GENERAL PRINCIPLES OF SYNCHRONOUS MOTORS 25 



Let us apply this notation to the generator and motor already con- 

 sidered. Let us direct the E.M.F. E l of the generator along the axis 

 OX. E 2 , lagging in phase by the angle 6, measured from the opposite 

 direction, will have the form 



2 (cos 6 j sin 6). 



The imaginary impedance is 



R+ttiLj. 



The resultant E.M.F. being 



EI- (E 2 cosO-jE 2 sin 0), 

 the current will be obtained by taking the quotient 



E l -E 2 cosO+jE 2 smO 



= l - E * C S 



Separating the real and imaginary portions, we have 

 _r [ R(Ei-E 2 cosff)+u>LE 2 sinO 



R 2 +to 2 L 2 \ + j[RE 2 sin 0-taL(E 1 -E 2 cos ff)] }' 



This equation, when transformed into finite values, and taking z to 

 represent the impedance, gives 



Z 2 / 2 = [R(Ei - E 2 cos 0) +toLE 2 sin O] 2 + [RE 2 sin Q-uL(E v - E 2 cos 0)] 2 



This equation defines the relation between I, E\, E 2 , and 6 in a syn- 

 chronous motor. 



The mean power, PI, is obtained by simply multiplying the real 

 portion by EI thus: 



i= 2 E \, r ~ [RE l -E 2 (R cos 0-ajL sin (?)] 

 ->"/>^ 



cos 7- E 2 cos 



or the expression for the E.M.F. The product is calculated, and then only the 

 real portion thereof is taken. M. Guilbert has also given the following rule (E. E., 

 10 Mar., 1900, p. 361): Change the sign of the variable which is out of phase 

 and the real portion gives the power, with its sign. 



