This calculation is another one of those tedious chores.
k0 is known as the zero sequence compensation factor. It is used in distance relay calculations to compensate for the difference between the phase impedance and the ground impedance. Only when compensation is applied to the residual (neutral) current can ground distance measurement be accurate.
The calculation to find the zero-sequence compensation factor is :
k0 = (Z0-Z1) / (3Z1)
The part that makes it tedious is the fact that "Z" has both magnitude and direction (vector).
To subtract one vector from another you must first convert both vectors into their rectangular coordinate equivalents. Then find the resulting horizontal component and the resulting vertical component.
Then convert this resultant into its polar form.
Once you have the resulting (Z0-Z1) back into polar form then you divide the resultant by (3Z1).
In division of vectors do not forget to subtract the denominator's angle, (the denominator is the bottom number of a fraction), from the numerator's angle.
The final number is a factor that has no units (it is no longer impedance).
The final number has an angle that can be thought of as an offset in one direction or the other.
The compensation factor will be used in phase-ground fault distance calculation:
Z = V / ( k0In + I )
If the Z0 and Z1 angles are equal then :
Z = V / I( 1 + k0 ) (This is the calculation that we like to use in relay testing.)