Transformer Total Voltage Drop

Total Approximate Voltage Drop of a Transformer

During the no-load condition, induced voltages at the primary and secondary windings are equal to the applied voltage and secondary terminal voltage respectively. If ₀V₂ be the secondary terminal voltage at no load, we can write E₂ = ₀V₂.

When the transformer is on no-load, then V₁ is approximately equal to E₁. Hence E₂ = KE₁ = KV₁. 

Also,
E₂ = ₀V₂ 

where ₀V₂ is the secondary terminal voltage on no-load, 

hence no-load secondary terminal voltage is KV₁.


The secondary voltage on load is V₂. The difference between the two is I₂ Z₀₂ as shown in Figure below. The approximate voltage drop of the transformer as referred to secondary is found thus.

With O as the center and radius, OC draws an arc-cutting OA produced at M. The total voltage drop I₂

Z₀₂ = AC = AM which is approximately equal to AN. From B draw BD perpendicular on OA produced.

Draw CN perpendicular to OM and draw BL parallel to OM.

Approximate voltage drop
= AN =AD+DN
= I₂R₀₂ cosφ + I₂X₀₂sinφ
where φ₁ = φ₂ = φ (approx).

This is the value of the approximate voltage drop for a lagging power factor.

The different figures for unity and leading power factors are shown below.

The approximate voltage drop for the leading power factor becomes (I₂R₀₂cosφ ± I₂X₀₂ sinφ).

In general, the approximate voltage drop is 

(I₂ R₀₂ cosφ ± I₂X₀₂ sin /φ).

It may be noted that approximate voltage drop as referred to as primary is=

(I₁R₀₁ cosφ ± I₁ X₀₁sinφ)

% voltage drop in the secondary is

=[(I₂ R₀₂ cosφ ± I₂X₀₂ sin /φ)/₀V₂]*100

=[(100*I₂R_o2)/₀V₂]cosφ ±[(100*I_2Xo2)/₀V₂]sinφ

=v_rcosφ ± v_xsinφ

where,

v_r= (100*I₂R_o2)/₀V₂  =percentage resistive drop=(100*I₁R₀₁)/V₁

_vx=(100*I_2Xo2)/₀V₂=percentage reactive drop=(100*I₁X₀₁)/V₁

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.