HEATING OB' SINGLE-PHASE CONVERTER 241 



traversing the armature winding must be the same in each case. Let 

 I, I', I", and I"' be the line currents corresponding to maximum 

 safe temperature rise of the armature when generating continuous, 

 single-, two-, and three-phase currents respectively. If V, Vi, V 2 , ami 

 V 3 denote the corresponding line voltages, then the relative outputs 

 are 



Continuous - i u 

 current Single-phase. Two-phase. Three-phase. 



V 1 V:I' = 0707 VI 2V 2 I" = 1-414VI V 8 I"\/3 = 0'612VI' \/3 



For the sake of simplicity, we may assume the machine to be a 

 two-pole one. This will not in any way affect the generality of our 

 conclusions, for an ordinary lap-wound multipolar armature is 

 equivalent to a number of simple two-pole armatures connected in 

 parallel, and any result deduced for a two-pole machine will apply to 

 a section of the multipolar winding under cover of two neighbouring 

 pole-pieces, and hence will also apply to the entire multipolar 

 armature. 



Assuming, then, a two-pole armature, we have, for the currents 

 in the armature windings, in the four cases under consideration 



ji 41- 



For equal heating, these currents must be equal. Hence 



= = -; 



\/2 ' 



Substituting these values in the expressions for the output in the 

 various cases, we obtain 



Continuous current. Single-phase. Two-phase. Three-phase. 



VI 0-707VI VI 0-918VI 



144. Heating oi* Single- phase Converter 



The heating of a converter armature is a very complicated 

 problem, due mainly to the fact that the rate of heat generation 

 is not uniform throughout the armature winding (as it was in the 

 cases just considered), but varies according to the position of a coil 

 relatively to the point of con.nection to a slip-ring, the greatest rate 

 of heat production occurring in the coils close to the slip-ring con- 

 nections. For the sake of simplicity, we shall, as before, assume the 

 armature to be a two-pole QJU^ the power factor to be unity, and 



a 



