72 SYNCHRONOUS MOTORS 



Economic Study of Compensation for the Line by Means of 

 Motors Running without Load. For simplicity, let us suppose the 

 following to be constant: the voltage at the sending and receiving 

 ends, the power to be transmitted, and the loss of energy in the line. 

 It is required to determine the economy resulting from compensation 

 by overexcited synchronous motors running without load, for the 

 different values of cos <. 



Two points have to be considered: 



(1) The saving in the capital invested; 



(2) The saving in annual cost of operation. 



These two points lead, as will be seen, to conclusions which are 

 appreciably different: 



(i) Saving in Cost of Equipment. Let (for a single-phase current), 

 Eo=the voltage at the transmitting end of the line; Ei=the voltage at 

 the receiving end; ^^the E.M.F. of the synchronous motors; I w = 

 the useful active current; i = the active current of the synchro- 

 nous motors; I,j=I w tan <$>= the reactive current when there is no 

 compensation; /=the reactive current of the synchronous motors; 

 /i=the resultant current of the synchronous motors; /> =the cost 

 of the generators per kilovolt-ampere; p\= the cost of the synchronous 

 motors per kilovolt-ampere; p%= the price of line-copper per kilovolt- 

 ampere transmitted. 



The price of line-copper, when there is no compensation, is given 

 by the formula 



E\Jw . . 



p2 ........ (27) 



(which includes the return-conductor). In this formula the factor 

 p2 is equal to 



(28) 



wherein /= length, in kilometers; b= price of copper per kilogram, 



(assumed=2.5o francs). 



e=the percentage of loss allowed in the line; =the initial 

 E.M.F. in volts. 



The voltage being supposed constant at the transmitting and receiv- 

 ing ends, it follows that, in order to transmit the same power with the 



