current 30 in advance voltage. of- terminal voltage. Zero Pozver Factor. At zero power factor, cos 6 = 0, sin 6= i. * ( ipa). The graphical construction for this case will usually be pre- ferred; an analytical expression for ET, derived from the figure, is ET = VJSo 2 (XI COS0 RI sin 0) z (RI cos 0-\-XI sin 0). 3-B] PREDETERMINATION. 85 From Figs. 4 and 5 it is seen that the RI drop becomes ineffec- tive, being at right angles to ET, and can be neglected. Hence, practically, ET = EO XI, for lagging current ; ET = Eo + XI, for leading current. For this case, the various voltages are combined algebraically. Practically, XI = ZI = Ez, and these expressions become This expression, approximate for = 90, would be exact for a value of 6 a little less than 90 ; so that, in Fig. 4, OB A forms a straight line and tan = XI- J r-RI. 22. Given the Terminal Voltage at One Power Factor, to Determine it at Any Other Power Factor. Given ET at any power factor, E is found by method (a) of the preceding para- graphs. With Eo thus known, the value of ET is readily found for any desired power factor by method (b). In conducting tests, it is often difficult or impossible to deter- mine ET at unity or high power factors, on account of the power required. The value of ET can, however, be found by test at a low power factor (52) and then determined by calculation for any desired high power factor. Usually Eo is found by test and resistance drop is known; the reactance drop is not known. In this case the procedure is as follows : In Fig. 4, lay off resistance drop BC; at right angles draw the indefinite line CA, the value of reactance drop being unknown. At an angle B with BC, lay off BO equal to the value of ET found by test at power factor cos 6. Draw OA = Eo, as found by test, cutting CA at A.. The point A being located and Eo known, values of ET at any power factor are determined by method (&) above. In this manner, if the regulation is known for one power fac- tor, it can be calculated for any power factor. At constant terminal voltage, the locus of the point O will be the arc of a 86 SYNCHRONOUS ALTERNATORS. [Exp. circle with B as a center ; at constant excitation, EQ is constant and the locus of O is the arc of a circle with A as a center. 23. Application of Electromotive Force Method. Knowing the armature resistance and synchronous reactance* obtained from the short-circuit test, the electromotive force method can be used for predetermining the regulation, the external charac- teristic and the full-load saturation curve for any power factor. 24. Predetermination of Regulation at Different Power Factors. By method (a) of 17-20, determine the open-circuit voltage Eo, corresponding to rated full-load voltage at rated full- load current, for different power factors. The values of arma- ture RI drop and XI drop corresponding to full-load current will be constant in all the computations, R and X being taken as con- stant. f Plot the values of EQ, thus obtained, with power factor (or 6) as abscissae, as in Fig. 6. This is to be done for lagging and for leading currents. Arrange, also, a scale as on the right of Fig. 6 to show the values of EQ as per cent, of full-load voltage. 25. The curves show the increase (or decrease) in voltage when full-load current is thrown off at different power factors; in per cent., this gives the regulation. At power factor i.o, the *(23a). Synchronous reactance is practically equal to synchronous impedance. In Figs. I and 2, synchronous impedance is Z = Eo -f- Is, and is more or less constant ; it can be computed for the value of Eo or for the value of Is corresponding to working conditions. Thus, for normal field excitation, corresponding to Eo = 627, we obtain Z 627-4- 116 = 5.4 ohms; the armature current 116 amp. is, however, far above normal. For normal full-load current, 43.4 amp., we obtain Z = 234 -f- 43.4 = 5.4 ohms; in this case the field excitation is far below normal. It is thus seen that Z can be computed from the short-circuit test either for normal field current or for normal armature current; but field and armature currents can not simultaneously be normal. When Z is constant, the two computations give identical results. When Z is not constant, the two computations give different results ; either may be used, but it is justifiable to use the method which gives the smallest value for Z as being least pessimistic. (See na and 33.) t See 26a. 3-B] PREDETERMINATION. 87 regulation is 9 per cent.; at power factor 0.5 (lagging current), it is 37 per cent. ; at power factor o.o, it is 40 per cent. At high power factors, it is seen that a small change in power factor causes a marked change in regulation ; while at lower power fac- tors the regulation is nearly constant. The reason for this will appear from a consideration of the construction in Figs. 4 and 5. This fact is made use of in 52. joad voltage, (lagging current) 1.0 0.9 0.8 0.7 O.C 0.5 0.4 0.3 0.2 0.1 POWER. FACTOR FIG. 6. Curves showing no-load voltage corresponding to a constant full-load voltage (575) for full-load current (43.4 amperes) at different power factors. 26. Predetermination of External Characteristics. For a definite open-circuit voltage EQ and various power factors, com- pute (by method (b) of 17-20) the terminal voltage ET, for different load currents. Armature XI drop and RI drop are to be taken as proportional to current; i. e., X and R are taken as constant.* Data are thus obtained for plotting the complete ex- ternal characteristic, from open circuit to short circuit, for differ- ent power factors. * (26a). In 24, 26 and 32, the same constant values of X and Z are to be used. In 26 it is proper that X and Z be considered constant for the reason that field excitation is constant. In 24 the armature current is constant, but not the field, and strictly speaking X and Z might not remain constant, although for simplicity and for ease in comparison they are so taken. In the case of 32, X and Z should only be taken as con- stant for a certain range, and for very high saturations should be taken as variable as in 33. 88 SYNCHRONOUS ALTERNATORS. [Exp. 2 7- Fig. 4, Exp. 3-A, shows the characteristic for unity power factor. Power is zero on open circuit and on short cir- cuit. Maximum power is, in this case, obtained at about twice full-load current ; at short circuit, the current is about 2 J times full-load current. A small short-circuit current* is an element ' 1200P 10 20 30 40 50 60 70 80 90 100 110 120 130 AMPERES ARMATURE FIG. 7. External characteristics at different power factors. of safety, obtained, however, by large impedance drop and poor regulation. Compare 24%, Exp. 5~C. 28. External characteristics for different power factors, with current lagging and leading, should be plotted as in Fig. 7. The lowest possible characteristic is a straight line; it is obtained for a power factor (cos 0) of such a value that tan 6= (armature reactance-drop) -r- (armature resistance-drop). See 21. The *(27a). This is the working part of the characteristic for constant current operation, see 8, Exp. 3-A. The armature should have a high reactance for constant current and low reactance for constant potential. 3-B1 PREDETERMINATION. 89 characteristic for zero power .factor is a little higher than the straight line for the limiting case ; the difference, however, is in- appreciable. When the scale used is such that the ordinate on open circuit is equal to the abscissa on short circuit, the characteristics are ellipses with a 45 line as axis (Steinmetz, Alternating Current Phenomena, 3d ed., p. 304). In any alternator, armature resistance is small and armature reactance relatively large, so that the armature impedance is practically all reactance; this gives curves as in Fig. 7. If the conditions were reversed, resistance being large and reactance negligible, the curves for cos 6 = i and cos = o would have to be interchanged. Unity power factor would give the poorest regulation and the straight line characteristic now obtained for zero power factor ; for, with reactance zero, ET = O RI, in place of ET = EQ XI, as in 21. 29. Predetermination of Full-load Saturation Curve from No-load Saturation Curve. By method (b) of 1720, com- pute the terminal voltage E? corresponding to the different open- circuit voltages of the no-load saturation curve ; this is to be done* for full-load current at unity power factor and at zero power factor, current lagging. In this manner, full-load satura- tion curves are plotted for unity power factor (Fig. 2, Exp. 3- A) and for zero power factor (Fig. I of this experiment). 30. The interpretation of the full-load saturation curve for unity power factor is given in 10, Exp. 3~A. The curve for zero power factor is capable of similar interpretation. It is seen that, for the same terminal voltage, the excitation must be much greater at zero than at unity power factor; or, for the same excitation, the terminal voltage is much lower. 31. In determining the full-load saturation curves for any power factor, X and Z can be taken as they are (somewhat vari- * It is unnecessary to construct intermediate curves for part load and for other power factors, unless a special study is to be made. 90 SYNCHRONOUS ALTERNATORS. [Exp. able, 33) or they can be assumed constant,* 32. The com- putations can be readily made by either method ; it is only above saturation that the results differ. This will be discussed in greater detail in the case of zero power factor. 32. For zero power factor, the terminal voltage (21) is ET = EQ Ez ; that is, the impedance drop, Ez is subtracted arithmetically from E. In Fig. i, if impedance drop Ez is taken as constant, we obtain Curve (4) differing from Curve (i) by a constant distance (Ez) vertically.f This is satisfactory below saturation, but above saturation is too pessimistic. 33. If we wish to extend the curve above saturation, it is better to take a variable value, Z = EQ -f- 7s, computed from Curves (i) and (2), Fig. i, for each value of 0, that is, for each excitation. This gives a decreasing value for Z and results in Curve (5) instead of (4). Instead of subtracting from Curve ( i ) a constant Ez, we now subtract Ez = ZI = ~-Eo. Is, Here 7 is full-load current (43.4 amp.) ; EQ is taken from Curve ( i ) and 7s is the corresponding short-circuit current from Curve (2). The formula can be interpreted thus: if a current 7s uses up in the armature a voltage EQ, a current 7 will use up a proportional voltage, Ez= (I-~Is)Eo> * See 26a. fBy the magnetomotive force method (Appendix I.), Curve (6) differs from Curve (i) by a constant distance (A/z) horizontally; at high satu- rations this is too optimistic. 3-B] PREDETERMINATION. 9 1 APPENDIX I. MAGNETOMOTIVE FORCE METHOD.* 34. In the magnetomotive force method, instead of combining vectorially various electromotive forces as was done in the electro- motive force method, Figs. 3, 4 and 5 the corresponding magneto- motive forces are so combined. 35. The magnetomotive force corresponding to any electromotive force is found by reference to the no-load saturation curve, and is commonly expressed in ampere-turns. For a given machine, with constant number of field turns, field amperes are proportional to field ampere-turns and may be used as a measure of magnetomotive force. In Fig. I of this experiment and Fig. 2 of Exp. 3~A, it is seen, for example, that 627 .volts corresponds to a field excitation of 7.33 field amperes, or 3,401 field ampere-turns, either of which may be taken as a numerical measure of magnetomotive force. 36. It is readily seen that a straight saturation curve gives mag- netomotive forces proportional to electromotive forces, so that the same results will be obtained from the use of either, if the procedure is otherwise identical. On the other hand, a saturation curve which is not straight gives values of magnetomotive forces not proportional to electromotive forces, so that different results will be obtained according to whether magnetomotive forces or electromotive forces are used. 37. Method.f The three magnetomotive forces Mo, Mz and MT are combined vectorially, as in Fig. 8; cos is the power factor of the load. These three quantities Mo, Mz and MT may be interpreted by their correspondence:}: to the three electromotive 'forces Eo, Ez and ET, * No additional data are required ; see 43 for the particular application of the method to be made. t (37a). This is the common interpretation of the method (see Rush- more, p. 740, Vol. I., St. Louis Elect Congress, 1904). In Franklin & Esty's Electrical Engineering, Mo is obtained as the resultant of two mag- netomotive forces which correspond not to ET and Ez, but to Ep and EQ (the in-phase and quadrature components of o). $(37b). If the saturation curve were a straight line and magneto- motive forces were proportional to electromotive forces, the triangles for magnetomotive forces and electromotive forces would be similar and each side of one triangle would be perpendicular to the corresponding side of the other. SYNCHRONOUS ALTERNATORS. [Exp. respectively. A magnetomotive force MT is required for a terminal voltage ET, corresponding values being taken from the saturation curve; at no load no other magnetomotive force is required. Under load, an additional magnetomotive force BA = Mz is required to overcome the magnetizing effect of the armature. In terms of mag- netomotive force, Mz is equal to the ampere-turns of the armature; p Cos 6-0 FIG. 8. Magnetomotive force method. in terms of its corresponding electromotive force, it is a magneto- motive force which will produce an electromotive force equal to the armature impedance drop, Ez. The total magnetomotive force which the field must provide is the vector sum, MQ. In this sense, Mo is the resultant of MT and Mz ( BA}, in the same way that Eo is the resultant of ET and Ez. Interpreting these quantities further as magnetomotive forces: Mo is the magnetomotive force produced by the field; Mz (=AB, in the direction of armature current, /) is the magnetomotive force produced by the armature ; MT is the combined magnetomotive force and produces the electromotive force ET. In this sense, MT is the resultant of Mo and Mz ( =AB). On open circuit the field ampere- 3-B] PREDETERMINATION. 93 turns (or amperes) give us the value of the magnetomotive force MT; for, in this- case, Mz = O. On short circuit, the field ampere-turns (or amperes) give us the value of Mz; for, in this case, MT = O. That is, on short circuit the field and armature ampere-turns are (practically) equal and oppo- site (compare 21). In Fig. i it is seen that, on short circuit, full-load current (43.4 amp.) is given by a magnetomotive force Mz = OG = 121 ampere- turns (2.6 amperes) ; the corresponding impedance voltage, as used in the electromotive force method, is Ez = GF = 234. 38. Procedure; Any Power Factor. The value of Mz is known, as in the preceding paragraph ; also the power factor, cos 0, of the load. Given ET to find EQ. Construct the triangle OBA, Fig. 8, from the known values of Mz and cos 0, and the value of MT corresponding to ET; the value of Mo and the corresponding value of EQ is thus determined. Given E.Q, the converse procedure is followed to obtain ET. The most important cases are for unity and. zero power factors. 39. Unity Power Factor. For this case, cos 0= i, and OBA (Fig. 8) becomes a right triangle. The same procedure is followed as in the preceding paragraph. 40. The following procedure, known as the Institute* Method (proposed by a committee but not adopted) differs from the fore- going by taking special account of the armature RI drop. Armature RI drop is significant at unity power factor; it becomes less so as the power factor decreases and becomes negligible at zero power factor. The Institute Rule is : " When in synchronous machines the regulatio'n is computed from the terminal voltage and impedance voltage, the exciting ampere-turns corre- sponding to terminal voltage plus armature resistance-drop, and the ampere-turns at short-circuit corresponding to the armature impedance- drop, should be combined vectorially to obtain the resultant ampere-turns, and the corresponding internal e.m.f. should be taken from the saturation curve." By the reverse procedure ET is determined when EQ is known. *Rule 71, p. 1087, Vol. XIX. 94 SYNCHRONOUS ALTERNATORS. [Exp. 41. Zero Power Factor. When cos# = o, it is seen that, by the construction of Fig. 8, Mz and MT are in one straight line; hence MT = Mo Mz ; or, Mo = MT + Mz. At no load MO = MT. Under load, if Mr (and ET} is to have the same value as at no load, the field excitation Mo is to be increased by an amount Mz added in this case arithmetically* 42. Determination of Full-load Saturation Curve. Given the no- load saturation curve, Fig. I ; the full-load saturation curve for zero power factor is found by adding the constant magnetomotive force Mz = OG. The two curves (i) and (6) are accordingly a constant distance apart, measured horizontally. 43. Application. To illustrate the use of the magnetomotive force method, it will suffice to apply the method, using observed data, to the following typical cases : 1. Using the Institute Method, 40, obtain EQ, corresponding to rated voltage, ET, at full load, unity power factor. Plot this as the point p, Fig. 6. Note that this point is a little lower than Eo obtained by the electromotive force method, i. e., the regulation is better. 2. Also, locate p by the method of 39. 3. By the method of 38 and 41, locate the point q, Fig. 6, that is Eo corresponding to rated ET at full load, zero power factor. Note that this is considerably lower than Eo obtained by the electromotive force method. 4. Construct a full-load saturation curve (42) for zero power factor. 44. Justification of the Magnetomotive Force Method. The con- struction of Fig. 8 shows that the armature ampere-turns are com- bined with the field ampere-turns in such a way as to have the great- est effect for power factor zero, cos# = o; the least effect for cos 0= i ; and intermediate effects for intermediate values of cos 9. This will be shown to be qualitatively correct, although quantitatively it is only correct approximately or under certain assumptions. 45. Fig. 9 shows two conductors of an armature coil, one midway under a north pole, the other midway under a south pole. In this position the electromotive force induced in the armature conductors * (4ia). The corresponding electromotive forces at zero power factor are likewise added arithmetically; Eo = T -f- Ez. (See 21.) 3-B] PREDETERMINATION. 95 is a maximum. The armature current will likewise be a maximum, if it is in phase with this electromotive force. In this position, the flux set up by the armature current has a cross-magnetizing effect; the flux passes transversely through the pole piece but does not pass through or link with the field winding and so does not directly oppose the field ampere-turns. Fig. 10 shows the armature conductors midway between poles; the coil, to which these conductors may be assumed to belong, is exactly opposite a pole. In this position the electromotive force induced in FIG. 9. Distortion of field by transverse magnetization, or cross- magnetizing effect of armature cur- rent ; produced by an in-phase cur- rent, or component of current. FIG. 10. Weakening of field by de- magnetizing effect of armature current ; produced by a wattless or quadrature current, or component of current. the armature conductors is zero; at zero power factor the armature current lagging 90 behind the electromotive force is a maximum. It will be seen from the figure that in this position the armature has the greatest demagnetizing effect, the flux produced by the armature passing through the field winding and directly opposing the field ampere-turns. 46. It is seen that when the armature current is in phase with the generated electromotive force it produces distortion and cross-mag- netization ; when the armature current is in 'quadrature it produces demagnetization without distortion, the armature ampere-turns being in direct opposition to the field ampere-turns. When the current has a phase displacement, with respect to the induced electromotive force, between o and 90, it may be considered as composed of two components, an in-phase component producing cross-magnetization and a quadrature component producing demag- netization. 47. On short circuit, the current in the armature lags 90 (or 9 6 SYNCHRONOUS ALTERNATORS. [Exp. nearly so, on account of high armature reactance). The armature and field ampere-turns on short circuit are, therefore, practically equal and opposite. If they were exactly equal and opposite, there would be no electromotive force generated ; as a matter of fact, there is a very small electromotive force equal to the armature RI drop. That the armature ampere-turns due to a current lagging 90 opposes or weakens (and does not aid or strengthen) the field is verified by this short-circuit test, and its resultant small electromotive force. 48. A leading current, on the other hand, directly aids and strengthens the field. 49. In the foregoing discussion of Figs. 9 and 10, the reaction of the armature has been considered for the particular moment and position when the armature current is a maximum. In reality, the armature assumes successively all positions and the current takes all values; in intermediate positions, demagnetization and cross-magneti- zation are both present in varying amounts dependent upon the posi- tion of the armature and the armature current at any instant. The general nature of the reaction, however, may be considered as defined by its character when the current is a maximum. The real effect is a summation of the effects at each instant through a cycle. A more complete discussion would involve some knowledge or assumption as to flux distribution in the pole pieces, and other design factors. As a matter of fact, a sinusoidal flux distribution has been assumed in order to make it possible to treat Mo as a vector in Fig. 8; the assumption tacitly made is that the field flux passing through an arma- ture coil varies as a sine function of time, so that the generated elec- tromotive force ( The admittance Y of an alternating current circuit, defined as the amperes per volt, is the reciprocal of impedance; Y = I-+-E. The unit of admittance is commonly called the mho. 6. Power factor, defined as the ratio of true power W to apparent power or volt-amperes El } is always less than (or equal to) unity. Power f actor = cos 0, where is the phase difference between E and / ; see Figs. 2 and 7 discussed later. In a circuit with resistance R and reactance X, The subject will be most readily understood by considering: first, circuits with R, only; second, circuits with X, only; and finally circuits with both R and X. 7. Series Circuit with Resistance Only. In an alternating current circuit "containing only a resistance R, the electromotive force required to make flow a current /, is as in a direct current circuit. The current is in phase with the electromotive force. As the electromotive force rises from zero to a maximum and falls again to zero, the current i at each instant is proportional to the electro- motive force e at that instant; e = Ri. The current is zero when the electromotive force is zero, and is a maximum when the electromotive force is a maximum. 8. If E is represented as a vector, Fig. 5, the current / is represented as a vector in the same direction or phase as E ; 4-A] SERIES AND PARALLEL CIRCUITS. 105 I that is, to cause a current / to flow through a resistance R, an in-phase electromotive force equal to RI is required. 9. Significance of Vectors. In developing the theory of vec- tor diagrams for alternating current quantities, the vectors rep- resent the maximum values of quantities which vary according to a sine law. In applying these diagrams, however, the vectors are usually drawn to represent the effective (or virtual) values, as measured by ammeter and voltmeter, the effective value of a sine wave being ^V 2 times its maximum value.* Furthermore, vectors are used for currents and electromotive forces which do not vary exactly as a sine law, although the results in these cases are not, in general, theoretically correct.f In drawing vector diagrams, it is implied, therefore, that the currents and electro- I motive forces have wave forms which are sine waves or may be represented by equivalent sine waves of the same effective values. The phase difference 0, between equivalent sine waves for cur- rent and electromotive force, is determined by the relation: cos = power f actor = W -f- EL 10. Direction of Rotation. Counter-clockwise rotation is usually taken as the direction of rotation of alternating current vector diagrams, and this convention will be here followed. By considering a diagram as making one complete revolution (360) in one cycle, the projections, from instant to instant, of the various lines of the diagram upon any fixed line of reference will be proportional to the instantaneous values of the quantities represented by those lines. By reversing -all diagrams as in a mirror, the corresponding diagrams for clock-wise rotation will be obtained. 11. Electrical Degrees. In alternating current vector dia- grams, " angle " is a measure of time, 360 indicating the time * See Bedell and Crehore's Alternating Currents, p. 38, and other text- books. t (Qa). Compare 60-64; for further discussion, see references given in gb, Exp. 5-C. 106 SINGLE-PHASE CURRENTS. [Exp. of one complete period or cycle, 90 indicating J period, etc. A degree is, therefore, a unit of time, being sometimes designated a "time-degree" or "electrical degree." This designation is, how- ever, unnecessary except in discussions where " space-degrees " are also used. 12. Series Circuit with Reactance Only. In an alternating current circuit containing only a reactance of X ohms, the electro- motive force required to make flow a current I, is E X = XI; and / = x -5-X, as shown in 14-17. When the reactance X, is due to inductance, the electromotive force to overcome reactance is Reactance is the same as resistance in that an electromotive force proportional to it is required to cause a current to flow, the electromotive force being XI for reactance and RI for resistance. Reactance is, however, different from resistance in that it consumes no energy ; when the current is increasing, energy is stored* in the magnetic field (as in a fly-wheel), this energy being returned to the circuit when the current is decreasing. In a reactance, the current and electromotive FIG. i. Vector diagram for circuit force are not in phase but are in quadrature with inductive re- with each other, i. e., the current and electro- actance. r , . ~, . t ,. motive force differ in phase by a quarter of a cycle or 90, and when one is a maximum the other is zero. * ( I2a). The energy of the magnetic field is equal to ^>L/ 2 , cor- responding to the energy of a moving body, J / 2 MF*. 4-A] SERIES AND PARALLEL CIRCUITS. 107 13. For inductive reactance,* the electromotive force to over- come reactance is in advance of the current by 90, as in Fig. I, and is not in phase as in Fig. 5. The current lags behind the electromotive force by 90, that is, the current reaches a positive maximum J cycle later than the electromotive force reaches its positive maximum. When R = o, tan 6 = X -f- R = oo ; #=90 ; power = EI cos Q = o. A current and electromotive force in quadrature represent no power and are said to be " wattless." 14. Theory. When a current flows in an inductive circuit, the current sets up magnetic flux which is linked with the circuit. When the current changes, this flux changes and a counter- electromotive force is induced in the circuit tending to oppose any change in the current, the current seemingly possessing inertia. The electromotive force produced by self-induction depends upon the rate of change of current,f and is e oc di/dt ; or, e L di/dt. The negative sign indicates that the electromotive force is counter to the impressed electromotive force. The equal and opposite impressed electromotive force to over- come self-induction is e = L di/dt. * ( I3a). For capacity reactance, the electromotive force to overcome reactance X = i/Cu is A7 = I -f- Cw and is 90 behind the current ; the current is 90 in advance of the electromotive force ; see 55. t ( I4a). The electromotive force produced by self-induction, expressed in terms of rate of change of flux, is * = S d/dt, ' (Compare 33, 33a, Exp. 5-A.) In the absence of iron, i and are proportional to each other and L is constant. In this case Li = S, and = S -=- i '; or s the inductance of a coil is equal to the flux-linkages or flux-turns S for unit current. Since ccSi, it follows that L^S 2 , other things (including dimensions of coil and leakage) being equal; the inductance of a coil is approximately proportional to the square of the number of turns. In the presence of iron, i and are not proportional, and L is not constant but varies with saturation. io8 SINGLE-PHASE CURRENTS. [Exp. 15. The inductance L of a circuit is defined by the foregoing equations. When e is in volts and i is in amperes, L is in henries. A circuit has an inductance of one henry when a change of cur- rent at the rate of one ampere per second induces an electro- motive force of one volt. 1 6. When the current varies according to a sine law, i = /max sin w/. The impressed electromotive force is, accordingly, e = L di/dt = Lw/ max cos o>t = La>/ max sin ( at + 90 ) . The impressed electromotive force to overcome self-induction is, therefore, 90 in advance of the current; the current, on the other hand, lags 90 behind the electromotive force. 17. The maximum value of this electromotive force is seen to be Lw times the maximum value of the current; hence, the effective value of this electromotive force is Lo> times the effective value of the current, that is, Ex = Lu>I = XI. Fig. I and the statements in 12, 13 are thus established. 1 8. Series Circuit with Resistance and Inductive React- ance. In a circuit with both R and X, the electromotive force required to cause a current / to flow consists of two components, which have been separately discussed in the preceding paragraphs : RI, in phase with /, to overcome resistance; XI, 90 ahead of I, to overcome reactance. Thus in Fig. 2, if OD is current, OC is the electromotive force to overcome resistance and CA is the electromotive force to over- come* reactance, OA being the total impressed electromotive force. These electromotive force relations are fundamental and *(i8a). These electromotive forces, CA and OC are components of the impressed electromotive force. In the opposite sense, as counter- electromotive forces, we have the counter-electromotive force AC, lagging 90 behind the current, produced by inductive reactance ; and, the counter- electromotive force CO, opposite in phase to the current, produced by resistance. Compare 15, Exp. 6-A. 4-A] SERIES AND PARALLEL CIRCUITS. 109 are shown by the electromotive force triangle, Fig. 2, and by the following equations : Lcol = The impedance triangle, Fig. 3, is derived by dividing the elec- tromotive forces, Fig. 2, by /. 19. It is seen that the electromotive forces XI and RI are added as vectors. If, instead of a single X and R, there were Resistance FIG. 2. Electromotive force triangle. FIG. 3. Impedance triangle. several, the same procedure could be followed: RJ, RJ, RJ, etc., Would be laid off in phase with / ; and XJ, XJ, XJ, etc., in quadrature with /. Electromotive forces in a series circuit are added as vectors. Impedances, resistances and reactances in a series circuit are added as vectors. 20. The total drop in phase with / is 2RI ', the total drop in quadrature with / is 2X1. Hence, for any series circuit, J , and Z = The total resistance of a series circuit is seen to be the arith- metical sum of the separate resistances; the total reactance is the arithmetical sum of the separate reactances. For further discussion of series circuits, see 38-50; for par- allel circuits see 51-58- no SINGLE-PHASE CURRENTS. [Exp. PART II. MEASUREMENTS. 21. The following tests require a resistance, which is non- inductive and is designated R l ; and a coil, which is inductive and is designated R 2 L 2 . It is desirable to have the resistance and the coil take currents which are comparable in value with each other, for the frequency at which the tests are made; thus, if at no volts, 60 cycles, the coil takes a current of 10 amperes, the resist- ance should be so selected that at no volts it takes a current of, say, from 5 to 20 amperes. Except for 28, the coil should not have an iron core, so that there are no losses except RI 2 . For the tests of 26a (which may precede the main tests), the windings of the coil should be divided in two equal parts, which can be connected in series and in parallel. 22. The instruments required consist of a voltmeter, capable of reading the supply voltage and lower voltages ; an ammeter capable of measuring the combined currents of the coil and resist- ance; and a wattmeter having a voltage range corresponding to the range of the voltmeter and a current range corresponding to the range of the ammeter. A voltmeter switch will be found convenient for the series tests ( 2 9~3 J ) an d an ammeter switch for the parallel tests ( 32-34) . On all tests the frequency should be known. 23. (a) Resistance Alone. With an adjusting resistance in series, as in Fig. 4, connect the resistance R l to the supply circuit (say no volts, 60 cycles) and measure the current I, the voltage E at the terminals of R lt and the watts W consumed by R lf The current coil of the wattmeter is connected in series as an ammeter and the potential coil in shunt as a voltmeter, the arrangement* of instruments being shown in Fig. i, Exp. 5-B. * (23a). In these tests no account is ordinarily to be taken of the fact that the instruments themselves consume a certain small amount of power, as fully discussed in Appendix III., Exp. S-A ; this fact, however, should not be neglected in accurate testing, as for example in the accurate determination of L by the impedance method, 47. 4-A] SERIES AND PARALLEL CIRCUITS. m 24. Vary the adjusting resistance,* and in this way take sev- eral sets of readings. If there is any question as to the accuracy of the instruments, assume the ammeter and voltmeter to be correct and determine a correction for the wattmeter, so that in (a) the watts as read by the wattmeter are equal to the product of volts and amperes, as read by the voltmeter and ammeter. This serves as a calibration of the wattmeter, to be used in this and subsequent tests. 25. Take readings, in a like manner, at a second frequency. 26. (&) Coil Alone.f Repeat (a) using the coil R 2 L 2 alone, as in Fig. 6, instead of the resistance R^. 27. Take readings at a second frequency. 28. Effect of Iron. Gradually introduce an iron core and watch the ammeter ; or, introduce iron wires, a few at a time, thus gradually increasing the amount of iron. At present, only the general effect of iron is to be noted and explained; a more com- plete study of iron in the form of a closed magnetic circuit is made in the subsequent experiments on the transformer. 29. (c) Resistance and Coil in Series. Connect the resist- ance R l and the coil R 2 L 2 in series, and, together with an adjust- ing resistance, connect to the supply, as in Fig. 8. For a certain current, take readings of the voltage drop, the current and the watts consumed as follows: first, for the resistance; second, for * (24a). This adjustment should be so made that the readings of the various instruments are taken at open parts of the scales. t(26a). Series and Parallel Connections. If is instructive to use a coil with two equal windings. In this case, the regular tests should be made with the two windings either in parallel or in series and additive, i. e., setting up magnetic flux in the same direction. If one winding is reversed, it will oppose the other so that the resultant flux (and hence the impedance) is small. A few volts may cause a very large current. Preliminary Test. With the resistance R-L in series as a safeguard, to avoid excessive current, measure the current and voltage and determine the impedance of each winding alone and of the two windings connected in series and in parallel, additively and differentially. The additive wind- ing is inductive; the differential winding is non-inductive, except so far as there is magnetic leakage. H2 SINGLE-PHASE CURRENTS. [Exp. the coil; and third, for the resistance and coil combined. Vary the current, by means of the adjusting resistance, and take several sets of readings, the current being kept constant for each set; see 24a. 30. The ammeter and current coil of the wattmeter are in series with the circuit for all readings and their location is un- changed. The voltmeter and the voltage coil of the wattmeter are in parallel with each other and are connected : first, across the terminals of the resistance ; second, across the terminals of the coil; and third, across the terminals of the resistance and coil combined. These changes can be most readily made by means of a voltmeter switch, the current being maintained constant during one set of readings by means of the adjusting resistance. Some error is here introduced on account of the power consumed in the instruments. 31. Repeat at a second frequency. 32. (d) Resistance and Coil in Parallel. Connect the resist- ance R and the coil R 2 L 2 in ' parallel, and, together with the adjusting resistance, connect to the supply as in Fig. 10. For a certain constant voltage E, take readings of current, voltage and watts: first, for the resistance alone; second, for the coil alone; and third, for the resistance and coil together in parallel. Vary the voltage by means of the adjusting resistance, and take several sets of readings, the voltage being kept constant for each set ; see 24a. 33. The voltmeter and potential coil of the wattmeter are not changed during the readings. The ammeter and the current coil of the wattmeter are shifted from one circuit to another, being: first, in series with the resistance ; second, in series with the coil ; and third, in the main circuit. Since, during one set of readings, the voltage is maintained constant, the readings thus obtained* *This would be true if the instruments themselves took no power; 233. 4 -A] SERIES AND PARALLEL CIRCUITS. ^3 will be the same as readings obtained simultaneously with three ammeters and three wattmeters. 34. Repeat at a second frequency. 35. (e) Measurement of Resistance. Measure the resist- ances R-L and R 2 by direct current, 17, Exp. i-A. PART III. RESULTS. 36. In each test, (a), (b), (c), and (d), select say two sets of readings at each frequency and construct vector diagrams showing the magnitude and relative phase positions of the various currents and voltages. Compute for the various circuits, and parts of circuits, the power factor and the phase difference between current and voltage. The prime object is to obtain a clear understanding of the relations between the various quanti- ties, rather than to obtain exact numerical values. Adjusting Resistance I FIG. 4. Circuit containing resistance 37. (a) Resistance Alone. For this case, the current and electromotive force are in phase, and true power is equal to the product, volts X amperes. Power f actor = W -=- EI= I ; cos 9= i ; = o. See Fig. 5. 38. (b) Coil Alone. The current I lags behind the electro- motive force E by an angle 0, as in Fig. 7. The true power W, indicated by the wattmeter, is less than the volt-amperes or apparent power, El ; thus 9 Hence SINGLE-PHASE CURRENTS. W = El X power factor = El cos 6. cos = power factor = W -=- EL [Exp. The angle is thus computed from the readings of the wattmeter, voltmeter and ammeter. In constructing Fig. 7, lay off OA = E ; then lay off OD = I, at an angle 6 determined as above, and construct the right tri- angle of electromotive forces, OCA. Adjusting Resistance -w^yvj" J 1 1 R 2 L 2 j T FIG. 6. Circuit containing coil R 2 L 2 . Compute the components of electromotive force and current, and verify the various relations discussed in the following paragraphs. 39. Components of Electromotive Force. In the manner just described, the electromotive force is resolved into the power com- ponent, Ep = OC, in phase with /, and the wattless component, EQ = CA, in quadrature with /. These components are Ep = E cos = E X power factor ; EQ = E s'mO = E X reactive factor.* The vector sum of these two components gives the total im- pressed electromotive force. * (39a). Designating power factor by p and reactive factor by q, it is seen that /> 2 + # 2= i. Compare Standardization Rule 56. 4-A] SERIES AND PARALLEL CIRCUITS. 115 40. From these electromotive forces, we have the definitions : Impedance is total electromotive force divided by current; Z = E-+-L Resistance is power or in-phase component of electromotive force divided by current; R = Ecos0^r-L (In general, when motors, transformers, etc., are included in the circuit, this gives apparent resistance.) Reactance* is the wattless or quadrature component of electro- motive force divided by current; X = Esm0-^I. 41. Components of Current.^ In a similar manner, the cur- rent may be resolved into a power component, / P = /cos0, in phase with E, and a wattless component /g = /sin0, in quadra- ture with E; the total current is I=^/Ip 2 -}- IQ Z . 42. From these currents, we have the definitions : . Admittance Y is total current divided by electromotive force; K=/-*-E. Conductance g is the power or in-phase component of current divided by electromotive force; g = IcosQ^-E. Susceptance b is the wattless or quadrature component of cur- rent divided by electromotive force; b = I sinO-^-E. We have, then, the following relations; Total current = I = E X Y. Power current = / cos 6 = E X 9> Wattless current = / sin = E X b. g=Ycos6. Admittance = V^ 2 + * This is the general definition, Lta, i/Cw, etc., being merely particular values; see paper on Reactance, by Steinmetz and Bedell, p. 640, Vol. XI., Transactions A. I. E. E., 1894. f (4ia). As an illustration of the resolution of current, see Fig. 2 and other figures 'in Exp. 5-C. It is usual to resolve electromotive force into components for series circuits and current into components for parallel circuits. n6 SINGLE-PHASE CURRENTS. [Exp. Admittance is the reciprocal of impedance; but conductance is not the reciprocal of resistance (as with direct currents), nor is susceptance the reciprocal of reactance. 43. Power. It is seen that the expression for true power, El cos 0, may be written in two ways: W = Ecos6y< I (resolving electromotive force); or, F=/cos#XE (resolving current). 44. Resolving the electromotive force into components, we have: True power is equal to the product of current (I) and the component of electromotive force (EcosO) which is in phase with the current. 45. Resolving the current into components, we have : True power is equal to the product of the impressed electromotive force (E) and the component of current (I cos 6) which is in phase with the electromotive force. 46. Calculation of L and X by Wattmeter Method. React- ance is by definition (40) equal to the quadrature electromotive force, Ex, divided by current. Referring to Fig. 7, the reactance and inductance of the coil R 2 L 2 are computed as follows: L 2 w ^X 2 = CA -r- 1, ohms ; L 2 = X 2 -f- w = X 2 -+- 2-n-n, henries. By this method, X 2 and L 2 are determined by measurements of E, I and W ' , and are independent of the measured value of R 2 . (See 47 and 49.) Note also that R 2 = OC-t-I= W-^-I 2 , and that tan 6 = X 2 -^-R 2 . 47. Calculation of L and X by Impedance Method. By the impedance method, L 2 depends upon E, I and the measured value of R 2 , and is independent of the wattmeter reading. The cal- culations are made as follows: Impedance ( ohms ) =Z 2 = E-^-I. Reactance (ohms) =X 2 = \/Z 2 2 R*. 4-A] SERIES AND PARALLEL CIRCUITS. 117 Here R 2 is the resistance of the coil, as measured by direct current. The inductance, in henries, is L 2 = X 2 -^~2Trn. For the accurate determination of L by either of these methods, the wave form of electromotive force should be sinusoidal and the losses in instruments should be taken into consideration, 23a. 48. (c) Resistance and Coil in Series. In a series circuit there is one current which is the same in all parts of the circuit; electromotive forces are added vectorially, i. e., the voltage drops around the separate parts of the circuit, when added as vectors, give the total impressed electromotive force of the circuit. FIG. 8. O / D Resistance and coil in series. The three readings of the voltmeter, E, E^ and E 2 , are, accord- ingly, drawn to scale so as to form the triangle OAB, in Fig. 9. The current / is laid off in phase with E lt since the current and electromotive force in the non-inductive resistance are in the same phase. OCA is then drawn as a right triangle. We have then the in-phase, electromotive forces, OB = RJ to overcome the resistance R^ and BC = R 2 I to overcome the resist- ance R 2 ; and the quadrature electromotive force, CA = L 2 ul = X 2 I, to overcome the reactance X 2 . It will be seen that Fig. 9 is the same as Figs. 5 and 7 combined in one diagram so drawn that the current in both parts of the circuit is the same in magni- tude and in phase. 49. Three-voltmeter Method. The foregoing construction, known as the three-voltmeter method, enables us to calculate L 2 n8 SINGLE-PHASE CURRENTS. [Exp. and X 2 , the results being dependent upon three voltmeter read- ings and current, and not dependent upon the wattmeter (as in the wattmeter method, 46), nor upon the measurement of resist- ance (as in the impedance method, 47). Referring to Fig. 9, we have hence and In applying the three-voltmeter method, greatest accuracy is obtained when 1 = 2 . If an electrostatic voltmeter is used, no error is introduced on account of power consumed in the instru- ment, 23a. 50. Three-voltmeter Method for Measuring Power. Before the perfection and general introduction of the wattmeter, the three-volt- meter method for measuring power was used ; this is now obsolete for practical testing. The procedure was as follows: Given a device R^L 2 (which might be, for example, a transformer) the power in which is to be measured. Connect* in series a non- inductive resistance -R lf as in Fig. 8, and read E, E v E 2 and /. The power in R 3 L 2 (see Fig. 9) is W z = EJ cos 2 = (I -r- 2EJ (E* - E* - 2 2 ). See Bedell and Crehore's Alternating Currents, p. 232. The weak point in the method is that small errors in observation make large errors in the result. The three-ammeter method, with a non-inductive resistance in parallel with the apparatus under test as in Fig. 10, is open to the same objection. 51. (d) Resistance and Coil in Parallel. In parallel cir- cuits,* currents combine vectorially, the main current being the vector sum of the branch currents. * (5ia). Currents are proportional to admittances; hence admittances may be added as vectors. The admittance of several circuits in parallel 4-A] SERIES AND PARALLEL CIRCUITS. The main current / is laid off, in Fig. n, as the diagonal of a parallelogram with sides equal to the branch currents 7 X and / 2 . The electromotive force E is laid off in the direction of I lf since Adjusting Resistance E FIG. 10. O I z #2/2 C FIG. ii. Resistance and coil in parallel. the current and electromotive force in the non-inductive branch are in phase. E is the common terminal electromotive force and is the same for both branches. For the inductive branch, the electromotive force triangle OCA is constructed, as in (&). For this branch, the power electro- motive force is-OC, in phase with / 2 ; the wattless electromotive force is CA in quadrature with / 2 . Fig. 1 1 is seen to be the same as Figs. 5 and 7, drawn with a common E and combined. In Fig. 9, these figures were combined with a common I. 52. The right triangle OC'A is the electromotive force tri- angle for an equivalent* single circuit, R'L', which could be sub- stituted for the two parallel circuits. Since OC' = R'I, and is the vector sum of the admittance of the separate branches. In parallel circuits we may add as vectors either currents or admittances; while in series circuits we may add as vectors either electromotive forces or im- pedances, 19 and 20. * (52a). For a more complete discussion of equivalent resistance and inductance, see Bedell and Crehore's Alternating Currents, pp. 238-41. Both R' and L' depend upon frequency and are not constants of the circuits; the equivalent resistance of parallel circuits is not the same for alternating as for direct current. 120 SINGLE-PHASE CURRENTS. [Exp. C'A=L'uI, the resistance and reactance of this equivalent cir- cuit are computed as follows : L'<=CA~I. 53. For any number of parallel circuits, the total current in phase with E is 2,1 cos ; the total quadrature current is 2/ sin 0. Hence 1= V (2/cos0) 2 + (S/ sin 0) 2 . Dividing by E, we have The total conductance of a number of parallel circuits is the arithmetical sum of the separate conductances; the total suscept- ance is the arithmetical sum of the separate susceptances. (Com- pare with 20 for series circuits.) APPENDIX I. CIRCUITS WITH CAPACITY. 54. It is not intended in this experiment that tests with capacity be included, the following summarized statements concerning capacity being made for reference and for comparison with the relations already discussed concerning inductance. 55. Circuits with Resistance and Capacity. In theory, circuits containing capacity (C) can be treated exactly the same as circuits containing inductance, if the following differences are noted: Inductive reactance = Leo ; current lags behind impressed electro- motive force. Capacity reactance = i -=- Cw ; current is in advance of impressed electromotive force. In either circuit, tan = X -f- R. All diagrams for inductive circuits can be applied to capacity cir- 4-A] SERIES AND PARALLEL CIRCUITS. 121 cults by writing i -=- C g ivm g a lo wer voltage than former or booster, using coils full line voltage while the motor is coming up to speed; see Fig. 6, ^^^ Exp. 7-A. A common use of the step-up arrangement of Fig. 3 is as a booster to raise the voltage on remote parts of a distribution system, say from 2,000 to 2,200 volts. For this a standard 2,000/200 volt transformer can be used, with the low-potential coil in series with the primary to boost the voltage, as in Fig.2, Exp. 7 B. This becomes a " negative booster " if the connec- tions of the low-potential coil (coil D in Fig. 3) are reversed. (If a standard transformer is to be tried in the laboratory, a loo-volt circuit may be boosted to no volts, or reduced to 90 volts.) 14. Constant Potential Operation. Transformers are usually operated from a constant potential circuit, so as to transform either step-up or step-down from a constant primary potential to a constant secondary potential. 15. Open Circuit. Connect a no-volt alternating current supply circuit across two of the transformer coils in series, as 5-AJ STUDY AND OPERATION. *37 a primary. Measure the no-load primary current, 7 , called the exciting current. Predict, and then measure, the value of / when the two primary coils are in parallel and connected to a 55-volt supply i. e., half the preceding voltage. Compare the relative values, for the two cases, of primary turns, ampere turns, volts, volts per turn and flux density. Measure / when the two primary coils are in series, and con- nected to a 55-volt supply; and interpret the results (see Fig. 2, Exp. 5-B). Commercial transformers are commonly built with two pri- maries for connection in series (for, say, 2,200 volts) or parallel (for i, 100 volts) ; and two secondaries for connection in series (for, say, 220 volts) or parallel (for no volts). 16. Operation Under Load* Join twof of the coils in series to form a primary and join the other two coils in series to form a secondary or make such other arrangement of coils as may be desired. Connect the primary with an alternating current supply say no volts, 60 cycles appropriate to the arrange- ment of coils adopted. A voltmeter, ammeter and wattmeter are connected J in the primary, as in Fig. i. 17. With the secondary on open circuit, measure the primary voltage, the primary current (in this case, the no-load current, 7 ) and the primary power (in this case, the no-load or core losses, W ). * Time should not be spent in an attempt to get very accurate results in this test, particularly if it is to be followed by* the more accurate test by the method of losses, Exp. 5-B. f ( i6a). Where there is a choice of coils, select an arrangement which avoids great magnetic leakage. If each coil forms one layer or section, to take the first two for primary and the other two for secondary would not be a good arrangement. In a commercial transformer, the primary and secondary windings are so placed as to reduce magnetic leakage ; to secure this end, however, all the windings should be used, that is, no coil should be left idle. An arrangement of coils commonly used is as follows : low, high, high, low, potential. $ With instruments arranged as in Fig. i, no corrections need be made. (See Appendix III.) 13 s TRANSFORMERS. [Exp. 18. Load the secondary by means of suitable non-inductive resistance. Change this resistance by steps so as to vary the secondary current between no load and 25 per cent, overload. At each step measure the primary voltage E lt current I lf and power, W i ; also the secondary* voltage E 2 , and secondary cur- rent I 2 . The product of the secondary voltage and current will give the secondary power W 2 , the secondary load being non- inductive. In practice, a load of incandescent lamps is non- inductive, but not so a motor load. 19. Measure the resistance of primary and secondary. (See 15, Exp. 5-B.) 20. For each load, compute the power factor (W^~-EJ^)\ also the angle by which the primary current lags behind the electromotive force. (Power f actor = cos 6.) Plot Jj, W, power factor, 6, E 2 and W 2 for different values of I a , as in Fig. 4. Plot, also, the copper loss for primary (RJi 2 ) and for secondary (R 2 I 2 2 ) and the core loss W Q (the value of W on open circuit) which is constant at all loads, as in Fig. 8, Exp. 5-B. Note that E 2 decreases with load. Determine the per cent, regulation the per cent, increase in E 2 in going from full load to no load. Note the current ratio for different loads. It will be seen that as the transformer becomes loaded (by decreasing resistance in the secondary) the secondary current becomes more nearly equal to the primary current (multiplied by 5 i 1 -v-.S 1 2 ). In a loaded transformer, primary and secondary ampere-turns are practically (but not exactly) equal. It is seen that in a transformer there is a loss in volts, a loss in amperes and a loss in watts, this last determining the efficiency. While best for illustrating the operation of a transformer, the * By means of suitable transfer switches one voltmeter and one ammeter may be used for both primary and secondary. 5-A] STUDY AND OPERATION. 139 loading method is not so good for the accurate determination of efficiency and regulation. These can be computed much more 100 90 70 1500 1000 500 5 10 15 20 25 SECONDARY CURRENT; AMPERES FIG. 4. Curves for 2,000/100 volt, 2 K.W. transformer ; see also Fig. 8, Exp. s-B. accurately from the losses, determined without loading, as in Exp. 5-B. 21. Load the transformer with an inductive load and take one reading of the instruments. It will be seen that the sec- ondary voltage is somewhat less than it was with non-inductive load that is, the regulation is poorer.* This happens when induction motors are operated from transformers. In this case the secondary current is lagging. If the secondary current were leading, the secondary voltage in some cases would increase, instead of decrease, with the load. The results are similar to those obtained for an alternator ; see Exp. 3-6, particularly Fig. 7. 22. Design Data and Computation of Flux Density. Note the construction and essential dimensions of the transformer, * (2ia). If the leakage reactance of a transformer is small, compared with its resistance, the regulation may be better at low than at high power factor ; compare 28, Exp. 3-B. 140 TRANSFORMERS. [Exp. including the cross section of the magnetic circuit and size of wire, but do not remove parts, destroy insulation or damage the transformer in any way in seeking this information. Data fur- nished by the maker can be used for this purpose. 23. Compute the current density in amperes per square inch and in circular mils per ampere, for the primary and the sec- ondary windings. Current densities from 1,000 to 2,000 circular mils per ampere are common, but less copper was often allowed in early transformers. 24. Compute the maximum value of the total flux in C.G.S. lines or maxwells (see 9a, Exp. i-B) ; thus where E is the voltage and 5 the number of turns for any coil, and n is frequency. The quantity E -r- S is the volts per turn. For proof of formulae, see Appendix II. Compute the maximum value of the flux density in gausses (flux per sq. cm.) ; thus R X io 8 Flux where A is the cross section* of the core in sq. cms. If A is in square inches, 5 max . is the flux density in lines per square inch. If A, in square inches, is multiplied by 6.45, the formula gives m ax. in gausses for, unfortunately, this mixture of C.G.S. and English units is in common use. 25. The computations for B should be made for standard frequency (60 cycles), and two other frequencies (30 and 120) with the same value of E. If values of A and 5 are not obtain- able, assumed values may be assigned for practice computations. If the cross section of the core is not uniform, B will have dif- * (24a). The net cross section is, say, 15 per cent, less than the gross cross section on account of lamination. 5 -A] STUDY AND OPERATION. H 1 ferent values for different parts of the magnetic circuit. From these computations it can be seen whether B will be more or less, if a transformer is operated at a higher or lower frequency than rated and at the same voltage. (Note in what manner E should be changed to maintain B the same at different frequencies.) Practically, transformers are run at different frequencies without changing E, if the frequency is not too far below the frequency for which the transformer is designed. For a discussion of the effect of frequency upon core loss, see 8-14, Exp. 5~B. In transformer design,* B is given a wide range (4,000-14,000 gausses at 60 cycles), being sometimes greater in small than in large transformers and greater in transformers designed for low than in those for high frequency. In design, E and n being given, B may be assumed and the product A X ^ determined. This product being fixed, the designer may adjust the values of A and 5 to suit his purpose, increasing A and decreasing 5 to use more iron and less copper, or vice versa. 26. From the formula for flux density, it will be seen that the electromotive force of any coil of a transformer is propor- tional to the number of turns in the coil, a fact already noted. The volts-per-turn should be computed as a constant for the transformer. For small transformers this may be one third or one half, being greater for large transformers, perhaps 2 to 4 for transformers above 30 K.W. The reciprocal gives the turns- per-volt. The volts-per-turn, when known for a certain type and size of transformer, may be used as a design constant. 27. Other data of interest to the designer (which may be de- termined when worth while) are the weight of copper and of iron, total and per K.W. This may range from 5 to 25 Ibs. per K.W. for either copper or iron. The space factor for copper is the * ( 2 5a). For more complete design data, see handbooks, etc. As mag- netic material is improved, higher magnetic densities are possible for the same loss. While densities of 4,000-8,000 were used with ordinary grades of iron, densities of 6,000-12,000 are now common with alloy steel. I4 2 . TRANSFORMERS. [Exp. ratio of the cross section of copper to the total cross section of the windings, i. e., to the cross section of copper plus insulation and air space. Similarly the space factor for the iron is the ratio of its net to gross section. APPENDIX I. POLARITY AND RATIO OF COMMERCIAL TRANSFORMER. 28. Polarity; Alternating Current Method. The coils are con- nected in series, two at a time, and notice is taken whether the voltage around the two is the sum or the difference of the separate voltages. There are several ways in which this can be carried out. As an example, let us take a transformer with two primaries for 1,000 volts each and two secondaries for 50 volts each. Connect the two i,ooo-volt primaries in series and con- nect the terminals of one* of the primaries to a low potential supply circuit, say 50 volts, as in Fig. 5. If a voltmeter across the two coils together reads zero, reverse FIG. 5. Polarity test the conne ctions of one of the coils. The by alternating current yoltmeter should then read IQQ vohs acrQSS method. the two coils together, and 50 volts across each one separately. Terminals A and B are now of one polarity; terminals A' and B' are of the opposite polarity, to be marked with a prime (') or X- Each secondary is then connected in series with one primary, the primary being connected to the 5o-volt supply circuit; the secondary in series with it is so connected that the voltmeter reading around the two coils in series is greater (52.5 volts) than the potential from the mains (50 volts). If the reading is less (47.5 volts), reverse the secondary. Secondary terminals are marked with a prime (') or X to correspond with the primary. Small transformers are commonly so wound that, when the primary and secondary leads on one side of the transformer are connected * If the two coils in series were connected to the supply circuit, a burn- out might result if the coils were opposed to each other. -A] STUDY AND OPERATION. H3 together, the voltage measured across the two primary and secondary leads on the opposite side will be the sum of the voltages of the two windings. 29. Polarity; Direct Current Method. The alternating current method is usually preferred, but sometimes the following method will be found convenient. The primary is supplied with a direct current sufficient to give a reading on a direct current voltmeter connected to the primary terminals. The voltmeter terminals are then con- . nected to what are supposed to be corresponding terminals of the secondary. If, when the primary circuit is closed,* the voltmeter needle is thrown in the same direction as the preceding reading, the voltmeter has been connected to the secondary terminals correspond^ ing to primary terminals; i. e., the voltmeter lead from the primary terminal (') or X is connected to the secondary terminal to be marked (') or X- If the voltmeter needle is thrown in the opposite direction, the reverse is true. 30. Potential Ratio. Where one transformer alone is to be tested, the transformer should be supplied with any convenient voltage and the voltage of each circuit measured either by two voltmeters, one of which has been calibrated in terms of the other, or by one voltmeter reading direct on the low potential side and with a multiplier on the high potential side.f When one transformer has been tested in this manner, or a small potential transformer of accurate ratio is available, two transformers can be run in parallel from the same circuit and their secondary voltages on open circuit compared by readings taken with one volt- meter or with two voltmeters whose relative calibration is known. If the secondaries of two similar transformers are connected in series and in opposition, any difference will be shown by a voltmeter connected across the two. 31. Current Ratio. For commercial testing of the ratio of a transformer, test may be made by comparison of primary and secondary currents instead of voltages. The secondary circuit is short-circuited through an ammeter of low resistance and the *The current should be small so as not to injure the voltmeter by slamming the needle when the circuit is made and broken. t It is not necessary to run the transformer at full rated potential. When high potentials are used, due caution should be observed. M4 TRANSFORMERS. [Exp. primary and secondary currents measured when a proper voltage (a few per cent, of normal primary voltage) is applied to the primary, so that about the normal current flows. 32. Circulating Current Test. As a shop test, after one standard transformer has been tested, other transformers designed for the same ratio may be operated from the same primary mains and tested one at a time by connecting each secondary to be tested in parallel with the secondary of the standard, terminals of the same polarity being connected together. If an ammeter shows a circulation of current through the secondaries, the two transformers are not of the same ratio. Commercially a small difference in ratio is allowable as shown by the circulating current, which, however, should never exceed one per cent, of the rated full-load current. Instead of an ammeter a suit- able fuse may be conveniently used, and more safely where much difference in ratio may exist. APPENDIX II. RELATION BETWEEN FLUX AND ELECTROMOTIVE FORCE. 33. The fundamental relation between flux and electromotive force is expressed by Faraday's law; that is, in a closed circuit* of 5 turns embracing a varying flux <, the induced electromotive force is S-d(f>/dt. In a transformer, this applies alike to primary or secondary. In the case of a primary coil this induced electromotive force is a counter electromotive force and requires to overcome it an equal and opposite impressedf electromotive force 34. Sine Assumption. Assuming the wave of electromotive force to be a sine wave, we have e = max . sin &t ; * Not limited to a transformer. t (33a). The actual terminal voltage includes also resistance drop, thus The resistance drop, however, is practically negligible in the primary of a transformer on open circuit. S-A] STUDY AND OPERATION. H5 = max . sin tot dt ; The maximum value of the flux is <*> =- and the flux per unit area is To express in terms of effective voltage, substitute \/2.E for E m&x . Multiplying by io 8 to change from C.G.S. units to volts, and remem- bering that w is 27T times the frequency (w), we have as a working formula for flux density 2*nSA It follows from this formula that a constant potential transformer is a constant flux transformer. It also follows that, if a certain flux is maintained in the transformer, the voltage in any coil is propor- tional to the number of turns in that coil. For further interpreta- tion, see 24-26. 35. Without Sine Assumption. We have the fundamental rela- tion d^ = edt/S. Integrating for half of a period T, during which time the flux changes from a minus to a plus maximum, T X+6 io~ 7 . Here ^ is a coefficient of hysteresis, equal:}: to about .002 for what was formerly good iron, but is now little more than half that value for the best alloy steel. The hysteretic exponent 1.6, first determined by Steinmetz, is only approximate, being less than this for low magnetic densities and considerably more than this for high densities. Referring to Fig. 5, if all the core loss were due to hysteresis, we would have (taking 1.6 as the hysteretic exponent) 0=1.6 and b= i a = 0.6. 51. In an actual transformer both hysteresis and eddy current loss are present, so that a has a value between 1.6 (hysteresis) and 2 (eddy currents), and b has a value between 0.6 (hysteresis) and o *(4Qa). In terms of B, eddy current loss in watts per cu. cm. is y(dnB) 2 io~ 21 , where d is the thickness of lamination expressed in mils and 7 is the conductance (the reciprocal of resistance in ohms per cu. cm.) of the material; for iron, 7 is about io 5 . There is a very slight change of eddy currents with frequency and wave form due to local inductance and " skin effect " in the local eddy current circuit. By decreasing the thickness of transformer plate, eddy current loss is diminished ; but hysteresis loss is increased, since some iron is wasted and B is greater in the remainder. A thickness between io and 15 mils gives the least total loss, according to particular conditions; see Elec, World, Dec. 31, 1898. t(4Qb). Hysteresis loss, also, decreases with increase in temperature. The total core loss of a transformer when hot may be 6 or 8 per cent, less than when cold. \ (5oa). By so called "aging " due to heat, this coefficient increases in the course of time Although not entirely eliminated, this effect has been reduced in the best steel now used. S-B] TEST BY LOSSES. '75 (eddy currents). Hysteresis is the chief loss and has most weight in determining a and b. Hysteresis loss*, and hence the values of a and b, are affected by wave form. It will be understood that the hysteresis exponent 1.6 is not a constant but represents a fair average value for moderate ranges of flux densities; at high densities the hysteretic exponent may have a value as high as 2 or more. 52. One-Foliage and One-Frequency Method. If a and b are known, it is possible, having determined the core loss at one voltage for a particular frequency, to compute the core loss for any other voltage and frequency. It then becomes unnecessary to test a trans- former at the exact rated voltage and frequency which is indeed difficult to do. Taking as average values a =1.666 and b = .4474, correction factorsf for variation of core loss with frequency and voltage are given in the following tables. CORRECTION TABLES. VARIATION OF CORE Loss WITH VOLTAGE. Volts (per cent, normal) 90 95 96 97 98 99 100 Core loss 83.7 91.7 93.3 95 96.7 98.4 100 Volts (per cent, normal) 101 102 103 104 105 no Core loss 101.6 103.3 105 106.6 108.3 116.6 VARIATION OF CORE Loss WITH FREQUENCY. Cycles 55 56 57 5$ 59 60 6 1 62 63 64 65 Loss 103.9 103.12 102.3 101.6 100.8 100 99.3 98.5 97.8 97 96.4 53. Separation of Hysteresis and Eddy Currents. To determine the eddy current loss in watts, the core loss is. to be measured at two frequencies and at the same flux density. Let W be total core loss at normal voltage E' and frequency n 1 '. At a lower frequency n" and a * (5ia). When the wave of electromotive force is peaked, the maxi- mum flux density and the core loss are less. t (52a). These are taken from a series of tests made in 1899 by W. F. Kelley and H. Spoehrer (see thesis, Cornell University Library). The transformers were small (1-15 K. W.) and were designed for 60 cycles and over. The writer has no data on most recent transformer iron. These tests also showed that each per cent, variation in voltage caused about .7 per cent. (.6945) variation in exciting current. i7 6 TRANSFORMERS. [Exp. n" lower* voltage E" = , E f , let the core loss be W". We may com- pute the watts eddy current loss at the higher frequency (n r ) and normal voltage by the formula W 4 W" Watts eddy currents = Eddy current loss is substantially the same for all frequencies, but varies as the square of the voltage and so can be computed for any frequency and voltage. Hysteresis loss is found by subtracting eddy loss from total loss. * ( 53a). If the wave form of electromotive force for the two frequen- cies is different, E" = (n"f 4- rif'}E', where the form factor / is the ratio of the effective to the average value. (For a sine wave, /=i.i.) The eddy current loss in watts at the higher frequency n' and normal voltage is then The above equations can be derived as follows : Eddy current loss, irrespective of frequency and wave form (49), varies as E 2 and equals aE 2 , where a is a constant. Similarly, for any wave form, hysteresis loss equals bnB*, where b and x are constant ; no assumption is made that x= 1.6. At the two frequencies the total losses are (1) W = a(E'Y+bn' (BT; (2) W" = a(E"Y + bn"(B"Y. For B", write B', this being the condition of the test; for E", write E'(E"-^E'). Multiply (2) by n' -=- n", subtract from (i) and solve for eddy current loss a(E') 2 . When the wave form of electromotive force is the same at the two frequencies, (E" -- E'} = (M"-T-W')- The separation of losses by measurements at two frequencies was first made by Steinmetz ; the influence of form factor was introduced by Roessler. There are various methods for making the calculations, differ- ing somewhat in detail. The formulae here given are from a paper by the author before the Cornell Electrical Society, May 4, 1898. Note 35, Exp. 5-A, and Appendix L, Exp. 2-B ; also Bedell's Transformer, p. 312 et seq. (Some of these references, following Roessler, use form factor as the reciprocal of /, as defined above.) M. G. Lloyd has recently pub- lished a very complete investigation of the subject; see Bull. Bureau oj Standards, February, 1909. 5-B] TEST BY LOSSES. i?7 54. Insulation and Temperature Tests. These tests are of com- mercial importance but need no full discussion here. The Standardi- zation Rules specify fully the conditions under which they are to be made; details of the tests are described in the usual handbooks. 55. Insulation. The insulation is tested between each winding and all other parts. The applied voltage is increased gradually, so as to avoid any excessive momentary strain. This is usually done by some means of primary control in a special testing transformer. Various companies make testing transformers for obtaining high potential for this test and furnish detailed instructions for their use. The voltage is preferably measured by means of a spark gap with a high protective resistance in series with it. The test consists in seeing that the apparatus withstands a specified over-voltage for a specified time without breaking down. 56. H eat Runs. These are made under full-load voltage and full-load current for a specified time, temperatures being found by thermometers and resistance measurements. The heat run could be made by actually loading the transformer, but is usually made by some kind of opposition or pumping back method, of which there are several. No load is then required and no power, except enough to supply the losses. A common form of opposition run employs two similar trans- formers: the two secondaries (low potential side) are connected in parallel to source A, of normal frequency and normal voltage, which supplies the core loss; the two primaries are connected in series, opposed to each other, and are then connected to source B, which supplies the normal full-load current. (Source B requires a voltage equal to twice the impedance voltage of one transformer and can be of any frequency, i. e., it may or may not be the same frequency as A.) All windings now have full-load current and normal voltage. Instruments in A will give, if desired, the core loss and exciting current; instruments in B will give copper loss and impedance voltage. Instead of connecting source B in the high potential side, a com- mon modification is to connect the high potential windings of the two transformers directly in opposition and to insert source B in series with the low potential winding of one of the transformers. This has 13 I7 8 TRANSFORMERS. [Exp. the advantage that all connections with supply lines and instruments are at low potential; see Electric Journal, p. 64, Vol. VI., and Fig. 322, KarapetofFs Exp. Elect. Engineering. A modified form of opposition test can be applied to a single transformer; see Foster's Handbook. 57. Note on Efficiency. If the rated secondary voltage is 2 =ioo, the customary and most simple procedure is to take the core loss for this voltage from Fig. 5 (thus, W Q = ^i. 6) and to compute the full load efficiency as in 31. To be accurate, however, the secondary core voltage or flux voltage, E s , should be taken as E 2 plus the secondary RI drop. Taking this drop as 1.28 (%r in 35), we have E s 101.28 and the corresponding core loss, W = 42.5; this gives the correct efficiency of 95.51 instead of 95.56. The difference between these values is so little that the method of 31 is usually sufficiently correct. Approached in another way, we might consider E B = 100 and W = 4i.6. Then 2=1001.28 = 98.72. To get the rated out- put of 2 K. W., since E 2 is decreased, the current must be increased by the factor I -f- 98.72. The copper loss must then be increased by the factor (i -=-98.72) 2 , giving an efficiency of about 95.5. 5-C] CIRCLE DIAGRAM. 179 EXPERIMENT 5-C. Circle Diagram for a Constant Poten- tial Transformer. i. Introductory. It has been seen, Exp. 4-6, that when the resistance is varied in a series circuit with constant reactance the vector representing the current follows the arc of a circle as a locus. In a similar manner, the primary current of a con- stant potential transformer follows the arc of a circle as a locus when the secondary resistance is varied. The same is true for an induction motor when its load is varied, and use is made of this fact in practical motor testing. The following experiment will, accordingly, serve to make clear certain principles of the induction motor as well as of the transformer; upon these prin- ciples is based the method of transformer testing developed in detail in Exp. 5-B. In Part I. the general principles governing the action of a transformer will be discussed; in Part II. these principles will be applied in constructing a circle diagram. The practical re- sults, so far as commercial testing is concerned, are all given in Exp. 5-B. The actual construction of a diagram to scale gives one a definite and concrete idea of what might otherwise be vague and abstract. Furthermore, the abstract diagrams given here (Figs, i-n) and elsewhere are so grossly exaggerated that they give very wrong ideas of real values. Even Fig. 12, which is more nearly to scale, is much exaggerated. 2. Data. The same data are required as in Exp. 5-6. See 25 of this experiment. PART I. GENERAL DISCUSSION OF THE ACTION OF A TRANSFORMER. 3. The action of a transformer will be most readily under- stood by considering its action first without a load i. e., on open circuit and then with a load. iSo TRANSFORMERS. [Exp. 4. Transformer on Open Circuit. When a transformer is on open circuit, the secondary winding has no current flowing in it and it accordingly has no magnetizing effect on the core. A small current flows in the primary which magnetizes the core. Let us see what determines the magnitude and phase of this open-circuit primary current. 5. Assuming No Core Loss. The open-circuit diagram for a perfect transformer, in which there are no losses, is shown in Fig. i. The primary electromotive force Ep causes a current J to flow and this current sets up a flux <. This flux, being alternating, causes a counter-electromotive force opposed to the primary impressed electromotive force. When the primary cir- cuit is closed, the current / , and the flux which it sets up, assume such values that the counter-electromotive force is just equal* to the impressed electromotive force. This primary counter-electro- motive force has, at any instant, the value e' = S^dQ-t-'dt), the equal and opposite im- pressed electromotive force be- ing e P = S 1 (d^-dt). It will be seen that the electromotive force is zero when the flux is a maximum and that the flux < lags 90 behind the impressed electromotive force EP, as in Fig. i. 6. In the absence of core loss, the current 7 is in phase with the flux <, which it produces. When permeability is constant, magnetizing force H is proportional to / and is in phase with \ * The primary resistance on open circuit is very small and can be neglected. Flux( Phase of ~B and H FIG. i. Open-circuit diagram for a transformer with no core loss. 5-C] CIRCLE DIAGRAM. 181 and proportional to the flux density B. The B-H curve is a straight line, instead of the familiar hysteresis loop, and there is no hysteresis loss. The current / , as shown in Fig. I, is in quadrature with the electromotive force and is wattless. 7. The flux links with the secondary circuit and induces in the secondary an electromotive force ES, lagging 90 behind the flux. The instantaneous value of the secondary electro- motive force is e$ = S 2 (d-+- dt). It is seen that Es is ex- actly opposite to EP in phase and is equal to Ep, multiplied by (S 9 -*-S& 8. The flux throughout this discussion refers to the flux which links with both primary and secondary, and Ep and Es are the induced or flux voltages,* proportional to . In an ideal transformer there is no other flux, but in an actual trans- former there is, in addition to this main flux, a relatively small local or leakage flux, which links with the turns or part of the turns of one winding only and causes a reactance called leakage reactance. On account of the drop due to leakage reactance and the drop due to the resistance of the transformer windings, as discussed later, the terminal voltages, E 1 and E 2 , are slightly dif- ferent from the flux voltages EP and E$. * ( 8a) . Strictly speaking Ep is not the flux voltage but is equal and opposite thereto. Core-loss J H Component '. r arfA O -B Magnetising Component Flux> FIG. 2. Open-circuit diagram for a transformer with core loss, show- ing the two components of exciting current and the angle a of hysteretic advance. 102 TRANSFORMERS. [Exp. 9. With Core Loss. A transformer with an iron core differs from the ideal transformer just discussed because there is a loss in the iron due to hysteresis and eddy currents. The open- circuit diagram now becomes as shown in Fig. 2. The flux is still in quadrature with EP and Es, in accordance with Faraday's fundamental law of induced electromotive force, e S(d(f>^-dt). The exciting current 7 , however, can no longer be a wattless quadrature current, for it must have an in-phase power component to supply the core losses due to hysteresis and eddy currents. This core loss component is / H = watts core loss-^Ep. The exciting current 7 is, accordingly, advanced in phase by an angle a, called the hysteretic* angle of advance. It is seen, therefore, that 7 consists of two components the core loss component 7n and the true magnetizing component 7n which is wattless and in phase with the flux. The total ex- citing currentf is the vector sum of these two components : 10. A constant potential transformer (one in which EP is constant) is a constant flux transformer. It therefore follows * (9 a )- As here defined, this angle includes the effect of eddy currents. t(Qb). The exciting current of a transformer is distorted, i. e., has a wave form different from that of the electromotive force, on account of harmonics introduced by hysteresis. (See Appendix II., Exp. 6-A.) These harmonics currents of 3, 5, 7, etc., times the fundamental fre- quency are necessarily wattless. They do not appear, therefore, in the power component In, but are included in the wattless component /M. Strictly speaking, alternating currents in which harmonics are present can not be represented by vectors in one plane ; for practical purposes, how- ever, the plane vector diagram, as here given, is sufficiently accurate. (See 47, Exp. 6-A; also "The Effect of Iron in Distorting Alternating Current Wave Form," by Bedell and Tuttle, A. I. E. E., Sept., 1906; and " Vector Representation of Non-Harmonic Alternating Currents," by B. Arakawa, Physical Review, 1909.) These harmonics have the same value at all loads; at full load they form such a small part of the total current that the distortion which they produce is very small. 5-C] CIRCLE DIAGRAM. /Circle Locus, Primary that 7 , /H and /M are constant, and remain constant under all loads. This would not be quite true in a transformer in which the primary line voltage E l (and not Ep) is constant ; the difference in the two cases is very small. ii. Transformer Under Load. The complete diagram for a constant potential transformer un- der non-inductive load is shown in Fig. 3. This will be seen to be exactly the same as Fig. 2, the open-circuit diagram, with certain additions. As in Fig. 2, we have the electromotive forces EP and E$ opposite to each other in phase and in quadrature with the con- stant flux (f>. On open circuit, the primary current / flows as al- ready discussed. 12. Secondary Quantities. When the secondary circuit is connected to a load, a secondary current I 2 flows, the value of which depends upon the load. With non-inductive load, this current would be in phase with E$, if the transformer were perfect. On account of leakage reactance, X 2 , the current I 2 lags a little behind E$, as shown in Fig. 3. It is to be kept in mind that Fig. 3 and other diagrams here given are not at all to scale, being exaggerated in order to show more clearly the rela- tions between the various quantities. / Circle Locus of / Secondary Current / FIG.. 3. Complete diagram for a transformer under non-induc- tive load. When a current 7 2 flows in the secondary, a load current I i2) flows in the pri- mary, opposite in phase and of equal ampere turns. 7 2 = /< 2) X ratio of turns. lS 4 TRANSFORMERS. [Exp. The secondary terminal voltage, E 2 , is a little (perhaps one per cent.) less than E$ on account of reactance drop X 2 I 2 , and resistance drop RJ 2 , the former in quadrature and the latter in phase with 7 2 . For a non-inductive load, the secondary cur- rent, 7 2 , is in phase with the terminal voltage, E 2 . (For an inductive load, 7 2 would lag behind E 2 by an angle 6, where cos 6 is the power factor of the load.) 13. In the secondary, it is seen that Es is constant (flux being constant) and the secondary may, accordingly, be treated as a simple constant potential circuit. The locus of the secondary current, as the load resistance varies, is, accordingly, the arc of a circle, as in any constant-potential circuit with constant react- ance. (See Exp. 4-B.) 14. Primary Quantities. It has been seen that on open cir- cuit the primary current assumes a certain value 7 , so as to produce a flux that generates a counter-electromotive force just equal and opposite to the impressed electromotive force. When a secondary current 7 2 flows, it disturbs this equilibrium by tending to demagnetize the core. This allows more current to flow in the primary. The primary current increases until (in addition to 7 ) a current 7 (2) flows in the primary, the magnet- izing effect of which (ampere turns) just balances the magnet- izing effect of the current 7 2 in the secondary. The magnet- izing effect of the secondary being thus neutralized, the flux has the same constant value as before (as though produced by 7 alone), so that the counter-electromotive force produced by the flux continues to be just equal and opposite to the impressed elec- tromotive force. In Fig. 3, the total primary current I lt is seen to be composed of the constant 7 (which is small) and the load current 7 (2) , which is opposite to the current 7 2 in the secondary and equal to 7 2 multiplied by ( S 2 -=- S 1 ) . In a i : I transformer, the pri- mary load current 7 (2) is equal to the secondary current 7 2 . 5-C] CIRCLE DIAGRAM. 185 15. Fig. 4 shows that, in a loaded transformer, the resultant ampere turns are constant; hence the flux is constant, so that the counter-electromotive force irrespective of load equals, the impressed electromotive force. As the load changes, the primary cur- rent assumes such a value that the resultant ampere turns remains constant and this condition of equilibrium is maintained. 16. The primary electromotive force, thus balanced by the counter-electromotive force, is Ep. Referring to Fig. 3, it will be seen that the terminal impressed electromotive force, E 15 is a little greater (say one per cent, greater) than Ep, on account of the R^^ and XJi drops, due to primary resistance ance. 17. The locus of the secondary current I 2 is the arc of a circle (13). Hence the locus of the primary load current, 7 (2 ) in Fig. 3, is the arc of a circle. The total primary current, /!, measured from O to P, follows this same locus. Some simplified diagrams will now be discussed. 1 8. Representation of Transformer Circuits. From the foregoing discussion, it will be seen that the circuits of a trans- former may be represented as in Fig. 5, in which the resistance and leakage reactance of the two windings are considered as external to the transformer. Furthermore, the exciting cur- rent, 7 , is considered as flowing in a shunt circuit, also external to the transformer. This shunt circuit consists of two branches : FIG. 4. Diagram of ampere and to leakage react- turns; the resultan t am P ere turns are constant. 1 86 TRANSFORMERS. [Exp. a non-inductive branch for the in-phase component, /H, and an inductive branch (without resistance) for the wattless quadra- ture component /M. The currents which would flow in such equivalent shunt circuits correspond exactly to the currents / , /H and /M which actually flow in a transformer. Load FIG. 5. Complete equivalent of a transformer. The exciting current / is considered as flowing in a shunt circuit. The resistance and leakage react- ance of primary and secondary are considered as external. Corresponds to Fig. 3. 19. The transformer proper, in Fig. 5, is considered as ideal, all the losses being treated as external; I (2 )=I 2 (S 2 -^-S 1 ) ; and Ep=:Es(S lL -T-S 2 ). The voltage at the primary terminals, E 19 is more than Ep on account of the drop in X and in R^. Likewise, the voltage at the secondary terminals, E 2 , is less than ES on account of the drop in X 2 and in R 2 . *1 ^JWJtr-A/VV\rt--i Load Mi FIG. 6. Equivalent circuits as level (i : i) transformer. Corresponds to Fig. 7. The total primary current 7 is seen to be equal to the load current 7 (2) , plus (vectorially) the small no-load current / . 20. Equivalent Circuits. The circuits of a transformer may be represented more simply by the equivalent circuits of Fig. 6, 5-C] CIRCLE DIAGRAM. 187 in which all quantities are expressed in terms* of the primary. This will be most readily understood by treating the transformer as a "level" (1:1) transformer; we have then, Ep = E$; and The diagram corresponding to Fig. 6 is shown in Fig. 7 and is seen to be the same as Fig. 3 with all secondary quantities expressed in terms of the pri- mary and drawn in the first quadrant. 21. Simplified Circuits. The equivalent circuits so far considered (Figs. 5 and 6) and the corresponding diagrams (Figs. 3 and 7) are prac- tically exact and may be used for the accurate solution of any transformer problem. It will be noted that the resistance and reactance for the two wind- ings are treated separately, R^XI in the primary and R 2 X 2 in the secondary. By com- bining these into a single equiv- alent R and X, the trans- former circuits can, with little error, be simplified in either of two ways : *(2oa). To express secondary quantities in terms of the primary: multiply current by (Sz-^Si) ; multiply voltage by (Si-^S 2 } ; multiply X and R by (Si-=-S 2 ) 2 . See i6a, Exp. 5-B. It will be understood that secondary quantities thus represented in the primary are not the real secondary quantities but the equivalent primary quantities which could produce the same results ; thus, in a 10 : 1 transformer, i ohm in the primary is equivalent to o.oi ohm in the secondary. To express primary quantities in terms of the secondary, divide instead of multiply by these factors. FIG. 7. Exact diagram as level transformer, corresponding to Fig. 6. The same as Fig. 3 with secondary quantities expressed in terms of the primary. i88 TRANSFORMERS. [Exp. i. All the resistance and leakage reactance are considered to be in the primary, as in Figs. 8 and 10. 7? i T B I __ x i ** R * t p a yw\r r TOfflF>^^ i L Ijmi Load ami FIG. 9. Simplified circuits; R and X all in secondary. Corresponds to Fig. u. R and X, this current being either 7 t (as in Fig. 8) or 7 (2) (as in Fig. 9). If 7 were zero, Figs. 8 and 9 would not differ from Fig. 6, and all the representations would be identical. In fact, 7 is so small that either simplification and its resultant diagram, Fig. FIG. 8. Simplified circuits; R and X all in primary. Corresponds to Fig. 10. 2. All the resistance and leakage reactance are considered to be in the secondary, as in Figs. 9 and n. Each of these simplifications differ very little from the more exact representations already discussed. In the actual transformer, as represented in Fig. 6, it is seen that the current which flows through X 2 R 2 is 7 (2) , while a dif- ferent current I (slightly larger, due to 7 ) flows through X^R^. In the simplifications, the same current is considered to flow through R^X-L and R 2 X 2 which are now combined into a single 5-C] CIRCLE DIAGRAM. 189 10 or n, may, for most practical purposes, be considered as correct. This makes it possible to use the single equivalent values for R and X obtained by the short-circuit test of Exp. 5-B, and does not require separate values of R and X for the primary and sec- ondary circuits. 22. Again, the voltage which causes EI I to flow is EP, as is seen in Fig. 6. In the simplifications, this voltage is taken as E 2 (Fig. 8) which is, say, I per cent. less, or as E^ (Fig. 9) which is, say, i per cent, more than the value of Ep in the actual cases of Fig. 6. This would make an insignificant change in the value of 7 which is itself small. In the latter case 7 depends only upon line voltage and is independ- ent of load. 23. Diagrams Compared. Let us FlG> I0> simplified dia- compare the exact diagram, Fig. 7, with gram; R and X all in pri- ,, . ,.,- T^. mary. Corresponds to Fig. 8. the simplifications, Figs. 10 and n. In Fig. 7, the primary and secondary RI drops are in phase with /! and 7 (2) , respectively, the XI drops being in quadrature. The phase difference between 7 t and 7 (2) is small much smaller in fact than shown in the figure. The primary and secondary drops may, accordingly, be combined with little error. This may be done by taking the combined resistance drop in phase with 7 t (Fig. 10), or in phase with 7 (2) (Fig. n). The com- bined reactance drop is, in each case, at right angles to the combined resistance drop. In an actual case little error is introduced by these simplifications and either may be used, as is most convenient. 190 TRANSFORMERS. [Exp. PART II. THE CIRCLE DIAGRAM AND ITS CONSTRUCTION. 24. The circle diagram for a transformer shows the varia- tion in the primary current for different values of load resist- ance with constant impressed voltage. In Fig. n, the primary "~ Circle Locus ol Primary Current Flu** FIG. ii. Simplified diagram; R and X all in secondary. Corresponds to Fig. 9. current is OP, being composed of the no-load current OA and the load current AP. As the load resistance is decreased from in- finity to zero, the point P will trace the arc of a circle, and will take the position P" on short circuit.* If it were possible to elimi- nate the resistance of the transformer windings, the point P * (243). If a transformer is constructed so as to have a large leakage reactance (or if a reactance is included in the circuit external to the transformer), the' short-circuit current and the diameter, E^-^X, are reduced. The transformer may then be operated at or near short circuit, in which case the current will be nearly constant. This method is used for obtaining constant current from a constant potential line. (See 4a, Exp. 5-A.) Large reactance or magnetic leakage in any apparatus tend towards constant current operation. See 8, Exp. 3-A, 27, 273, Exp. 3-B, and 14, Exp. 4-6. 5-C1 CIRCLE DIAGRAM. 19 l would complete the semi-circle and assume the position P'" t the current in this case (E^-~X) being limited only by the leakage reactance, X. The short-circuit current of a transformer oper- ated at full voltage would be, however, greatly in excess of the carrying capacity of the transformer windings, and, in actual operation, the point P does not go far beyond the full-load point P'. See also Fig. 12, which is more nearly to scale. 25. Data Necessary. The data necessary are the values of / , /H and /M, to locate the point A, and the leakage reactance X, to determine the diameter of the semicircle. f These data are obtained from the open-circuit and short-circuit tests of Exp. 5-B. I IP' All quantities are to be in terms of the pri- mary (high-potential) side; thus, in Fig. 2. Exp. 5-B, the values of 7 , /H and /M, meas- I pi ured on the loo-volt coil, are divided by 20 to obtain the corresponding values for the 2,000- volt primary. This give us: / = -03025 ; /H = .0208 ; /M = .0220. The reactance X for the same transformer, is 35.2 ohms; see Fig. 7, Exp. 5-8. 26. Construction of Diagram from Experi- mental Data. From the data given above, lay off (Fig. 12) : ~ FIG. 12. Con- , ,., . , ~ . r struction of cir- OB = / H ; BA=I M ; OA=I V cle diagram. The diameter of the circle is E. L ~X = 2,000-^-35. 2 ^56. 8 amperes. The radius p = E^ -+- 2 X = 28.4. These values are large compared with'/ =>.O3 and full-load current 7 (2) = i ampere. It is, accordingly, not practicable to construct the whole semicircle, as in Fig. n, which is not at all to scale. 1 9 2 TRANSFORMERS. [Exp. For a working range it can be readily constructed, as in Fig. 12, which is more nearly to scale, as follows: Lay off A'D = I (2) for T fo, T V, J, J, f, i and ij load. (It is to be noted that, in Fig. 12, the angle DAP is small ; hence AD is taken as practically equal to AP or / (2) .) Thus, for a 2,000- volt, 2 K.W., transformer, AD is laid off, successively, equal to .01, o.i, .25, .50, .75, i.o and 1.25 amperes. For each value of AD, the point P is located by laying off = p Vf Aff which can be derived from the figure and is the equation of a circle referred to A as an origin. The line DP represents the quadrature component of primary current due to leakage re- actance. This is always small and would be zero when X = o t for the diameter of the semicircle (see Fig. n) is then infinite. The power component AD is, therefore, practically equal to AP. It is to be noted that and OC=OB + AD. From these values, compute* for different loads Primary current = OP = VOC+ C? . Power factor =OC-- OP. The curves in Fig. 4, Exp. 5~A were thus computed. Note . 4ia, Exp. 5-B. * (26a). It will be seen, also, that Watts input, ZTi = OC X 1 ; Watts output, W-i = Wi losses ; This gives a possible method for determining the total voltage drop. 5-C] CIRCLE DIAGRAM. J 93 APPENDIX I. NOTE ON REGULATION. 27. Definition of Terms. Regulation is defined by the Institute as follows: In constant-potential transformers, the regulation is the ratio of the rise of secondary terminal voltage from rated non-inductive load to no load (at constant primary impressed terminal voltage) to the secondary ter- minal voltage at rated load. (Compare 34, Exp. 5-B.) If the secondary terminal voltage is E Q at no load and E 2 at full load, the regulation is, Regulation^ (E E 2 ) --E 2 The drop on which regulation depends is E ,, which we may term the regulation drop. This drop, expressed as per cent, of E 2 , i gives the regulation. 28. The total voltage drop, in terms of a I : I transformer, is E^ E 2 and is a little more than the regulation drop, because E l is a little more than E on account of the drop due to exciting current in the primary winding. The per cent, voltage drop is (E 1 2 ) -=-.,, taking E 2 as 100 per cent.; or, (, ,) -t-E lt taking E l as 100 per cent. 29. Numerically, the difference between' " regulation " and " per cent, voltage drop " is small. In earlier usage,* the term regulation was commonly employed to designate " per cent, voltage drop." This confusion is one cause for the differences between various methods which have been used (and still are used) for determining regulation. A difference arises, also, according to whether t or E 2 is taken as 100 per cent. *(2ga). See the following articles, in the Elec. World, on the pre- determination of transformer regulation : Bedell, Chandler and Sherwood, August 14, 1897; A. R. Everest, June 4, 1898; F. Bedell, October 8, 1898. See also Foster's Electrical Eng. Pocket Book, p. 492, fifth edition, 1908. 14 194 TRANSFORMERS. [Exp. 30. An illustration will make this clear. Let ,= 100; = 99.9; 2 = 97- Regulation drop ., = 2.9 volts. Per cent, regulation = 2.9 -=- 97 = 2.99 per cent. Total voltage drop t 2 = 3 volts. Per cent, voltage drop = 3-^-100 = 3 per cent.; or = 3 -+- 97 = 3- 1 P er cent - 31. Regulation drop depends upon the difference between and 2 . This drop is due to load current, and does not include any drop due to exciting current, which affects E and E 2 alike and, practically, does not affect their difference. The total voltage drop depends upon the difference between E l and 2 . This drop is chiefly due to load current, but includes, in addition, a small drop due to exciting current which affects 2 but not x and so directly affects their difference. 32. Computations. To compute regulation drop, we have the problem: Given ,, to compute E . To compute total voltage drop, we have the problem: Given 2 , to compute a . 33. Regulation. For determing regulation, we compute E = V T7+>T~+? ; where in-phase drop =p = RI (2) , quadrature drop =.q = XI (2) . It is seen that exciting current does not enter. The various drops may be expressed either in volts or in per cent. The working details of the method are discussed in 34-43, Exp. 5~B. 34. Total Voltage Drop. For determining total voltage drop, we compute The in-phase drop p, consists principally of /?/ (2) , but includes the small additional terms RJu and XJu, which are drops caused by the two components of the exciting current flowing through X v R r Without much error, X v R^ may be taken as half of X, R. Hence 5-C] CIRCLE DIAGRAM. 195 In a like manner q = XI (2) 4- -^/H The last two terms are small and nearly cancel each other. 35. Other methods of analysis may be employed for determining the total voltage drop, and the form in which the results are ex- pressed will vary according 4:o the manner in which the various terms are combined and the approximations which are introduced. In any case some small and troublesome terms are introduced, which affect the result very little and which do not enter in the determination of " regulation," as denned by the Institute. The results are affected less by these small terms than by variations in the value of R, depend- ing upon whether, in its determination, load losses were included or not, and whether steady temperature conditions were maintained during the test. 36. It might well be held that regulation should be so denned that magnetising current should enter into its determination, particularly since magnetising current has been much increased by the use of improved iron worked at 'higher densities; on the other hand, it is much simpler to define regulation independently of magnetizing cur- rent and to specify the value of the magnetizing or exciting current as a separate item. CHAPTER VI.. POLYPHASE CURRENTS. EXPERIMENT 6-A. A General Study of Polyphase Cur- rents.* PART I. I. Introductory. In a polyphase system, several single- phase currents differing in phase from each other are combined into one system. The circuits for each phase may be independ- ent, without electrical connection, or interconnected. The phase difference between the currents of the several phases is usually 90 or 120, the corresponding systems being called two-phase or three-phase. (a) FIG. i. Two-phase connections for generator or receiver circuits, a, 4-wire system with independent phases. b, 3-wire system. c, Quarter-phase, star- connected ; or, 4-wire system with interconnected neutral, d, Quarter-phase, mesh-connected ; or, ring-connected. To form a polyphase system we must have several sources of single-phase electromotive force which differ in phase by proper amounts. For a symmetrical polyphase system these electro- motive forces must be equal and differ from each other by equal phase angles, as in the 3-phase and quarter-phase systems soon *(ia). In making polyphase measurements, some form of voltmeter and ammeter switches will be found convenient, so that all readings can be made with one voltmeter and one ammeter. The same switches will serve to transfer one wattmeter from one circuit to another. 196 6-A] GENERAL STUDY. ! 97 to be discussed. The sources of these electromotive forces are in principle several rigidly connected single-phase generators, but in practice they are generator coils on a single armature. The secondary coil of a transformer may be considered as a generator coil. The currents from these sources may be utilized separately as single-phase currents (as in lighting), or jointly as polyphase currents (as in an induction motor). (<*) FIG. 2. Three-phase connections for generator or receiver circuits, a, Inde- pendent circuits ; see 3a. b, Star- or F-connected. c, Mesh- or delta- (A) connected. d, T-connected. e, F-connected ; or, open delta. 2. The load on a polyphase system is balanced when each phase has an equal load with equal power factor. In a balanced polyphase system the flow of energy is uniform, which is a bet- ter and more general definition of such a system; (see Steinmetz, Alternating Current Phenomena). In a single-phase system or unbalanced polyphase system, the flow of energy is pulsating, discussed further in I, Exp. 7-A. The torque is, accordingly, pulsating in all single-phase machinery; whereas it is uniform in polyphase motors and in polyphase generators on balanced load. Furthermore, a polyphase induction motor on account of its rotating field can be given a good starting torque, whereas a single-phase induction motor has none in itself and has only a small starting torque when auxiliary starting devices are used. Polyphase machinery has a greater output than single phase for a given size, or has a smaller size for a given output. These features, together with the copper economy of 3-phase as com- pared with single-phase transmission, all favor the use of poly- phase systems ; see Appendix III. I9 S POLYPHASE CURRENTS. [Exp. 3. Methods of Connecting Phases. Generating or receiving coils or circuits may be combined in various ways, the common ones being shown* diagrammatically in Figs. I and 2. In Figs. I and 2, the relative positions of the various coils represent the relative phase positions of their several electromotive forces.f The black dotsj may be taken as line wires in cross-section. On paper the distance between any two dots is the difference of potential between them ; phase, as well as magnitude, is shown in this way. To the same polyphase system, a number of differently con- nected polyphase generators and receivers may be connected at the same time ; thus, on a 3-phase system, some apparatus may be delta- and some star-connected. From a 4-wire 2-phase system, induction motors may be run simultaneously when connected as (a), (c) or (d), Fig. i. Connection (b) can be combined on the same system with (a), but not with (c) or (d). This is an objection to 3~wire 2-phase distribution, inasmuch as synchron- ous motors and converters as well as generators are frequently wound quarter-phase and so cannot be run from a 3-wire system. A further objection, that the line drop in the common wire makes the voltages unsymmetrical, is discussed later, 14. 4. Object. In performing this experiment, the object is to gain a knowledge of the connections of polyphase circuits and polyphase apparatus, and to understand their electrical relations and various diagrammatic methods for representing them. Make a study of whatever polyphase supply circuits are available and by means of transformers obtain, so far as possible, all the systems indicated in Figs. I and 2. * (3 a )- The arrangement of Fig. 2 (a) is never used for independent 3-phase circuits ; it is used only for connecting transformer secondaries to so-called 6-phase synchronous converters, 27. f(3b). Although the diagram of connections can not in general be taken as the vector diagram of electromotive forces, this can be done in the simpler cases and makes the introduction to the subject more clear. $ (3c). This representation by dot's is called by Steinmetz the topo- graphic method. 6-A] GENERAL STUDY. 199 Note also the connections on various pieces of polyphase apparatus (as generators, motors, etc.) which may be available, and note for what kind of polyphase system the apparatus is intended. PART II. 5. Two-phase Measurement. Take two transformers* with the same ratio of transformation (say 1:1). Connect the primary of one transformer to phase A of a 2-phase circuit,f and the primary of the other transformer to phase B. Measure the secondary voltages when the secondary circuits are inde- pendent, thus forming a 4~wire system with independent phases, Fig. i (a). 6. Addition of Electromotive Forces. Connect the two sec- ondaries as a 3-wire system, Fig. I (&), and measure the voltage of each phase (A and EB) and the voltage E between outside wires. Lay off these voltages as a triangle and note how nearly EA and EE are at right angles, so making a true 2-phase system. This triangle may be drawn as in Fig. 3, 4 or 5. FIG. 3. Topographic method. FIG. 4. Addition method. FIG. 5. Subtraction method. 7. If we use the topographic method of Steinmetz and omit arrows, we can represent the electromotive forces of the 2-phase 3-wire system by Fig. 3 (see Appendix I.). This electromotive * It is preferable that each secondary consists of two equal coils : thus, we might have primary no volts; secondaries 55 volts each, giving in series no volts with a middle or neutral point. Note the various possible voltage transformations for each transformer. t It matters not whether the supply circuit is 3-wire or 4-wire, or how connected. If several kinds of supply circuits are available, use each one in turn. Compare Fig. 6. 200 POLYPHASE CURRENTS. [Exp. force diagram is seen to be similar to the circuit diagram (b) of Fig. i. 8. If we take one outside line, say B, as our starting point (imagining if we wish that it is grounded, but this is unneces- sary), we have the electromotive forces EE and A represented by the vectors, BO and OA, in the direction shown by arrows in Fig. 4. The sum of these two vectors is BA. 9. If, as is common, we take the neutral O as the starting point (say ground), the differences of potential between the side wires and ground are OA and OB, the direction of the vectors being from the starting point as in Fig. 5. The difference in potential between A and B is now the difference between OB and OA, Fig. 5; which is the same as the sum of BO (equal -OB) and OA, Fig. 4. 10. In general, if we take electromotive forces in sequence as BO, OA they must be added (Fig. 4) ; if, however, we con- sider each electromotive force in a direction away from a com- mon joining point as OB, OA they must be subtracted (Fig. 5). For the simple case at hand, involving only two elec- tromotive forces connected to a common point, the difference method may be readily applied. For more complicated networks the addition method is used, as it is capable of more general application ; it is based on the statement of Kirchhoff 's Law ( 32, Appendix I.) that the differences of potential around any mesh add up to zero. For this addition method, all arrows are taken consecutively, from feather to tip. ii. If each transformer has a secondary winding, consisting of two equal coils, connect the secondary coils of the two trans- formers so as to form a star-connected and a mesh-connected quarter-phase system, as in (c) and (d) of Fig. I. Measure all voltages and draw diagrams of voltages for the star and for the mesh connection. In the mesh connection, the two secondaries of one trans- former are connected as the opposite sides of a square, -due 6-A] GENERAL STUDY. 201 attention being given to polarity; the two secondaries of the other transformer form the remaining two sides. Before clos- ing the square, connect a voltmeter between the two points about to be connected and proceed to connect them only in case the voltmeter reads zero. This precaution should be taken in mak- ing any mesh connection. 12. A convenient laboratory supply board is obtained from 2-phase secondaries, the secondary circuit on each phase consist- ing of four equal coils in series so as to form a 5-wire system on each phase. With the neutrals of the two phases intercon- nected, this gives supply voltages, as Fig. 6. If the total volt- age of each phase is 220 volts, this gives 2-phase voltages as follows: 4-wire no and 220 volts; 3~wire 55, no, 77.8 and 155.6 volts; also additional single-phase *i i voltages, 123 and 165 volts. The voltage between any two points can be scaled off from the drawing in Fig. 6, as shown in the discussion of Figs. 3, 4 and 5. When FlG - 6. Two-phase , , j , , laboratory supply volt- the transformer secondaries cannot be so ages. subdivided, the result can be obtained by connecting across each phase of a 4-wire system an autotrans- former made of four equal coils. Verify these voltages by calcu- lation or by measurement. The preceding study has brought out the fact that in poly- phase circuits, the single-phase voltages of interconnected gen- erator or receiver coils are combined geometrically to give re- sultant voltages. Although this was shown particularly for 2-phase circuits, it will be understood to be general and to apply as well to a 3-phase circuit or to any circuit whatsoever. 13. Addition of Currents. Currents, also, when of differ- ent phases, are added* vectorially to obtain the resultant current. To show this proceed as follows: * Branch currents, flowing to or from a common point, always combine by addition not by subtraction to give the total current. See Appendix I. 202 POLYPHASE CURRENTS. [Exp. From a 3-wire 2-phase supply, connect two resistances as load, one on each phase. Measure the currents, I A and IE, in each resistance and the total current / in the common conductor. If the two currents I A and IE differ in phase by 90, we will have /= V^A 2 + /B 2 . This will be true for an inductive as well as A for a non-inductive load, provided the load on each phase has the same power factor, i. e., OA = OE. If EA and E E are not at right angles, or OA and OE are not equal, the currents I A and IE will no longer be at right angles; the branch currents will still, however, add as vectors to give the total current, as in Fig. 7. 14. Line drop. To illustrate line drop, with the same circuits and re- sistances just used, insert a small additional non-inductive resist- ance in the supply wires to represent resistance in a long supply line. Construct a triangle OAB for the supply voltage and O'A'B' for the delivered voltage for the following three cases: A A' FIG. 7. Addition of currents. O IB B' B FIG. 8. Resistance in FIG. 9. Resistance in FIG. 10. Resistance in lines A and B. common conductor. all three lines. With resistances in lines A and B only, Fig. 8; With a resistance in the common conductor O only, Fig. 9; With resistances in all three lines, Fig. 10; in this third case measurements of voltages O'A and O'B are also to be taken. For the first case (Fig. 8), the supply voltages, OA and OB, 6-A] GENERAL STUDY. 203 shrink to the delivered voltages, OA' and OB' \ the drop due to resistance in lines A and B is in phase with the currents /A and IE- There is the same phase difference (90) between the deliv- ered voltages as between the supply voltages. For the second case (Fig. 9), the line drop in the common conductor is in phase with I, and it is seen that, on account of this drop, the phase angle between the delivered voltages is greater than between the supply voltages. This, also, is true in Fig. 10. This lack of symmetry in delivered voltages is one dis- advantage of the 3-wire system; see 3. 15. These diagrams illustrate the topographic or mesh method for representing electromotive forces. The direction assigned to any line depends upon the sense in which it is taken. Resistance drop consumed by resistance is in phase with cur- rent; resistance drop produced by a resistance is opposite to the current, as discussed in Exp. 4~A. It is taken in this latter sense in applying the mesh principle, Law (i) of Appendix I. that the electromotive forces around any mesh have a vector sum of zero and can be represented as a closed polygon. Thus, in Fig. 10, proceeding around the mesh OAA'O', we have the fol- lowing electromotive forces : OA produced by the generator ; AA' produced by resistance in line A and opposite to /A; A'O' the counter electromotive force produced by the load (the elec- tromotive force delivered to the load being O'A') ; O'O pro- duced by resistance in the common line O and opposite to 7. The line drop for a single-phase circuit can be similarly repre- sented. With inductance in the lines, besides the resistance drop just discussed, there is a reactance drop at right angles to the cur- rent; this reactance drop is 90 ahead of the current when con- sidered as consumed by reactance, and 90 behind the current when considered as produced by reactance. (See i8a and Fig. 2, Exp. 4-A, and Figs. 3, 4 and 5, Exp. 3-B.) 1 6. The line drop diagram, Fig. 10, is true for any 3-wire 204 POLYPHASE CURRENTS. [Exp. system, and may be applied to a 3-phase system by making the triangles more or less equilateral. A 4-wire system or any other system can be treated in a similar manner. Furthermore, the method just discussed for treating the effect of resistance drop and reactance drop in line conductors is not limited to non-inductive loads, but is applicable as well to other loads, either with leading or lagging currents. (See 56. Exp. 3-B.) 17. Conclusion. In the main it has been seen that 2-phase circuits are essentially the same as two single-phase circuits and can be so treated. Three-phase circuits are likewise essentially three single-phase circuits and the conception of polyphase cir- cuits is thus made simple. In any polyphase circuit the funda- mental principles for the vector addition of currents and electro- motive forces apply as in single-phase circuits. For 3-phase circuits, however, there are modified forms of treatment that are found practically convenient; these will now be considered. PART III. 1 8. Three-phase Measurement. The most important 3-phase connections (Fig. 2) are the star and delta connections, the elec- trical relations of which will first be studied. Other 3-phase connections will then be stud- ied with reference to various arrangements of transformers on 3-phase circuits. 19. Star-connection. On a 3-phase line, connect three approximately equal resist- ances* in star-connection ; see Fig. ii. Measure the line voltages XY, YZ and ZX; these are also called delta voltages * Some measurements should also be made with unequal resistances. Line Vohtage FIG. ii. Star- or y-connection of load resistances. 6-A] GENERAL STUDY. 205 and for clearness may be designated by the subscript D thus, ED. When nothing further is specified than the voltage E of a 3-phase line or machine, it is this delta or line voltage that is meant. Measure* the star voltage Es (called also voltage per phase or phase voltage, 30) from each line to the junction O, Fig. n. Also measure the star current /s for each phase. The line cur- rent is always the star current, as is evident for this case. Compare the measured values of ED and ES with the expres- sion (which should be proved) 20. Compute the power for each resistance. This is obvi- ously, as in a single-phase circuit, equal to the product of volts X amperes (for a non-inductive load), i. e., the product of star voltage and star current (s/s) for each phase. For an inductive load in which the current lags by an angle 6, as in Fig. 12, the power for each star circuit is Es Is cos 0. When ES, Is and 6 are the same for each phase, we can multiply the power for each phase by 3 to obtain the total power; thus, Total power But hence cos 9. = D-^ V3; FIG. 12. Currents and voltages in a star-con- nected 3-phase circuit, radial method of represen- tation. Total power = \/^D/S cos 0. *(iga). If the neutral point of the supply is available, measure the voltage between it and O, and test with a telephone as described in Appen- dix II., 44. This can be done either in connection with the present test or later in connection with Appendix II. 206 POLYPHASE CURRENTS. [Exp/ Since line voltage is ED and line current is /s, we may drop the subscripts and write Total power = V3 El cos 6= V3 El X power factor, where E is line voltage and / is line current. This is the custo- mary formula for power in any balanced 3-phase system, no Line Voltage matter how connected. In the next paragraph it will be de- rived for a delta-connection. 21 Delta-connection. Con- nect the same three equal* re- sistances in delta to a 3-phase supply, as in Fig. 13. Measure the current and voltage for each 7 resistance, namely the delta F.O. 13. Delta- or mesh-connection of ^^ j ^ ^ ^^ (]jne) load resistances. voltage ED. Also measure the line current / and the star voltage Es, if the neutral O of the supply system is accessible. It is seen, as above, ES = ED-+- V3- Compare the measured values of / and ID with the expression (which should be proved) /= V3/D. Compute the power for each resistance ED!D, and compare with the power found for the same resistances in star-connection. For an inductive load, we should multiply by cos 6 to obtain the true power in each resistance. If ED, ID and 6 are the same for each phase, we find total power by multiplying by 3 ; hence Total power = 3^0/0 cos 6. But hence * Some measurements should also be made with unequal resistances. 6-A] GENERAL STUDY. 207 Total power =V3 D/ cos 0, = V3 El cos 0, = V3 -El X power > factor, where E and / are line voltage and line current. This is the customary power formula for any balanced 3-phase system, as has already been found for the star-connection. 22. The currents and voltages for the delta-connection can be laid off by the radial method (see Appendix I.) from a com- mon center, giving a diagram similar to Fig. 12. Another method is shown in Fig. 14, in which the voltages are laid off as a triangle (polygon method) and the currents radially from the corners. The cur- rents in Fig. 14 are drawn as lagging. These currents are /XY (from X to Y), IYZ (from Y to Z), and /zx (from Z to X). With sign reversed, the latter becomes /xz, meas- ured from X to Z. The sum* of /XY and /xz gives /. If we wish to select signs so that the sum of these three vectors is zero, we must reverse the FIG. 14. Currents and voltages in a sign of I so as to give the line ****<"* 3-phase circui.,- P oly- gon or mesh method of representation. current /' ; we now have /', /XY and /xz all measured from X, so that Law (3) of Appendix I. is satisfied. 23. Transformer-connections on 3-Phase Circuits. Trans- former secondaries and primaries like any generating or re- ceiving circuits can be connected to a 3-phase circuit by A-, Y-, T- or F-connections, shown in Fig. 2. *(22a). The current / is the sum of /xz and /XY (both measured from X), or the difference between /zx and /XY (measured one towards and the other away from X). See Laws (3) and (4), Appendix I. 208 POLYPHASE CURRENTS. [Exp. The most convenient and instructive method for studying the electrical relations of these connections is to use three trans- formers with the same ratio of transformation (say i: i), the primaries and secondaries of which can be connected in any desired manner. With three such transformers and with a 3-phase supply given, make connections in the following six ways : With three transformers: (i) Primaries star-connected. Secondaries star-connected. (2) " " " " delta (3) " delta " " star .(4) " " " " delta With two transformers: - (5) Primaries T-connected. Secondaries T-connected. (6) " V V In each case measure all electromotive forces and construct electromotive force diagrams, _ v IT comparing computed and meas- ured results. The star- and delta-connec- tions have already been dis- cussed; the special relations of the T- and F-connections, will , now be considered. * ta 24. T -connection. For the F.O. ,5. Relation between currents r _ connect ; ffleasure the yo , t . and voltages in a ./-connection. age OZ, Fig. 15, and note that it is 86.6 when XY is 100. For a balanced load, the three cur- rents, /x, /Y, /z, are equal. For a non-inductive* load, Fig. 15, the current in transformer XY is out of phase with the elctro- motive force by 30 and the power factor (cos 30) is 0.866; * (243). For an inductive load, the currents take the positions shown by dotted lines in Fig. 15; 7x is now out of phase more than 30, and /Y less than 30. 6-A] GENERAL STUDY. 209 in transformer OZ the current is in phase with the voltage, giving unity power factor. For a current of 100 amperes, on non-inductive load, we have Volt- E I Power Factor. Watts. amperes. Transformer XY 100 100 0.866 8,666 10,000 Transformer OZ 86.6 100 i.oo 8,666 8,666 17,333 18,666 This shows that the power output of each transformer is the same ; for non-inductive load the two transformers require about 8 per cent, more transformer capacity (volt-amperes) than watts power transmitted. For delta- and star-connection, on non- inductive load, no excess of transformer capacity is needed. The T-connection is discussed further under Polyphase Trans- formation, Exp. 7- A, where it is shown (8) that, for good regulation, the windings OX and OF on one transformer must be interspaced so as to reduce the magnetic leakage between them. The neutral point in a T-connection can be obtained by a tap at N in the coil OZ (see Fig. 9, Exp. 7~A), dividing the coil into 4 and . 25. V-connection or Open Delta. Draw a diagram similar to Fig. 15, for the F-connection, and from the power factor of each transformer show that for non-inductive* load this connec- tion requires 15 J per cent, more transformer capacity than power transmitted. Obviously a F-connection can be replaced to ad- vantage by a T-connection ; even using the same two transform- ers, there will be an advantage in the change, for there will be less voltage on one of the transformers and hence less core loss. It is seen that, as a general principle, apparatus in which cur- rents and voltages are out of phase require greater volt-ampere * (253). Note that an inductive load will cause the power factor for one transformer to become more and for the other less than cos 30, which will make the regulation better on one and worse on the other. 15 210 POLYPHASE CURRENTS. [Exp. capacity for the same power than apparatus in which currents and voltages are in phase. 26. A Comparison. In comparing the relative advantages of transformer-connections, it is to be borne in mind that three transformers (even though of somewhat smaller aggregate capacity) will usually cost more than two. The F-connection gives the least voltage per transformer and the least insulation strain, particularly if the neutral is grounded; for this reason it is to be preferred on high potential lines, say, 20,000 volts or over. On the other hand, the delta-connection has the advan- tage that, if one transformer breaks down, the remaining two will operate F-connected; at moderate voltages (say, under 20,000 volts) the delta-connection is accordingly to be preferred. In the delta-connection, if one transformer breaks down, each remaining transformer will have J instead of ^ of the whole power and will have to carry the line current instead of the delta current. By what per centages are current and power in each transformer thus increased? This increase would cause abnormal heating. For the same heating (same current) show that the two transformers F-connected will carry 57! per cent, as much load -as the three delta-connected transformers. With transformers delta-connected, the voltage of the system can be increased by using the same transformers F-connected. In a new system, the delta-connection is sometimes installed with a view to changing later to a F-connection and a higher voltage. A single 3-phase transformer requires less material than three single-phase transformers of the same aggregate capacity, and is more efficient. (See Handbooks.) The three single-phase transformers may be cheaper or more readily obtained because more nearly standard, and in case of breakdown one third and not all the equipment needs be replaced ; in other respects the single 3-phase transformer is preferable and is coming more and more into use. 27. SLv-Phase Circuits. A 6-phase circuit is a 6-wire cir- 6-A] GENERAL STUDY. 211 cuit, the potential diagram of which forms a hexagon. Its only use is in connecting transformer secondaries to 6-phase syn- chronous converters.* The usual and best method for obtaining a 6-phase circuit is by means of the diametrical-connection, as follows. Three transformers have primaries connected to a 3-phase circuit. The six wires of the 6-phase circuit may be represented by the apices of a hexagon; the three transformer secondaries, Fig. 2 (a), are connected so as to form diagonals or diameters of the hexagon. The three neutral or middle points of the secondaries may, or may not, be interconnected. Connect transformers in this manner, with the neutrals interconnected, and test with a. voltmeter; for present purposes this one test will be sufficient. If each transformer has two separate secondaries of equal voltage, these six coils can be used as a 6-phase supply by a ring- or mesh-connection (each coil forming diagrammatically one side of a hexagon) ; or, a 6-phase supply can be obtained, by a double T or double delta, one T or delta being reversed with respect to the other. A double F-connection is the same as the diametral-connection. One advantage of the diametral-con- nection is that it gives a neutral which may be used as a " derived neutral " for a 3-wire system on the direct current service from the converter; this is particularly useful in lighting systems. PART IV. 28. Equivalent Single-phase Quantities. Polyphase quan- tities are sometimes reduced to equivalent single-phase values for * (273). A 3-phase converter may be increased in rating 40 or 50 per cent, with no increased losses and with a corresponding higher efficiency when changed to 6-phase by the addition of three more collector rings and (if necessary) an extension of the commutator. A most valuable paper on this subject is one by Woodbridge (A. I. E. E., February 14, 1908), who states that of 1,000,000 K. W. of railway converters, one. third are 6-phase; above 500 K. W. one company makes all converters 6-phase. See also Chap. XI., Alternating Current Motors, by A. S. McAllister, where 6-phase transformer connections are given in detail. 212 POLYPHASE CURRENTS. [Exp. simplicity in working up and comparing data relating to poly- phase machinery. The equivalent single-phase current I' (sometimes called total current) in any balanced polyphase system is the current which, multiplied by the line voltage and power factor, gives the true (total) power; hence Total power El' X power factor. For a 2-phase circuit, the equivalent single-phase current /' is evidently twice the line current. For a 3-phase circuit, the equivalent single-phase current is V~3 times the line current. (In a delta-connection, it is seen that this is three times the delta current, hence the significance of total current.) 29. Equivalent single-phase resistance R f is the resistance which, multiplied by the square of the equivalent single-phase current, gives the total copper loss (=RT 2 ). It will be found* that for star- or mesh-connection, or any symmetrical combination of star and mesh, 2-phase as well as 3-phase, R' is one half the resistance measured between lines of one phase. For a 2-phase circuit, this becomes apparent upon inspection. For a 3-phase circuit, with the three equal resistances r under test connected star and connected delta, determine R' and /' ; in each case compare R with r and with the resistance measured between any two line-wires. Equivalent single-phase reactance and impedance are likewise one half the measured values between lines of one phase. 30. Current and Voltage per Phase. Current per phase and voltage per phase (or phase voltage) are more commonly used than equivalent single-phase quantities ; the meaning is not so definite, but can generally be told from the context. The terms * See Standard Electrical Handbook ; or Alternating Current Motors, by A. S. McAllister, in which equivalent single-phase quantities are exten- sively used. 6-A] GENERAL STUDY. 213 are usually so used that the total power in a 2-phase circuit is twice the product of current per phase, voltage per phase and power factor; the total power in a 3-phase circuit is three times the product of current and voltage per phase, and power factor. In a 2-phase system, there is little chance for ambiguity. In a 3-phase system, the current and voltage per phase (as denned above) may be either the star (line) current and star voltage, or the delta current and delta (line) voltage. In either case, the total power is three times the power per phase. Using line current, we must use star voltage ; using line voltage, we must use delta current. It will be remembered that, if line cur- rent and line voltage are used, the total power is \/3 times their product multiplied by power factor. APPENDIX I. VECTOR ADDITION OF ALTERNATING CURRENTS AND ELECTRO- MOTIVE FORCES IN A NETWORK OF CONDUCTORS. 31. Laws of Vector Addition and Subtraction. Any hill may be considered to be up or down according to the direction in which one is walking; the difference in level may be considered positive or negative. In the same way difference of potential may be considered as positive or negative according to the sense in which it is taken that is, according to the direction one takes in proceeding around a circuit or from point to point in a circuit. Consider a network of highways in a hilly country. If from any starting point one proceeds by any route or circuit back to the starting point, he will find himself at the original level the plus hills and the minus hills adding up to zero. On different trips he may traverse the same hill in opposite directions, giving it one time a plus and the other time a minus sign. This would be true at any instant, even if the surface were rising and falling, as in an imaginary earthquake or on the surface of the ocean. Consider now a network of conductors. If from any starting point one proceeds by any route or circuit back to the starting point, he will 214 POLYPHASE CURRENTS. [Exp. reach the original potential ; the algebraic sum of the potential differ- ences at any instant, taken in the proper sense, adding up to zero. For an alternating current circuit in which currents and potential differences vary harmonically and can be represented by vectors, algebraic addition is used for instantaneous values and vector addi- tion for maximum or for effective values; hence, for maximum or effective values we have the modified statement of Kirchhoff's Law: 32. Law (/). Vector Addition of Electromotive Forces: Gen- eral Law. In proceeding completely around any mesh or number of meshes in an alternating current system of conductors, the vector sum of all the differences in potential is zero; such vectors form a closed polygon. For this vector addition, electromotive forces are represented by arrows, the tip of one to the feather of the next, which must be in sequence according to the direction in which we proceed around the circuit. A coil xy may have an electromotive force represented by a vector XY, as measured from x to y. Taken in the opposite sense (by traversing the circuit in the opposite direction) the electromotive force would be YX, the same vector with arrow reversed. To illustrate* further this addition, from a point O on the side of a hill, let two paths ascend: one to the point A (elevation 100) ; the other to B (elevation 90). If a man starts at A, descends to 0, ascends to B and back to A f the ascents and descents add to zero (100; +90; + 10). To illustrate the special case of subtraction, if the sense or sign of one quantity be reversed: let two men start from O, one ascending to A (-{- 100) and the other to B (+90). The difference in their level is now the difference between -f- 100 and + 90, which illustrates the following law : 33. Law (/3 ? What per cent, is EH of E-i- V3? 46. With a voltmeter* measure the line voltage XYZ and con- struct a triangle as in Fig. 16. Measure also the three star voltages O'X, O'Y, O'Z and lay them off as shown, each one twice. A supply neutral is not necessary for this test. Cut out the diagram on the heavy lines and fold on the light lines, bringing the three points 0' together so as to form a pyramid. The height of the pyramid represents the voltage EH due to hysteresis harmonics. 47. The foregoing illustrates the fact that vectors in a plane can exactly represent only currents and electromotive forces which are simple sine functions; the error due to harmonics is commonly neglected. 48. Generator Coils. If there is a third harmonic in the generated electromotive force, with the generator coils delta-connected it cannot appear in the line but will appear as a circulating current in the delta. This may cause appreciable heating if the harmonic is large. 49. The third harmonic can appear on the line only in case the generator coils are F-connected and have the neutral connected to ground or a 4th wire. If the line is not grounded also at the receiv- * Use an electrostatic voltmeter ; although this is not important with large transformers, it becomes necessary in case the coils or transformers are small, as the current taken by an ordinary voltmeter may cause con- siderable error. 220 POLYPHASE CURRENTS. [Exp. ing end or a 4th wire return used, the potential of the line as a whole will be raised by this electromotive force of triple frequency. APPENDIX III. COPPER ECONOMY OF VARIOUS SYSTEMS. 50. In figuring copper economy, it is to be assumed that all sys- tems compared are to have the same line loss and per cent, resistance drop. As a general principle, in any given system, the amount of copper necessary varies inversely as the square of the voltage; thus, if the voltage is doubled, the current will be halved and the copper reduced to one fourth, increasing R four-fold. This gives the same RI 2 loss in the line and the same per cent. RI drop. Any comparison of systems should, therefore, be made on the basis of equal voltage; this may mean either the greatest voltage between any two line wires or the voltage between any wire and the neutral. This latter becomes more significant when the neutral is grounded. 51. On the Basis of the Same Voltage E$ from the Line Wire to Neutral. On this basis all symmetrical alternating systems give the same copper economy, as will be seen from the following. Let us consider all wires to be of a given size and to carry a given current I, thus giving the same drop and loss per wire. We then have Single-phase, 2 wires: amount of copper 2; power = 2 E$I. Three-phase, 3 wires : amount of copper 3 ; power = 3 Quarter-phase, 4 wires : amount of copper 4 ; power = 4 w-phase, n wires : amount of copper n ; power = The amount of power is seen to be proportional to the amount of copper, giving therefore equal copper economy for all systems on the basis of equal voltage between the line and the neutral or ground. 52. On the Basis of the Same Voltage Between Line Wires. Between line wires the voltage is 2s for the single-phase (or quarter-phase) system and V3-Es for the 3-phase system. To make the voltage between line wires equal in these systems, the voltage in the 3-phase system can be increased in the ratio \/3 : 2. The amount of copper can accordingly be reduced (see 50) inversely as the square of this ratio, namely, 4:3. Hence, for the same line voltage, a 3-phase system requires 75 per cent, as much copper as a single- phase or quarter-phase system. 6-A] GENERAL STUDY. 221 53. Direct Currrent System. A direct current system has the same copper economy as a single-phase system, when the direct cur- rent voltage is made equal to the effective (sq. rt. of mean sq.) value of the alternating voltage. If, however, the direct current voltage is increased so as to equal the maximum value of the alternating current voltage, the direct current voltage is increased in the ratio of I : \/2 and the copper is decreased as the inverse square of this ratio. The direct current system then requires only one half the copper of a single-phase or two thirds the copper of a 3-phase system, on the basis of equal volt- age between wires. A direct current system would, therefore, be more economical of copper than any other system, at the same voltage. 54. Choice of Systems. On account of copper economy and the simplicity due to the use of only two wires, direct current would be superior to any alternating current system, if it were not for lack of simple and suitable means for transforming direct current so as to obtain the advantage of high potential transmission with low potential generation and utilization. In the case of alternating cur- rents, these means are provided for by the transformer which makes alternating current systems so flexible that they are practically always* used for long distance transmission, instead of direct current. In comparing alternating current transmission systems, the choice is to be made between single-phase with its simpler line construction, fewer insulators, etc. and 3-phase, requiring only 75 per cent, as much copper. If these were all the factors, single-phase transmission systems would be more common than they are, the simplicity offsetting the poorer copper economy. An important and perhaps a determin- ing factor, however, is the superiority of polyphase as compared with single-phase machinery (2) ; for this reason a polyphase system is commonly preferred, quite aside from considerations of copper econ- omy. Of polyphase systems, the 3-phase system is most economical and is therefore the system in general use. * ( 54 a )- I n a f W cases high potential direct current has been used for power transmission, notably in the Thury system. This is essentially a constant current system. The high potential is obtained by generators in series ; the motors are likewise in series. See Land. Electrician, March 19, 1897; New York Elect. Rev., January, 1901. 222 POLYPHASE CURRENTS. [Exp. EXPERIMENT 6-B. Measurement of Power and Power Fac- tor in Polyphase Circuits. PART I. GENERAL DISCUSSION. . i. Preliminary. For measuring power in any 3-wire sys- tem, the best method is the two-wattmeter method 23 ; for the particular case of a balanced 3-phase load, some one-wattmeter method, 32-9, may be used. For measuring power in systems with more than three wires, the n i wattmeter method of 16 is correct for all cases; for the particular case of a balanced 2-phase load, on a 4-wire sys- tem, the method of 10, employing two wattmeters, may be used. An unknown load should not be assumed to be balanced. It will be understood that, in cases where several wattmeters are described as being required, a single instrument may be used and shifted by suitable switches from circuit to circuit, readings being taken successively in the different positions. 2. Separate Phase Loads. In any single-phase system power is measured by means of a wattmeter, the current coil being connected in series and the potential coil in parallel with the circuit, as discussed in Appendix III., Exp. 5-A. An exten- sion of this method can be applied to a polyphase system, if the phases are separately accessible so that the load of each phase can be separately measured. A wattmeter is then used for each phase load, with current coil in series and potential coil in parallel with the particular load being measured, the total power being the arithmetical sum of the several wattmeter readings. For example, to measure the power in three star-connected re- sistances on a 3-phase circuit by this method, three wattmeters would be required, each current coil carrying the star (or line) current and each potential coil being subjected to the star voltage. With three resistances delta connected, three wattmeters would 6-B] MEASUREMENT OF POWER. 223 also be required, each current coil carrying the delta current and each potential coil being subjected to the delta (or line) voltage. 3. This method of measuring the separate phase loads is simple in principle and is commonly used on a 2-phase circuit (6), but it is not capable of general application inasmuch as phase loads are not always separable. On a 3-phase circuit in testing, for example, a 3-phase induction motor it may be impossible to measure delta current or star voltage, so that some method not requiring either of these measurements becomes necessary; furthermore, the method is open to objection on account of the number of measurements required, unless the assumption is made that all phases are alike, so that measure- ments are necessary on one phase only. 4. Polyphase Power Factor. A polyphase system is a com- bination of single-phase elements. If E, I and W are, respectively, the voltage, current and power for any separate element, the power factor for that element is W -~EI, by definition. When the separate elements or phases of a polyphase system have the same power factor, this is the power factor for the whole system. 5. When, however, the separate elements have different power factors, there is no one power factor that has a definite value or physical significance for the whole system. It is convenient, however, to obtain a kind of average power factor for the system, the value of which will depend upon the method used in its determination.* An average power factor may be satisfactorily determined when the separate phases are nearly alike, but has little meaning when they are widely different. 6. Two-phase Load. Two-phase power is usually measured by two wattmeters, one on each phase, as just described. 7. When the phases are independent, as in a, Fig. I, Exp. 6-A, the measurements differ in no respect from measurements made on single-phase circuits. *(5a). See A. S. McAlliser, Alternating Current Motors, p. 12; A. Burt, Three-phase Power Factor, A. I. E. E., p. 613, Vol. XXVIL, 1908. 224 POLYPHASE CURRENTS. [Exp. 8. On a 3-wire, 2-phase circuit, as in b, Fig. i, Exp. 6-A, the same method may also be used, the two wattmeter current coils being located in the two " outer " conductors, A and B, respectively. With the wattmeters thus located, the sum of their two readings will give the true power (23) for any load whatsoever, even when part of the load is between A and B. (These connections are seen in Fig. I, in which X and Y are the outer conductors and Z is the common conductor or return.) 9. When the load in a 3-wire 2-phase system is balanced and there is no load between the two outer conductors A and B, one wattmeter may ; be conveniently used by connecting the current coil in the common conductor; one end of the potential coil is connected to the common conductor and the other end connected first to one and then to the other outer conductor. A reading* is taken in each position and the algebraicf sum gives the total power. (The connections are seen in Fig. 7, in which Z is the common conductor.) A 3-wire 2-phase circuit is likely not to be balanced ( 14, Exp. 6-A) and the method should be used with caution. 10. On a 4-wire, quarter-phase, 2-phase system, as in c and d, Fig. i, Exp. 6-A, two wattmeters, one on each phase, will give the correct power only when the load is balanced. The method may be used for testing a single machine, but not for measuring the power of a circuit when the character of its load is unknown. * (9a). For a balanced load, power can be determined from a single reading of the wattmeter by connecting the current coil in the common conductor and connecting the potential circuit from the common conductor to the middle point of two approximately equal non-inductive resistances, Ri Rz, connected across the two outer conductors as in Fig. 5. A single reading of the wattmeter gives one half the total power, if the wattmeter is calibrated as a single-phase instrument with Rt and R 2 connected in parallel with each other and in series with the potential circuit (36a). See also 33a. t (Qb). For low power factors, when exceeds 45, the reading of the wattmeter in one position is negative. The similar case for a 3-phase circuit is fully discussed later. 6-B] MEASUREMENT OF POWER. 225 That the method is not generally correct will be seen by assum- ing the current coils of the two wattmeters to be connected in two of the lines, as A and B ; neither wattmeter would then record a single-phase load drawing current from the other two lines, A'B'. On a 4-wire system, with unbalanced load, at least three watt- meters must be used, 16. ii. Po^ver Factor in a Tzvo-phase Circuit. If E, I and W are measured on one phase of a 2-phase circuit, W -f- El is the power factor for that phase, 4. This may be called the cosine method for determining power factor, since W -7- El = cos 6 when currents and electromotive forces are represented by sine waves. 12. The following tangent method for determining power factor from two readings of the wattmeter will be found simple and often convenient. The current coil of the wattmeter is connected in one line of phase A ; the potential coil is connected across phase A, whose voltage is EA. The wattmeter now reads the power volt-amperes or true watts (1) W i = E A I A cosO. Transfer the potential coil to phase B, whose voltage is E-B. The wattmeter now reads the wattless or quadrature volt- amperes (sometimes called wattless, or quadrature, watts), (2) ^ 2 = B /Asin0. Dividing the second reading by the first, (3) 5= a Tan 0, and hence power factor (cos0), is determined by the ratio of the two readings. Usually EB = A, so that tan = W 2 _r_ w. The power factor thus determined is the power 16 226 POLYPHASE CURRENTS. [Exp. factor of phase A ; 6 is the phase difference between JA and E&. The method assumes that EA and EE differ 90 in phase and that electromotive forces and currents follow a sine law. The advantage of the tangent method is its simplicity and inde- pendence of the calibration of instruments. The method can be used for determining the power factor of a single-phase load, drawn from a 2-phase supply, and a somewhat similar method can be used for determining the power factor of a 3-phase load, 28, 38, 41. 13. The value of 6 and power factor can be found by the sine method directly from (2); thus, sin = W 2 -f- B/A. For a single-phase or 2-phase load there is little advantage in this method, which is useful, however, on 3-phase circuits, 43. 14. The " cosine " method gives correct power factor by definition and is general, being independent of wave form. The " tangent " and " sine " methods are based on the assumption that voltages and currents follow a sine* law. The " cosine " and " sine " methods require carefully calibrated instruments. 15. The three methods are seen to be based on the relation, power volt-amperes total volt-amperes wattless volt-amperes sin = total volt-amperes wattless volt-amperes tan 9 = - . power volt-amperes 1 6. General Method for Measuring Power; n i Watt- meters. This method consists in selecting any one conductor of a system and considering it as a common return for all the others. One wattmeter is then used for each conductor, except *(i4a). With non-sine waves, the value of power factor by the tangent method would, theoretically, be a little larger than the true value by the cosine method; the value by the sine method would be a little larger than the value by the tangent method. 6-B] MEASUREMENT OF POWER. 227 this common return. No wattmeter is required for a return circuit ; thus, for a 2-wire system, one wattmeter only is needed, no wattmeter being needed in the return conductor; in a 3~wire system, two wattmeters are used, none being needed in the re- turn conductor, etc. If n is the number of line conductors, n i wattmeters are, accordingly, required. For a 3~wire sys- tem, the connections are shown in Fig. i. To measure power in any system, connect a wattmeter in every line circuit except one (considered as the return conductor), each wattmeter having its current coil in series with one of the lines and its potential coil connected from this line to the return conductor. One less wattmeter is required than the number of line wires; the total power is the algebraic sum of the individual wattmeter readings. 17. To read positive power each wattmeter is to be connected in the positive sense, that is, connected in the same way as for measuring power in a 2-wire system, direct or alternating. If, when connected in this manner, the needle of any wattmeter deflects the wrong way, the connections of its potential or current coil are to be reversed and its reading is to be considered negative. Compare 25. 18. This method of measuring power is absolutely general; the current may be direct or alternating and may vary by any law whatsoever ; the system may be single-phase or polyphase, balanced or unbalanced, symmetrical or unsymmetrical. As a particular case, the two-wattmeter method for a 3-wire system is of special importance with reference to 3-phase circuits and will be considered later (23) in detail. 19. The foregoing method -has been explained by considering one cpnductor as a common return for all the others, and for most purposes this explanation is sufficient. The method with n i wattmeters can be rigorously established (22) by first developing the method with n wattmeters, 20. 228 POLYPHASE CURRENTS. [Exp. 20. General Method, n Wattmeters. In any star-connected system, if a wattmeter is connected in each line the current coil connected in series with the line and the two ends of the potential coil connected, respectively, to the line wire and to the junction or neutral point of the system the total power of the system will be the sum of the separate wattmeter readings, as discussed in 2. 21. This arrangement of wattmeters, however, is not limited to star-connected circuits ; nor is it necessary to have the neutral point accessible. The true power of any system whatsoever may be measured by connecting one wattmeter in each line, with cur- rent coil in series with the line and potential coil with one end connected to the line and the other end to any point P of the system, which may or may not be the neutral. To this potential point P is connected the potential coil of every wattmeter. The algebraic sum of the wattmeter readings gives the true power. A general proof of this is given in 53 ; it can be verified by ex- periment, 45-49- 22. The fact that any point of the system may be taken as the potential point P leads to the practical simplification by which one wattmeter is omitted. In a system of line wires, a } b, c - n } let the line wire n be taken as the potential point. Wattmeters A, B, C, etc., will have current coils connected in series with a, b, c, etc., and potential coils connected from a to n, from b to n, etc. Wattmeter N would, accordingly, have its potential coil connected from n to ; as both ends of the pressure coil would thus be connected to the same point, this wattmeter would always read zero and, accordingly, can be omitted. The method of n i wattmeters, 16, is thus established. 23. Two Wattmeter Method for any 3-wire system. This is the method generally used for measuring 3-phase power. Be- ing a particular application of the n I wattmeter method, 1 6, the two-wattmeter method can be applied to any 3-wire 6-B] MEASUREMENT OF POWER. 229 system* and is independent of any assumptions as to wave form or the nature of the load. 24. The arrangement of instruments is shown in Fig. i. The wattmetersf are inserted in any two lines, as X and Y , the third wire Z being considered as a common return. LJL < w l V [ j Y Wo 1! FIG. i. Two-wattmeter method for measuring power in any 3-phase or other 3-wire circuit. The total power is the algebraic sum of the readings of the two wattmeters. For high power factors (more than 0.5) this will be the arithmetical sum, both wattmeter readings being posi- tive. For low power factors (less than 0.5), the reading of one wattmeter is to be considered negative, the total power in this case being the arithmetical difference of the two readings, as shown later in 31. 25. There are several ways for telling whether one reading is negative or not, the principal ones being as follows : (a) From the sense of the connections, 17. * ( 2 3a). If each end of a 3-phase line has its neutral well grounded, it becomes virtually a 4-wire system; the ground circuit can not be neglected unless the load' is practically balanced. t (243). Polyphase Wattmeter. Instead of two single-phase watt- meters, a single instrument combining the two is commonly used. This consists of two wattmeters, one above the other, with the moving elements mounted upon a common shaft. The reading of such an instrument gives the total power. The electrical connections are the same as for two separate instruments. 230 POLYPHASE CURRENTS. [Exp. (b) For the given load substitute a load that is non-inductive or is known to have high power factor; if, with certain connec- tions, both wattmeters deflect properly, their readings for these connections are positive. When one connection needs to be re- versed to obtain proper deflection, one reading is negative. (c) Disconnect one* potential circuit from the middle wire Z and connect it to the outside wire, X or Y ; if the wattmeter re- verses, the readings of one of the wattmeters must be considered negative. > Method (c) can be readily applied during test, when using the two-wattmeter method on a 3-wire system, but does not apply to a system with more than three wires. Method (a) is general and can be applied to a system with any number of wires. The polarity of the wattmeter circuits may be marked once for all, instruments of one make being similar. The instruments can be properly connected in the posi- tive sensef in advance and confusion during the test avoided. 26. Two-wattmeter Method with Balanced Three-Phase Load. As has been already stated, the two-wattmeter method is general for any kind of 3-wire circuit. Detailed proof for each particular case is, accordingly, unnecessary. A discussion of its application to measuring a balanced 3-phase load will, however, prove instructive as an illustration and will serve to make clear the negative reading of one wattmeter at low power factors. Furthermore, it will show a method for obtaining 3-phase power factor. 27. Fig. 2 is the diagram for a balanced 3-phase load, it being assumed that currents and voltages follow a sine law. For unity *(25a). On a 3-phase circuit it is sufficient to do -this with one potential circuit only; but in general it should be done, successively, with each potential circuit, a reversal of either instrument indicating that one reading is negative. t(2Sb). This also indicates the direction of the. flow of power; see " Polyphase Power Measurements," by C. A. Adams, Elect. World, p. 143, January 19, 1907. 6-B] MEASUREMENT OF POWER. 231 power factor (0 = o), the three line currents are shown by the heavy arrows /x, /Y, Iz. The dotted arrows show these currents for lower power factors, # = 30, = 6o and = 90. FIG. 2. Currents and voltages in a balanced 3-phase system. If two wattmeters are connected as in Fig. i, wattmeter (i) has a current !x in its current coil and a voltage Exz across its potential coil, the phase difference between this current and voltage being 6 30. The component of Ix in phase with Exz is, accordingly, Ix cos (6 30) ; hence writing E for Exz and / for Ix wattmeter (i) reads W t = EI cos (0 3 o)=7 (cos 30 cos + sin 30 sin 0). In a like manner, wattmeter (2) has a voltage EYZ and a cur- rent /Y, having a component /Y cos (0 + 30) in phase with EYZ. Hence writing E for Eyz and / for /Y wattmeter (2) reads PF 2 = /cos (0 + 30)=7 (cos 30 cos sin 30 sin 0). Adding W z to W lf we have Wi+W 2 = 2EI cos 30 cos = V3/ cos 0, 23 2 POLYPHASE CURRENTS. [Exp. which is seen to be the expression for the total power in a 3-phase circuit (20, 21, Exp. 6-A). The two-wattmeter method for a balanced 3-phase load is thus established. 28. Power Factor. Subtracting W 2 from W lf we have W 1 W 2 = 2EI sin 30 sin = EI sin 0. Hence, by dividing, we have . Wi EF 2 tan0 ~ The value of and of power factor (cos 6) for a balanced 3-phase circuit is, accordingly, determined by the tangent formula The larger reading is W lf and is always positive; the smaller reading, W z , may be positive or negative. 29. To save labor in com- putation, it is convenient to plot a curve, Fig. 3, with power factor (cos 6) as or- dinates and the ratio of watt- meter readings, W z -f- W lt as abscissae. Points on this curve are determined by the relation jgative 30 By means of this curve, the -1.00 -.SO -.liO -.40 -.20 +.iJO +.40 ^ .60 +.80+J.OO Ratio of Wattmeter Readings, IF-f^ W l FIG. 3. Power factor of balanced P Ower fact r f r a balanced 3-phase circuit for different ratios of load is readily determined wattmeter readings in two-wattmeter method. from the ratio of the two wattmeter readings. For plot- ting the curve in Fig. 3, the following points were determined: 6-B] MEASUREMENT OF POWER. 233 W**-Wi I. .80 .60 40 .20 O +.20 +40 +.60 +.80 +1. cos o .064 .143 .240 .359 .5 .655 .803 .918 .982 I. Intermediate values can be found by interpolation. It is seen that the curve is not symmetrical. 30. Errors of calibration are avoided if one wattmeter is used, successively, in the two positions to determine W and W 2 . Since the assumption is made that the current in the wattmeter is the same for the two readings (/X = /Y = /), greater accuracy is obtained if the current in the two cases is actually the same current. This is accomplished by using the one wattmeter method of Fig. 7, which is more accurate for determining power factor than is the two-wattmeter method. In either case, corrections may be made (42) for slight variations in voltage. 31. Negative Reading of Wattmeter. Referring to Fig. 2, it is seen that for all values of 6 from o to 90, the projections of /Y upon Ezx have the same sign; the wattmeter reading W^ is, therefore, in all cases positive. The projection of Iy upon EYZ decreases as 6 increases, be- comes zero when = 6o, and then changes sign. The watt- meter reading W 2t accordingly, changes sign, being positive when 6 is less than 60 (power factor more than 0.5) and negative when 6 is more than 60 (power factor less than 0.5). In all cases W is the larger, and W 2 is the smaller, reading. On non-inductive load, 6 = and IV^ = W 2 ', each wattmeter reads half the total power. When # = 90, W^ = W 2 and the total power is zero. 32. Three-Phase Power with One Wattmeter. With only one wattmeter, 3-phase power can be measured by the two-watt- meter method (23) by using suitable switches for throwing the wattmeter from one position to the other. This procedure gives the true power for unbalanced as well as balanced loads and is generally the best one to follow. The transfer of the current coil of the wattmeter from one line to another is not always convenient or possible and, when 234 POLYPHASE CURRENTS. [Exp. the load is balanced, the power in a 3-phase system can be measured with only one wattmeter without such transfer by one of the following methods. 33- With Neutral Available. When the neutral is available, the current coil of the wattmeter can be connected in any one line circuit and the potential coil connected from that line to the neutral. For a balanced load, the total power will be three times the reading* of the wattmeter. The power factor is equal to W .-El, where / is the line current and E is the star voltage. When the load is not balanced the total power will be the sum of three readings, one on each phase. 34. With Artificial Neutral. When the neutral is not avail- able, an artificial neutral can be created, as by means of three equal star-connected non-inductive resistances, R^ R 2 , R 3 in Fig. 4. The method of 33 can then be applied. It is necessary that these resistances be relatively low, as com- pared with the resistance of the potential circuit Rw of the wattmeter. The current in them will then be relatively large, so that the potential of the neutral will not be dis- turbed by the connection of the potential circuit of the FIG. 4. Measuring power with one wattmeter. The power taken wattmeter connected to the neutral in ; n the resistances may be in- a balanced 3-phase circuit. eluded or not in the measured power as desired ; correction for this power can be made when necessary. 35. Strictly speaking R { and R 2 should each be equal to the joint resistance of R 3 and Rw in parallel. In this case there is no need of making the resistances low ; this leads to the method of 36 in which R s is omitted entirely, that is, R 3 = oo. *(33a). Calibration for Total Power. -In this method, or in any method depending upon a single reading, the wattmeter can be calibrated to read total power. 6-B] MEASUREMENT OF POWER. 2 35 36. With Y -Multiplier. With a balanced load and with one wattmeter, the current coil of the wattmeter is connected in one line. One end of the potential circuit is connected to the same line, the other end being con- nected to the junction of two resistances R and R 2 , which are connected to the other two lines, as shown in Fig. 5. The resistances R : and R 2 are non- inductive and are each equal* to Rw, the resistance of the X X Y i t ^ Llij Y FIG. 5. Measuring power with one wattmeter and a Y-multiplier in a bal- anced 3-phase system. potential circuit of the watt- meter. True power is three times the reading of the wattmeter, cali- brated as a single-phase instrument. The resistances are some- times put up in a special volt-box or Y-multiplier for 3-phase cir- cuits ; the instrument may then be calibrated so as to read total power, 33a. 37. By Means of T-connection. In a 3-phase system, with three lines X, Y, Z, connect the current coil of the wattmeter in any one line, as Z, Fig. 6. Connect the potential coil from Z to a point O, the middle point of a transformer coil across XY. See Fig. 15, Exp. 6-A. In any balanced 3-phase system, how- ever the load is connected, the wattmeter will now give one half the total power. (This may be seen as follows: If the wattmeter *(36a). Provided Ri and R 2 are approximately equal to each other, this same method may be used without having R 1 and R 2 equal to /?\v. The instrument is calibrated as a single-phase wattmeter with R! and R 2 in parallel with each other and in series with Rw, a single reading then gives one half the total power. Compare Qa, 33a. FIG. 6. Measuring power with one wattmeter, !T-con- nected, in a balanced 3- phase circuit. I 236 POLYPHASE CURRENTS. [Exp. were connected with its potential coil on the star voltage, the watt- meter would read one third the total power; with its potential increased 50 per cent. see Fig. 2, it will read one half the total power.) 38. The power factor is W -i- oz/z. The power factor can be found from the tangent formula, by taking one reading, WK of the wattmeter with the connections as described and a second reading, W 2 , with the potential circuit of the wattmeter transferred to XY. W 2 XY/Z sin 6 . n ; nence tan = 39. Two-reading Method. This is one of the simplest and most satisfactory methods for measuring power and power fac- tor with one wattmeter in a balanced 3-phase circuit. The , current coil is connected in one line, as V Z, Fig. 7, one end of the potential circuit being connected to the same line. The other end of the potential coil .is con- nected, successively, to X and Y ' , and a Y reading taken in each position. The FIG. 7 . Measuring power algebraic sum of the two readings gives by two readings of one the total power. (The smaller readings, wattmeter in a balanced w ^ conside red negative whenever it 3-phase circuit. is necessary to reverse the potential or current coil of the wattmeter to obtain a proper deflection.) 40. The proof of the method will be seen by referring to Fig. 2, which assumes that voltages and currents follow a sine law. The two readings of the wattmeter are Wi = El cos (0 30 ) ; W* = EIcos(e + 30 ) . Hence, the sum of the two readings gives the total power, 27. 41. The power factor (cos0) is determined from the tangent formula, 28, 6-B] MEASUREMENT OF POWER. 237 By referring to Fig. 3, power factor can be found directly from the ratio W 2 -i- W t . 42. When there is an appreciable difference between the phase voltages (which we may term E^ and E 2 ) across which the potential circuit is connected when W and W z are read, a more accurate value of power factor will be obtained by correcting W^ or W 2 by direct proportion to obtain values correspond- ing to equal voltages. The ratio W z -=- W^ then becomes EJW 2 EJV^ The power factor thus determined is quite accurate, being independent of the calibration of any instrument and of any slight inequality in the phases. Even for an un- balanced load, it gives accurately the value of cos 6 for /z, where is the phase difference between /z and the voltage OZ (Fig. 2) midway in phase between XZ and FZ. The method is more accurate with one than with two wattmeters, 28. 43. Power Factor by Sine Method. The power factor of a balanced 3-phase circuit 'can be determined by the sine method (13) with only a single reading of voltmeter, ammeter and wattmeter. The method does not require the neutral to be available, nor does it require any auxiliary resistances or other devices. Representing the three line wires as X, Y and Z, the ammeter and the current coil of the wattmeter are connected in one line, as Z. The voltmeter and the potential coil of the wattmeter are connected across the other two lines, X and Y. The watt- meter reading gives the wattless or quadrature volt-amperes, sin 0, from which and cos are determined. 238 POLYPHASE CURRENTS. [Exp. PART II. MEASUREMENTS. 44. Many of the methods just described for measuring poly- phase power and power factor can best be taken up as occasion arises for their use. Without undertaking in the present experi- ment to subject all of these methods to test, it will be well to select a few of them for trial in the laboratory in order to illus- trate and make clear the methods as a whole. For this the following tests are suggested. 45. Verification of Methods for Measuring Polyphase Power. With a single-phase non-inductive load, forming a 2-wire sys- tem, measure the total power with two wattmeters. Each line is to contain the current coil of one wattmeter, the potential coil of which is connected from the line to a common point P, as in 21. The experiment consists in connecting P to different parts of the circuit, of various potentials, and noting that the algebraic sum of the two wattmeter readings is constant. When the power indicated by one wattmeter becomes greater, as P is changed, the power indicated by the other wattmeter be- comes less.* 46. For example, let the supply lines be a^a^ as in Fig. 6, Exp. 6- A. Connect P, successively, to points of different po- tential, as a lt a 2 , the neutral O, A^ and A 2 , these points being all on phase A. When phase B of a two phase supply is avail- able, proceed, also, to connect P successively to points B lt b lf b 2 , B 2 on phase B. 47. Repeat with an inductive load. 48. Repeat in some modified manner, as by using ajb^ as supply lines and connecting P, successively, to various points as described above. 49. When points, as in Fig. 6, Exp. 6- A, are not available, a resistance can be bridged across the circuit and the point P * A positive reading decreases ; a negative reading increases. 6-B] MEASUREMENT OF POWER. 239 connected to different points on this resistance. The load re- sistance itself can be thus utilized. The experiment might be extended to using 3 wattmeters on a 3-wire system, 4 wattmeters on a 4-wire system, etc., but this seems hardly necessary. The method of n wattmeters, n I wattmeters and two wattmeters may, in this way, be experi- mentally verified. 50. Two-phase Power Factor. From one phase, A, of a 2-phase supply draw a single-phase load. Take measurements with a voltmeter, ammeter and wattmeter and determine the power factor by the " cosine method," 14. Transfer the voltmeter and potential coil of the wattmeter to the other phase, B, and determine the power factor by the "sine method," 13, and by the "tangent method," 12. 51. Three-phase Power and Power Factor. With a 3-phase balanced load supplied from a 3-phase circuit, take two readings of a wattmeter connected as in Fig. 7. Determine the total power ; calculate the power factor by the tangent formula, 28, and by the ratio of wattmeter reading, Fig. 3. 52. Transfer the potential coil of the wattmeter to the third phase, so as to read the " quadrature " volt-amperes ; take the necessary readings of the wattmeter, voltmeter and ammeter, and determine power factor by the " sine method," 43. APPENDIX I. MISCELLANEOUS NOTES. 53. General Proof. In any system, with any number of con- ductors a, b, c, etc., let the instantaneous values of the currents in these conductors be i a , t' B , i c , etc. Designate by e a , e b , e c , etc., the instantaneous values of the potentials of the several conductors. The currents and electromotive forces may vary in any manner what- soever. There is no limitation as to the arrangement or method of connection of the generator and receiver circuits. 240 POLYPHASE CURRENTS. [Exp. The total power at any instant is (1) w e a i a + e b i b + e c i c . . . =2ei. Let e p be the instantaneous potential of any point P of the system. Since it is known that ^i = o, it follows that (2) e p i a + e p ii> + e p i c . . . = * P 2 = o. Since (2) is equal to zero, it may be subtracted from (i) without affecting its value; hence (3) w= (*o -*p)*'o + Ob *p)*& + (e c e v }i c . . = S( speed control of, 32-34 stopping of, 34 Shunt turns, determination of, 25 Sine method, of measuring power fac- tor, 226, 237 Single-phase currents, 102-122 Six-phase circuits, 210-211 Smith, S. P., on alternator regula- tion, 99 Space degrees, 106 Sparking at brushes, 6, 22 Speed control of motors, 32 Speed equation of motors, 30 Speed regulation, 37. Speed, relation to frequency, 65 Split-field method of alternator test- ing, 98 Star-connected 2-phase system, 196 3-phase system, 197, 204 Star current, 205 xStar voltage, 205 Starting boxes, 34 Static torque, 29 Steam turbine, influence on design of alternators, 62 Steinmetz, C. P., on choice of fre- quency, 64 on definition of a balanced poly- phase system, 197 on form of external alternator characteristics, 89 on hysteresis exponent, 174 on monocyclic transformation, 247 on separation of iron losses, 176 on topographic method, 198, 199 on wave form, 217 Steinmetz and Bedell, on reactance, US Stray power, 47 method of motor testing, 41-61 Susceptance, 115 of parallel circuits, 120 Swenson and Frankenfield, on motor testing, 56 Symmetrical polyphase system, 196 Synchronous machine, definition, 62 Synchronous generators, see Genera- tors Synchronous impedance, 79, 80 Synchronous reactance, 80 Synchronous watt, 29 T-connected transformers, delta equiv- alent of, 249 for 2- to 3-phase transforma- tion, 243 star equivalent of, 249 voltage and current relations, 248 T-connection of 3-phase circuits, 197, 208 Tangent method of measuring power factor, 225, 232, 237 Teaser circuit of monocyclic sys- tem, 247 Temperature coefficients of copper, n Temperature corrections, formula for, 10 Temperature of transformers, see Transformers Temperature rise, computed from change in resistance, n Third harmonic, in delta-connections, 217 in generator coils, 219 in star-connections, 218 Thompson, S. P., on regulation of alternators, 100 Three-phase systems, 197 delta and star currents and vol- tages, 204 measurement of power in, 228, 230, 233 power in, 205 transformation to 2-phase, 243 Thury system of direct current power transmission, 221 Time degrees, 106 Tirrell regulator, 13, 70, 251 Topographic method, 199, 203 Torda-Heymann, on regulation of alternators, 100 Torque, expressions for, 28 how created, 28 in a generator, 27 in a motor, 30 in compound motor, 35 in differential motor, 36 264 INDEX. Torque, in series motor, 39, 40 in single-phase and polyphase machinery, 197 static, 29 Total characteristics (see Character- istics), 7, 8, 19 Transformer, adjustment of voltage in testing, 172 aging of iron in, 130 all-day efficiency, 167 auto-transformers, 134-136 best frequency for, 64 circle diagram, 179-195 circulating current test, 144 computation of efficiency, 166 constant current, 127 constant current from constant potential, 190 copper loss, 165 core loss, 155 current density in, 140 current ratio of, 143 design data, 139-142 electromotive force and flux, 144, 146 efficiency, 139, 178 equivalent circuits of, 186-192 equivalent leakage reactance of, 150 equivalent primary quantities, 187 equivalent resistance of, 150, 159, 160 exciting current, 137, 151, 153 154 flux density in, 140 form-factor, effect of, 176 general discussion of, 179-189 harmonics due to hysteresis, 182 heat runs, 177 heating of, 130 hysteresis in, see Hysteresis insulation tests, 177 impedance, 163 impedance ratio, 165 impedance voltage, 162 instruments for testing, 171 load losses in, 161 loading back method, 177 losses in, 129 magnetic densities in, 141 magnetic leakage in, 137 magnetizing .current in, 154, 180 maximum efficiency of, 167 net and gross cross-sections, 140 normal current and voltage in, 173 open circuit test, 151 operation and study of, 128-149 Transformer, phase of primary and secondary electromotive forces and currents, 134 polarity of coils, 132, 133 polarity test by alternating cur- rent, 142 polarity test by direct current, 143 polyphase, 131, 210 potential ratio of, 143 ratio of transformation of, 133 reactance drop in, 129 reactance of, 163 resistance drop in, 129 resistance of, 163 regulation of, 139, 167, 193, 194 secondary quantities in terms of primary, 187 separation of hysteresis and eddy current losses in, 175 series, 131 short-circuit test, 160 step-up and step-down, 128 systems of polyphase connections, 210 T-connection of, 243 test by the method of losses, 150-178 total voltage drop in, 194 tub type, 131 types of, 130 variation of core losses in, 156-158, 173-176 voltage and current transforma- tion, 128 volts per turn, 141 weight of copper and iron in, 141 Transmission lines, regulation of, 101 Two-phase system, 196 laboratory supply, 201 transformation to 3-phase, 243 transformation to 6-phase, 248 Unipolar dynamo, 2 V-connection, of 3-phase circuits, 197, 209 of auto-transformers for starting motors, 248 Vectors, addition and subtraction of, 213-216 direction of rotation of, 105 for representing admittances, 118 for representing currents and electromotive forces, 105 for representing impedance, re- sistance and reactance, 109 for representing non-harmonic quantities, 122 INDEX. 265 Vectors, in magnetomotive force method of predetermining al- ternator characteristics, 96 relative accuracy when applied to inductive and capacity circuits, 122 significance of, 105 Voltage adjustment, 10 Voltage per phase, 212 Voltmeters, damage due to induced electromotive force, 12 methods of connecting when used with a wattmeter, 148 multipliers for, 149 power consumed in, 148 Wattless current, 115 Wattless power, 107 Wattmeters, correction for power consumed in instrument, 151 errors in, 146-149 multipliers for, 149 n wattmeter method of measuring power, 228, 240 n-i wattmeter method of meas- uring power, 226, 240 negative reading of, in 3-phase power measurements, 233 one wattmeter methods of meas- uring 3-phase power, 233 polyphase, 229 two wattmeter method of meas- uring power, 228 Wave winding, 3 Woodbridge, on converters, 211 Workman, motor testing, 56, 61 Y-connected, see Star-connected THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. 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