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Calculate power value from a input current peak

Discussion in 'Power Electronics' started by Chatanas, Nov 28, 2020.

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  1. Chatanas

    Chatanas

    3
    0
    Nov 28, 2020
    Hello folks,

    I have a really simple problem.
    I'm probing the input current peak of a system and I'd like to calculate the equivalent power consumption.

    This peak current is about 3.3A for 2ms approximately and the system is powered by a 12V power-supply. The signal form is not exactly this one but I simplified it for the sake of the exercise. I attached the screenshot of the real one to this post (and before you ask, the unit is actually in A, but I forgot to change the unit in the oscilloscope).

    If the peak lasted 1s it would be simple and I would only have to write the traditional equation P = I x V = 3.3A x 12V = 39.6W. But as this peak last only 2ms, then it cannot be that high.

    Then, I would have written something like (3.3A x 2ms) x 12V... However, it would not define a power anymore, but an energy, unless I say it is a normalization to 1s like in the following formula: upload_2020-11-28_10-30-13.png

    Did I write this equation right?

    I acquired the value samples from an oscilloscope to calculate the power by transcripted the equation in the discrete-domain. Here is how I computed it:
    upload_2020-11-28_11-29-49.png
    With N the number of sample during the peak and M the total number of sample during 1s.
    I considered Vn and Vm as constants equals to 12V since the voltage value barely changed during the current peak.

    However, summing the first part of the equation ( upload_2020-11-28_11-32-25.png ) already gives me a result too high to be realistic.
    Indeed, in my example I have M = 10^5 samples, N = 127 sample and sum(VnxIn) = 1700W.
    Then it gives a result of 2.16W, for only 2ms (while it has to be 39.6W for a full second).

    I am a little bit confused and lost in my equations right now... Could you please help me solve this issue? Otherwise, could you please give me some advices or document I could read to learn more about this subject?

    Thanks a lot for your help!
     

    Attached Files:

  2. Kabelsalat

    Kabelsalat

    164
    29
    Jul 5, 2011
    Well - this doesn't look like an ordinary RC discharge curve, so it's tricky if you cannot describe this area with some ordinary math function.
    Have you considering using Simpsons formula ?
     
  3. Harald Kapp

    Harald Kapp Moderator Moderator

    11,646
    2,691
    Nov 17, 2011
    I think that is where you err. The equation should look like this:
    upload_2020-11-28_18-4-31.png

    Reason:
    1. count starts at 1 if you have M samples. If count started at 0, the total number of samples is M+1
    2. Assume Vn and In are constant, not time variable. Then sum(Vn × In)1N = N × Vn × In. In your equation you have N². That's where your too large value comes from.
     
  4. Chatanas

    Chatanas

    3
    0
    Nov 28, 2020
    Hello Kabelsalat and Harald Kapp and thanks for your replies.

    I didn't, but after reading some more about it, it is a good method, indeed :)
    As I was looking for more information (mainly to know why the equation takes this form) I found this website, which performs the mathematical demonstration... Very interesting!
    I won't necessarily use it for this application, but I'll keep it in mind if ever I need extra accuracy in my calculation for the future.
    Thanks a lot for your help!

    1- Indeed, I didn't write properly the formula. Sorry about it and thanks for the correction!
    2- You're absolutely right! I knew there was something wrong in this equation, but I did not found what it was. I correct it in my equation and it worked! Now I'm looking at the equation this way, it's just a basic equation to find the average and I feel a bit stupid to not have thought about it... I should not have been properly awake :oops:
    In any case, it's exactly what I was looking for! Thanks again!

    Beside these methods, I slept on my issue and came with this equation, which seemed to work properly, too:
    upload_2020-11-29_11-29-18.png
    (edit: replace the 2 under the epsilon by 1)

    With Tn the time when the sample In has been measured, V = 12V and T = 1s.

    This way, the equation sums the successive rectangles with a length of In and a width of (Tn - Tn-1) composing the total area covers by the curve.
    Then, to remove the part in excess (or missing) of each rectangle when the curve is falling (or rising), I would write this equation:
    upload_2020-11-29_11-34-26.png
    (edit: replace the 2 under the epsilon by 1)

    It is not as accurate as the Simpson's method, but I think it is a bit more accurate than the average equation.
    What do you think about it?
     
  5. Chatanas

    Chatanas

    3
    0
    Nov 28, 2020
    And my bad: it is of course not an epsilon but a sigma :oops:
    Shame on me ;)
     
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