# Voltage Regulation transformer

## Homework Statement

5. 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.
(a) Determine the % regulation of the transformer at 0.8 power factor lagging.

(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.

## The Attempt at a Solution

(a) (200*10^3) / (415^2) * (0.014* 0.8 +0.057 * √(1-0.8^2)) * 100% =
5.27%

(b) P.F = 1

Not sure where to start. I can't find a direct link equation wise between the primary winding resistance and the secondary resistance. Any push in the right direction appreciated.

gneill
Mentor
Impedance in the secondary circuit is "reflected" into the primary circuit. The secondary's winding resistance is equivalent to a resistance in the secondary circuit. A search on terms like "transformer impedance reflection" should turn something up.

The primary resistance is determined by the secondary load resistance (Rl) and the turns ration i.e R'p =(1/n)^2*Rl . If we solve for Rl since the turns ration is 415/11k =0.037,
0.01=((415/11000)^2)*Rl , Rl= 7.026 ohms. Which for a step up transformer makes sense. Not sure where power factor at unity and 2% Vreg come into play.

At unity power factor, 2% = (200000/415^2)*R'p*100 , R'p=0.017

Hello,
Again I have the same question and feel it can't be that easy. Part a) is no problem. Part b) however I used the voltage regulation equation used in part a) to find the resistance as 0.017Ω at PF 1. As 0.01Ω of this is for the primary winding can I assume that the other 0.007Ω is the secondary winding resistance reflected onto the primary winding? Putting the numbers back into the voltage regulation equation comes out as 1.97% (close enough to 2%!).
I am struggling to find any information in the texts provided, books and on-line searches so again, any guidance is greatly appreciated.

Ive got a feeling part (A) is wrong.

VA/V1^2 X (R'p cos (theta) + X'p sin (theta)) x 100 is an approximation. Has anyone handed it in and got it correct this way? It just seems too easy.

the exact equation is:

(E2-V2)/V2

Where:

E2= V2^2 + I2^2 (R's^2 + X's^2) +2 x V2 x I2 x (R's cos (theta) + X's sin (theta))

it also states that:

R's= Rs + (Rp/n^2)
X's/L's = Xs + (Xp/n^2)

This is where i get stuck.

how can i calculate Rs and Xs?

For (b). Think about reflected impedance theory. If at unity power factor, Primary resistance is calculated to 0.017ohms, and the designed transformer requires 0.01ohms, whats the secondary winding resistance? no complex arithmatic required!

I have three answers for b. Can anyone point me in the right direction.

Rs= 0.007
Rs= 4.92
Rs= 9.963x10^-6

Do any of these match anyone else's?

NascentOxygen
Staff Emeritus
I have three answers for b. Can anyone point me in the right direction.

Rs= 0.007
Rs= 4.92
Rs= 9.963x10^-6

Do any of these match anyone else's?
It's not 0.007 Ω because that the secondary resistance when reflected to the primary. So how should you proceed to determine actual secondary resistance?

R's x a = rs?

NascentOxygen
Staff Emeritus
R's x a = rs?
I don't recognize these abbreviations. Perhaps put it in words, or a comprehensible expression.

I don't recognize these abbreviations. Perhaps put it in words, or a comprehensible expression.

Is it correct to then say

Reflected = Rsecondary + (Rprimary / n^2)

Where n = (N1 / N2)

Which gives me RS = (0.007 - (0.010 / n^2)

Problem is I've failed to lose n^2 so I'm left with numerals only

NascentOxygen
Staff Emeritus
Is it correct to then say

Reflected = Rsecondary + (Rprimary / n^2)

Where n = (N1 / N2)

Which gives me RS = (0.007 - (0.010 / n^2)

Problem is I've failed to lose n^2 so I'm left with numerals only
You know n, it's the transformer's voltage ratio.

You know n, it's the transformer's voltage ratio.

Thanx, Yea I had done that but my answer is coming out as negative value. Is that correct?

NascentOxygen
Staff Emeritus