Transformer switch on saturation

[trobbins]

Transformer inrush has been studied intensely over the decades - as it is a major issue for large 3ph power transformers and protection circuit design. If you google there are many many detailed references, most with an introduction or summary that goes to the matter, without having to wade through all the modelling and tests and paper reviews that fill out such papers.

So yes, core saturation is the main cause, with residual flux, application voltage and a variety of static and dynamic impedances within the transformer determining the actual current waveforms observed.

A number of forums threads have broached the subject. Simple testing of single events provides examples of the responses to be expected for a particular transformer and test scheme. But you'd have to be lucky to observe a worst-case peak current level, as there are many variables that influence the response.

[R.G.]

Is this effect purely due to core saturation? I had a thought experiment (feel free to shoot it down ): Would not an un-energized transformer look like just the coil resistance? Until current starts flowing and there's some back EMF happening due to inductance, it's just a 3.1 ohm resistance.

It's a little more complicated than that. Inductors are still inductors even when the current through them is zero, just like resistors still have a resistance at zero voltage/current. In fact, the field inside a transformer goes to zero twice per AC line cycle. It's the change in field that couples voltage from input to output. The field in the core is the price to be paid to set up that transfer. So no, an un-energized transformer still looks like the coil resistance in series with the inductance, although just like with a resistor, you have to expend some voltage and current to measure the inductance.

In the real world, the coil also has some self-capacitance, and leakage inductance, so there is the current in those parasitics that has to be accounted for; also, the core is almost certain to be left with some magnetic field remanence from the last time it was turned off. Ferromagnetic materials do not relax to zero field when they've been energized. Permanent magnets are just materials that have quite high remanence. Transformer iron is designed to have little, but it's not zero. So the remanence adds on top of the self capacitance and leakage inductance, as well as core saturation from too much volt-time integral.

I'm pretty sure all inductors surge a bit when AC is first applied; once a field forms (a continually varying field in the case of AC), then the inductive reactance kicks in.

They all do to some extent, but not that way. I used to run pulse-inductance tests on ferrites to see where they saturated. I would set up a wound core with a 0.1R resistor to sample current, and a function generator to apply a rectangular wave of voltage with varying on-times to the coil. Depending on the coil, there would be an excruciatingly narrow capacitive spike, then the current would ramp up at a rate of di/dt = V/L. The advantage of the pulse inductance test is that by varying the on-time of the applied voltage pulse, I could twist the knob and see the current start turning upwards from it's linear ramp as the core reached the first flitters of saturation.

Yeah - what we're seeing is almost all remanence and volt-time integral caused saturation.

[Mike Sulzer]

Regarding the inductance of the transformer, let's look at this plot again:

This is the monetization current, that is, the current that flows with open secondaries after the inrush transient has died out. What are the states of the transformer core? I think it is quite close to symmetrical. If saturation occurred on the first inrush spike, then the remanent magnetization was nearly completely removed after recovery from that spike. From the previous plot, it appears that the following spikes do not push the transformer into complete saturation since transformer operation is not interrupted, but rather into the region near saturation so that the permeability drops and the primary current increases somewhat. These continuing decaying spikes further reduce the remanent magnetization. Then the result is operation about the initial magnetization curve of the steel. Current rises quickly because the initial permeability is not so high, but rather increases with the applied field, resulting in a nearly flat-topped current waveform.

Thus the inductance is not constant over a cycle.

[R.G.]

Regarding the inductance of the transformer, let's look at this plot again:
This is the monetization current, that is, the current that flows with open secondaries after the inrush transient has died out. What are the states of the transformer core? I think it is quite close to symmetrical. If saturation occurred on the first inrush spike, then the remanent magnetization was nearly completely removed after recovery from that spike. From the previous plot, it appears that the following spikes do not push the transformer into complete saturation since transformer operation is not interrupted, but rather into the region near saturation so that the permeability drops and the primary current increases somewhat. These continuing decaying spikes further reduce the remanent magnetization. Then the result is operation about the initial magnetization curve of the steel. Current rises quickly because the initial permeability is not so high, but rather increases with the applied field, resulting in a nearly flat-topped current waveform.

Thus the inductance is not constant over a cycle.

No, inductance is indeed not constant over a cycle.

One reason is that economics and the sloppy, soft way that good transformer iron enters saturation encourages transformer designers to push the excitation right up to the edges of saturation. Inductance is proportional to the slope of the BH curve at a given point, and this constantly changes. With ferromagnetic materials, the BH curve is almost never a simple line, so even way below saturation, the inductance changes. This is one source of distortion that was known and accounted for in transformer-output amplifiers back in the tube Golden Age. RDH4 even talks about transformer distortion in a specific topic. I'd have to go dig out the book to get the reference, but it's generally a low third-order term. Generally, high-quality OTs were designed to never get even close to saturation, both for the effects of saturation and to keep the inductance change down.

There are other sources of non-constant inductance. When an AC power trannie is running, it is mostly symmetrical because the applied voltage is mostly symmetrical. I say "mostly" because this is not always strictly true. Odd loads on local wiring can cause equivalent DC offsets on the incoming AC line. I remember an article in some audio mag I read about a fellow who started having a small, but noticeable hum in his carefully hand-crafted amplifier. This just about drove him mad until he noticed that it never happened in daylight, only at night. He eventually tracked it down to the life/power savers he put in his porch and garage exterior lights. These are simple diode pellets and run the light on half-wave-rectified DC to cut the filament temperature and make the bulb last longer. But they do load one cycle of the AC line and not the other, and they were giving him a small DC offset on the inputs of his toroidal power transformers. A voltage offset into an inductor causes a current (and hence H) offset that is limited only by externals, in this case the accumulated wiring of the power lines and transformer primary resistance.

Remanence comes from turn *off* timing. If the primary voltage/current is interrupted, the core energy is sucked out by secondary load and pushed, by inductive kickback changing the voltage. But this can only happen until B=0. Even for soft ferromagnetic materials, this leaves the core with a non-zero remanent field, as the field collapses and runs down a minor BH loop to the B=0 axis, then stays there. The amount of remanence is determined by both the BH curve of the material (including its minor-loop behavior) and by when in the AC cycle the exciting voltage is turned off. To get close to zero remanence, you have to gently turn the AC voltage down, decreasing the excitation and letting the excitation force the field into smaller and smaller loops around zero.

[SoulFetish]

You guys never disappoint. It's been a little while since I've checked in here, and I forgot how much I love this joint. All it took was a little bit of magnetizing flux/core saturation talk to really hit the spot.
Mike and Nickb, you guys always seem to contribute really detailed analytical data with graphic illustrations for circuits under test. I really appreciate the work and the info you guys, RG, JM, and others share here (I'm fairly new, so I'm sure there are many more). I don't know if this is a loaded question, but, where can I go for resources on learning which tools are standard for this kind of testing, diagnostics, and analysis? Obviously, the equipment is useless unless one understands what the important parameters are, and the what the criteria is for testing a particular device or network. Mike(or anyone), in this particular topic, would you mind a quick run-through of how you set up and tested this transformer? Or if this would question would be better suited for somewhere else, that is okay. I don't want to hamstring the conversation. Thanks.

[Mike Sulzer]

You guys never disappoint. It's been a little while since I've checked in here, and I forgot how much I love this joint. All it took was a little bit of magnetizing flux/core saturation talk to really hit the spot.
Mike and Nickb, you guys always seem to contribute really detailed analytical data with graphic illustrations for circuits under test. I really appreciate the work and the info you guys, RG, JM, and others share here (I'm fairly new, so I'm sure there are many more). I don't know if this is a loaded question, but, where can I go for resources on learning which tools are standard for this kind of testing, diagnostics, and analysis? Obviously, the equipment is useless unless one understands what the important parameters are, and the what the criteria is for testing a particular device or network. Mike(or anyone), in this particular topic, would you mind a quick run-through of how you set up and tested this transformer? Or if this would question would be better suited for somewhere else, that is okay. I don't want to hamstring the conversation. Thanks.

Have you looked at Post #2? If that is not clear or complete, I would be happy to add to it.

nickb has the best way: Use a dc coupled current probe and a good scope. My approach is ac coupled and so as stated above, you have to subtract out the negative overshoot and recovery. But you just need your recording interface, your computer, and some software. The advantage is that when you save the data, you have it right there on your disk for further analysis. I use interactive Python for that, which can function as a kind of a free, but better, Matlab.

[Richard]

Is the point of this to measure inrush current for sizing fuses? Beyond not understanding any of this I don't understand what this data are used for.

[SoulFetish]

Have you looked at Post #2? If that is not clear or complete, I would be happy to add to it.

nickb has the best way: Use a dc coupled current probe and a good scope. My approach is ac coupled and so as stated above, you have to subtract out the negative overshoot and recovery. But you just need your recording interface, your computer, and some software. The advantage is that when you save the data, you have it right there on your disk for further analysis. I use interactive Python for that, which can function as a kind of a free, but better, Matlab.

I apologize mike, you spell it out quite clearly there. I must have missed it .
In fact after looking it over, I see why you did what you did(If I understand it correctly). The voltage/current measurements of transformer under test could not be plotted into a digital format for analysis directly, therefore, a second stepdown transformer was used to provide suitable voltages for the A/D converter. the clipper was used to clamp the voltages so not to exceed +1.2V and -1.2V for the (typical?-->) 0-5V input range of A/D converter. This is your scaling network. RG giving you a threshold figure of 60A without clipping, was for testing the full range the manufacturer VA rating without exceeding it(ie. 60A @ ~2V for a 120VA transformer)? How'd I do?

[nickb]

Is the point of this to measure inrush current for sizing fuses? Beyond not understanding any of this I don't understand what this data are used for.

IIRC it was a question about fuse ratings that started this off. You probably don't need to understand the details but just be aware that the phenomenon exists. As far as using it to determine a fuse rating let me try to work through an example.

First, here is a capture from my 2KVA bench variac:



I put the data into a spreadsheet and did a numerical integration to calculate I^2*t - a number that is important to the fuse selection:



You can see that the I^2.t value is about 3.3.

For a 1KVA load on the 240V line (UK) would be about 4 amps. A fuse of 5A would be a conservative choice as a 4 amp would blow too soon.

The i^2 rating for a particular fast blow 5A fuse in the first attached pdf is 27.4 i.e about 8 eight times the expected value of 3.3 so we know the fuse will not blow. However, every time you hit the fuse with one of these current pulses it weakens a little, so chart II in the second pdf tells us that at 1/8 of I^2.t the fuse can withstand > 100,000 pulses. Thus a fast acting fuse will be suitable. For comparison a 5A delay fuse I^2.t rating is 111.

This is just for the transformer. Add a rectifier and capacitor and the surge while the heaters warm up and you'll get a different figure but hopefully you can see how the process works. When I get a chance I will measure a real amp and get some more practically useful figures for you.

[trobbins]

Using the I2t value for fuse selection is appropriate for checking the fuse capability for a transformer inrush event, as the in-rush characteristic is typically a very high initial current pulse, with further pulses much attenuated. The I2t value is only really valid for comparison of such a short mains half-cycle current pulse, and for US type UL248 is aligned with an 8ms time assessment.

Assessing a fuse for capacitor inrush and heaters needs longer time frame assessment, and goes more to the I-t curve than a I2t value comparison. All those influences - PT inrush, capacitor inrush and heater inrush - should be combined if they are relevant.

A UL-248 spec fuse shouldn't be used at more than 80% of rating, so 4A continuous is max for a 5A fuse rating.

[SoulFetish]

I apologize mike, you spell it out quite clearly there. I must have missed it .
In fact after looking it over, I see why you did what you did(If I understand it correctly). The voltage/current measurements of transformer under test could not be plotted into a digital format for analysis directly, therefore, a second stepdown transformer was used to provide suitable voltages for the A/D converter. the clipper was used to clamp the voltages so not to exceed +1.2V and -1.2V for the (typical?-->) 0-5V input range of A/D converter. This is your scaling network. RG giving you a threshold figure of 60A without clipping, was for testing the full range the manufacturer VA rating without exceeding it(ie. 60A @ ~2V for a 120VA transformer)? How'd I do?

Everybody, please disregard any of this nonsense I posted above. I don't have time to go into it, but I was not right at all about this test setup. Let me just answer myself here: quote "RG giving you a threshold figure of 60A without clipping, was for testing the full range the manufacturer VA rating without exceeding it(ie. 60A @ ~2V for a 120VA transformer)? How'd I do?"
Well, RG gives a threshold of 60A because of Ohm's friggin law, which he clearly states given a voltage of the unlikely 125AC and a resistance of 3(3.1) presented by the primary winding of the TUT.
Ugh, I should go stand in the corner and think about what I've done for that one. I lost a reply I was writing earlier to automatic logout, but long story short, I'm pretty sure I now know what you actually set up for a test and how you tested it.

[nickb]

Here is the data for a Vibro-Champ captured over the first 40 seconds after power on. This has a tube rectifier so there is no capacitive surge. Also interestingly the heater surge is of no consequence as initially the rectifier is cold and non-conducting. By the time it has warmed up so have the other heaters and so the current demand ramp is quite orderly.

Steady state power consumption is about 70VA.

This time, I calculated i^2.t using an 8ms interval, primarily because the sample interval was 4ms and it was close enough to a half cycle at line frequency. The red trace is i^2.t and the blue is the rms current calculated over a moving 1 second interval.




The steady state current is abut 0.25A so you would need to choose at least a 0.25*1.25 = 0.3125A fuse. The nearest fast blow (in the 235 pdf above) is 400mA with a i^2.t rating of 0.058. The transformer surge is about 0.18 so this fast blow is not suitable. Attached is the data for a slow blow series. The 400mA is rated at 1.32. 20% of 1.32 is 0.26 and so give at least a 100,000 pulse withstand for out i^2.t of 0.18.

Fender went for 500mA anti-surge fuse (240V version), probably a good choice of compromise between protection, reliability and availability.

Next, I aim to get the data on a 130W AB amp with a solid state rectifier.

[trobbins]

Does the mains current vary for 'cranked' output?

[Mike Sulzer]

Here are the data for the transformer sold by tube depot.com for the JTM45 Clone:


In the first plot there is no load on the transformer as before. This transformer has about 2.2 ohms primary resistance. The plot shown is near to the highest measured; one measurement that I did not record peaked at about 21 amps. However, no measurement came close to the much higher values one would expect if true saturation was achieved. So there are two indications that, although there are current spikes short of complete saturation, the peaks do not really get there:
1. The peak values are too low.
2. Tranformer action, although modified during the transient, does not cease.

This is a very heavy transformer; that is, it has a lot of steel.

The second plot shows the results of a full wave rectifier supplying a 100 microfarad capacitor. Note that:
1. It takes several cycles to charge the capacitor.
2. The secondary voltage (5 volt winding) is reduced during the charging process, but this indicates that the primary voltage is reduced..

This brings up an interesting question. It is the primary voltage that is reduced during the charge. Saturation is critically dependent on the primary voltage. So, in a different transformer, where saturation is an issue with no load, does the capacitor charging eliminate the possibility of saturation?

[nickb]

Does the mains current vary for 'cranked' output?

Surely. But not more than about +10%.