24 o ALTERNATING CURRENTS 



142. Ratio of Currents 



We shall next consider the ratio of the continuous current to the 

 line currents on the alternating-current side. An approximate value 

 for this ratio may be easily obtained by assuming that the power 

 factor is unity, and that the losses in the converter are negligible ; 

 the latter supposition requiring equality of power on the two sides of 

 the converter. 



Let V, I stand for the voltage and current respectively on the 

 continuous-current side ; and Vi, Ii ; V 2 , 1% ; V 3 , I 3 for the voltages 

 and currents on the alternating-current side of a single-, two-, and 

 three-phase converter respectively. The power factor being unity, 

 and the losses being neglected, we must have 



VI = Vilx = 2V 2 I 2 = v/3 V 3 I 3 .* 



Now since, as we have just seen, Vi = 0707V, V 2 = 0707V, and 

 V 3 = 0-61 2V, we get 



- l! = 1-4141 ; I a = 07071 ; I 3 = 0'943I 

 Exhibited in tabular form, these results are 



Alternating Line Currents. 



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



100 141-4 70-7 94-3 



143. Relative Outputs of Armature when gene- 

 rating Continuous, Single=, Two=, and Three- 

 phase Currents 



One of the most important problems in connection with converters 

 is the question of heating. Before proceeding with this problem, 

 however, we shall investigate the relative output of a continuous- 

 current armature when used to generate continuous, single-, two-, 

 and three-phase currents, the limit of output being determined by the 

 greatest permissible rise of temperature. As a basis of our com- 

 parison we therefore adopt the same temperature rise in each case, 

 assuming also that the speed and the effective flux per pole are 

 maintained constant. 



It is evident that to obtain the same temperature rise the current 



* The three-phase power = 3V 3 I 3 ', where I 3 ' is the phase current ; now I 3 ' = ==. I a 

 ( 16), so that the power = ^3 . V 3 I,. 



