76 CONSTANT-VOLTAGE TRANSMISSION 



as a negative quantity. The vector diagram for a lag- 

 ging current is the same as Fig. 9, except that Q is 

 always drawn in the opposite direction. It is shown in 

 Fig. 4, Chapter IV. The quantities shown in Fig. 9 are 

 the same as those in Fig. 4, except that Q represents a 

 leading current instead of lagging. 



The difference between the voltages E 8 and E is 

 equal to the voltage drop in the conductors, and is made 

 up of the resistance drop, I R, in phase with /, and the 

 reactance drop, / Xj in quadrature with 7. Using com- 

 ponents which are at right angles to one another, we ob- 

 tain the relationship 



E*=(E + PR-QX)*+(PX + QR)* . (i) 



In a constant-voltage line, E and E 8 are constant, and 

 P and Q vary as the load changes. The above equation, 

 therefore, reduces to the following equation between P 

 andQ: 



This is seen to be the equation of a circle. This circle is 

 easily drawn on cross-section paper, and it gives a satis- 

 factory graphical solution of an important problem in 

 connection with a constant-voltage line, namely, that of 

 finding the ratings in synchronous motors required for 

 various loads, with given terminal voltages. The best 

 units to use are Kw. and Kva. It is recommended that 

 the circle diagram of a constant-voltage line be drawn 

 in all cases, because it is a short operation and because 

 it gives a comprehensive idea of relative magnitudes and 

 of certain limits to the power load of the line. With 

 fine section paper, very close results may be obtained. 



