Transformer with Resistance and Leakage Reactance Calculation

Transformer with Resistance and Leakage Reactance

What do you mean by Transformer Resistance and Leakage Reactance?

The Transformer resistance means the resistance of the primary and secondary winding of the transformer. 

Transformer Leakage Reactance means there is some magnetic leaking in both of the primary and secondary windings that should be equal to inductive coils connected in both primary & secondary windings.

The figure above shows the primary and secondary windings of a transformer with reactance taken out of the windings. 

The primary impedance is given by
Z₁ = sqr(R₁²+X₁²)

Similarly, secondary impedance is given by
Z₂ = sqr(R₂²+X₂²)

The resistance and leakage reactance of each winding is responsible for some voltage drop in each winding. 

The primary leakage reactance drop is I₁X₁(usually 1 or 2% of V₁).

Hence,
V₁= E₁+ I₁(R₁+jX₁) =E₁+I₁Z₁

Similarly, I2R2 and I2X2 drops in secondary ₂R₂ and I₂X₂ drops in secondary which combine with V₂ to give E₂.

E2 = V2 + I₂(R2+jX2) =V₂+ I₂Z₂

It may be noted that leakage reactance can also be transferred from one winding to the other in the same way as resistance.

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.