Unbalanced faults
Phase-to-phase fault current I″k2
- where
- line-to-line fault current (kA)
- IEC 60909 voltage factor
- nominal line-to-line voltage (kV)
- positive-sequence resistance and reactance, equal to negative sequence (Ω)
Explain this equation
Gives the line-to-line fault current. It is often the minimum fault level used to check that overcurrent protection at the end of a feeder will still operate.
c·Un is the line voltage driving the fault, multiplied by the IEC 60909 voltage factor. Z1 = R1 + jX1 is the positive-sequence impedance; far from rotating machines the negative-sequence impedance is the same, so the loop is 2·Z1.
In a line-to-line fault the current goes out on one phase and returns on another, through two phase impedances, driven by the full line voltage. The same answer comes from connecting the positive and negative sequence networks in parallel at the fault.
Sense check: I″k2 is √3/2, or 86.6%, of the three-phase value, so about 13% lower. A 13.9 kA three-phase level gives about 12 kA phase-to-phase.
Watch out: for minimum-fault protection checks use cmin = 1.00 and conductor resistance at the end-of-fault temperature.
Line-to-line (unearthed) fault current; with Z2 = Z1 it is √3/2 (86.6%) of the three-phase value.
Enter your values to see the result.
Good to know
Often the minimum fault current for overcurrent protection sensitivity at the remote end of a feeder: use cmin = 1.00 and conductor resistance at the end-of-fault temperature for that check.
Common mistake
Assuming the three-phase fault is always the minimum fault for setting overcurrent relays. The phase-to-phase fault is about 13% lower.
Limits
Far from rotating machines, so Z2 = Z1. Near generators Z2 differs and the ratio changes.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.