TRANSFORMERS 425 



which means that a current equal to 50 per cent of normal circulates 

 between the transformers in both high- and low-voltage windings. 

 It adds to the load current in the transformer having the higher 

 induced voltage and subtracts in the other, causing the former to 

 carry the greater load. 



The impedance Z\ can be found for the first transformer by 

 impressing a voltage on the low-voltage winding with the high- 

 voltage winding short-circuited. The current is then read, and if 



E 



I is the current and E the voltage, then z\ = -=. In the same man- 

 ner 22 is determined. 



With three-phase delta-delta-connected transformers different 

 voltage ratios will cause unbalanced voltages and set up a circu- 

 lating current within the delta in both the high- and low-voltage 

 windings. Unbalanced voltages outside the delta can, however, 

 not produce any circulating currents within the delta, and un- 

 balanced voltages applied to a delta-connected transformer bank 

 cannot be equalized on the low-voltage side by the introduction 

 of additional voltage in the delta. 



As with single-phase transformers the value of the circulating 

 current is obtained by dividing the voltage difference by the total 

 impedance of the transformer bank. For example, if three trans- 

 formers having impedances of 4 per cent are connected delta- 

 delta, and one has a ratio 1 per cent greater than the other two, the 

 resulting circulating current will be 



Per cent 7=^|X100 = 8.33 per cent. 



When the load is taken from such a bank, the load currents and 

 circulating currents are superimposed, and the transformer having 

 the highest secondary voltage will carry the greatest load, as 

 before. 



With delta- Y-connected transformers a slight difference in the 

 ratios has a very small effect compared with a delta-delta-con- 

 nected bank. This is due to the shifting of the neutral point, 

 causing an equalization of the voltages. 



Effect of Impedance on Parallel Operation. In addition to 

 identical polarities and voltage ratios a successful parallel opera- 

 tion of transformers requires that their impedances are in inverse 

 proportion to the load which they are to carry, so that the voltage 



