PETERSEN SYSTEM OF GROUNDING 55 



and the residual voltage is 



Vr = S (Foi - I„Z'„ - V„) 



3 V 

 = I _ fn^ ^\' z' approximately. (11) 



The corresponding expressions for solidly grounded neutral are ob- 

 tained by omitting m- in the denominator for each of the equations 

 just derived. Thus the advantage of grounding through the reactor 

 relative to grounding directly depends on the magnitude of F'Z'^ as 

 compared to the square of the order of the harmonic. Z'„ depends 

 upon the voltage and the kva. capacity of the transformers and is 

 mostly inductive reactance. For high voltage transformer banks 

 of small capacity feeding very extensive networks, the gain indicated 

 by equations (10) and (11) from the use of" the reactor would prob- 

 ably not be large. It would be important, however, where the aggre- 

 gate capacity of the supply transformers is moderate or large and the 

 connected network is of moderate extent and voltage. For instance, 

 using the data of the example considered in an earlier part of this 



paper and taking Z'„, = jL'^w' = -. j 9,000 as an appropriate value 



o 



for a total transformer capacity of 7,000 to 8,000 kva., with line voltage 

 from 20,000 to 30,000, we should have L'^Coi'^ equal to about 4 at 

 180 cycles/sec. In other words, in this case, the employment of the 

 reactor would reduce the residual voltage and the neutral current of 

 the third harmonic frequency due to a star-star solidly grounded 

 transformer bank by about 75 per cent., and residuals of other fre- 

 quencies belonging to the same series probably by larger amounts. 



In the earlier discussion relating to harmonics not belonging to the 

 triple series, comparison was made between a system grounded through 

 a Petersen reactor and the isolated system. In a similar comparison 

 with respect to the triple harmonic series, the isolated system has the 

 advantage, since residuals of this series theoretically do not appear 

 in such a system, as the voltages are not impressed between wires. 

 As a practical matter, an isolated system would probably not be 

 entirely free of triple harmonic residuals, owing to dissimilarities in 

 transformers or elsewhere. Such accidental effects can hardly be 

 taken into account in a theoretical discussion. However, in setting 

 up a comparison between the isolated system and that grounded 

 through the reactor, an idea of the relative importance of the triple 

 harmonic residual voltages existing in the latter case can perhaps be 

 obtained by comparing their theoretical magnitudes with the theoreti- 



