# Voltage Regulation - Transformer

• Gremlin
In summary: Thank you for your help. You're welcome. Yes, that's the correct formula. You can also think of it as RS = (R'P - RP)/n² because if you multiply both top and bottom of this fraction by n², you obtain the first formula.So now you can go back and re-do the earlier steps, and also do the calculations with the correct formula. Your earlier values (e.g. 1.488) will no longer be correct, so you'll have to start again from scratch.The correct value for RS will agree with the answer you were given earlier in this thread. The (2%) difference you obtained may have been due to rounding off of the intermediate values,
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 = Rp x n2 Rs

## 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?

Thanks.

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:
Gremlin said:

## Homework Equations

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

n = N1 / N2 = E1 / E2

R'p = Rp x n2 Rs
That expression for R'p looks a bit odd. The units don't make sense (Ohms squared on the right hand side).

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?

James Goodchild said:
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.

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.

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

KatieMariie said:
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
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

NascentOxygen said:
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

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

casper12 said:
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

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.

## 1. What is voltage regulation?

Voltage regulation is the process of maintaining a stable output voltage from a transformer despite changes in input voltage or load. It ensures that the desired voltage is delivered to the load within a specific range of variation.

## 2. How does a transformer regulate voltage?

A transformer regulates voltage through the principle of electromagnetic induction. The transformer has two coils, a primary coil that receives the input voltage and a secondary coil that delivers the output voltage. The ratio of the number of turns in the primary and secondary coils determines the output voltage. By adjusting the number of turns in the coils, the transformer can regulate the output voltage.

## 3. What is the purpose of voltage regulation in a transformer?

The purpose of voltage regulation is to provide a stable output voltage for the load. This is especially important in electrical systems where sensitive equipment or devices require consistent power supply to function properly. Voltage regulation also helps to prevent damage to the load due to voltage fluctuations.

## 4. How is voltage regulation measured?

Voltage regulation is measured as a percentage of the difference between the no-load voltage and the full-load voltage. It is calculated using the formula: ((VNL – VFL) / VFL) * 100%, where VNL is the no-load voltage and VFL is the full-load voltage. A lower percentage indicates better voltage regulation.

## 5. What factors can affect voltage regulation in a transformer?

Several factors can affect voltage regulation in a transformer, including the quality of the transformer's design and construction, the type and quality of materials used, the size and length of the transformer's conductors, and the ambient temperature. Poor design or materials, as well as environmental conditions, can result in a decrease in voltage regulation, leading to potential issues for the load.

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