HEATING OF SINGLE-PHASE CONVERTER 245 



This result shows that the heating effect at P depends on $, 

 i.e. on the position of P relatively to the slip-ring attachments. The 



heating is least when = , or when P is halfway between the 



f 



slip-rings, and it is greatest when <f> = Q, i.e. when P is in direct 

 connection with a slip-ring. In the first case, the mean square of 



the current at P is Jlm^T - -) = i-I a x 0-113, and in the second, 



0'75 

 1 1 ,- X 075, the ratio of the latter to the former being ^ = 6'6. 



Thus, in a single-phase converter, heat is generated in a coil in direct 

 connection with a slip-ring at 6*6 times the rate at which it is gene- 

 rated in a coil halfway between the slip-rings. There is thus great 

 local heating of certain coils. 



In Fig. 153 is plotted a curve, marked N = 2, whose abscissae 



are different values of A, and whose ordinates represent the mean 



2 

 square of the corresponding current \Im\4 -- sin 0). In order 



to find the average rate of heating of the coils, we must determine 

 the area of this curve. This may be done either graphically or by 

 integration. Adopting the latter method, we get for the area 



+ \ 



- - 



and for its mean ordinate (the mean value of the mean square of the 

 current in the various coils) 



t - 4) -iVx 0-8448 



7T 2 



So far, therefore, as the average rise of temperature of the 

 armature coils is concerned, the effect is the same as if they were 

 traversed by a continuous current, in each half of the winding, of 

 amount AI m \/0'3448 = 0'2929I WI , or by a total continuous current 

 (which divides equally between the two parallel paths of the 

 winding) of amount 0'5858I m . 



For the same average rise of temperature, therefore, as that 

 which occurs in the single-phase converter, the armature could be 

 loaded with a continuous current of amount 0'5858I,n, and if V 

 = continuous voltage at the given speed, the output of the armature 



