Voltage Regulation transformer

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Discussion Overview

The discussion revolves around the voltage regulation of a transformer, specifically a 415V to 11 kV transformer with a 200 kVA rating. Participants explore calculations related to winding resistance, leakage reactance, and the implications of power factor on voltage regulation. The conversation includes both theoretical and practical aspects of transformer design and performance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the % regulation of the transformer at 0.8 power factor lagging to be approximately 5.27% using a specific formula.
  • Another participant discusses the concept of impedance reflection in transformers, suggesting that secondary winding resistance can be reflected into the primary circuit.
  • A participant derives the primary resistance based on the secondary load resistance and the turns ratio, arriving at a value of 0.017Ω for the primary resistance at unity power factor.
  • Concerns are raised about the simplicity of the calculations in part (a), with a participant questioning the validity of their approach and suggesting a more complex equation for voltage regulation.
  • Multiple participants express uncertainty about the correct secondary winding resistance, with various values proposed, including 0.007Ω, 4.92Ω, and 9.963x10^-6Ω.
  • There is confusion regarding the use of abbreviations and the correct formulation for reflected resistance, with participants seeking clarification on the relationships between primary and secondary resistances.
  • One participant mentions obtaining a negative value for resistance, prompting a discussion about the correctness of such a result.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct secondary winding resistance or the validity of the calculations presented. Multiple competing views and values are expressed, indicating ongoing uncertainty and debate.

Contextual Notes

Participants reference various equations and concepts related to transformer design, including the effects of power factor and the implications of reflected impedance. Some calculations appear to depend on assumptions that are not fully clarified, and there are unresolved steps in the mathematical reasoning.

Who May Find This Useful

This discussion may be useful for students and professionals interested in transformer design, electrical engineering concepts, and voltage regulation principles.

his_tonyness
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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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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, what's 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?
 
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?
 
R's x a = rs?
 
  • #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
 

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