RELAYS 101

In-Depth Create B-C 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).
B-C Fault. Visit the Page for B-C Fault with no V0 for a demonstration of the math shown on this page. A phase-to-phase fault is a bit more involved to simulate properly for relay testing. Keeping in mind that there is no Zero Sequence during a phase-to-phase fault. If you end up creating a simulation that has some Zero Sequence then it is possible that the relay will behave differently than expected. Some relay manufacturers allow you to "Disable Loss of Potential" circuits. However, if you think about it then you are acknowledging that you are creating a fault that is not true-to-life. Isn't it better to create true-to-life faults and test accordingly? 
On this page you can enter different values of your desired test voltage and test impedance. You can then calculate what is needed to produce the phase voltage, current and angles for B and C phases. The calculations should produce test values that produce no Zero Sequence current or voltage.

Enter (unfaulted) VA magnitude: @: degrees

Enter magnitude of (faulted) VBC: @: degrees

Fault Z Magnitude: Fault Z Angle: degrees

Step 1: Enter a desired test phase voltage (VBC) and the desired impedance to the fault. Divide the voltage by the impedance. The resultant will be the test current.

(Itest = Vtest/Ztest)

Your calculated test current: amps

Step 2: The current test angle will be the Fault Z Angle subtracted from the VBC phase angle (IB Angle will be -90 degrees - Fault Z Angle)

Your calculated test current angle: degrees

Step 3: When calculating the faulted phase voltages remember that VB=VC and the sum of VA + VB + VC must = zero.

VB = √(((0.5VBC)x(0.5VBC)) + ((0.5VA)x(0.5VA))) = and VC = VB =

Step 4: VB angle will be the ArcCosine function of the quantity (0.5VA/VB) then subtract 180 degrees from that angle (this yields a lagging phase angle for VB angle).

VB angle = and VC angle= (ACos(0.5VA/VB) + 180) x -1 =

Step 5: IB = Calculated test current divided by 2 = And IC = IB =

Step 6: IB angle = test current angle = degrees. And IC angle = IB angle - 180 degrees = degrees.

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

The diagram below is a snapshot in time of a sampled B-C fault. Here you can see the B and C phase voltages are smaller in value than the Phase-A voltage magnitude. You can see that the B and C phase voltages are collapsing towards one another. This is demonstration in real life that there is no Zero Sequence produced in a phase-to-phase fault. At any time, under any condition of a phase-to-phase fault the sum of the two faulted voltages will be equal in magnitude to the third unfaulted phase, and opposite in direction from the third unfaulted phase.
Concerning the production of Zero Sequence, the same is also true of the fault currents. Although in this real time example, there was load on all three phases and the snapshot of the B-C fault also captured some Phase-A load. Thus the system responded with a B and C phases slightly offset from a perfect 180 degrees. The sum of the three currents add up to show no Zero Sequence current. During a simulated B-C fault relay test it is easy (yet still true-to-life) to simply keep Phase-A current at 0 amps, then you can have B and C phase currents set up to be 180 degrees away from one-another.
With a little imagination one can visualize that this "Collapsing Phase Angle Between Faulted Voltages" will be closer and closer to 120 degrees the closer the fault is to the "Perfect Bus" or to the generator. If the phase angle were to be measured right at the point of the fault then it would be zero degrees. Just as if the voltage were to be measured directly at the point of the fault then the PHASE-TO-PHASE VOLTAGE would be ZERO. The phase to neutral voltage of each of the faulted phases can thus be seen as one-half of the magnitude of the unfaulted phase. The voltage measured moves from nominal to fault value as seen from Bus to point of fault. Likewise (in a phase-to-phase fault) the phase angle (between phases) moves from 120 degrees to zero degrees as measured from the bus (or generator) to the fault.

Faulted Phase vectors during a sampled B-C Fault — Faulted phase vectors during a sampled B-C Fault