354 PRINCIPLES OF ELECTRICAL DESIGN 



angle = 54 degrees (Figs. 137 and 142) was based on certain 

 conditions that may not actually be fulfilled. A closer determina- 

 tion of the external power factor corresponding to the conditions 

 that have been studied is easily made as follows. 



The angle a of Fig. 137 was determined on page 349 and found 

 to be 11 degrees. The angle \[/' is therefore /? a = 54 11 = 

 43 degrees, instead of the previously obtained value of 40 40' 

 (see calculations under items (52) to (54)). The vector OE' g is 

 known, and its value is 4,000 volts, since this is the e.m.f. devel- 

 oped by the flux distribution C of Fig. 141. In order to obtain 

 the corrected values for the angle 6 and the length of the vector 

 OE t in Fig. 137, we have: 



OB = OE' cos <// = 4,000 cos 43 



= 2,925 



whence OA = 2,917 



Also, BE' g = OE' g sin V = 4,000 sin 43 



= 2,725 

 whence AE t = 2,419 



Thus, tan = ^r= = 0.83, which corresponds to 6 = 39 40'. 



The external power factor is therefore cos 6 0.77 and the 



r- OA % X 2,917 



terminal voltage = V3 - 7 = -- Q~ff - = 6,570. 



Thus, the condition that has actually been worked out by 

 graphical methods corresponds to a terminal voltage of 6,570 with 

 full-load current on an external power factor of 0.77. This is 

 sufficiently close to the specified condition with figures 6,600 and 

 0.8 to show that the machine will comply with the requirements. 



Applying these corrections to the regulation, we have: 



Inherent regulation with full-load current 

 on an external power factor of 0.77 



_ \/3 X 4625 - 6570 



6570 

 = 22 per cent. 



Item (71). On the assumption that the inductance of the 

 armature windings can be correctly calculated, the short-circuit 

 current corresponding to any given field excitation can readily be 

 determined by the method described in Art. 107. The curve 

 marked volts in Fig. 146 is the open-circuit characteristic of the 

 machine, the scale of ordinates being on the left-hand side of the 

 diagram. The construction shows that, in order to develop the 



