# How to calculate transformer inrush current?

I have a transformer with 220 V primary and three secondaries;

1. 24 V | 1.2 A
2. 24 V | 600 mA
3. 12 V | 200 mA


Each secondary have 4400uF capacitor and 100mH inductor after the bridge rectifier.

How can I estimate the inrush current and pick the proper thermistor value for limiting the inrush current?

• Simulation would probably be easiest. Jan 19 '20 at 21:23
• Measure the resistance of the primary winding. That's what limits the inrush current in case the transformer was fully magnetized on turn-on. Jan 19 '20 at 21:47
• This is not a job for the apparent simulator since I can almost guarantee that most of the worst case inrush will be from the transformer alone, and while this inrush happens the secondary starts at and progresses from being decoupled from the primary. So when the inrush begins, the secondary winding is “not even there”. Modelling inrush requires measuring parameters of the transformer and developing an equivalent circuit model for it. Maybe such models are widely availble nowadays, but nothing like that comes stock with, say, LTspice. Maybe the (now free) microcap would have one. Jan 20 '20 at 1:00
• Well, I have to disagree with the above. It's eminently suitable for modelling with a simulator. Jan 20 '20 at 9:17
• All Power transformers of these small sizes have a 10% typical Vac at rated current. This is due to winding resistance. Similarily most DC motors have rated current of 10% of the start/stall current based on DCR then the no load current is 1% of the stall current. For Ripple filters if the ripple is 10% of Vdc the peak current fully charged is ~10x load current and for 5% ripple voltage the current pulse duty cycle is also 5% but now 1/5% or 20x the rated discharge current unless limited by the winding DCR. Jan 20 '20 at 10:52

There are two inrush currents, capacitor charging, and transformer saturation.

Unfortunately, they both depend on the resistance of the transformer, and the saturation inrush depends on the detail of the transformer magnetising curve, so it's somewhat easier to measure them than to gather enough good data to calculate them.

It's possible to measure the transformer saturation current independently of the capacitor charge current, as it exists even when the transformer is unloaded.

A transformer is designed for the flux to swing between nearly saturated in one direction, and nearly saturated in the other. At switch on, a good transformer will have zero flux in the core. If the transformer is switched on at a point in the mains voltage for when the flux would normally be zero, so maximum voltage, then it will start up with no inrush. If it's switched on a point when transformer flux would be maximum, at the voltage zero crossings, then it will attempt to swing to nearly 2x the saturation flux, which is not possible. The inductance collapses, and a huge current in drawn, causing an extra voltage drop in the transformer resistance which serves to correct the flux a little. The higher the transformer resistance, the more the flux will be corrected each cycle, and the quicker it will reach its eventual balanced flux operating condition. Paradoxically therefore, the 'better' the transformer, the longer it will spend drawing this saturation inrush current. Note that 'zero crossing' switches, normally ideal for resistive loads, are exactly the wrong thing for transformer loads.

If you don't have test gear capable of timing the switch-ons, then just switch on and off repeatedly, and record the maximum inrush current.

Once you've connected the rectifier/capacitor load, switch on and off repeatedly, and record the minimum inrush current. The capacitor inrush will be the same every switching cycle, so the total will be minimum when there is zero saturation inrush current.

In practice, inrush tends to be a manageable problem, at least for smallish power supplies. Silicon rectifier diodes tend to have surge capabilities an order of magnitude or more greater than their steady ratings (1N400x 30A versus 1A, 1N540x 200A versus 3A for half a mains cycle) so shrug off the initial capacitor charging spike. Time delay mains fuses will usually ride out the transformer saturation spike. Your PSU ratings are definitely in the 'smallish' range.

• Can we guesstimate the inrush current? If capacitors act as short circuit and transformer pull x10-15 times it's nominal current, for a 2A transformer it will be ~20 A. a 10 ohm thermistor for that is more than enough. right? Jan 20 '20 at 8:58
• Yes, a 10 ohm resistor sounds like it would be adequate, under the assumptions you've made. Jan 20 '20 at 9:00
• What about the assumption? are they reasonable if not accurate enough? Jan 20 '20 at 9:00
• Read my last paragraph, and stop worrying. Jan 20 '20 at 9:04

You have two reasons for the inrush:

1) the iron core has been left to saturated state since the last usage.

2) the initial charging of the capacitors.

Reason 1 causes an inrush pulse which must be measured. Your linked story that you said to be too advanced is the way to find a way around it. Do not have any load when you test the inrush caused by saturation

Reason 2 can be estimated with a circuit simulator if you have a short circuit test data of the transformer. The losses and stray inductance limit the inrush to empty capacitors.

How these 2 inrush mechanisms interfere when there are rectifiers + capacitors connected is difficult to estimate. I guess you can sum the energies of the pulses and place the initial charging pulse to happen after the demagnetization has happened at least 50%.

Unfortunately I cannot calculate anything exact of the transition between the demagnetization and initial charging, to be sure it should be measured with parts that can take the punishment.

ADD due a comment: Hot NTC resistor and repowering the system is a risk of inrush. If inrushes must be absolutely prevented you must have a soft-start circuit which doesn't get fooled by short off-periods.

• Reason 1 demands worst case saturation of core which may only happen 10 to 20% of the random power cycles depending on the core primary inductance and core flux levels relative to rated saturation level. It can be eliminated if the power off and on are coincidentally in the same conduction angle which is rare. . Reason 3 depends on power dropout duration and the hot NTC thermistor still running hot while the caps may have discharged in a few cycles. So this is the worst case. where you have Remanence surge for core saturation plus Cap charge and no surge relief for a few cycle outage. Jan 20 '20 at 0:50