Confused about transformer saturation

Discussion in 'General Electronics Chat' started by daviddeakin, Apr 21, 2010.

  1. daviddeakin

    Thread Starter Active Member

    Aug 6, 2009
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    I have just had a major mental failure regarding transformers! Seems I don't know as much as I thought (hoped) I did!

    If we take a lossless power transformer, for simplicity:

    You apply mains voltage, and a magnetising current is set up in the primary, which lags the voltage. So you now have a certain amount of magnetic flux in the core. The secondary voltage is in phase with the primary voltage.

    When you attach a resistive load to the secondary then the secondary load current is in phase with the secondary voltage. This causes additional current to flow in the primary, which must also be in phase with the primary voltage.

    However, the secondary current does not cause additional flux because the secondary magnetomotive force (MMF) is cancelled by an opposing MMF in the primary, so the net flux remains unchanged by loading.

    So how the heck does a core saturate if you apply too much load, where does the extra flux come from?!
     
  2. The Electrician

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    Where did you read that a transformer core will saturate if you apply too much load (or who told you this)?

    This won't happen as long as the load is purely resistive.

    If DC is caused to pass through the secondary, such as would happen with a half-wave rectifier load, this could happen.
     
  3. daviddeakin

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    I don't know, I thought it was 'common knowledge', but now I am looking into it you see why I had to ask the question!

    I can see why exceeding the rated mains voltage, or lowering the frequency, would cause saturation. So you're saying that even with the secondary short-circuited, the transformer will not saturate? (Though presumably it will get hot from copper losses) Am I on the right track?

    This is a big revelation to me! Thanks for any help!
     
  4. Ghar

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    Mar 8, 2010
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    The flux is the integral of applied voltage, which is proportional to the magnetizing current, like an inductor, because a transformer is very high value inductor.

    Lower frequency or higher amplitude makes the integral reach a higher value and the core saturates at some value.

    http://ludens.cl/Electron/Magnet.html

    DC voltage saturates a transformer because the current just keeps building until it's limited by the external circuit.

    Though I have to admit, the one time I actually ran into transformer saturation (haven't used them much) I didn't get it to work, so please someone correct me where I'm wrong.
     
  5. The Electrician

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    A resistive load on the secondary, up to and including a short, will not increase the flux in the core. In fact, drawing current from the secondary will slightly decrease the core flux due to the IR drop in the primary.
     
  6. retched

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    Its like a sponge. Saturated is full of water.

    The secondary can pull water out of the sponge while under load.

    If the current exceeds the coppers rating, you will start to have excessive heat which increases resistivity which increases heat which increases resistiv.....ect.
     
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  7. daviddeakin

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    Aug 6, 2009
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    I think a light has finally turned on in my head- thanks everyone!

    New question:
    Does that mean that a net DC current in primary or secondary, no matter how small, will push the core into saturation? Even 1mA?

    Surely there is enough DC offset on the mains alone to do that, and we would all end up with hot, noisy transformers?
     
  8. The Electrician

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    The onset of saturation is a gradual thing. A little DC will only push the core a little way into saturation.
     
  9. t_n_k

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    That's true. I guess Ghar was considering what happens when a DC source is connected to the input of an "ideal" transformer - in which case the absence of any primary resistance would see [at first thought] the primary current increasing in an unbounded manner. Of course if the transformer core was also ideal it would never saturate and it would be infinitely permeable. Being infinitely permeable would imply that the mmf required to magnetise the core would be zero and the primary current, in an unloaded secondary condition, would never increase beyond zero. An ideal transformer is a perfect transformer of both AC and DC. Now there's a nice conundrum.

    The ideal transformer is an abstract concept rather than a realisable physical entity.
     
    Last edited: Apr 22, 2010
  10. The Electrician

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    Here are some scope captures from a loaded rectifier power supply (capacitor input filter) with a standard bridge (full wave) rectifier configuration, and also with a single diode, half wave configuration.

    The blue trace is the line voltage applied to the primary; the green trace is the DC output voltage. There is substantial ripple voltage because the filter capacitance is only 1800 μF.

    The purple trace is the secondary current, and the orange trace is the primary current.

    The first image shows the situation with the bridge rectifier. The secondary current reaches a peak of about 9 amps, and the primary reaches a little over 2 amps.

    The second image shows the half wave rectifier performance. The load current was adjusted so that the RMS value of the primary current was the same as in the full wave case.

    You can see the primary current occurring at the same time as the secondary current, but then the primary current has a substantial peak of about 1.8 amps when there is no secondary current. The transformer core has been driven well into saturation.

    We're only getting about half the DC output current for the same RMS primary current (and therefore the same transformer heating due to primary copper loss) in the half wave case. Additional disadvantages of half wave rectification are more ripple in the output voltage (for the same filter capacitance) and a noisy transformer (it's buzzing a lot).
     
  11. Ghar

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    Well my reasoning was that the magnetizing current was proportional to flux, and that current gets limited. You don't have access to the magnetizing inductance directly, so just like an inductor cannot go to very high currents due to series resistance, neither can this magnetizing current (i.e. current peak at same time as zero crossing of voltage)

    My only experience with this is when I built an inverter and had a transformer on the end of it. I could vary DC offset +/- and amplitude very easily and it would saturate all the time. Sadly I didn't know enough about it then to experiment properly and since then the inverter was junked.

    Has anybody measured the DC offset on the grid?

    I just found this interesting site but it doesn't explicitly talk about saturation:
    http://www.vias.org/eltransformers/wrapnt_introduction8.html

    Edit:
    Looking at The Electrician's saturation plots it does suggest the integral at least.
    Look at the applied voltage (blue) vs the primary current (orange).
    At some point during the cycle saturation starts happening and current begins to increase. It keeps increasing until the voltage crosses zero and becomes negative. (i.e. current peak at the same time as voltage zero crossing)
     
    Last edited: Apr 22, 2010
  12. t_n_k

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    There's nothing wrong with your reasoning - I was just suggesting a thought experiment.

    Presumably power supply authorities do their best to remove any DC offset from the mains supply. Considering that most consumers are connected to sub-stations with transformers it's unlikely under normal circumstances that a DC offset in the mains supply would be observed or if it did exist, it could not propagate very far down the distribution system. The next transformer lower down in the system network would not pass the DC onwards.
     
  13. The Electrician

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    t_n_k is right. Since the power distribution grid is transformer isolated in many layers from generator to home, there is no way to know what DC offset there may be in the various parts. And, if there is one somewhere along the way, it will be eliminated by the last transformer supplying your home.

    However, it is well known that there may be a small DC offset in any one particular person's home. The golden ears audio people know about it; it can cause buzzing in toroidal power transformers found in some audio power amps. There are accessories sold to eliminate it, and plans for making such a device yourself, which basically consists of a big non-polar electrolytic in series with the primary of the toroidal transformer.

    One common cause of measurable DC offset in the home is the use of hair dryers on medium power setting. The usual way the low cost dryers achieve medium power is to place a diode in series with the heating element, so a half wave load is applied to the distribution transformer (pole pig). If more than one home is supplied from a particular transformer, then your home may experience a DC offset due to half wave loads in use at a neighbor's home.
     
  14. Ghar

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    What order of magnitude is this offset do you think?

    This issue of limited magnetizing flux has been bugging me for a while.
     
  15. The Electrician

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    It's not just a suggestion; it's Faraday's law. It is indeed what is happening.

    I didn't respond to what you said about the integral of applied voltage because I assumed from Alberto's comments in post #3, and the OP's comments in post #4 that it was understood.

    To be very specific, the flux in the core is determined by the integral of the applied voltage, the primary voltage. If that voltage is (essentially) constant, the the flux excursions will be constant, independent of load.

    Note, however, as I said, if a large current is drawn from the secondary, and hence from the primary, that current will cause an IR drop in the resistance of the primary, and that slight loss of voltage will reduce the voltage seen by the core. So the flux excursions will be slightly reduced, not increased; loading a transformer reduces the flux excursions in the core.

    The magnetizing current is not directly proportional to the flux (flux density, actually), but is related in a non-linear way because of the shape of the B-H curve of the core material, the iron.

    If the core material were linear (air, for example), and if we applied a sine wave of voltage to the primary (with the secondary unloaded), we would expect a 90° shifted sine wave of current. But with an iron core, the current wave is highly distorted if the flux density goes much above 10,000 gauss.

    Passing DC through the secondary pushes the flux excursions off to one side of the hysteresis loop of the core, and leads to saturation in one direction only.
     
  16. Ghar

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    I had most of that but thanks for confirming it.
    The part I'm still curious about is this issue of DC voltage on the primary.
    If the magnetizing current is the integral of voltage then it will increase until limited by series resistance.
    That resistance isn't very high so a small DC offset could saturate a transformer.

    This is why I asked about the magnitude of the offsets on the grid.
     
  17. The Electrician

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    Well, just for you, I measured it. It's easy to do. Just connect an 18k (use one 4 times larger if your line voltage is 240) resistor in series with a 50 μF motor run capacitor and plug in to an outlet. This RC low pass filter gets rid of most of the AC voltage, and then my Fluke 187, on millivolts DC range, can get a good reading across the capacitor with its 60 Hz rejection capability not not being overwhelmed.

    I see some bobble in the reading, but it stays below 1 millivolt. I then plugged in a hair dryer at that same outlet. With the dryer on high, there was no change. With the dryer on half power, I have about 100 millivolts of DC present.

    I should ask my neighbor to plug in a hair dryer and put it on half power to see if I can detect the offset! Maybe later.
     
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  18. Ghar

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    I think you're my favourite person on these forums now.
     
  19. The Electrician

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    Flattery will get you nowhere! :D

    http://dictionary.cambridge.org/dictionary/british/flattery-will-get-you-nowhere

    The hair dryer is about a 750 watt load at half power; that's something like 6 amps drawn from the outlet.

    A low resistance transformer primary plugged in at that outlet could have something like 1 amp of DC in the primary when the hair dryer is running at half power.
     
  20. The Electrician

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    Remember, it's the flux that is proportional to the integral of voltage. The magnetizing current is related to flux by the properties of the core.

    In the case of DC, the core will only have an effect on current for a very short time. Ultimately, the (DC) current is determined by the DC circuit parameters.
     
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