88 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



as the frequency and the square of the current. Assume that 

 the core loss due to the mutual flux varies as the product of the 

 frequency and the square of the flux density. 



(a) What is the total output when the slip of the second is 

 1.55 per cent, and the voltage generated by the air-gap flux in 

 the rotor winding of the second motor is 430 volts per phase? 



(b) What power do they receive from the line and at what 

 power factor do they operate? 



(c) What is the power developed by each motor? 



69. A 1000-h.p. induction motor is operated as an induction 

 generator in parallel with a synchronous generator having a 

 full-load capacity of 1000 kv.-a. The induction machine, which 

 is wound for 12 poles, is driven at a constant speed of 250.5 rev. 

 per min. The speed of the synchronous generator falls uni- 

 formly from 1530 rev. per min. at no load to 1500 rev. per min. 

 at full load, when the frequency is 25 cycles. The load deliv- 

 ered by the induction generator is proportional to the slip which 

 at full load is 1.7 per cent. 



When the total load supplied is 1500 kw. what is the load 

 delivered by each? At what speed should the induction gener- 

 ator be driven so that both will deliver their rated loads at the 

 same time? 



70. An induction generator and a synchronous generator, each 

 rated to deliver 2500 kv.-a., are operated in parallel. The speed 

 of the induction generator falls from 1520 at no load to 1498 at 

 full load, and the speed of the synchronous generator falls 

 from 1525 at no load to 1490 at full load. The load on the 

 induction generator is proportional to the slip which at full 

 load is 1.8 per cent. 



What is the greatest load that can be delivered without over 

 loading either generator? To what value should the full-load 

 speed of the synchronous generator be adjusted so that both gen- 

 erators will deliver their rated loads at the same time? 



71. A 4-pole induction generator and a 2-pole synchronous 

 generator are operating in parallel. The induction generator is 

 driven at a constant speed, but the speed of the synchronous 

 generator falls from 3660 rev. per min. at no load to 3590 at 

 full load of 2000 kw. The resistance of the rotor windings 

 between terminals refered to the stator is 0.73 ohm. Neglect 

 the_stator resistance and reactance, the rotor reactance, and the 

 losses. The excitation of the synchronous generator is adjusted 



