192 TREATISE ON ALTERNATING CURRENTS. 



THE MEASUREMENT OF POWER IN TRI-PHASE CIRCUITS. 



135. The following theory, due to Mr. A. Russell,* gives 

 methods of measuring power in tri-phase circuits : 



The Measurement of Power in Three-phase 

 Circuits. Suppose that there is both a mesh and a star wind- 

 ing as in Fig. 81. Let i, a 2 , and a 3 ; ii, i%, and i$ ; i xt i yt and i z be 

 the instantaneous values of the currents in the mains, in the 

 mesh winding and in the star winding respectively. 



Then 



a 3 = i 2 - ii 4- 



Let w be the instantaneous value of the watts, then 

 w = flints 4- 2 . 8 ii + Vfriiz -f Vii x + v& y + v 



Now 



v 3 .i = 0i.2 #2-3 

 and 



*>, = ~ i* - i* 

 also 



Vi - V Z = Vi.fr 



.'. w = fli. a (i 3 - i 2 + ^) + v 3 . 2 (i' 2 - *i + C^ (1) 

 By symmetry 



= fli.2i 4- ^3.2^3] 



= 02.802 + V l-3 tt l I ......... ( 2 ) 



= 03.103 + ffcioj 

 Similarly 



W = 0ii + V 2 2 + %^3 ...... : . (3) 



The formulae (2) and (3) give the ordinary methods of measuring 

 power in three-phase circuits. 



The first method is to use two wattmeters. The ampere coil 

 of one of them is put in the main 0,1, and the volt- coil is connected 

 across 1 and 2. The ampere coil of the other is put in the main 



* " The Elements of Three-phase Theory," by A. Russell, M A., Electrician, 

 vol. xlvii. pp. 639-643, August 16, 1901. The author wishes to express his 

 indebtedness to Mr. A. Eussell and The Electrician Printing and Publishing 

 Company, Limited, for kind permission to reproduce the text and diagrams of 

 135, and also for the loan of the blocks. 



