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Current Transformer Magnetic Behavior

  1. Apr 24, 2015 #1


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    Hi friends..I am very confused with the magnetic behavior of a CT. CT secondary should never be left open.Okay I understand why. But how exactly does a shorted secondary cancel the primary flux? For that the primary and secondary currents must be 180 degrees out of phase while Lenz's law states it should be 90 degrees due to the di/dt of Ip. In power transformers,primary draws excess current on loading and 180 degree phase difference is established. But in CT,primary current is fixed. Also,if CT is somehow switched on at the zero-crossing instant of primary current, CT will tend to oppose the increase in flux but if it is switched on just after the peak of Ip, it will oppose the decrease in the flux and try to maintain the previous flux. This is baffling me. What does the secondary do exactly?? Does it oppose the primary flux or the change in primary flux?? What is the steady state waveform of secondary current?? What is its phase relationship with Ip?? Please help me with actual physics behind this..I am sick of the usual 'equivalent circuit' method and bunch of formulae..Please could anybody explain the actual physics?? I am eagerly waiting..
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  3. Apr 24, 2015 #2

    jim hardy

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    Sneaky, aren't they?


    For simplicity think about it temporarily as DC.
    Apply right hand rule to both windings.
    Ip pushes flux UP
    Is pushes flux UP
    and those two mmf's oppose, one is clockwise and the other counterclockwise.
    If amp-turns are equal , mmf's will be equal and opposite, so flux will be zero.(Φ=mmf/reluctance)

    Are you confusing Lenz with Faraday ?

    So far as operating principle goes, the only difference between a current transformer and a voltage transformer is the external circuit.
    In a current transformer something in the circuit sets primary current. There'd be a motor or light or something in series with Vp.
    In a voltage transformer the transformer's counter-emf limits the current.

    Aha - not much counter emf in a current transformer? That means not much flux.
    Secondary current must be allowed to flow freely so that it can cancel primary flux.

    Now - since it takes some amp-turns to push flux around the core, a typical current transformer will have a better core than a typical power transformer. That's to minimize primary amp-turns that get lost because they were spent magnetizing the core. You want them all to cause secondary amp-turns instead.

    Most common hangup in understanding CT's is the concept that primary current is set by whatever is the machine whose current you're measuring with the CT. Ideally Vprimary would be zero hence the shorted secondary.

    EDIT: edited by moderator per OP request
    Last edited by a moderator: Apr 24, 2015
  4. Apr 24, 2015 #3


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    Thanks for your reply Jim..But what still confuses me is that the secondary amp-turns must be generated by thesecondary emf which is induced by the changing primary current. So, Ip and Is should be 90 degrees apart. Does the self inductance of secondary have anything to do with this? Because if that inductance is large enough, it will provide the next 90 degree displacement between induced secondary voltage and secondary current . Without that if I directly assume both the currents to be 180 degrees apart, that would violate the math of Lenz's law.
  5. Apr 24, 2015 #4

    jim hardy

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    e =
    hmmm i sense your confusion and am searching for the fewest words to clarify .

    CT's have phase shift of typically six degrees or less, not ninety.

    Taking it to the extreme limit:
    Basically, shorted secondary means zero volts across both windings
    so primary and secondary amp-turns must cancel each other immediately, without time delay, else there'd be induced voltage
    and for sinewaves time delay is phase shift.

    The closer to zero flux you can operate the transformer the better it'll do.

    Will be back when i have the words for it.

    old jim
    Last edited: Apr 24, 2015
  6. Apr 24, 2015 #5

    jim hardy

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    ps thanks, moderator for edit of post 2 !
  7. Apr 24, 2015 #6

    jim hardy

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    ps , late entry
    maybe this train of thought will lead to a math-less explanation, to which we can then apply math.

    A winding on a core is inductance.
    Definition of inductance is flux X turns per amp.
    Presence of secondary amp-turns , by cancelling primary amp-turns reduces flux.
    Flux-turns per amp is inductance, and we reduce inductance by shorting secondary.
    So the CT appears less like an inductor and more like a low ohm resistor.

    Try a search on CT Phase shift, maybe you'll have better luck than i did.

    old jim
  8. Apr 24, 2015 #7


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    Okay ..This is interesting..I'm getting your idea, especially that inductance part...Thanks a lot..:smile:Got to think on it...
  9. Apr 25, 2015 #8

    jim hardy

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    let's try this train of thought.

    It's hard to swap our mind from a voltage transformer to a current transformer.

    Here's the concept

    Voltage Transformer:
    Voltage determines flux, even though current is what makes flux.
    That's because while mmf = amp-turns
    voltage = ndΦ/dt , Faraday
    so flux Φ = 1/n X ∫voltage
    and integral of sine is cosine...
    That derivative-integral relationship is important.

    Flux is measured in Webers or Maxwells

    but volts per turn (at a known frequency) works just as well.
    One weber per second induces one volt in one turn
    so volts per turn is webers per second

    Anyhow to keep it math-less,
    applying a fixed voltage to an inductor locks the flux at a level that'll make equal counter-emf.
    There's some current level that'll make that amount of flux, and let's call that the "magnetizing current".
    The more the inductance the less the magnetizing current.

    If i add a second winding to that inductor i have made a transformer.
    A good transformer will have lots of inductance so as to not waste too much current magnetizing the core.
    Magnetizing current is 90 degrees (well around ninety) out of phase with applied voltage because it's inductive, and that derivative-integral relation holds.

    If i now allow current to flow in secondary, that current immediately produces mmf that opposes primary mmf.
    Immediately ? Yes, immediately because mmf is amp turns with no derivative-integral relationship.
    Aha - secondary amp0turns must be immediately overcome(?)corrected(?)(choose a verb) by primary amp-turns,, else flux would drop and counter emf wouldn't balance applied voltage.
    So - secondary current(let's call it load curent) is reflected into primary with no delay, and no delay=no phase shift.
    So - load current is not in phase with magnetizing current.
    Primary current will be sum of magnetizing and load current phasors.
    Sum of primary and secondary mmf's will produce mmf equal to magnetizing current mmf, because voltage is fixed.


    In your original post you were thinking of secondary current being out of phase with primary magnetizing current, which it is,
    but load current in secondar windings is in phase with load current reflected into primary. (i hope that wording is okay)

    So - in a voltage transformer, primary mmf will be whatever is necessary to support counter-emf.
    Sum of mmf's is constant , and is substantial. Power transformers operate high up the B-H curve, near the knee.


    Now to the humble current transformer.


    Hollow refers to the donut shaped core, which is not a hollow circular shell .

    The current transformer is an inductor as was the voltage transformer.
    Since it goes in series with whatever device for whgich we wish to measure the current,
    it is desirable to have low voltage across the CT so as to not impede current to our device.
    That's true for any ammeter. How can i determine my awshing machine's current if the CT blocks current?
    So we must keep flux in our CT as low as possible so it won't make any counter EMF.

    Well that's easy, just short circuit the secondary.
    Since the secondary mmf will cancel the primary mmf there'll be no flux to oppose primary current.
    Why doesn't current rush in like in a voltage transformer, to restore flux? Because primary current is fixed by the circuit we're measuring.

    Okay, that's cool.
    What about phase?
    Remember from the voltage transformer that mmf's cancel immediately with no phase shift...
    So the secondary current ought to be in phase with primary current, since it's all "load current".

    Okay, but as you said there's got to be some magnetizing current in the CT else it couldn't make secondary current.
    Quite so.

    How much magnetizing current?
    system is ignoring preview and upload and post buttons again and i'm about to smash the screen

    will be abck when things work better
  10. Apr 25, 2015 #9

    jim hardy

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    how much magnetizing current in a ct ?


    so our mmf's ( currents) in a CT will be more like tnis

    well cant up load again so see next post

    had to reboot to get it to see buttons
  11. Apr 25, 2015 #10


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    You are awesome man...! What a lucid explanation... Really I wish you were my professor:smile: Can't wait to see next post...
  12. Apr 25, 2015 #11

    jim hardy

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    darn lost half this post in reboot to fight the "Button Ignore War"

    So how much magnetizing current in a ct ?

    not much. Remember we're on the bottom of the curve
    and CT;s use high quality extreme permeability cores that are easily magnetized

    It helped me to think of primary current as two components - magnetizing and reflected from load if you will.

    I use "current" and "MMF" amost interchangeably, because they're in direct proportion - hope that didnt muddy anything for you.

    So i think the answer to your original dilemma is - secondary current is 90 degrees out of phase with the magnetizing component of primary current, just as it is in the voltage transformer
    but the CT consumes only a little bit of its primary current as magnetizing current, remainder shows up as secondary current.

    And grade school geometry tells us that in a right triangle with such a small "opposite side", adjacent and hypotenuse are almost equal.

    That's the best math-less explanation i can come up with, and the frustration with system ignoring buttons has been awful. So i apologize if this presentation is less than my best.

    With those principles in mind one can figure out how the textbook formulas came about, and understand their application.

    i hope this is coherent . As i said i lost some of it and it's difficult for one as scrambled as i to retrace his "stream of consciousness babble."
    It seemed to make sense as i went along

    maybe if the system behaves better for me you'd post some of the math of your textbook.

    Anyhow - when CT's become intuitive you're getting clloser to understanding transformers in general.

    Thanks for the kind words, i hope i helped you. Makes an old guy feel less useless.

    If system accepts this post button - i gotta get a break from it. Going out to shed and finish my TV antenna (yagi specific to PBS station 60 miles away)

    old jim

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  13. Apr 25, 2015 #12

    jim hardy

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    remember primary current magnitude is set by the circuit
    so you're dividing the available primary current pie between magnetizing current (consumed by core) and secondary current for the meters.
    Meters are the important part so designer assures they get the lion's share of primary mmf, amp-turns, current, whatever you choose to call it. Why not call it "the pie" ? I need alll the memory aids i can conjure.

    And do not shy away from the math. It is important to bounce your understanding of the formulas against your understanding of the physical processes. That'll train you mind to avoid false "word salads" .
    "Dancing with the Stars" is a good time to think about transformers instead of cheesecake.

    old jim
  14. Apr 25, 2015 #13


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    Hats off to you Jim...You are really an expert on this...Thank you very much for all this brilliant stuff above..:smile::smile:
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