Transformer Inrush Current Formulas

Transformer inrush formulas: rated current, peak inrush as a multiple of rated current, comparison with the rated peak and the effect on protection.

The formulas

S is the rating in kVA, V the line voltage in volts and k the inrush multiple of the RMS rated current, which the manufacturer gives. Typical values are 6 to 12 for distribution transformers, and larger for small units. The inrush appears when a transformer is energised and depends on the point on the voltage wave and the residual flux in the core. It is a short pulse with a high content of second harmonic, and it decays over several cycles to seconds. The multiple of 10 in the example is an illustration, not a data sheet value.

Worked example: 1,000 kVA at 11 kV

1. In = 1000 × 1000 / (√3 × 11,000) = 52.49 A
2. With k = 10, Ipeak = 10 × 52.49 = 524.9 A
3. The rated peak is 52.49 × √2 = 74.23 A, so the inrush is 7.071 times the rated peak

Peak inrush for different multiples

Frequently asked questions

Why does a transformer draw inrush current?

The core can be driven into saturation in the first half cycle when the flux from the supply adds to the residual flux. The magnetising current then becomes very large.

How does inrush affect the protection?

The overcurrent relay or fuse on the primary must not trip on the inrush, so the instantaneous setting is above the peak or the relay is restrained by the second harmonic.

Does the inrush depend on the supply impedance?

Yes. A stiff supply gives a higher and longer inrush, and the resistance of the source and the transformer damps it.

How can I reduce it?

Use point-on-wave switching, a pre-insertion resistor or soft-start equipment for large units.

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