THREE-PHASE POWER MEASUREMENT 57 



the line wires, while its pressure coil is connected between this line 

 wire and the neutral point. The wattmeter will then evidently 

 measure the power in one phase, and since the system is balanced, 

 the total power is given by three times the reading of the 

 instrument. 



In this connection it may be mentioned that, with an accessible 

 neutral point, the total power of an unbalanced system may be 

 measured by means of three wattmeters, connected as just explained, 

 each wattmeter measuring the power in one phase. The total power 

 is the sum of the three wattmeter readings. This method, whose 

 applicability is limited by the accessibility of the neutral point, is 

 known as the three-wattmeter method. 



29. Power Measurement by Ammeters and 



Voltmeters 



The case of an unbalanced non-inductive load is of considerable 

 interest, not only on account of its frequent occurrence in practice, 

 but also because in this case the power may be found from the 

 readings of three voltmeters and three ammeters, connected so as to 

 read the three line p.d.'s and three line currents, without the use of 

 any wattmeter. 



A reference to the vector diagram of Fig. 37 shows that the 

 directions of the current vectors must in this case coincide with those 

 of the star p.d. vectors, with which they are co-phasaL From this 

 it is evident that, if the current vector diagram (showing the 

 magnitudes and phase relations of the line currents) be given in the 

 form of three vectors radiating from a point, it must be possible to 

 so fit this diagram into the triangle ABC, Fig. 37, of the line p.d. 

 vectors as to cause the current vectors, or those vectors produced, to 

 pass through the angular points of the triangle. 



Assuming, therefore, that the three line voltages and three line 

 currents have been measured, we may proceed to find the power as 

 follows. Construct the triangle ABC, Fig. 40 (a), of the line 

 voltages, and the triangle of line currents, Fig. 40 (&). From this 

 latter obtain the star of currents, Fig. 40 (c). Produce the rays of 

 the star, if necessary, and, having made a tracing of it, fit it over the 

 triangle of voltages. By means of a needle-point, mark the position 

 of the centre O of the star inside the triangle. Eemove the tracing, 

 and from each of the vertices A, B, and C of the angle draw lines 

 radiating from ; along these lines lay off lengths representing the 

 line currents. Then the power is given by 



V 8 ' x Ii cos x + Vi'la cos fr = AB x AD + CB x CE 



