54 BELL SYSTEM TECHNICAL JOURNAL 



the residual current except when only one line is supplied from the 

 transformer bank, the effect upon the former should in general be at 

 least approximately proportional to the effect upon the residual cur- 

 rent in any line supplied from the bank. 



In writing equation (7), any difference between the induced voltage 

 jEoi and the voltage appearing between line and neutral has been 

 ignored. To the extent that this is justifiable, the expressions for the 

 case of the solidly grounded neutral may be obtained by making the 

 denominators of the right hand sides of (8) and (9) each unity. If 

 the transformer bank is provided with a delta winding of low im- 

 pedance, in particular if it is connected delta on one side, this pro- 

 cedure gives a fair approximation to the correct expressions, since 

 the impedance through which the voltage £oi regulates is in this 

 case merely the transformer leakage impedance. The resulting 

 conclusions with respect to the advantage of the reactor — for ex- 

 ample, that the third harmonic residual voltage or neutral current is 

 1/8 as large, the ninth 1/80 as large, etc., with the reactor as with 

 solidly grounded neutral — should not, in any event, be unfavorable to 

 the latter method of grounding unless the electrical length of the line 

 approaches the point at which its reactance to ground becomes 

 positive. 



If the transformers are so connected as to provide no path for triple 

 harmonic magnetizing currents other than through line admittance 

 to ground and the impedance between neutral and ground, the in- 

 duced voltage jEoi is not the same for the two methods of grounding 

 under consideration, because the impedance to the triple harmonic 

 magnetizing currents is appreciably different in two cases. A con- 

 venient method of taking this effect into account is to regard the in- 

 duced voltage as due to a fictitious impedanceless generator of de- 

 terminate voltage regulating through the mutual impedance of the 

 transformer windings for the frequency in question.'' If Z'^ is one- 

 third of this mutual impedance and Vo\^ is the voltage of the fictitious 

 generator, the expression for the neutral current with ground con- 

 nection through the reactor becomes 



'H. S. Osborne, Trans. A. I. E. E. 34, p. 2175, 1915. 



'The voltage thus assumed is, of course, not identical with the induced voltage 

 for which the symbol Eoi has hitherto been used, and for this reason the new symbol 

 Foi is used for it. The corresponding 7?oi would be Foi diminished by the drop through 

 the mutual impedance. 



