316 SYNCHRONOUS MACHINES. [Exr. 



EXPERIMENT IO-B. Special Study of a Synchronous Motor. 



i. Electromotive Force Method. The complete action of a 

 synchronous motor can be simply explained* by considering that 

 the line electromotive force E and counter-electromotive force E' 

 combine to make a resultant electromotive force Ez. The arma- 

 ture current / is equal to Ez~Z and lags behind Ez by an angle 

 Oz whose tangent is X-^-R, where Z is the synchronous inped- 

 ance, X the synchronous reactance and R the resistance of the 

 armature circuit. 



In Fig. i, suppose the motor is thrown into circuit at a time 

 when E' is exactly opposite to E in phase. Ez is then a minimum, 

 being the arithmetical difference between E and E' ; the current 

 7 that flows is zero or small and generally will not produce enough 

 powerf for the motor to maintain rotation. The armature tends to 

 stop or slow down, but as the armature drops back in its running 

 position E' drops back in phase, thus increasing Ez, I and the 

 power. A balance is reached at some point as d, when the power 

 developed is just sufficient to meet the demand. 



2. The electrical power input is the vector product of E 

 and I, which is E times Oe, the projection of / upon E. The 

 mechanical power developed is the vector product of E r and I, 

 which is E' times Of, the projection of 7 upon the continuation of 

 E'. Furthermore, the mechanical power developed is equal to the 



* ( ia). Following a paper by Bedell and Ryan, Journal of the Franklin 

 Institute, March, 1895, the first complete discussion of the synchronous 

 motor with graphical diagrams and experimental verification, based upon 

 preliminary papers in A. I. E. E. and Sibley Journal, May, 1894. A dis- 

 cussion of the circular current locus will be found in McAllister's Alter- 

 nating Current Motors. For an elaborate discussion of the magneto- 

 motive force or ampere turn method, see a series of articles by C. A. 

 Adams, Harvard Engineering Journal, Jan., 1908, April, 1908, Jan., 1909. 

 (A translation of Blondel's treatise on the synchronous motor is in prepa- 

 ration.) 



t When E' is opposite to E, there will be no power at all as a motor 

 unless E' is less than E, as the subsequent discussion will show; see 43. 



