488 



BELL SYSTEM TECHNICAL JOURNAL 



In addition to the effect of residuals in increasing the inductive 

 influence of a power Une, the induction due to residuals is not affected 

 by transposing the power line (as was pointed out in connection with 

 the discussion of coupling). 



SUPPLY LINE 



IN PARALLEL 



Fig. 12 — Arrangement for comparing balanced and residual voltages or currents. 



It may be of interest to examine briefly some of the causes of residual 

 voltages and currents. For example, in a three-phase system, har- 

 monic currents or voltages-to-neutral which are odd multiples of three 

 times the fundamental frequency are in phase in all three line wires and 

 hence tend to be residual. Such triples can be present in appreciable 

 amounts only with certain types of power apparatus and connections. 



POWER LINE 



IN EXPOSURE 



AA/V 



SUPPLY 



-VvV 



AM^ 



Fig. 13 — Arrangement for showing added inductive influence due to triple harmonic 



voltages. 



Perhaps the most important condition giving rise to triple harmonic 

 frequency residual currents or voltages is the connection of grounded- 

 neutral Y-connected generators which have triple harmonic voltages 

 between line and neutral, directly or through Y-Y connected trans- 

 former or Y-connected auto-transformer banks (with no or small 

 tertiary windings, and with grounded neutrals) to power lines. The 

 use of Y-Y banks may also cause triple frequency residuals on the lines 

 due to the magnetization characteristics of the transformers themselves 

 although when used with Y-connected grounded generators, the 



