Unbalanced faults
Single-phase-to-earth fault current I″k1
- where
- line-to-earth fault current (kA)
- IEC 60909 voltage factor
- nominal line-to-line voltage (kV)
- positive-sequence resistance and reactance, equal to negative sequence (Ω)
- zero-sequence resistance and reactance (Ω)
- neutral earthing resistance (Ω)
- fault resistance (Ω)
Explain this equation
Calculates single-phase-to-earth fault current from sequence impedances, with optional neutral earthing resistance and fault resistance. Use it for earth fault protection settings, earthing system design and neutral resistor sizing.
Z1 = R1 + jX1 is the positive-sequence impedance and is taken equal to the negative-sequence impedance, hence the 2. R0 and X0 are the zero-sequence impedance, which depends on transformer winding connections and the earth or sheath return path. RN is the neutral earthing resistor and Rf the resistance at the fault.
For an earth fault the three sequence networks connect in series. The phase current is three times the sequence current, which turns c·Un/√3 into √3·c·Un over the loop. Any resistance in the neutral or the fault carries all three sequence currents, so it appears as 3RN and 3Rf.
Sense check: on a solidly earthed system with Z0 close to Z1 the earth fault current is about the same as the three-phase value. A 6.35 Ω resistor at 11 kV limits it to roughly 1 kA.
Watch out: IEC 60909 itself assumes a bolted fault (Rf = 0). Not valid for isolated or Petersen-coil earthed systems.
Earth fault current from sequence impedances (Z2 = Z1), with optional neutral earthing resistor and fault resistance.
Enter your values to see the result.
Good to know
Z0 depends on transformer vector group and earthing: a delta winding blocks zero sequence, a Dyn transformer passes it to the LV star side only. A neutral earthing resistor RN appears as 3RN in the zero-sequence path. UK 11 kV systems are often resistance earthed to limit earth fault current to around the transformer full-load current.
Common mistake
Adding RN once instead of 3RN, or using the positive-sequence cable impedance for Z0 (cable Z0 is typically 3–10 times Z1 and depends on the sheath return path).
Limits
IEC 60909 itself treats bolted faults (Rf = 0); the Rf term is the standard symmetrical-component extension (Grainger & Stevenson). Far from generators (Z2 = Z1). Not for isolated or resonant-earthed (Petersen coil) systems.
Sources
- IEC 60909-0:2016 Short-circuit currents in three-phase a.c. systems – Part 0: Calculation of currents
- Schneider Electric Cahier Technique 158: Calculation of short-circuit currents
- Grainger & Stevenson, Power System Analysis, McGraw-Hill 1994 (per-unit, symmetrical faults, symmetrical components)
- GE Grid Solutions: Network Protection & Automation Guide (NPAG), chapters 3–4
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.