Transformer Through-Fault Current Formulas

Transformer through-fault formulas: the rated currents, the fault current with an infinite source or a finite source and the I²t over the rated fault duration.

The formulas

S is the rating of the transformer in MVA, V the line voltage on the side that you study, Zt% its impedance in per cent, Ssc the short-circuit power of the source in MVA and t the duration. The fault is a three-phase fault at the terminals of the secondary, and the current on the primary side follows the same ratio. The forces on the windings follow the square of the current, and the heating follows I²t. The standard IEC 60076-5 states a rated duration of 2 s unless the buyer asks for another. The ratings and the source here are examples.

Worked example: a 1 MVA, 11 kV / 415 V transformer with 5% impedance

1. HV rated current = 1,000 / (√3 × 11) = 52.49 A, and LV rated current = 1,000 / (√3 × 0.415) = 1,391 A
2. Infinite source: LV If = 1,391 / 0.05 = 27,820 A, and HV If = 1,050 A
3. With a source of 250 MVA, Zs% = 1 / 250 × 100 = 0.4%, so the total is 5.4%
4. LV If = 1,391 / 0.054 = 25,760 A, and HV If = 972 A
5. The finite source cuts the force to 85.73% of the infinite-source value (the square of the ratio of the currents)
6. Over 2 s on the HV side, I²t = 972² × 2 = 1,889,000 A²s

LV fault current with an infinite source by impedance

Frequently asked questions

Why is the rated duration 2 s?

The standard takes it as the longest time the fault is likely to last before the protection clears it. A transformer built for a longer duration says so on the nameplate.

What does the source impedance change?

It adds to the impedance of the transformer and cuts the fault current. A strong source gives a result close to the infinite-source value.

Why do the forces follow the square of the current?

The force on a winding is from the current in it and the field of the neighbouring winding, and both are proportional to the current.

Is the cable impedance included?

No. The cable and the busbars add impedance and lower the current at the load, so this is the fault at the transformer terminals.

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