Where  
I
j
is the capacitive earth fault current at a non-resistive phase-to-earth fault
X
c
is the capacitive reactance to earth
In a system with a neutral point resistor (resistance earthed system) the impedance
Z
0
 can be calculated as:
IECEQUATION16032 V1 EN-US (Equation 45)
Where  
R
n
is the resistance of the neutral point resistor
In many systems there is also a neutral point reactor (Petersen coil) connected to
one or more transformer neutral points. In such a system the impedance Z
0
 can be
calculated as:
0
4
//2 // 2
222
nnc
cn n
nc n n c
RXX
ZjXRjX
XX jR X X
 
IECEQUATION16033 V1 EN-US (Equation 46)
Where  
X
n
is the reactance of the Petersen coil. If the Petersen coil is well tuned we have 2X
n
 = X
c
 In
this case the impedance Z
0
 will be: Z
0
 = 2R
n
Now consider a system with an earthing via a resistor giving higher earth fault
current than the high impedance earthing
. The series impedances in the system can
no longer be neglected. The system with a single phase to earth fault can be
described as in Figure 
58.
1MRK 506 375-UEN A Section 8
Current protection
Railway application RER670 2.2 IEC 177
Application manual