178 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 



Let R= resistance of primary circuit of converter; 

 X=co(L+l + s) = reactance of same; 



Z=V / .R 2 + X 2 = impedance of same; 

 X 



tan r== reactance-coefficient; 

 K 



27T 



o)= = frequency. 



The " primary " circuit in this case includes the armature. The 

 reactance constant X must therefore include the following: The 

 reactance (coL) of the reactance-coils connected in series with the 

 converter; also the reactance (col) of the alternator and of the line 

 if the current is supplied directly by an alternator, and not by a 

 distribution-system; and, finally, the reactance (cos) corresponding to 

 the effect of the magnetic leakage at the armature itself. 



For each value, 6, of the phase-angle between the E.M.F.'s E 

 and , the third side, BC, of the triangle COB, represents the resultant 

 E.M.F. of E and e, which is equal to the product of the impedance Z 

 by the primary alternating current / corresponding to and passing 

 through this impedance. Constructing the triangle CBH, on BC as 

 the hypothenuse, with the angle f at B we will have 



BH=XI and HC=RI. 



In the diagrams (f> will always represent the angle of lag of the current 

 behind the voltage at the terminals. 



In order that the vector BC may measure the current / itself, 

 both in magnitude and in phase, it is only necessary to take, for the 

 amperes, a scale which is Z times greater than for the volts, and to 

 take, as the origin of phase-angles ((j>), a reference line BDY, making, 

 with the line OX, the angle f denned hereinabove. The angle DEC 

 then measures a phase-angle (</>), representing a " lag " if it be to 

 the right of BD, and a "lead " if it be to the left. We therefore count 

 the reactive current, Id, as positive on the right-hand side of D and as 

 negative on the left-hand side. 



If, from C (Fig. 3) a perpendicular CD be drawn to the line of 

 reference BY, the segments CD and BD will measure the reactive and 

 active currents for each position of C. The active current I w can, 

 itself, be considered as equal to the sum of two parts. One of these 

 parts (/o), represented by the segment Bd, is practically constant and 





