RELAYS 101

In-Depth Learn to Calculate K0

Enter Z0 and Z1 magnitudes and angles. Output is an example calculation for K0. Different protective relay manufacturers may have different methods of computing K0. GE has used the simple relationship of K0=Z0/Z1, and then designed their circuits and programming to reflect this factor in the phase-ground relaying. Many other relay manufacturers have used K0=(Z0-Z1)/3Z1. This factor is the harder factor to calculate thus this K0 is the one featured in the In-Depth learning.
In reality one can see that the first part of the equation (Z0-Z1) is really the same calculation that is used to find a phase-phase value (VAB=VA-VB).
K0 is the value known as Zero Sequence Compensation Factor. This is the value used in ground fault relaying to allow for accurate distance measurement. Compensation is needed because the phase and ground impedances are different. Unlike the phase fault distance measurements where (typically) both phases involved in the fault have the same impedance. K0 is only needed for accurate distance measurement in phase to ground faults.

K0 = (Z0-Z1)/3Z1

Z0 Magnitude : Z0 Angle (deg) :

Z1 Magnitude : Z1 Angle (deg) :

Z0 Rectangular Coordinates Horizontal (X): Vertical (Y):

Z1 Rectangular Coordinates - Horizontal (X): Vertical (Y):

Subtraction of Horizontal (X): and Vertical (Y):

Resultant Hypotenuse using Pythagorean Theorum (Z= √((X*X)+(Y*Y)):

Hypotenuse Angle using Trigonometry ArcTan (Opp/Adj) or (Vert/Horiz):

Resultant Calculation Divided By 3Z1: / (3* ) =

Resulting Angle Minus Z1 Angle: - =

K0 Magnitude : K0 Angle (deg) :