Fault level
X/R, R and X from fault level and impedance angle
- where
- fault impedance magnitude (Ω)
- nominal voltage (kV)
- fault level (MVA)
- reactance to resistance ratio
- fault impedance angle (°)
- series resistance and reactance (Ω)
Explain this equation
Converts a fault level and its impedance angle, as often given in network operator data or study outputs, into X/R and series R and X.
Z is the magnitude of the fault impedance seen at the point, taken as Un²/S″k. φ is the angle by which the fault current lags the voltage. On the impedance triangle R is the adjacent side, X the opposite side, and X/R their ratio.
Since R = Z·cos φ and X = Z·sin φ, the ratio X/R is simply tan φ. No voltage factor is included here: this is a straight conversion of the stated fault level. The calculator also gives κ from the X/R for a quick peak estimate.
Sense check: 80° gives X/R ≈ 5.7, 84.3° gives 10 and 85° gives about 11.4. Near 90° small angle errors make big changes in X/R, so take angles to at least one decimal place.
Watch out: if you need the IEC 60909 source impedance including c, use the source impedance calculator instead.
Converts a fault level and its angle (as given in DNO data or a study printout) into X/R and series R and X.
Enter your values to see the result.
Good to know
The angle is that of the fault impedance, so X/R = tan φ and the power factor of the fault current is cos φ. 80° gives X/R ≈ 5.7; 85° gives ≈ 11.4. Z here is Un²/S″k without c; use the source impedance calculator if you need the IEC 60909 ZQ including c.
Common mistake
Taking the angle of the fault MVA as a load power-factor angle measured the other way, giving R/X instead of X/R.
Limits
Simple Thevenin conversion with Z = Un²/S″k. Angle must be between 0° and 90°.
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.