What is transformer inrush current, and why does it happen?

In this guide we switch on one transformer and follow its core flux, with animated diagrams, to see why the current jumps and how relays stay calm.

The problem: a big current with no load

A transformer changes voltage from one level to another. It needs a magnetic field inside its iron core to do this. We call this field the magnetic flux.

The current that builds the flux is the magnetizing current. In normal running it is tiny. In a large power transformer it is often below 1% of the rated current. With no load connected, this is almost all the current the transformer draws.

Now we close the breaker on a transformer with no load. For a short time, it can draw 10 times its rated current, or even more. So why does a device that normally sips current suddenly gulp it?

This short surge is called inrush current. It causes real trouble. Protection relays can mistake it for a fault and trip. Fuses can blow. The big current also causes a short voltage dip for other customers on the same network.

What is inside: the core and the windings

A transformer has two main parts. The first is the core. It is a closed loop of thin steel sheets, called laminations. The vertical parts are the limbs. The horizontal parts that join them are the yokes.

The second part is the windings. These are coils of copper or aluminium wire around the limbs. The high-voltage winding has many turns. The low-voltage winding has fewer turns. It usually sits on the inside, next to the steel.

The flux runs in a closed loop through the steel. It links both windings. This link is how energy moves from one winding to the other.

The core idea: flux cannot jump

Two simple facts explain inrush. The first is about the steel. The second is about time.

Fact one: the steel can get full. Up to a point, a small current makes a lot of flux. But steel can hold only so much flux. Above a level called the knee point, the steel is nearly full. We say the core is saturated. Now each extra bit of flux needs a very large current. The flux then has to go through air as well as steel, and air is a poor path for flux.

Designers run the core fairly close to the knee. This keeps the transformer small and cheap. In our example, normal peak flux is 1.0 per unit (pu), which means 1.0 times the normal value. The knee is near 1.2 pu. That leaves only about 20% of headroom.

Fact two: the flux follows the voltage, but it cannot jump. The flux in the core is built up from the applied voltage over time. In steady running, the flux is a smooth wave. It swings evenly from −1 to +1 pu. Its peaks come a quarter cycle after the voltage peaks.

At switch-on, the flux must start from wherever it is. In a core with no leftover magnetism, that is zero. Suppose we close the breaker as the voltage crosses zero. In steady running, the flux would be at its negative peak at that instant. But it is at zero instead. So the whole flux wave is lifted up by 1 pu. It now swings from 0 to +2 pu.

Two per unit is far above the knee. So for part of each cycle the core is saturated, and a huge current flows. That is inrush.

There is one more factor. When a transformer is switched off, some magnetism stays in the steel. This is the residual flux. It is often 50% to 90% of the normal peak. If it points the same way as the offset, the first peak can reach 2.5 pu or more. The inrush is then even larger.

Step by step: one switch-on, four moments

Let us follow one worst-case switch-on from start to finish. Each card shows one moment.

How fast do the spikes fade? It depends on the ratio of inductance to resistance in the circuit. Small distribution transformers settle in a few cycles. Large power transformers have very low resistance, so their inrush can last several seconds.

Why the closing moment matters

Inrush is not the same every time. It depends on where the voltage wave is when the contacts close. Engineers call this the point on wave, and measure it as an angle. Zero degrees is a voltage zero. Ninety degrees is a voltage peak.

Close at a voltage peak, and the flux happens to be at zero in steady running too. So the flux starts in its normal place. There is no offset and, with no residual flux, no inrush. Close at a voltage zero, and the offset is the full 1 pu. That is the worst case. Use the slider to see the effect.

The curve is a V. The middle band is safe. Near either voltage zero, the inrush is large. This is the idea behind controlled switching. A controller times the breaker so it closes at the best point on the wave. Good controllers also take the residual flux into account.

Inrush or fault? A worked example

The main protection on a large transformer is the differential relay. It compares the current going into the transformer with the current coming out. If they do not match, it decides there is an internal fault and trips.

During inrush, current flows into the transformer but none comes out. To a differential relay this looks exactly like a fault. So how does the relay tell the difference?

Worked example. Take a 20 MVA, 132/33 kV transformer. On the 132 kV side, rated current is 20,000 kVA ÷ (√3 × 132 kV) = 87.5 A. Its magnetizing current in normal running is about 0.5% of that, or 0.4 A.

Now energize it from the 132 kV side at a voltage zero. Let the residual flux be 0.6 pu in the same direction. The peak flux is 1 + 1 + 0.6 = 2.6 pu. That is 1.4 pu above the 1.2 pu knee. Above the knee, the core acts almost like an air coil. Its air-core reactance, the opposition of the winding with no help from the steel, is about 0.2 pu here. So the peak inrush is about (√2 ÷ 0.2) × 1.4 ≈ 9.9 times rated current. That is about 870 A.

A typical differential relay picks up at 0.3 × rated, or 26 A. The inrush is 33 times bigger. Size alone cannot tell it from a fault.

So the relay looks at the shape of the current. Inrush is one-sided. A one-sided wave contains a strong second harmonic, a component at twice the supply frequency (100 Hz on a 50 Hz grid). A fault current is a near-perfect sine, with very little second harmonic.

The relay measures the second harmonic as a percentage of the main 50 Hz part. If it is above a setting, often 15% to 20%, the relay blocks the trip. This is called second-harmonic restraint. If the ratio is low, it is a real fault, and the relay trips.

One warning. Modern low-loss core steel can give inrush with very little second harmonic, in some cases near 5%. So modern relays add extra checks, such as looking at all three phases together, or at the gaps in the waveform.

Where inrush matters in practice

Inrush shapes many everyday design choices. Differential relays on power transformers all use some form of harmonic restraint. Overcurrent relays and fuses on distribution transformers must ride through it. A common check point is 12 times rated current for 0.1 second.

Inrush also matters in wind and solar farms, where many transformers are switched on together. Large inrush can cause voltage dips for nearby customers. There is also sympathetic inrush. Switching on one transformer can make a second one, already in service nearby, draw inrush too.

The fixes are well known. We can close the breaker at the best point on the wave. We can add a pre-insertion resistor, a resistor switched in for the first few milliseconds to limit the current. Or we can energize from the high-voltage side, where the air-core reactance is larger.

Key takeaways

• Inrush current is a large, short current a transformer draws when it is switched on. It is normal, not a fault.
• It happens because the core flux cannot jump. It starts offset and can reach about 2 pu, far above the knee near 1.2 pu.
• Residual flux left in the core can push the peak higher still, and the inrush grows with it.
• Closing at a voltage zero gives the worst inrush. Closing at a voltage peak gives the least. Controlled switching uses this.
• Peak inrush is often 5 to 10 times rated current or more. It fades over a few cycles to several seconds.
• Inrush is one-sided and rich in second harmonic, so differential relays use second-harmonic restraint to avoid tripping.