WAZIPOINT Engineering Science & Technology: Transformer Total Voltage Drop

Wednesday, March 31, 2021

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

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.

Total Approximate Voltage Drop of a  Transformer at Lagging Power Factor

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
= 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.

Total Approximate Voltage Drop of a  Transformer at Unity Power Factor

Total Approximate Voltage Drop of a  Transformer at Leading Power Factor

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*I2Ro2)/0V2]cosφ ±[(100*I2Xo2)/0V2]sinφ
=vrcosφ ± vxsinφ

vr= (100*I2Ro2)/0V2  =percentage resistive drop=(100*I1R01)/V1
vx=(100*I2Xo2)/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.

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