(°ru tcb*A- &■ f drajuo- 
 
 of the American Institute of Electrical Engin- 
 eers , Buffalo , August 22nd , iqoi . 
 
 
 [advance copy subject to revision] 
 POWER FACTOR INDICATORS. 
 
 BY WILLIAM HAND BROWNE, JR. 
 
 The introduction of induction motors in factories brings with 
 
 it a power factor considerably less than unity. Since this re- 
 quires a larger current for a given power delivered, the total 
 available output of the generating plant is less, and the efficiency 
 of the system is lower than if the load were non-inductive. Fui- 
 ther, the wattless component of the current causes increased 
 armature reactions, and consequently seriously affects the regula- 
 tion of the system. 
 
 It therefore may be thought desirable to balance wholly or in 
 part the wattless component of current, due to the induction 
 motors, by the use of synchronous motors or converters, and it 
 then becomes necessary to have some means of knowing when 
 this has been accomplished. 
 
 Methods of Determining Balance . — One method of judging 
 the conditions of the system, which is used to some extent, is to 
 place an ammeter in the line carrying the current for both in- 
 duction and synchronous motors. Then to secure a balance, the 
 excitation of the synchronous motor is changed until the line cur- 
 rent is a minimum. This method, while simple, is exceedingly 
 crude, and becomes entirely unreliable when the synchronous 
 motor is fairly well loaded. As the power factor of the system 
 approaches unity under these conditions, a comparatively large 
 change in the excitation of the synchronous motor produces little 
 or no apparent change in the ammeter reading. This is because 
 the characteristic v curve of the synchronous motor, i. e ., arma- 
 
 475 
 
476 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 ture current on a field current base, is quite flat for large loads. 
 The wattless component of current, however, changes very rapidly 
 as will be shown later. The same criticism applies to the use of 
 an indicating wattmeter for securing balance. Here the excita- 
 tion of the synchronous motor is changed until the volt amperes 
 as found from the ammeter and voltmeter readings are equal to 
 the true watts as indicated by the wattmeter. 
 
 To show that both of these methods are unreliable, suppose a 
 small error has been made in reading the ammeter or wattmeter, 
 due to carelessness or to instrumental errors. Fig. 1 illustrates the 
 effect of this error on the wattless component of current, or what 
 
 Fig. 1. — Curve showing the rate of change of the sine with the cosine. 
 
 is the same thing on sin the inductance factor ; k l represents 
 the power factor for different percentage differences between the 
 true and apparent watts, m n is the corresponding inductance factor 
 curve. For an error of 1 per cent, the inductance factor is .14. 
 For an error of 2 per cent, the wattless component of current is 
 nearly 20 per cent, of the total current. That is to say, when the 
 attendant thinks he has secured a balance, the wattless current fnay 
 still be a very considerable fraction of the whole, and seriously 
 affect the regulation of the generator. 
 
 Behavior of a Synchronous Motor.— Fig. 2 shows how a syn- 
 chronous motor will behave under these conditions. Here a con- 
 
1901. J BROWNE ON POWER FACTOR INDICATORS. 477 
 
 Btant applied voltage and a constant true watts input have been 
 assumed, with a variable inductance factor. That is to say, 
 El cos (p is constant, at 5 kilowatts, represented by the horizontal 
 line fa . (Fig. 2). 
 
 The base taken here is El sin <p. The curve b c is cos <p for diff- 
 erent values of El sin ip. The curve o d shows the corresponding 
 values of sin ip ; f q is the armature current. These curves show 
 
 that as we approach unity power factor cos ip changes slowly and 
 the total current changes slowly, but sin ip (and hence / sin ip) 
 changes very rapidly. 
 
 The need of an instrument which will indicate accurately the 
 condition of the system as regards balance being evident, it be- 
 comes worth while examining the methods and instruments 
 available for such determinations, as well as the quantities to be 
 measured. The phase difference of two waves is usually defined 
 as the displacement in degrees between the points where they 
 
478 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 pass, in the same direction, through zero or their maximum 
 values. In alternating current theory, where the two waves are 
 assumed sinusoids and one is the e.m.f. and the other the cur- 
 rent, the cosine of the phase angle is called the power factor. It 
 is equal to the ratio of true watts to volt amperes. In practice 
 while we may not have sinusoids, this ratio is still called the 
 power factor and may be considered as the cosine of the phase 
 angle of the equivalent sinusoids. 
 
 As pointed out above, measurements for determining the phase 
 angle are unsatisfactory when involving the cosine, if the cosine 
 approaches unity. We must measure either the phase angle 
 directly or indirectly, or what in most cases would be equally 
 satisfactory, the wattless volt amperes ; that quantity Mr. Stein- 
 metz has called the “ wattless power.” 
 
 Unfortunately few of the methods suggested for measuring 
 these quantities are more than laboratory methods, and the in- 
 struments used are unsuitable for practical work. The split 
 dynamometer of Blakesley, the three voltmeter method of Flem- 
 ing, and the three ammeter method of Sumpner are too familiar 
 to need description here, and are hardly applicable under the 
 usual operating conditions. There are, however, two or three 
 instruments which give satisfactory gervice under proper con- 
 ditions. 
 
 Glassification .. — Power factor indicators may be divided into 
 four classes : 
 
 1. Phase meters, by which the phase angle is determined 
 directly. 
 
 2. Power factor meters, measuring a function of the phase 
 angle. 
 
 3 Wattless power meters, measuring El sin ip. 
 
 A. Wattless current meters, measuring 1 sin ip. 
 
 In the first class we may include, in addition to types to be 
 described below, all forms of oscillographs and curve tracers. 
 
 In the second class we may include all instruments measuring 
 sin ^.and tan (p as well as cos ip. 
 
 These classes may be further subdivided, according to the 
 means employed to obtain an indication, into four types : 
 
 (a.) Electromagnetic, using the force of attraction of electro- 
 magnets. 
 
 (i b .) Electro-dynamic, utilizing the reaction between coils carry- 
 ing currents. 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 47& 
 
 ( c .) Induction, a rotating magnetic field is set up and used to 
 deflect a disk. 
 
 ( d ) Electrolytic, depending upon electrolysis to secure a 
 record. 
 
 Phase Meters . — The various types of oscillographs and curve 
 tracers are too well known to need description. In general they 
 are laboratory instruments and not applicable to commercial 
 working. 
 
 Tumtfs Phase Meter 1 (1&).— Let the pair of coils a b (Fig. 3) 
 carry the current whose phase angle, referred to the e. m. f. is 
 desired. 
 
 Within the space between the two, suspended freely, is the 
 movable system c d, consisting of two independent windings con- 
 nected together mechanically at right angles. Let a be the angle 
 
 which d makes with the axis of a b. 
 
 When a current i x — l x sin (co t — <p ) passes through a b; this 
 sets up an alternating flux in the space between them equal to 
 
 N = sin (co t — <p) 
 
 JV 0 being the maximum value of the flux and co times the fre- 
 quency. Through d pass a current in phase with the e. m. f. 
 This will be 
 
 i. z = f 2 sin co t 
 
 1. J. Tuma in Sitzungsberichte der K. Preussischen Akademie dev Wissen- 
 schaften, vol. 106, p. 521, 1897. M. Brieger in Bulletin de V Association des 
 Ingenieurs Elcctriciens, vol. 11, p. 79, 1899. Aug. J. Bowie, Jr., in Electri- 
 cal World a.nd Engineer, vol. 86, p. 644, 1900. (Mr. Bowie works out the gen- 
 eral condition and shows the application to two and three-phase circuits.) H. 
 Armangat in L Eclair age Electriqne , vol. 25, p. 339. (Hartmann and Braun 
 instrument.) 
 
480 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 And through c pass a current in quadrature with this 
 h = h sin (co t — ^ 
 
 The torque set up between a b and d will be 
 
 T x — N i 2 sin a 
 
 Between a b and c 
 
 T 2 = N % cos a 
 
 Substituting for n, i 2 and i 3 , the values given above, the effec- 
 tive values are 
 
 rji jVq L • 
 
 1 1 = — - — * sin a cos (p 
 2 y 
 
 T — ^ ) 
 
 cos a sin (p 
 
 Since the coil is free to turn, the angle a will be such that 
 T x = T 2 , then 
 
 #0 
 
 sin a cos (p 
 
 n q i 2 
 
 cos a sin (p 
 
 tan a :: tan ip 
 
 The angle a is the phase angle. 
 
 Induction Phase Meters (Id). — If we pass through two coils, 
 concentric but set at an angle with each other, currents which 
 set up equal fluxes differing, however, in phase, a rotating mag- 
 netic field of elliptical form will in general be created. If the 
 two coils are inclined at an angle which is the supplement of the 
 phase angle, the resulting field will have a constant value. An 
 armature suitably placed in such a field will cause a ray of light 
 reflected from an attached mirror to travel in a circle. In apply- 
 ing this method it is necessary to have the fluxes of equal value 
 and to change the angle between the coils until the ellipse be- 
 comes a circle when the phase angle is read off directly. The 
 instruments of Angelmeyer 1 2 , Korda 1 , Hess 1 , Rossi 3 and one of 
 Arno 3 , make use of this principle. 
 
 1. (a) “Mesure des Differences de Phase.” P. Fontaine in Bulletin de V As- 
 sociation des Ingenieurs Electriciens , Nov. 1899. 
 
 2. L'Edairage Electrique, vol 15, pp. 133, 322, 355, 1898. 
 
 3. Ibid , vol. 21, p. 225, 1899. 
 
1901.] BROWNE ON POWER FACTOR INDICATORS . 
 
 481 
 
 Electrolytic Phase Indicator (16?.) — A very simple device, due 
 to Janet 1 , consists of a metallic drum upon which rest two styli 
 of iron. One of these is connected so as to have a difference of 
 potential between it and the drum which is in phase with the 
 current, the other one which is in phase with the e. m. f. On 
 the drum is stretched a sheet of paper which has been soaked in 
 potassium ferrocyanide and ammonium acetate. 
 
 When the difference of potential between either stylus and the 
 drum reaches a certain positive value, electrolysis begins and the 
 paper under that stylus turns blue. Now if the drum be turned, 
 each stylus traces a broken blue line on the paper, each blue 
 mark representing part of a positive half wave. The angular dis- 
 tance from the center of one of these short lines and that of the 
 corresponding mark made by the other stylus, expressed in elec- 
 trical degrees, is the phase angle. This is true only when the 
 two waves have the same form. 
 
 Power Factor Meters (2). — Two harmonic motions acting at 
 right angles and having the same frequency and amplitude but a 
 difference in phase of 90°, will produce, if acting at the same 
 time, a uniform circular motion. If the amplitudes are not the 
 same, the result is an ellipse, the major and minor axes of which 
 are the respective paths of the two harmonic motions. 
 
 If the phase difference is not 90° the two axes of the resulting 
 ellipse do not coincide in direction with the two harmonic mo- 
 tions. 
 
 Puluy's Power Factor Meter (2a). — The principle just de- 
 scribed has been made use of by Puluy. Two electro-magnets, 
 through the winding of each of which, one of the currents, the 
 phase difference of which is desired, is passed, act upon two ar- 
 matures causing them to vibrate in planes normal to each other. 
 A ray of light falling upon a mirror attached to one of these and 
 reflected to a second mirror on the other, and thence to a screen, 
 will describe an ellipse, the shape and position of which is de- 
 termined by the values of the two currents and the phase differ- 
 ence. 
 
 Let X be the amplitude of one vibration and Y that of the 
 other. It is evident that a rectangle, the sides of which are re- 
 spectively 2 X and 2 Y, can be circumscribed about this ellipse, 
 Fig. 4. Now when either one of the magnets is acting alone, a 
 
 1. See reference ( a ) above. 
 
482 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 straight line will be described, 2 X or - 2 Y in length. The inter- 
 section of these lines will be the center of the ellipse. 
 
 The co-ordinates of any point on the ellipse, referred to^ these 
 two lines, will be 
 
 x = X sin to t (1) 
 
 y — Y sin {to t — <p) (2) 
 
 tp being the difference in phase 
 In equation (1) let x = 0, then 
 
 to t — n n 
 
 n being some whole number. 
 
 Substituting in (2) 
 
 Vo = Y sin (n it — tp) 
 
 = ± Y sin tp = OC (Fig. 4) (3) 
 
 Again let y = 0 in (2), then 
 
 to t — tp = n 7i 
 x 0 = X sin {n tt -)- <p) 
 
 — ± X sin tp — 0 D ^Fig. 4) 0 v (4) 
 From (3) and (4) it follows that 
 
 sin tp 
 
 o c _ o_d 
 
 O B ' 0~A 
 
 MorlancPs Power Factor Meter . — In an apparatus described 
 by Mr. Morland 1 , the two conductors carrying the two currents 
 pass between the poles of a permanent magnet. Each of these 
 causes a small mirror to vibrate, producing the result just des- 
 cribed. 
 
 Claude's Power Factor Meter. — Claude 2 places the two elec- 
 tro-magnets in direct opposition and causes them to actuate the 
 same armature. Let the maximum flux set up by each coil be N. 
 The ray of light reflected from the mirror will under the influ- 
 ence of the flux X oscillate along a path in length K X, K being 
 a constant. If both coils were acting and if the currents were in 
 phase, the length of this path would be 2 K X. 
 
 1. Apparatus for illustrating change of phase, S. I. Moreland, Electrical En- 
 gineer , Vol. 28, p. 237. Sept. 8, 1898. 
 
 2. See reference ( a ) above. 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 483 
 
 Call this d x . At any instant the flux due to one coil will be 
 
 
 JV t = N sin (o t 
 
 (1) 
 
 That due to the other will be 
 
 
 
 N 2 = N sin (a) t — (f) 
 
 (2) 
 
 Writing (1) 
 
 f 
 
 + 
 
 I 
 
 3 
 
 *QQ 
 
 tei 
 
 II 
 
 
 and (2) 
 
 N % = N sill [(cot — I] — 1 1 
 
 
 
 L\ -A 2 J 
 
 
 and taking the sum we have 
 
 N, + = 2N sin (co t — cos | 
 
 and the path to the ray is 
 
 Call this d 2 . 
 
 Then it follows that 
 
 2 N K cos 2. 
 
 2 
 
 It is evident from what has been said above that this method 
 will not be accurate when <p approaches zero. 
 
 Rayleighs Power Factor Meter (2a). — Lord Rayleigh’s ap- 
 paratus 1 for measuring phase angles is somewhat similar to the 
 above. The movable loop is replaced by a soft iron needle and 
 the two coils are placed on opposite sides of this. The equation 
 then becomes 
 
 + ^2 + 2 \/d t d 2 cos <p = d s 
 
 The deflections are measured as in a reflecting galvanometer. 
 Mr. Edwin Place 2 gives the results of a great number of experi- 
 ments made with an instrument of this type. He shows that the 
 angle found in this way is that between the equivalent sine waves. 
 The cosine of this angle, however, is not given by the ratio of 
 true watts to volt amperes, the true power factor. 
 
 Tuma 3 describes an instrument similar to the above but with 
 
 1. Philosophical Magazine, May, 1897. 
 
 2 Electrical World and Engineer , May 13, 1899. p. 614. 
 
 3. Sitz u n guberichte der K. Preussischen Akademie der Wi sens haf ten (Berlin) 
 vol. 106, p. 442, 1897. 
 
484 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 the coils at right angles. One of these lies in the magnetic 
 meridian. 
 
 He shows that, with specially wound coils, if ip is the phase 
 angle and ip the angle between the needle and that coil which 
 lies in the magnetic meridian, then 
 
 cos ip = tan 2 p. 
 
 Dynamometer Types. — A Siemens electro-dynamometer 1 hav- 
 ing two fixed coils may be used for phase angle measurements 
 if the movable system be replaced by a coil closed upon itself 
 and suspended in the plane of the other two. 
 
 1. If a current i x — I x sin to t be passed through one coil, 
 
 it will set up an e. m. f. in the movable loop 
 
 e x — — M a) 1 \ cos io't. 
 
 2. When the current i 2 = 1 2 sin (to t — ip) passes through 
 
 the second coil it will set up in the movable coil an e. m. f. 
 
 e 2 — — M o) / 2 cos (to t — ip) 
 
 M is the mutual inductance and is assumed the same in each 
 case. 
 
 3. If the two currents are flowing at the same time, we have 
 in the movable coil 
 
 e \ + e 2 — — il/ co [/j cos it) t -|- I 2 cos {to — ip) J 
 
 Denoting the angles of torsion necessary to keep the mova- 
 able coil in its zero position in the three cases by d h d 2 and 
 <# 3 , respectively, and by t the constant of the instrument by K, 
 we have 
 
 Kd x = M 2 to 2 1'\ efl 
 
 Kd 2 = M 2 to 2 7 2 2eff . 
 
 jK dz= M 2 (O 2 ( K l\ efl -f- 1\ e ff — 2 I\ 1% eff. COS ip) 
 
 Hence 
 
 d\-\- d 2 — 2 s/ d x cos <p = d s 
 
 and the phase angle is deduced from this relation. 
 
 . See reference (a) above. 
 
1901.] BROWNE ON POWER FACTOR INDICATORS . 
 
 485 
 
 Arno’s “ Tangent Phase Meter ” (2 b ). — A second power meter 
 of Arno’s 1 consists of a Siemens electro-dynamometer with an 
 additional pair of coils closed upon themselves and fastened to- 
 gether at right angles. The pair as a whole is suspended within 
 the two other coils and may be held in any position by a torsion 
 spring. In Fig. 5 let a and b be the two coils of the dynamom- 
 eter and c and d the pair of short-circuited loops. 
 
 Passing the two currents through a and b respectively, the in- 
 strument becomes a wattmeter and we have 
 
 l x / 2 cos cp = ici d x (1) 
 
 where d x is the angle of torsion required to keep the movable 
 coil in position. h x is the constant for this system. 
 
 Now fix b and pass the current I x through a, this will set up 
 in c an e. m. f. 
 
 
 M L x CO cos CO t 
 
 M l x co sin 
 
 (" 
 
 This will cause in c a current 
 
 i x = — I x co sin (cot — 
 
 r x . . 1 V 2/ 
 
 1. L’ Eclair age Electrique, vol. 12, p. 5. J 0; vol. 21, p. 226; vo], 25, p. 484; 
 also reference (a) above. 
 
486 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 The inductance of the loop is assumed negligible ; r x is the re- 
 sistance. 
 
 This current being in quadrature with that in a will set up no 
 torque. 
 
 The current in a will have no inductive effect upon the loop n 
 since they are kept at right angles. 
 
 If at the same instant a current I 2 is passed through b, we will 
 have at this instant in b > 
 
 h 
 
 1 2 sin (co t — cp ) 
 
 e 2 = M / 2 a) sin (co t — - — cp) 
 
 and a current 
 
 M T . , . 7T 
 — 1 2 co sin (co t — - 
 r 2 
 
 — 9) 
 
 This assumes the same mutual inductance for each pair of coils 
 and the same resistance for the two loops c and d. 
 
 This current will react with that in a and set up a torque pro- 
 portional to their product 
 
 ^ ^ I* co sin co t sin (co t — - — cp) 
 v 2 
 
 The effective value of this torque is 
 
 M l, I 2 
 2 r 
 
 co cos 
 
 2 r 
 
 co sin cp 
 
 It is evident that the couple existing between b and c will have 
 the same value but have an opposite sign, since the current in c 
 being in quadrature with that in a will be less than 90° behind 
 b, while that in d will be more than 90° behind a. 
 
 The resulting torque of the system is proportional to I x I 2 sin cp 
 and may be written 
 
 I x 1 2 sin = Jc 2 d 2 (2) 
 
 where k 2 is a constant and d 2 the angle of torsion. 
 
 Dividing (2) by (1) we have 
 
 h d 2 
 
 = tan cp 
 
 giving the phase angle in terms of its tangent. 
 
1901.] BROWNE ON POWER FACTOR INDICATORS. 487 
 
 Breitfield's Method (2b). — Mr. C. Breitfield 1 has suggested an 
 application of an ordinary wattmeter for measuring the power 
 factor of a three-phase system. The current coil is placed in one 
 line and one end of the pressure coil also connected to this line. 
 The other end is first connected to the second line and then to 
 the third. In the first case we have the deflection 
 
 d x = El cos (<p — 30°) 
 
 In the second 
 
 d % = E I cos (<p -|- 30°) 
 
 From these equations we have 
 
 d\ — d 2 = E I sin <p sin 30° 
 
 Hence 
 
 di + d 2 = E I cos <p cos 30° 
 
 tan <p 
 
 VS 
 
 d\ — d* 
 —d\ + d^ 
 
 General Electric Company's Instrument (2b). — The well- 
 known fact that the ratio of the readings of the two wattmeters 
 used to measure the power of a three-phase system changes with 
 the power factor and is unity when the power factor is unity, has 
 been made use of by the General Flectric Company to indicate 
 the power factor. The instrument 2 is simply two wattmeters of 
 the dynamometer type, the movable coils of which are attached 
 to the same spindle. The instrument deflects to the right or left 
 according as the current lags or leads, and stands at zero when 
 the system is balanced and the power factor unity. 
 
 Eerraris ’ Power Factor Meter (2c.). — Ferraris 3 combines two 
 harmonic fields, producing a rotating field of elliptical form. 
 Within this field is suspended a short-circuited coil which can be 
 held in any position, by a torsion spring, as is the movable coil of 
 a Siemens dynamometer. The force required and therefore the 
 angle through which the spring must be turned, to hold the coil 
 in any position is proportional to the square of the intensity of 
 the flux in that direction. Points can thus be determined and 
 
 1. Electrotechnische Zeitschrift, vol. 20, p. 120, 1899. 
 
 2. Electrical World and Engineer , vol. 67, p. 688, April 27, 1901 . 
 
 3. See reference (a) above. 
 
488 
 
 BRO WISE ON PO WER FA GTOR INDIG A TORS. [Aug. 22, 
 
 the ellipse plotted and the sine of the phase angle deduced as 
 above. (See Puluy’s Method, page 481.) 
 
 Power Factor Indicators (3). — In the methods described 
 above, the object sought was the determination of the phase angle. 
 But few of these are applicable under the usual operating condi- 
 tions. We might mention as useful forms, those of Turaa and 
 the General Electric Co. In most cases, however, we are more 
 concerned with the magnitude of the wattless component of cur- 
 rent than with the power factor. We care less about the decrease 
 in the total output than about the poor regulation caused by in- 
 ductive loads. Instruments which will indicate the wattless 
 current, or rather the wattless volt amperes are easily made in 
 commercial form. 
 
 “ Wattless Wattmeters .” Dynamometer Type (3b). — A Sie- 
 mens dynamometer becomes a wattmeter indicating E I cos (p 
 when the current is passed through one coil and a current pro- 
 portional to and in phase with the e. m. f. through the other. 
 
 If the current in the pressure coil be in quadrature with the 
 e. m. f. the instrument indicates El sin <p , the wattless volt am- 
 peres. 
 
 This is easily done with a two-phase system. With a single- 
 phase system it is necessary to place a proper condenser or induc- 
 tive reactance in series with the pressure coil. 
 
 “ Wattless Wattmeter sP Induction Type (3c). DobrowolskVs 
 Power Factor Indicator 1 . — In a fully compensated induction 
 meter the shunt flux is in quadrature with the series flux, the 
 result of the two being a rotating or shifting field. If the shunt 
 flux be brought into phase with the series flux an alternating field 
 only will be set up as long as the current and e. m. f. are in phase. 
 If, however, the current lags, the field will rotate in one direc- 
 tion. If it leads, the field will rotate in the opposite direction. 
 The torque developed on a disk placed in this field is, in either 
 case proportional to El sin <p , the wattless volt amperes. This is 
 the principle of Dobrowolski’s apparatus. 
 
 The movable disk is held in its zero position by a spring when 
 the wattless volt amperes are zero, but deflects one way or the 
 other, when the current is out of phase, an amount proportional 
 to El sin (p. 
 
 Any induction wattmeter can be used in this way provided the 
 flux through the pressure coil be brought into phase with the 
 
 E. M. F. 
 
 1. U. S. latent No. 549,449, 1896. 
 
1901.] 
 
 BRO WNE ON POWER EAR TOR INDICATORS. 
 
 489 
 
 Wattless Current Meters (4 ). — The Allegemeine Electricitats 
 Gesellschaft make an instrument 1 which indicates the wattless 
 current. This is really an induction wattmeter having the shunt 
 flux in phase with the e. m. f. and indicates therefore only when 
 there is a phase difference. As an instrument of this type indi- 
 cates El sin <p , it is presumed that this meter is graduated to read 
 
 200 
 
 600 
 
 800 
 
 I sin (p at normal voltage, and should properly come under 
 “ wattless wattmeters” (3c.) 
 
 Behavior of Power Factor Indicators. 
 
 The Siemens Electro-dynamometer. = Th.Q following set of 
 curves (Fig. 6) were taken with a Siemens dynamometer, the 
 
 1. L' Eclairage Electrique, vol. 35, p. 389. 
 
490 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 movable coil of which was in series with a capacity of 3.5 micro- 
 farads. The values of cos <p, sin <p and El sin y plotted have been 
 computed from ammeter, voltmeter and wattmeter readings given 
 in Table I. 
 
 El sin (p is a straight line and is plotted above and below the 
 axis todndicate lagging and leading currents respectively. The 
 base^is the deflection in degrees. These curves were taken for a 
 constant power delivered, of 500 true watts. The displacement 
 of current was obtained by means of a phasing transformer. For 
 comparison between El sin <p and cos <p the axis of .abscissae is 
 taken as^unity for the latter, and the decreasing values plotted 
 above and below this. 
 
 TABLE. 1. 
 
 Siemens Dynamometer as Power Factor Indicator. 
 
 Amp. 
 
 / 
 
 Volts 
 
 E 
 
 Watts 
 El cos (j) 
 
 Deflec- 
 
 tion. 
 
 Direc- 
 
 tion. 
 
 Phase 
 
 Apparent 
 
 watts 
 
 El 
 
 Power fac- 
 tors 
 COS <t> 
 
 Induct- 
 ance fact- 
 ors sin 0 
 
 AYsinc 
 
 10.15 
 
 108 
 
 500 
 
 213 
 
 Right 
 
 Lead 
 
 1096 
 
 • 456 
 
 .889 
 
 975 
 
 8.4 
 
 108 
 
 500 
 
 158 
 
 
 “ 
 
 907 
 
 • 552 
 
 • 834 
 
 755 
 
 7-58 
 
 107.9 
 
 500 
 
 141 
 
 “ 
 
 *■ 
 
 818 
 
 .611 
 
 .791 
 
 647 
 
 6.51 
 
 108 
 
 500 
 
 106 
 
 “ 
 
 “ 
 
 703 
 
 .711 
 
 •703 
 
 494 
 
 5-63 
 
 107.8 
 
 500 
 
 78 
 
 “ 
 
 “ 
 
 607 
 
 .823 
 
 .568 
 
 294 
 
 5-25 
 
 107.8 
 
 500 
 
 53 
 
 “ 
 
 “ 
 
 516 
 
 .884 
 
 .467 
 
 241 
 
 4.78 
 
 105.5 
 
 500 
 
 13 
 
 Left 
 
 Lag 
 
 504 
 
 .992 
 
 .126 
 
 63 
 
 5.05 
 
 105.7 
 
 500 
 
 44 
 
 “ 
 
 “ 
 
 533 
 
 •938 
 
 •346 
 
 185 
 
 5-67 
 
 106. 1 
 
 500 
 
 76 
 
 “ 
 
 “ 
 
 602 
 
 .831 
 
 •555 
 
 334 
 
 8.17 
 
 106 
 
 500 
 
 155 
 
 “ 
 
 11 
 
 866 
 
 •577 
 
 .817 
 
 707 
 
 9.61 
 
 105.9 
 
 500 
 
 197 
 
 U 
 
 
 1007 
 
 •497 
 
 .867 
 
 873 
 
 Note. — Pressure coil in series with 3.5 microfarads capacity. 
 
 We notice first that these lines do not pass through the origin. 
 The resistance of the pressure coil is not negligible, as the in- 
 strument shows a slight deflection at unity power factor. The 
 curves show verjr clearly that a slight change in the power factor 
 when near unity caused a comparatively large change in the 
 value of El sin <p. 
 
 This fact is very striking when working with the instrument. 
 It may be made to deflect considerably to the right or left with- 
 out producing any appreciable change in the reading of the 
 Weston wattmeter, the current and voltage remaining constant 
 the while. 
 
1901.] 
 
 BROWNE ON POWER FAC 'LOR INDICATORS. 
 
 491 
 
 Power factors for larger power delivered, lie below the one 
 just considered and hence are still flatter when approaching 
 unity. One for 1,000 true watts has been plotted from calculated 
 values only. It shows that it would be practically impossible to 
 say from ammeter, voltmeter and wattmeter readings alone, 
 when the current was in phase with the e. m. f. With the power 
 factor indicator, however, there would be no difficulty in getting 
 an almost exact adjustment. 
 
 Fig. 7. 
 
 f" Weston Wattmeter as Power Factor Indicator . — In Fig. 7 is 
 given the characteristic of a Weston wattmeter of 150 volts, 50 
 amperes capacity, used on a two-phase system in the manner 
 described above. The characteristic is a straight line, but does 
 not pass through the origin. 
 
 This may be due either to the slight inductance of the pressure 
 coil, or to a slight change in the phase angle between the im- 
 pressed e. m. f.’s or to both. 
 
492 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 The method of calibrating consisted in connecting the pressure 
 coils of the power factor indicator and wattmeter respectively to 
 the two primary windings of a two-phase induction motor, used 
 as a phasing transformer. The current coils of the meters were in 
 series and connected to the movable secondary. As the secondary 
 is shifted, the load is partially shifted from one phase of the primary 
 winding to the other. This doubtless caused a slight change in the 
 phase angle between the e. m. f.’s at the motor terminals. The 
 motor used was rated at two horse-power. The supply was drawn 
 from two 4 k. w. transformers, both partially loaded in addition 
 with lights. 
 
 TABLE II. 
 
 Weston Wattmeters as Power Factor Indicator. 
 
 True 
 
 Watts. 
 
 Vcltage. 
 
 Amperes. 
 
 Wattless 
 volt am- 
 peres ob- 
 served. 
 
 Phase 
 
 relation. 
 
 Volt-am- 
 
 peres. 
 
 Power 
 
 factor. 
 
 Induct- 
 ance fac- 
 tor com- 
 puted. 
 
 Wattless 
 volt-am- 
 peres com- 
 puted. 
 
 IQ70 
 
 in . 5 
 
 44.4 
 
 4530 
 
 Lag 
 
 4950 
 
 •398 
 
 . - 9^7 
 
 4540 
 
 
 “ 
 
 34 -7 
 
 3325 
 
 ‘ 
 
 3 8 7 «> ■ 
 
 .509 
 
 .860 
 
 3330 
 
 
 “ 
 
 29.8 
 
 2690 
 
 
 334 ° 
 
 .590 
 
 .807 
 
 2690 
 
 
 “ 
 
 25.0 
 
 1950 
 
 “ 
 
 2790 
 
 .706 
 
 .708 
 
 z 975 
 
 
 “ 
 
 20.1 
 
 1050 
 
 “ 
 
 2240 
 
 .879 
 
 •477 
 
 1070 
 
 
 “ 
 
 17.7 
 
 180 
 
 “ 
 
 1975 
 
 •997 
 
 .071 
 
 140 
 
 
 “ 
 
 17.65 
 
 0 
 
 - 
 
 1970 
 
 1.0 
 
 .0 
 
 0 
 
 
 
 20.1 
 
 1130 
 
 Lead 
 
 2240 
 
 .879 
 
 •477 
 
 1070 
 
 
 
 25.0 
 
 2050 
 
 “ 
 
 2790 
 
 .706 
 
 .708 
 
 x 975 
 
 
 
 29.8 
 
 2785 
 
 “ 
 
 3340 
 
 •590 
 
 .807 
 
 269 1 
 
 
 “ 
 
 34-7 
 
 3420 
 
 “ 
 
 3870 
 
 •509 
 
 .860 
 
 333 ° 
 
 44 
 
 “ 
 
 44.4 
 
 461c 
 
 “ 
 
 4950 
 
 •398 
 
 .917 
 
 454° 
 
 The agreement between observed and calculated values of El 
 sin <p is good. Table II gives observed and computed values for 
 this instrument. 
 
 Induction Meters . — In Fig. 8 are shown a set of curves ob- 
 tained from a Shallenberger integrating wattmeter used as a power 
 factor indicator. The instrument is a 500-volt, 10-ampere meter 
 of the older type (1898). The reactive coil was replaced by a 
 non-inductive resistance of 2, 000 ohms. In series with this was a 
 capacity of 3 mf., this being found to balance the inductance of 
 the shunt coil at a frequency of 60 cycles. In this case the in- 
 strument was used as a recording meter. The curves plotted are {} 
 
1901 .] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 493 
 
 AT sin (p, cos <p and <p, all on a revolutions per minute base, for a 
 delivered power of 500 true watts. Table III gives the instru- 
 mental readings and computed values for these curves. 
 
 Fig. 9 shows the results from the same meter under somewhat 
 different conditions. Here the recording train was removed to 
 lessen the friction, and a light steel spring attached to the 
 spindle of the revolving disk. A pointer attached to the disk 
 
 CD 
 
 Fig. 8. 
 
 -e- 
 
 z 
 
 co 
 
 LU 
 
 0 
 
 300 
 
 400 
 
 800 
 
 1000 
 
 passed over a scale marked in degrees. The curves plotted are, 
 as before, El sin y>, cos <p and cp, for a delivered power of 500 
 true watts. The base is degrees deflection. It will be noticed 
 that from 20° lag to 20° lead the deflection is almost directly 
 proportional to the phase angle. The flattening of the curve for 
 cos <p is very marked. This instrument was even more sensitive 
 than the dynamometer and besides was dead beat, as the damping 
 
4 
 
 494 BRO WNE ON BO WER FACTOR 1NDICA10RS. [Aug. 21, 
 
 magnets were left in. Table IY gives tlie instrumental readings 
 and computed values for these curves. 
 
 Application of Power Factor Indicator . — To illustrate the 
 application of a power factor indicator, the Weston wattmeter 
 mentioned above was used to measure the wattless volt amperes 
 taken by a General Electric 7^-kilowatt, 125-volt, four-pole, 
 synchronous converter for different values of field current. The 
 converter was run on a two-phase system at constant input. The 
 supply was drawn from two Westinghouse 7-J-kilowatt trans- 
 formers, o. d. type, fitted with a Hartford regulator. The 
 
 TABLE III. 
 
 Shallenberger Wattmeter as Power Factor Indicator. 10 amp. 400 volts. 
 
 No. 
 
 Amp. 
 
 Volts. 
 
 Watts 
 
 r.p.m. 
 
 Direc- 
 
 tion. 
 
 1 
 
 Phase. 
 
 Appar- 
 
 ent 
 
 watts 
 
 El 
 
 Power 
 factor 
 COS (j) 
 
 Phase 
 
 Angle 
 
 <p. 
 
 Induct- 
 ance fac- 
 tor 
 
 sin <j> 
 
 E /sin (p 
 
 1 
 
 10. 01 
 
 111.3 
 
 505 
 
 30.8 
 
 Left 
 
 Lagging 
 
 1114 
 
 •449 
 
 63° — io' 
 
 .898 
 
 996 
 
 2 
 
 8 
 
 hi . 5 
 
 5°5 
 
 23-4 
 
 “ 
 
 “ 
 
 891 
 
 •567 
 
 55—27 
 
 .824 
 
 734 
 
 3 
 
 6 
 
 hi . 5 
 
 505 
 
 13-45 
 
 “ 
 
 “ 
 
 669 
 
 •75 6 
 
 4o—53 
 
 .655 
 
 438 
 
 4 
 
 5-°7 
 
 iri.o 
 
 5°5 
 
 7-45 
 
 “ 
 
 “ 
 
 563 
 
 .898 
 
 26-^06 
 
 .440 
 
 248 
 
 5 
 
 4.78 
 
 1 10. 3 
 
 5°S 
 
 4.68 
 
 “ 
 
 “ 
 
 527 
 
 •954 
 
 17 — 26 
 
 .300 
 
 158 
 
 6 
 
 4-5 
 
 hi. 9 
 
 5°5 
 
 0 
 
 — 
 
 - 
 
 5°4 
 
 1. 00 
 
 0 
 
 0 
 
 0 
 
 7 
 
 4-58 
 
 ”4-5 
 
 505 
 
 5-29 
 
 Right 
 
 Leading 
 
 525 
 
 .962 
 
 15—50 
 
 •273 
 
 M3 
 
 8 
 
 S-oo 
 
 II4-3 
 
 5°4 
 
 8.7 
 
 4 - 
 
 “ 
 
 572 
 
 .881 
 
 28 — 14 
 
 •473 
 
 270 
 
 9 
 
 6.09 
 
 112. 2 
 
 5°5 
 
 14.6 
 
 “ 
 
 “ 
 
 684 
 
 •738 
 
 42 — 26 
 
 •675 
 
 462 
 
 10 
 
 8.0 
 
 hi. 3 
 
 5°5 
 
 22.8 
 
 “ 
 
 “ 
 
 890 
 
 •567 
 
 55- 28 
 
 .824 
 
 733 
 
 11 
 
 10. 0 
 
 nr. 2 
 
 505 
 
 30.6 
 
 “ 
 
 
 1112 
 
 •454 
 
 63— CO 
 
 .891 
 
 992 
 
 Note. — Impedance coil cut out and shunt coil in series with three microfarads and 2,000 ohms. 
 
 output was absorbed by a lamp bank and water rheostat. 
 
 In Fig. 10, armature, current and wattless volt amperes have 
 been plotted as ordinates, the base being field current. The input 
 was 3J k. w. per phase. The flatness of the current curve alluded 
 to above is quite noticeable here. The characteristic for wattless 
 volt amperes is plotted above and below the axis of abscissae to 
 indicate lagging and leading currents respectively. 
 
 The instruments were quite steady, a condition indicating but 
 little hunting of the armature, although there were no devices on 
 the machine to prevent this phenomenon. The power factor in- 
 dicator, although exactly like the wattmeter, was even steadier 
 than the latter. There was no difficulty in setting the indicator 
 to read any desired value by adjusting the field current. 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 495 
 
 It was stated’ at a recent meeting of the National Electric 
 Light Association, during the discussion of a paper on synchronous 
 converters, that it was practically impossible to operate a syn- 
 chronous motor or converter at unity power factor. The reasons 
 given were hunting of the armature and dissimilar e. m. f. waves 
 of motor and generator. In the above experiment it was found 
 that the power factor indicator could be set at zero and under 
 these conditions the true watts and the volt amperes were equal. 
 This condition would seem to be that of practically unity power 
 factor. 
 
 800 
 
 TOO 
 
 600 
 
 500 
 
 400 
 
 300 
 
 200 
 
 .100 
 
 0 
 
 o 
 
 5 
 
 .■©• 
 
 z 
 
 CO 
 
 HH 
 
 LxJ 
 
 Fig. 9. 
 
 A number of power factor curves of synchronous converters 
 have been published recently in which the current passes from 
 lag to lead without the power factor passing through unity. Even 
 if it were impossible to hold the power factor at unity, it must 
 pass through this value as it swings across the line. 
 
 In Fig. 11 are plotted, on an excitation base, curves of power 
 factor from wattmeter readings and inductance factor from the 
 
 1. Western Electrician , Feb. 9, 1901. 
 
496 BRO WNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 “wattless wattmeter” readings. In addition there have been 
 plotted two curves obtained by assuming these values to be cosines 
 and ^ines of phase angles and the corresponding values of sines 
 and cosines taken from tables and plotted on the same base. 
 These deduced values do not agree at all with the observed ones. 
 The discrepancy is greater for leading than lagging currents. 
 This discrepancy, as has been pointed out by Mr. Steinmetz 1 , is: 
 
 TABLE IV. 
 
 Shallenberger Wattmeter as Power Factor Indicator. 
 
 No. 
 
 Amp- 
 
 eres. 
 
 Volts. 
 
 True 
 
 watts. 
 
 Degrees 
 
 deflection. 
 
 Direc- 
 
 tion. 
 
 Phase 
 
 Apparent 
 
 watts. 
 
 COS (p 
 
 0 
 
 sin 0 
 
 El sin (j> 
 
 i 
 
 8.29 
 
 no. 
 
 500 
 
 75° 
 
 Left 
 
 Lag. 
 
 9 11 
 
 •549 
 
 56 0 — 42' 
 
 .836 
 
 761 
 
 2 
 
 7.27 
 
 108.5 
 
 500 
 
 60 
 
 
 “ 
 
 788 
 
 •634 
 
 50—39 
 
 •773 
 
 608 
 
 3 
 
 6.54 
 
 icg. 
 
 500 
 
 50 
 
 “ 
 
 
 712 
 
 .702 
 
 45—35 
 
 .712 
 
 507 
 
 4 
 
 5-85 
 
 110.5 
 
 500 
 
 40 
 
 “ 
 
 
 646 
 
 • 774 
 
 39—17 
 
 •633 
 
 409 
 
 5 
 
 5-41 
 
 109.2 
 
 500 
 
 30 
 
 “ 
 
 
 590 
 
 .848 
 
 32 — 00 
 
 •530 
 
 3*3 
 
 6 
 
 4.94 
 
 109.9 
 
 500 
 
 20 
 
 “ 
 
 
 543 
 
 .921 
 
 22 — 56 
 
 •39° 
 
 212 
 
 7 
 
 4-57 
 
 nr. 1 
 
 500 
 
 IC 
 
 “ 
 
 
 507 
 
 .987 
 
 9—04 
 
 .158 
 
 80 
 
 8 
 
 4-59 
 
 108.4 
 
 500 
 
 0 
 
 - 
 
 - 
 
 498 
 
 1. 
 
 0 
 
 0 
 
 0 
 
 9 
 
 4-67 
 
 109. 
 
 500 
 
 10 
 
 Right 
 
 Lead 
 
 509 
 
 .982 
 
 10—53 
 
 .189 
 
 96 
 
 IO 
 
 5-35 
 
 108. 
 
 500 
 
 30 
 
 “ 
 
 “ 
 
 578 
 
 .865 
 
 30—07 
 
 .502 
 
 290 
 
 1 1 
 
 5-87 
 
 109.4 
 
 500 
 
 40 
 
 “ 
 
 “ 
 
 642 
 
 .78 
 
 38—44 
 
 .626 
 
 402 
 
 12 
 
 6-45 
 
 109.7 
 
 500 
 
 50 
 
 “ 
 
 “ 
 
 707 
 
 .708 
 
 45—05 
 
 .706 
 
 498 
 
 13 
 
 7-44 
 
 107.4 
 
 500 
 
 60 
 
 
 *• 
 
 799 
 
 .626 
 
 5i—i3 
 
 •779 
 
 623 
 
 i4 
 
 8.16 
 
 108.7 
 
 500 
 
 70 
 
 “ 
 
 
 886 
 
 •564 
 
 55—40 
 
 .826 
 
 732 
 
 Note.— Impedance coil removed and shunt coil in series with three microfarads and 2,000 ohms 
 non-inductive resistance. Recording gear removed and light torsion spring attached to disk. 
 
 due to the distortion of the e. m. f. and current waves. 
 
 Table Y gives observed and computed values for these 
 curves. 
 
 Conclusions .— It would seem from the above that there is a 
 decided need of an accurate power factor indicator in all large 
 installations, but especially in those in which induction and syn- 
 chronous motors are used together. This method of operation 
 has been adopted by the Deering Harvester Company, where ad- 
 justment of the exciting current of the synchronous machine is 
 
 1 . Symbolic Representation of General Alternating Waves and of Double- 
 
 Frequency Products. C. P. Steinmetz, Transactions, vol. 16, p. 289, 1899. 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 497 
 
 made by means of a wattmeter, and at Butte, Montana 1 , where 
 adjustment is made from ammeter readings. The advisability of 
 adopting this composite system is not in question here. We are 
 considering merely the best method of attaining the end sought. 
 
 70 
 
 7000 
 
 
 
 
 
 
 
 
 
 Ij 
 
 
 60 
 
 6000 
 
 V 
 
 
 
 
 
 
 
 
 
 
 50 
 
 o 
 
 5000 § 
 
 Il\ ' 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 40 £ 
 
 _j 
 
 h 
 
 4000 < 
 
 
 
 
 
 
 
 
 
 
 
 S 
 
 AMP 
 
 CO 
 
 1x1 
 
 3000 t 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 $ 
 
 2000 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 1000 
 
 
 
 
 
 
 
 
 
 
 
 0 
 
 0 o 
 
 5 
 
 1 
 
 0 
 
 \l 
 
 5 
 
 2 
 
 ,0 
 
 2 
 
 5 
 
 3 
 
 
 1000 
 
 
 AMPERES 
 
 
 
 
 
 EXCITA1 
 
 ION 
 
 
 
 
 2000 
 
 
 
 
 
 
 
 
 
 
 
 
 3000 
 
 
 
 
 
 
 
 
 
 
 
 
 LEADING 
 
 
 
 
 
 
 
 \o 
 
 
 
 
 
 5000 
 
 
 
 
 
 
 
 
 
 
 
 
 6000 
 
 GENERAL ELECTRIC SYNCHRONOUS CONVERTER 
 7-K KW. 125 V. 4 POLE, 60 A/ 
 
 I- I ARMATURE CURRENT 
 
 II- II “WATTLESS WATTS” 
 
 
 
 
 
 7000 
 
 
 
 n 
 
 Fig. 10. 
 
 For accurate adjusting of the system the indications of the in- 
 strument should depend upon the values of <p or sin <p and not 
 upon cos (p. 
 
 Instruments of the dynamometer or the induction type seem 
 more suitable for operating conditions. If the meter be of the 
 
 1. Elec. Lt. & Power at Butte, Mont. J. R. Cravath, Elec. W. & E., vol 
 37, p. 149, Jan. 26, 1901. 
 
498 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 dynamometer type the resistance of the pressure coil must be 
 negligible if it is to be used on a single-phase system, as the cur- 
 
 o 
 
 < 
 
 -J 
 
 o 
 
 0.9 5 
 
 
 
 
 
 
 
 
 
 
 
 -SF 
 
 CO 
 
 O 
 
 o 
 
 ■€P 
 
 0.8 g 
 
 
 
 'GENERAL ELECTRIC SYNCHRONOUS CONVERTER 
 1-Yz KW. 125 V. 4 POLE 60 A J 
 
 T-I POWER FACTOR, OBSERVED 
 
 II- II INDUCTANCE FACTOR, “ 
 
 III- III SIN 0 FROM CURVE I 
 
 IV- IV COS 0 FROM CURVE II 
 
 
 ce 
 
 O 
 
 o 
 
 < 
 
 u. 
 
 o 
 
 < 
 
 0.7 o 
 
 
 
 
 5 
 
 o 
 
 CL 
 
 0.4 
 
 < 
 
 0.6 1 
 
 
 
 
 
 
 
 
 
 
 
 0.5 
 
 0.5 > 
 
 
 
 
 
 
 
 
 
 
 
 0.6 
 
 0.4 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 0.7 
 
 0.3 
 
 
 
 
 
 
 
 
 
 
 
 0.8 
 
 0.2 
 
 
 
 
 
 
 
 
 
 
 
 0.9 
 
 0.1 
 
 
 
 
 
 
 
 
 • 
 
 
 
 1.0 
 
 0 0 
 
 5 
 
 1 
 
 ,0 
 
 o\ 
 
 .5 
 
 2 
 
 ,0 
 
 2 
 
 5 
 
 3 
 
 0.9 
 
 0.1 
 
 
 AMPERES 
 
 
 
 
 
 EXCIT/ 
 
 mON 
 
 
 
 0.8 
 
 0.2 
 
 
 
 
 
 
 \ ° 
 
 
 
 
 
 0.7 
 
 0.3 
 
 
 
 
 
 
 
 \ o 
 
 
 
 
 0.6 
 
 0.4 
 
 
 
 
 
 
 
 
 
 
 
 0.5 
 
 0.5 
 
 
 
 
 
 
 
 
 
 
 
 0.4 
 
 0.6 
 
 
 
 
 
 
 r\\ 
 
 
 
 
 
 0.3 
 
 0.7 
 
 
 
 
 
 
 o \ 
 
 \ + 
 
 
 
 
 
 0.8 
 
 
 
 • 
 
 
 
 
 
 
 /s 
 
 
 LEAD 
 
 P 1 
 
 ° leadI 
 
 
 
 
 
 
 
 
 
 
 
 
 1.0 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 11. 
 
 rent in this coil must be in quadrature with the e. m. f. 
 
 If the meter is to be used on a two or a three-phase system, 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 499 
 
 the inductance of the pressure coil must be negligibly small, and 
 meter connected in one of the methods described above. In this 
 case care must be taken that the loads on the different phases be 
 kept equal. In a two-phase system, unbalancing the phases will 
 shift the e. m. f.’s relatively to each other. In a three-phase sys- 
 tem, since the meters used are really wattmeters, unbalancing the 
 phases will vitiate the indications of the instrument. 
 
 If the meter be of the induction type the inductance of the 
 pressure coil must be negligible, since not only is it undesirable 
 
 TABLE V. 
 
 General Electric Synchronous Converter. 7-^k.w., 125 v., 4-pole, 60 2-phase. 
 Input 3.5 k.w. per phase. 
 
 Wattless 
 kilo- volt 
 amperes. 
 
 Amperes 
 
 armature 
 
 current. 
 
 Voltage 
 
 at 
 
 brushes. 
 
 Amp- 
 
 eresfield 
 
 current. 
 
 Phase 
 
 relation. 
 
 Kilovolt 
 
 amperes 
 
 Power 
 
 factor. 
 
 Induc- 
 
 tance 
 
 factor. 
 
 sin < j > 
 
 computed 
 from pow- 
 er factor. 
 
 COS (p 
 computed 
 from in- 
 ductance 
 factor. 
 
 5-55 
 
 6t.6 
 
 109.9 
 
 0.57 
 
 Lag 
 
 6 76 
 
 .518 
 
 822 
 
 •855 
 
 .569 
 
 4-23 
 
 51*3 
 
 1 10.0 
 
 O 
 
 00 
 
 
 5-64 
 
 .621 
 
 •750 
 
 •784 
 
 .661 
 
 2.62 
 
 40.9 
 
 109.9 
 
 r.03 
 
 “ 
 
 4-5 
 
 .778 
 
 ■583 
 
 .628 
 
 .812 
 
 1 45 
 
 35 7 
 
 109.7 
 
 1.2 
 
 “ 
 
 3 9 1 
 
 .895 
 
 •37i 
 
 .446 
 
 .929 
 
 o-45 
 
 32 0 
 
 109.8 
 
 1.36 
 
 “ 
 
 3-5i 
 
 •997 
 
 .128 
 
 .077 
 
 .992 
 
 — 0.05 
 
 3*-9 
 
 109.8 
 
 1.47 
 
 Lead 
 
 3-5° 
 
 1.0 
 
 .014 
 
 .0 
 
 •999 
 
 — o-45 
 
 32.1 
 
 1 ie.o 
 
 r.55 
 
 “ 
 
 3-53 
 
 992 
 
 .128 
 
 .126 
 
 .992 
 
 — 1.20 
 
 35-7 
 
 no. 4 
 
 1.69 
 
 “ 
 
 3-94 
 
 .888 
 
 .306 
 
 .460 
 
 •952 
 
 — 2.22 
 
 40.9 
 
 O 
 
 bo 
 
 1.88 
 
 “ 
 
 4-49 
 
 •779 
 
 •495 
 
 .627 
 
 .869 
 
 — 365 
 
 5i-3 
 
 IIO.O 
 
 2.22 
 
 “ 
 
 5-64 
 
 .621 
 
 .648 
 
 .784 
 
 .762 
 
 — 5 3° 
 
 6r.6 
 
 IIO. 2 
 
 2.5 
 
 “ 
 
 6.78 
 
 .516 
 
 .782 
 
 •857 
 
 .623 
 
 — 6 65 
 
 71.9 
 
 ■ 0&8 
 
 ••75 
 
 “ 
 
 7 89 
 
 •444 
 
 • 844 
 
 .896 
 
 .536 
 
 to use condensers to compensate for this, both from their bulki- 
 ness and expense, but the presence of any reactance makes the 
 deflection dependent upon the frequency. An attempt was made 
 to improve upon the induction meter described above by remov- 
 ing the three-legged stampings of iron upon which the pressure 
 coil was wound. The inductance was still too large for satisfac- 
 tory working and as the condensers in the laboratory were not 
 sufficient to compensate for this, it was necessary, to make up 
 for this lack of capacity and to avoid the use of iron, to add an 
 auxiliary inductance wound on a wooden bobbin. The instru- 
 ment thus modified was found to be so sensitive to slight changes 
 in frequency that it was impossible to use it with any degree of 
 
600 
 
 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22, 
 
 satisfaction in the laboratory. Any change of load on the prime 
 mover would so change the reading of the instrument as to make 
 its indications extremely unreliable. 
 
 Dobrowolski shows, in the reference given above, the applica- 
 tion of his instrument for automatically adjusting the excitation 
 of the synchronous machine so as to keep the power factor at 
 unity at all times. 
 
 The use of an instrument of this kind emphasizes the fact that, 
 when induction motors are used alone, the inductance factor is 
 always a large percentage of the power factor. For instance, 
 when the power factor is .85 the inductance factor, assuming 
 sinusoidal waves, is nearly 62 % of this. That is, for every kilo- 
 watt used by the motor, 620 c£ wattless watts ” are, so to speak, 
 borrowed. It would seem but fair that those who use induction 
 motors should at least pay rental for the wattless volt amperes 
 required. It is true this does not represent energy consumed, 
 but it does, in a sense, represent energy borrowed and returned 
 and the station must have sufficient capacity in generators to 
 meet all such calls for loans. 
 
 The additional charge could be taken care of by over-com- 
 pensating integrating wattmeters of the induction type, as sug- 
 gested by Mr. Benischke. They would then read high on lagging 
 reactive loads and low on leading reactive loads. This would put 
 a premium on the use of synchronous motors as they, if not too 
 greatly over-excited, help out in the regulation of the plant. The 
 induction motor has so many points in its favor it can well 
 afford to pay for what it needs— a large wattless component of 
 current. 
 
1901.] 
 
 BROWNE ON POWER FACTOR INDICATORS. 
 
 499 
 
 the inductance of the pressure coil must be negligibly small, and 
 meter connected in one of the methods described above. In this 
 case care must be taken that the loads on the different phases be 
 kept equal. In a two-phase system, unbalancing the phases will 
 shift the e. m. f.’s relatively to each other. In a three-phase sys- 
 tem, since the meters used are really wattmeters, unbalancing the 
 phases will vitiate the indications of the instrument. 
 
 If the meter be of the induction type the inductance of the 
 pressure coil must be negligible, since not only is it undesirable 
 
 TABLE V. 
 
 General Electric Synchronous Converter. 7-Jk.w., 125 v., 4-pole, 60 2- phase. 
 
 Input 3.5 k.w. per phase. 
 
 Wattless 
 kilo- volt 
 amperes. 
 
 Amperes 
 
 armature 
 
 current. 
 
 Voltage 
 
 at 
 
 brushes. 
 
 Amp- 
 eres field 
 current. 
 
 Phase 
 
 relation. 
 
 Kilovolt 
 
 amperes 
 
 Power 
 
 factor. 
 
 Induc- 
 
 tance 
 
 factor. 
 
 sin ( j ) 
 
 computed 
 from pow- 
 er factor. 
 
 COS (p 
 computed 
 from in- 
 ductance 
 factor. 
 
 5-55 
 
 6t.6 
 
 109.9 
 
 o -57 
 
 Lag 
 
 6 76 
 
 .518 
 
 822 
 
 •855 
 
 •569 
 
 4-23 
 
 5 T -3 
 
 I 10.0 
 
 0.78 
 
 
 5-64 
 
 .621 
 
 • 75 ° 
 
 .784 
 
 .661 
 
 2.62 
 
 40.9 
 
 109.9 
 
 1.03 
 
 “ 
 
 4-5 
 
 .778 
 
 •583 
 
 .628 
 
 .8x2 
 
 1 45 
 
 35 7 
 
 109 7 
 
 1.2 
 
 “ 
 
 3 91 
 
 .895 
 
 • 37 i 
 
 .446 
 
 .929 
 
 0-45 
 
 32 0 
 
 109.8 
 
 T.36 
 
 “ 
 
 3 - 5 i 
 
 •997 
 
 .128 
 
 .077 
 
 .992 
 
 — 0.05 
 
 3 i -9 
 
 icg.8 
 
 I.47 
 
 Lead 
 
 3 - 5 ° 
 
 1.0 
 
 .014 
 
 .0 
 
 •999 
 
 — o -45 
 
 32.1 
 
 I IC.O 
 
 t -55 
 
 “ 
 
 3-53 
 
 992 
 
 .128 
 
 .126 
 
 .992 
 
 — 1.20 
 
 35-7 
 
 1 10.4 
 
 I.69 
 
 “ 
 
 3-94 
 
 .888 
 
 .306 
 
 .460 
 
 •952 
 
 — 2.22 
 
 40.9 
 
 109.8 
 
 1.88 
 
 “ 
 
 4-49 
 
 •779 
 
 •495 
 
 .627 
 
 .869 
 
 — 3 65 
 
 5 t -3 
 
 rio.o 
 
 2.22 
 
 “ 
 
 5-64 
 
 .621 
 
 .648 
 
 .784 
 
 .762 
 
 — 5 30 
 
 6r.6 
 
 no. 2 
 
 2.5 
 
 
 6.78 
 
 • 5*6 
 
 .782 
 
 •857 
 
 .623 
 
 — 6 65 
 
 71.9 
 
 io >.8 
 
 -•75 
 
 “ 
 
 7 89 
 
 •444 
 
 .844 
 
 .896 
 
 •536 
 
 to use condensers to compensate for this, both from their bulki- 
 ness and expense, but the presence of any reactance makes the 
 deflection dependent upon the frequency. An attempt was made 
 to improve upon the induction meter described above by remov- 
 ing the three-legged stampings of iron upon which the pressure 
 coil was wound. The inductance was still too large for satisfac- 
 tory working and as the condensers in the laboratory were not 
 sufficient to compensate for this, it was necessary, to make up 
 for this lack of capacity and to avoid the use of iron, to add an 
 auxiliary inductance wound on a wooden bobbin. The instru- 
 ment thus modified was found to be so sensitive to slight changes 
 in frequency that it was impossible to use it with any degree of 
 
600 BROWNE ON POWER FACTOR INDICATORS. [Aug. 22 
 
 satisfaction in the laboratory. Any change of load on the prime 
 mover would so change the reading of the instrument as to make 
 its indications extremely unreliable. 
 
 Dobrowolski shows, in the reference given above, the applica- 
 tion of his instrument for automatically adjusting the excitation 
 of the synchronous machine so as to keep the power factor at 
 unity at all times. 
 
 The use of an instrument of this kind emphasizes the fact that, 
 when induction motors are used alone, the inductance factor is 
 always a large percentage of the power factor. For instance, 
 when the power factor is .85 the inductance factor, assuming 
 sinusoidal waves, is nearly 62 % of this. That is, for every kilo- 
 watt used by the motor, 620 “ wattless watts ” are, so to speak, 
 borrowed. It would seem but fair that those who use induction 
 motors should at least pay rental for the wattless volt amperes 
 required. It is true this does not represent energy consumed, 
 but it does, in a sense, represent energy borrowed and returned 
 and the station must have sufficient capacity in generators to 
 meet all such calls for loans. 
 
 The additional charge could be taken care of by over-com- 
 pensating integrating wattmeters of the induction type, as sug- 
 gested by Mr. Benischke. They would then read high on lagging 
 reactive loads and low on leading reactive loads. This would put 
 a premium on the use of synchronous motors as they, if not too 
 greatly over-excited, help out in the regulation of the plant. The 
 induction motor has so many points in its favor it can well 
 afford to pay for what it needs — a large wattless component of 
 current.