RELAYS 101

In-Depth Create A-G Fault

Whenever you attempt to simulate a fault for a relay test you must ensure that the phase current value(s) are equal to or greater than any overcurrent supervision involved in the circuit (or trip equation).
The phase-to-ground simulated fault relay test is perhaps the most difficult to calculate.
On this page you can enter your desired parameters and click to calculate. Or before you look at the answers you can practice your math and predict the values in the step-by-step calculations.
Part of the needed calculations are to find "K0" from "K0 = (Z0-Z1)/3Z1". To make things less difficult on this page K0 is an entry text field. Learning to calculate K0 is on the "In-Depth Learn to Calculate K0" page.
There is still plenty of tedious calculations though because:
Zfault = Vfault / (Ifault + K0IN) 
or to find the current value if you have a known fault Z:
Iflt = Vflt / (Zflt + K0Zflt) where K0=(Z0-Z1)/3Z1
Fault current equals the fault voltage divided by the sum of fault impedance plus the "Compensated Fault Impedance".
You can see an equivalence diagram depicting this calculation on the "Lecture Notes" page.

Enter Faulted VA magnitude: Angle: degrees

Enter Unfaulted VA magnitude: Angle: degrees

Enter Fault Z Magnitude and Angle: Z Fault Angle: degrees

Enter K0 Magnitude and Angle: Angle: degrees

Iflt = Vflt / (Zflt + K0Zflt)

Fault Current equals the Fault Voltage divided by the sum of the Fault Impedance and the Compensated Fault Impedance.

Step 1 - Find the "Compensated Impedance (K0Zflt)". Multiply the Fault Z by the K0 =

Step 2 - Find the Angle of K0Zflt. Add the K0 angle to the Z fault angle =

To add the Zflt to the K0Zflt we must convert to rectangular, add the components then convert back to polar

Step 3 - (K0Zflt horizontal coordinate = ) Multiply K0Zflt by cosine of K0Zflt angle =

Step 4 - (K0Zflt vertical coordinate =) Multiply K0Zflt by sine of K0Zflt angle =

Step 5 - (Zflt horizontal coordinate = ) Multiply Zflt magnitude by cosine of Zflt angle =

Step 6 - (Zflt vertical coordinate = ) Multiply Zflt magnitude by sine of Zflt angle =

Step 7 - Add the two horizontal coordinates together =

Step 8 - Add the two vertical coordinates together =

Step 9 - Convert back to polar (Ztotal magnitude = √((Ztotalhoriz*Ztotalhoriz)+(Ztotalvert*Ztotalvert)) = ohms

Step 10 - Finish the conversion, find the Fault Z angle (Ztotal angle = arcTan(vert/horiz) = degrees

Almost done, the rest is easier.

Step 11 - Calculate the current. Divide the fault voltage by the fault impedance (Iflt = Vflt / Zflt) amps

Step 12 - Calculate the current angle. Subtract the Fault Z angle from the Fault Voltage angle (Iang = Vang - Zang) degrees

Relay Test Set Values

VA: volts VA Angle: degrees

VB: volts VB Angle: degrees

VC: volts VC Angle: degrees

IA: amps IA Angle: degrees

IB: amps IB Angle: degrees

IC: amps IC Angle: degrees

In the phasor diagram below Phase-A is colored black, Phase-B is colored green, Phase-C is colored red. In this particular microprocessor relay there is also a channel for "Compensated Neutral Current" (K0IN). This diagrm has KOIN colored blue. Note that the KOIN Angle is slightly off from the faulted phase current, a subsequent change in relay settings could bring the "KOIN" closer to the fault angle. Some relay engineers will routinely analyze the relay fault recordings to determine if their relay settings are close enough. There are even utilities that will change their ground current relay settings from the dry season to the rainy season.
In this display of a fault recording one can readily see that Phase-A voltage is faulted substantially, Phases B&C voltages still appear to be nominal. The faulted current is lagging from Phase-A voltage (yet still less than 90 degrees- it cannot be at 90 degrees as there must be some resistance).
As this is obviously a phase-to-ground fault then it is known that there will be Positive, Negative and Zero Sequence Components. You can see the diagram of the symmetrical components for this fault by visiting the "In-Depth Zero Sequence" page.