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Homework Help: Voltage Regulation - Transformer

  1. Jun 3, 2015 #1
    1. The problem statement, all variables and given/known data

    A 415V to 11 kV transformer has a rating of 200 kVA. The winding resistance and leakage reactance when referred to the primary are 0.014 Ω and 0.057 Ω respectively.

    (b) In designing a particular 415V to 11 kV, 200 kVA transformer, the primary winding resistance is to be 10 mΩ. Find the maximum winding resistance of the secondary winding if the transformer is to have 2% regulation at unity power factor.

    2. Relevant equations

    Voltage Regulation ≈ (VA Rating / V12) x R'p x 100

    n = N1 / N2 = E1 / E2

    R'p = Rp x n2 Rs

    3. The attempt at a solution

    Voltage Regulation = 2%
    VA Rating = 200000
    V1 = 415
    V2 = 11000
    Rp = 0.01
    Cosθ = 1

    2 ≈ (200000 / 4152) x R'p x 100

    2/100 ≈ 1.161271 x R'p

    0.02 / 1.161271 ≈ R'p

    R'p ≈ 0.01722

    E1 / E2 = 415/11000 = 0.037727

    0.01722 = 0.01 x 0.0377272 x Rs

    0.01722 / 1.42333 x 10-3 = Rs

    Rs = 1209.84Ω

    I'm sure i'm wrong, but am i in the correct ball park in the way i'm going about answering the question?

  2. jcsd
  3. Jun 4, 2015 #2
    The maths is wrong but i'm happy i've got the right idea - and the right answer when the maths is corrected.
    Last edited: Jun 4, 2015
  4. Jun 4, 2015 #3


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    Staff: Mentor

    That expression for R'p looks a bit odd. The units don't make sense (Ohms squared on the right hand side).
  5. Jul 26, 2015 #4
    n = N1/N2 = E1/E2

    Is n = V1/V2? In other words, E1 = V1? E2 = V2?

    If they are, n = 415/11000 = 0.0377

    Is this correct?
  6. Jul 26, 2015 #5


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    Staff: Mentor

    Yes, that's correct. Although sometimes you'll see an author use V2/V1 instead, as it yields values greater than 1 (a convenience only) for step-up transformer situations. Formulas employing 'n' will be adjusted accordingly, using 1/n in place of n.
  7. Jul 26, 2015 #6
    Thank you Gneill. I was not sure, as the winding resistance and leakage reactance connected in series with the primary winding suggest that V1 is not equal E1.

  8. Jul 28, 2015 #7
    I was also instructed to use the above formula (OP) by my tutor; however i'm somewhat concerned that the R'p equation looks odd.

    I have completed the calculations as instructed and found b) = 1210.19 Ohms (2 dp), i had not questioned my answer until i came across this post. Can anyone confirm if there is an error in the R'p = Rp x (n^2 x Rs) forumla so i can go back and re-do the question?

    Thanks, Kate
  9. Jul 29, 2015 #8


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    Staff: Mentor

    The units there don't match, so it can't be right.

    The total winding resistance referred to the primary side would be Rp + n²·Rs
  10. May 7, 2016 #9
    Hi, I have a value for Rs of 1.488 ohms, Could somebody please tell me if I am wildly incorrect?

    Many thanks
  11. Dec 25, 2016 #10
    hi i am new to the forum and trying to complete the electrical and electronic engineering course but the learning material provided does not seem to provide adequate knowledge to complete some of the questions being asked. I rearranged the formula R'P = RP + n^2 * RS to RS = R'P / (RP + n^2) which resulted in RS = 1.50744 ohms but with so many values being suggested on the forums I am doubting the result. cheers
  12. Dec 25, 2016 #11


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    Staff: Mentor

    Hi casper12. smiley_sign_welcome.gif

    In future, please start a new thread for your question, unless it is a follow-on to an earlier thread dealing with the same question. This saves readers having to wade through old unrelated posts before reaching yours.

    If in doubt of your re-arrangement, you can always check to confirm it is correct!

    Here's how: Take any convenient arbitrary value for RP, RS and n, and evaluate what those values would make for R'P in your first equation. Now, using these values work out what the right-hand side of your second equation would be.

    ◾Is that value almost the same as your original value for RS? If so, your rearrangement is confirmed, but if there is no agreement, then your rearrangement is definitely wrong.

    Show the steps in your working here.

  13. Dec 26, 2016 #12
    Hi thank you for fast response and sorry for double posting, I checked my re arrangement as you suggested and it was incorrect. I have had some further feedback and been advised that the calculation to find RS is RS = [ R'P - RP ] * n^2 with this I will hopefully complete the question.
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