52 BELL SYSTEM TECHNICAL JOURNAL 



question. For small losses x' may be neglected in comparison with 

 unity, as before, giving 



\yn\ = -4^, approximately. (5) 



For isolated neutral 



\Vn\ = \y'E,,\. (6) 



Thus, even for the fifth harmonic, the right hand side of (5) is only 

 4 per cent, in excess of the value it would have if the neutral were 

 isolated. 



For harmonics whose orders are not divisible by three the residual 

 voltage is three times F„. Thus from the standpoint of noise inter- 

 ference from voltages, a system grounded through a Petersen coil 

 behaves practically as though the neutral were isolated, so far as these 

 harmonics are concerned. As with the fundamental, power circuit 

 transpositions are available for the reduction of residual voltages of 

 these frequencies. 



Residual currents of frequencies belonging to this series of har- 

 monics, which are not present at the ends of the line with isolated 

 neutral, are introduced by grounding through the reactor, but they 

 are of minor importance, as may be judged by comparing the neutral 

 currents with the reactor and with dead grounded neutral. With the 

 reactor, the neutral current of a harmonic of order m not a multiple 

 of 3 is found from (5) to be, in absolute value, 



I ^" I = rJ^-1"|Z.| ' approximately, 



Z„ being the coil impedance at fundamental frequency, while with 

 dead-grounded neutral, it would be 



I 7„ 1 = I EQiy'mY\, approximately, 



in which Y is the total admittance to ground at fundamental fre- 

 quency. Thus the magnitude of the neutral current with the reactor 

 is approximately l/(m^ — 1) of its magnitude with dead-grounded 

 neutral. The noise effects of residual currents of these magnitudes 

 will generally be insignificant compared to those arising from other 

 sources, particularly if the power circuit capacities to ground are well 

 balanced. 



For the third harmonic, or one of its odd multiples, we get 



■rr 7' T ^ n-i 



Vn - z. „i„ - ^ ^2'„r ' 



