360 ELECTRICAL ENGINEERING 



The power factor under running conditions is 

 COS6 S + Kr.+r/) 



but & = kn&, where $ is the maximum value of the flux per pole, 

 n is the motor speed in revolutions per second and k is a constant 

 depending on the number of turns in the armature winding and on 

 the shape of the flux wave. The flux < is almost proportional to 

 the current 7 and the generated e.m.f . may be expressed as 



& = k'nL 

 Substituting this value for in equation and eliminating 7 



k'n + r a + r f 



cos <t> = = ; . . (338) 



' 



the power factor, therefore, increases with increasing speed and 

 approaches unity. At low speed and at standstill it is low on 

 account of the reactances in the field and armature and for satis- 

 factory operation it is necessary to make these reactances as low 

 as possible. 



228. Design for Minimum Reactance. The inductance of 

 any coil is proportional to the square of the number of turns and 

 is inversely proportional to the reluctance of the magnetic circuit 

 through it. To reduce the inductance L/ of the field winding it 

 is designed with a small number of turns but this reduces the field 

 m.m.f. and in order to obtain the required flux the reluctance of 

 the magnetic circuit must be made very low. For this purpose 

 large sections of high permeability are used, the slots are partially 

 closed and the air gap is made as short as possible. 



The reactance of the winding is proportional to the product of 

 the inductance and the frequency and therefore the frequency 

 should be low. Motors are usually designed for 25 cycles since 

 that is the lowest standard frequency, but they will operate on 

 15 cycles or on direct current with a much improved efficiency and 

 power factor and a larger output. The frequency of the supply 

 does not affect the speed of the motor directly, but it does indi- 

 rectly since the reactance drop decreases with the frequency and, 

 therefore, the speed for a given current increases. 



229. Compensating Windings. The armature inductance 

 and reactance cannot be decreased by reducing the number of 



