PETERSEN SYSTEM OF GROUNDING 51 



In substance, this means that, at fundamental frequency and with 

 small losses, the fractional admittance unbalance should be kept small 

 compared to the ratio of the resistance to the reactance of the coil, if 

 unduly high voltages to ground are to be avoided. (It is supposed 

 that g'oiC is of the order of r„/wL„, or smaller — a condition probably 

 satisfied even with the best practiable design of coil, except under 

 very wet line conditions.) The point involved here is, of course, an 

 important one from the standpoint of power system operation. It 

 is also important from the standpoint of electrically induced voltages 

 in exposed communication circuits. The admittance unbalance can 

 be kept within the necessary limits by suitable power circuit trans- 

 positions. 



The absolute magnitude of the fundamental frequency neutral 

 current is obtained from the expression for ] F„ ] by dividing by the 

 coil impedance (or directly from equation (3), and is, approximately, 



' yEoi I 



In = 





For a system with dead-grounded neutral the fundamental frequency 

 residual current is yEoiY and is thus smaller than that just found for 

 the case of the reactor in the ratio of j x | to 1, approximately. It is 

 evident, how^ever, that the magnitude of the neutral current with 

 reactor is controllable by means of transpositions, as in the case of 

 the neutral and residual voltages. The inductive effects of this 

 current should be of small consequence with an amount of transposing 

 sufficient to keep the line voltages to ground within limits desirable 

 from the standpoint of power system operation. 



2. Harmonics 



In the following discussion, we retain the assumption of lumped 

 constants, so that the results are not applicable to extensive networks 

 without modification. 



With this restriction, at harmonic frequencies other than the third 

 or one of its odd multiples, the above approximate equation for V„ 

 becomes 



y (x' — 1) 

 V„ = — — . Eoi, approximately, 



- 1 -f — 2 + x' 



m being the order and £oi the voltage of the harmonic and x and y 

 accented to denote that they are to be taken for the frequency in 



