Fault level
LV-side fault through a transformer and the current seen on the HV side
- where
- HV source impedance referred to the LV side, split by the source X/R (Ω)
- IEC 60909 voltage factor (also used as cmax in KT)
- LV nominal voltage (kV)
- HV fault level (MVA)
- transformer impedance on the LV side, split by the transformer X/R (Ω)
- transformer impedance (%)
- transformer rating (MVA)
- IEC 60909 correction factor
- relative reactance, uk/100 × X/R ÷ √(1 + (X/R)²)
- LV fault current (kA)
- corresponding HV line current (kA)
- HV nominal voltage (kV)
Explain this equation
Calculates a three-phase fault on the LV side of a transformer fed from an HV network, and the current the HV side carries for that fault. Use it for LV switchgear duty and for grading HV overcurrent protection against LV faults.
ZQt is the HV source impedance referred to the LV voltage, using the transformer ratio taken as UnHV/UnLV. ZT is the transformer impedance on the LV side, and KT the IEC 60909 correction factor, with xT the per-unit transformer reactance. Each impedance is split into R and X using its own X/R before adding.
Referring impedances through a transformer scales them by the square of the voltage ratio, which is why UnLV² appears in both ZQt and ZT. The source and corrected transformer impedances are in series. The HV current is the LV current scaled down by the voltage ratio, since power is conserved through the transformer.
Sense check: a 20 MVA, 10% transformer on a 1000 MVA 33 kV source gives about 9.6 kA at 11 kV and about 3.2 kA on the 33 kV side. Even an infinite source cannot push more than about 11.7 kA here, set by the transformer alone.
Watch out: the HV scaling holds for balanced faults only. For LV earth faults on a Dyn transformer the HV currents are distributed differently.
Three-phase fault on the LV terminals of a transformer, with the HV source referred through the transformer, and the corresponding current flowing on the HV side for grading upstream protection.
Enter your values to see the result.
Good to know
The HV source is referred to the LV side using the transformation ratio (here taken as UnHV/UnLV), so ZQt = c·UnLV²/S″kQ. KT is applied to the transformer impedance. The HV-side current is the LV current scaled by the voltage ratio, which is what an HV overcurrent relay sees for a three-phase LV fault.
Common mistake
Using the three-phase scaling for an LV earth fault on a Dyn transformer. For a single-phase LV fault, the HV line currents of a Dyn11 unit are only 1/√3 of the scaled value in two phases.
Limits
Two-winding network transformer at principal tap with rated voltages equal to the nominal system voltages; balanced three-phase fault; no LV infeed. For off-nominal ratios use IEC 60909 with tr = UrHV/UrLV.
Sources
- IEC 60909-0:2016 Short-circuit currents in three-phase a.c. systems – Part 0: Calculation of currents
- GE Grid Solutions: Network Protection & Automation Guide (NPAG), chapters 3–4
- ENA Engineering Recommendation G74 Issue 2: Procedure to meet the requirements of IEC 60909 for the calculation of short-circuit currents
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.