Transformer Equivalent Resistance

Fig-1: Transformer Equivalent Resistance

Fig-2: Transformer Equivalent Reactance

How to Calculate the Transformer Equivalent Resistance and Reactance?

The transformer’s impedance is given in percentage or per unit system. It is because of the reason that the impedance value for the transformer is represented as two values one wrt to low voltage winding and the other is high voltage winding. Both values are different but represent the very same physical quantity.

Transformer equivalent impedance contains two-part, one is equivalent resistance and the other is equivalent reactance. The vector sum of these two parts is known as equivalent impedance.

Transformer Equivalent Resistance

Considering the figure-1 the above

Let

R₁ = primary winding resistance;

R₂ = secondary winding resistance;

K = transformation ratio.

The equivalent resistance of the transformer referred to as the primary is represented by R₀₁.

 

Therefore, R₀₁ = R₁ + R₂' = R₁ + R₂/K².

The equivalent resistance of the transformer referred to as the secondary is represented by R02.

 

Therefore, R₀₂ = R2 + R1' = R2 + K²R1.

Transformer Equivalent Reactance

Considering the figure-2 the above

Let

X1 = primary winding reactance;

X2= secondary winding reactance;

K = transformation ratio.

The equivalent reactance of the transformer referred to as the primary is represented by X₀₁.

 

Therefore, X₀₁ = X1 + X2' = X1 + X₂/K²

The equivalent reactance of the transformer referred to as the secondary is represented by X02.

 

Therefore, X₀₂ = X2 + X1' = X2 + K²X₁.

The impedance of the Transformer

Impedance(Z) = Resistance(R) + j Reactance(X)

The primary impedance Z1 = R1 + jX1

And secondary impedance Z2 = R2 + jX2

 

The transfer of impedances takes place on the same lines as that of the resistances. The transfer of impedances can take place from primary to secondary and vice versa.

Percentage Resistance is the resistance drop in volts at rated current and frequency as a percentage of the rated voltage.

%R = ( IR/V)*100

Percentage Reactance is the reactance drop in volts at rated current and frequency as a percentage of the rated voltage.

%X = ( IX/V)*100

Percentage impedance is nothing but a measure of the volt drops when the transformer is on full load due to the winding resistance and leakage reactance expressed as a percentage of the rated voltage.

%Z = ( IZ/V)*100

 

Z₀₁ = (R₀₁² + X₀₁2)^1/2 impedance referred to primary side.

Z₀₂ = (R₀₂² + X₀₂2)^1/2  impedance referred to secondary side.

The important advantages of expressing resistance and reactance of a transformer in percentage are that the percentage resistance and percentage reactance have the same values whether determined and referred to as primary or secondary whereas expressed in ohms they have different values when referred to as primary and secondary.

You may know the details about the electrical transformer from the following articles:

 

1. Working Principle of Transformer;
2. Transformer Construction;
3. Core-type Transformers;
4. Shell-type Transformers;
5. Elementary Theory of an Ideal Transformer;
6. E.M.F. Equation of Transformer;
7. Voltage Transformation Ratio;
8. Transformer with losses but no Magnetic Leakage;
9. Transformer on No-load;
10. Transformer on Load;
11. Transformer with Winding Resistance but no Magnetic Leakage;
12. Equivalent Resistance;
13. Magnetic Leakage;
14. Transformer with Resistance and Leakage Reactance;
15. Simplified Diagram;
16. Total Approximate Voltage Drop in Transformer;
17. Exact Voltage Drop;
18. Equivalent Circuit Transformer Tests;
19. Open-circuit or No-load Test;
20. Separation of Core Losses;
21. Short-Circuit or Impedance Test;
22. Why Transformer Rating in KVA?;
23. Regulation of a Transformer;
24. Percentage Resistance, Reactance, and Impedance;
25. Kapp Regulation Diagram;
26. Sumpner or Back-to-back-Test;
    
27. The efficiency of a Transformer;
28. Condition for Maximum Efficiency;
29. Variation of Efficiency with Power Factor;
30. All-day Efficiency;
31. Auto-transformer;
32. Conversion of 2-Winding Transformer into Auto-transformer;
33. Parallel Operation of Single-phase Transformers;
34. Questions and Answers on Transformers;
35. Three-phase Transformers;
36. Three-phase Transformer Connections;
37. Star/Star or Y/Y Connection;
38. Delta-Delta or ∆/∆ Connection;
39. Wye/Delta or Y/ Connection;
40. Delta/Wye or ∆/Y Connection;
41. Open-Delta or V-V Connection;
42. Power Supplied by V-V Bank;
43. Scott Connection or T-T Connection;
44. Three-phase to Two-Phase Conversion and vice-versa;
45. Parallel Operation of 3-phase Transformers;
46. Instrument Transformers;
47. Current Transformers;
48. Potential or Voltage Transformers.