PETERSEN SYSTEM OE GROUNDING 41 



Y Y Y 



Ic = -^ (-^01 — -Eos) + -o (-^02 — -Eos) = "o" (Eoi + £o2 — 2£o2), 



= FEso = (g+jCco) £30. (1) 



The current through the coil and fault is 



r _ ^^ — '" ( • r ^ 



r ^ 

 or, neglecting " in comparison with unity, 



io'Ln' 



In = -jj-^ {r„ - JcoL„). 



Thus the total fault current is 



/, + /. = /, = £3.[s + ^+i(.C-J-)]. 

 and, if the coil is adjusted for resonance. 



"^^+-i). (2) 



(t)L„ VwLn 0}C 



On comparison of this expression with the above equation (1) for 

 the charging current, which constitutes the fault current if the system 

 is isolated, it is seen that, if the losses in the system are small, the 

 effect of the coil is to reduce the magnitude of the current in the fault 



approximately in the ratio of ("YTl + ^jto 1^1' ^•^•' neglecting 



terms of the second and higher orders, in the ratio i-j- H ^j to 



unity. Further, as equation (2) shows, the phase of the fault current 

 coincides with that of the voltage impressed between the faulty wire 

 and ground to the degree of approximation here used, i.e., to the 

 second order of small quantities. (The bracket on the right-hand 

 side of (2), if written in full, would include quadrature terms in the 

 square and higher even powers of r„/uL„.) With the system isolated, 

 the phase displacement is nearly 90". 



The action of the coil may be described as a transfer of the charging 

 current from the fault to the coil, leaving nothing but the component 

 of current to supply losses at the fault. With suitable design of the 

 coil, this energy current can be made small. 



The coincidence in phase of the fault current and the voltage im- 

 pressed by the transformer on the faulty wire, together with the small 

 magnitude of the former, are very farorable to the suppression of the 



k 



