320 ELECTRICAL EQUIPMENT 



but there is a limit hereto also, as with a very high reactance the 

 total cross current would be reduced, and thus also the syn- 

 chronizing current. 



The synchronizing force is a function of the short-circuit cur- 

 rent ratio of the generator and may be defined as the torque per 

 degree displacement. 



The torque in foot-pounds corresponding to a given Kw. 

 energy load is: 



Kw.X 33,000 = Kw.X7040 

 R.P.M.X27TX.746 R.P.M. ' 



The synchronizing torque is then equal to 



Kw.X7040 

 R.P.M. XO' 



where 6 is the angle of displacement. 



Assume a generator rated ATB-72-125Q Kw. 1.0 P.F.-100- 

 2300 V. having a synchronous impedance limiting the short-cir- 

 cuit current to three times normal. The current flowing can, with 

 sufficient accuracy, be assumed to be proportional to the sine of 

 the displacement between the terminal or bus-bar e.m.f. and the 

 induced generator e.m.f. At short circuit, this displacement 

 would be approximately 90, thus the short-circuit current would 

 correspond to sin 90 =1. As this current has been assumed to 

 be three times full-load current, the latter would correspond to a 

 displacement of 6, the sine of which would be equal to f . 



Sine 6=1 and = 19.5 degrees. 



The synchronizing torque of this generator with a certain dis- 

 placement, for example, 10 degrees, would be: 



, 1250X7040 



Ts= 100X19.5 =4525 foot -P ounds - 



The cross current of the above generator with a certain dis- 

 placement, for example, 10, would be: 

 Sin. 10 = 0.17. 

 Full-load current = 3 15 amp. 



Cross current = ^^ X 315 = 160 amperes. 



Strictly speaking, this is not a cross current but the transfer 

 of current to the generator in question from the others, which are 

 relieved of a corresponding amount. 



