What is Inrush Restraint?

In brief, inrush restraint is a temporary modification to protection elements to allow for transformer re-energisation without spurious tripping. It’s achieved in two major ways:

  1. By applying a temporary multiplier to overcurrent settings thresholds
  2. By looking for symptoms of inrush, more than overcurrent alone.

Where does Transformer Inrush come from?

Our greatest ally for the success of the global AC power grid has been transformers. Transformers allow us to transform the voltage level of a power supply to facilitate the large-scale transmission and distribution of electricity.

When a transformer has been de-energised, from an outage or a temporary fault, such as an upstream circuit breaker operation, it needs extra energy on start-up to energise the magnetic core. To an outsider, looking into the transformer, this manifests as a relatively large spike in current drawn over a few power cycles (~100ms).

Figure 1 - Transformer Inrush on a 25 MVA Transformer [1]

Figure 1 - Transformer Inrush on a 25 MVA Transformer [1]


While this inrush current quickly subsides, and the transformer reaches operating steady state, this initial “inrush” of energization current can be higher than the steady state overcurrent limit.

This is a significant problem – if each attempt to close a circuit causes a current spike, your relays and breakers will operate to stop the current and the network cannot be safely closed. Inrush restraint was invented to address this problem.

Without Inrush Restraint, some overcurrent protection schemes will operate on this spike, even though it isn’t a real fault.

How Big will the Transformer Inrush Current Be?

As with most things in electrical engineering, it depends.

Transformer inrush currents depend on the amount of residual flux in the transformer, and the transformer specifications. A common range is from 8 to a 14 times multiplier to the nominal current. The smaller the transformer, the bigger the inrush, but the shorter the decay time [2].

Bigger transformers have more inductance, leading to lower but longer inrush currents. You can consult your transformer supplier for these specifications.

Figure 2 shows an overlay of the peak inrush current calculation.

Figure 2 – Peak Inrush Calculation [2]

Figure 2 – Peak Inrush Calculation [2]


Techniques for Inrush Restraint

Now that we know that inrush restraint is a fast decaying, but large asymmetric increase in current when energizing a transformer, how do we design protection schemes to handle this phenomenon?

There are two common techniques for inrush restraint in electrical equipment.

Inrush Restraint Multipliers/Modifiers

One method for handling inrush is to add a temporary multiplier to the overcurrent pickup level. This is a simple method that raises the overcurrent pickup during the first few cycles after a re-energisation, allowing the transient to pass before settling into a steady state.

This keeps the overcurrent pickup above the inrush transient, a simple solution to the problem. And since it only applies to Overcurrent, we can still detect asymmetric fault conditions such as Earth Faults. This makes the technique both safe and reliable.

2nd and 5th Harmonic Inrush Restraint

The alternative technique for inrush restraint relies on the asymmetric nature of the inrush current waveform.

If we look at Figure 1, we can see that the waveform is not symmetrical around the time axis. A Fourier Transform of this waveform shows a second harmonic component.

Therefore, if we block overcurrent trips based on the presence of 2nd Harmonics in the signal, we can achieve the same outcome as an Inrush Restraint multiplier.

But 2nd and 5th Harmonic Inrush Restraint has a problem.

The second harmonic component of a transformer inrush depends on the hysteresis loop of a transformer. Older transformers used lower flux density materials, that cause higher second harmonic components on inrush. Newer transformers use high flux density materials to improve efficiency and reduce losses [1], [3], [4].

Figure 3 – A simplified view of Traditional vs Modern Transformers[1]

Figure 3 – A simplified view of Traditional vs Modern Transformers[1]


As the power system adopts more modern and efficient transformers, this 2nd harmonic technique becomes less reliable. A traditional signal requirement of 20% 2nd harmonic vs fundamental current was used as a gate, but new transformers may struggle to reach this threshold in the worst-case scenario. The inrush will still be present, but the blocking won’t, leading to spurious trips.

Which technique to use?

When implementing a differential protection scheme across a transformer, the 2nd harmonic method has been the traditional technique. However, deployment of modern transformers is causing active research for a replacement. For technical readers, Randy Hamilton published an excellent paper on the topic available here.

For distribution applications outside of the substation, using the multiplier-based Inrush Restraint technique is superior, and more likely to handle modern efficient transformers. By applying the multiplier to overcurrent alone, sensitivity to other faults are preserved (earth faults or other unbalanced types).

NOJA Power’s implementation uses the multiplier-based approach, because it is better for medium voltage distribution networks in most cases.

“Protection coordination on distribution networks is becoming increasingly challenging as fault levels drop on networks with more inverter connected generation,” says NOJA Power Group Managing Director Neil O’Sullivan.

“An important tool available to protection engineers is our inrush restraint and cold load pickup multipliers that ensures transformer magnetising current does not cause nuisance tripping on re-energisation combined with cold load multiplier which can ensure protection reach is maintained while load diversity rebalances.”


The electricity distribution grid couldn’t function without AC transformers, but their energization behaviour means that transformer inrush is a fact of electrical engineering life.

Inrush currents can be very large but operate only on a small timescale. They can be a nuisance for spurious tripping, but we can address their effects with two fundamental techniques.

These are Inrush Restraint Multipliers, and Harmonic Blocking.

Multipliers apply a temporary increase to Overcurrent levels, allowing the transient to pass without tripping. Harmonic blocking techniques look for the asymmetry of inrush currents.

Harmonic blocking has an issue in modern transformers because the improved transformer materials result in much lower harmonics on energization. On distribution networks, the more reliable technique is to apply multiplier-based inrush restraint.

NOJA Power’s OSM Recloser is used in over 95 countries worldwide, with over 65,000 installations. This system includes Inrush Restraint based on a multiplier technique, which is the most reliable method for distribution network operation at medium voltage.  If you’d like to learn more, you can visit www.nojapower.com.au or contact your local NOJA Power Distributor.


[1] R. Hamilton, ‘Analysis of Transformer Inrush Current and Comparison of Harmonic Restraint Methods in Transformer Protection’, IEEE Trans. Ind. Appl., vol. 49, no. 4, pp. 1890–1899, Jul. 2013, doi: 10.1109/TIA.2013.2257155.

[2] ‘Protection of Network Elements’, in Protection of Electrical Networks, John Wiley & Sons, Ltd, 2006, pp. 361–486.

[3] E. Cardelli and A. Faba, ‘Numerical modeling of transformer inrush currents’, Phys. B Condens. Matter, vol. 435, pp. 116–119, Feb. 2014, doi: 10.1016/j.physb.2013.06.020.

[4] F. de Leon, A. Farazmand, and P. Joseph, ‘Comparing the T and π Equivalent Circuits for the Calculation of Transformer Inrush Currents’, IEEE Trans. Power Deliv., vol. 27, no. 4, pp. 2390–2398, Oct. 2012, doi: 10.1109/TPWRD.2012.2208229.