Voltage Regulation - Transformer

[Gremlin]

Homework Statement

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.

Homework Equations

Voltage Regulation ≈ (VA _Rating / V₁²) x R'_p x 100

n = N₁ / N₂ = E₁ / E₂

R'_p = R_p x n² R_s

The Attempt at a Solution

Voltage Regulation = 2%
VA _Rating = 200000
V₁ = 415
V₂ = 11000
R_p = 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 R_s

0.01722 / 1.42333 x 10^-3 = R_s

R_s = 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?

Thanks.

 

[Gremlin]

The maths is wrong but I'm happy I've got the right idea - and the right answer when the maths is corrected.

 

[gneill]

Homework Equations

Voltage Regulation ≈ (VA _Rating / V₁²) x R'_p x 100

n = N₁ / N₂ = E₁ / E₂

R'_p = R_p x n² R_s

That expression for R'_p looks a bit odd. The units don't make sense (Ohms squared on the right hand side).

 

[James Goodchild]

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?

 

[gneill]

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?

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.

 

[James Goodchild]

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.

 

[KatieMariie]

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) formula so i can go back and re-do the question?

Thanks, Kate

 

[NascentOxygen]

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) formula so i can go back and re-do the question?

Thanks, Kate

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

 

[kjkj]

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

Hi, I have a value for Rs of 1.488 ohms, Could somebody please tell me if I am wildly incorrect?

Many thanks

 

[casper12]

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

 

[NascentOxygen]

I rearranged the formula R'P = RP + n^2 * RS to RS = R'P / (RP + n^2)

Hi casper12.

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.

[emoji422] 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.

https://www.physicsforums.com/attachments/110502.gif

 

[casper12]

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.