Voltage Regulation transformer

In summary: I don't recognize these abbreviations. Perhaps put it in words, or a comprehensible expression.R's= Rs + (Rp/n^2)X's/L's = Xs + (Xp/n^2)RS = (0.007 - (0.010 / n^2))RS = 1.488
  • #1

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.

Homework Equations



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.
 
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  • #2
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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?
 
  • #6
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, what's the secondary winding resistance? no complex arithmatic required!
 
  • #7
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?
 
  • #8
The_daddy_2012 said:
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?
 
  • #10
The_daddy_2012 said:
R's x a = rs?
I don't recognize these abbreviations. Perhaps put it in words, or a comprehensible expression.
 
  • #11
NascentOxygen said:
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
 
  • #12
MrBondx said:
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.
 
  • #13
NascentOxygen said:
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?
 
  • #14
A negative resistance value won't be correct. Take another look back over your working, likely there's a mistake.
 
  • #17
Hi, I have a value for Rs of 1.488 ohms, Could somebody please tell me if I am wildly incorrect?

Many thanks
 

1. What is a voltage regulation transformer?

A voltage regulation transformer is a type of transformer that is used to regulate or control the voltage of an electrical circuit. It can either increase or decrease the input voltage to a desired output voltage.

2. How does a voltage regulation transformer work?

A voltage regulation transformer works by using a primary and secondary winding, connected to a magnetic core, to transfer electrical energy from one circuit to another. By adjusting the number of turns in each winding, the output voltage can be regulated.

3. What are the different types of voltage regulation transformers?

There are several types of voltage regulation transformers, including autotransformers, buck-boost transformers, and tap-changing transformers. Each type has its own unique design and function, but all are used to regulate voltage in some way.

4. What are the benefits of using a voltage regulation transformer?

Using a voltage regulation transformer can provide a stable and consistent voltage output, even when the input voltage fluctuates. This can protect sensitive electrical equipment from damage and ensure efficient operation.

5. How do I choose the right voltage regulation transformer for my application?

The type and size of voltage regulation transformer you need will depend on your specific application and the voltage requirements of your equipment. It is important to consult with a professional or do thorough research to determine the best option for your needs.

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