Condition for Maximum Efficiency of Transformer

The ordinary or commercial efficiency of a transformer is defined as the ratio of output power to input power.

Efficiency = η = Output / Input

Efficiency = η= Output / (Output + Losses) 

As Input = Output + Losses.

Maximum Efficiency of Transformer

Ideally, the Maximum Efficiency of the Transformer is 100% considering no loss and zero voltage regulation. As there is no moving part in the transformer, there will be no frictional losses so it will be around 97–99%.

The efficiency will eventually go down for a number of reasons.

• Copper losses 
• Copper losses 
• Core and eddy current losses

Efficiency is maximum in a transformer when Copper losses = Iron losses.

V2= Secondary terminal voltage.

I2= Full load secondary current.

Cosϕ2= Power factor of the load.

pi= Iron loss= eddy current loss + Hysteresis loss = Constant loss.

Pc= Full load Copper losses.

The efficiency is a load function i.e., load current I2 assuming cos Φ constant. The secondary terminal voltage V2 is also taken constantly.

So for maximum efficiency,

Case Study of Transformer Efficiency

A 500 KVA transformer has 2500 watts iron loss, and 7500 watts copper loss at full load. The power factor is 0.8 lagging. Calculate transformer efficiency at full load,

maximum efficiency of the transformer,

output KVA corresponding to maximum efficiency,

transformer efficiency at half load.

Solution: Transformer rating = 500 KVA

Transformer output power = 500,000 x 0.8 = 400,000 watts

Iron losses (Pi) = 2500 W

Total load copper loss (Pcu) = 7500 W

 

Transformer Efficiency at Full Load

= [(output power)/(output power + Pi +Pcu)] x 100

 

= [(400,000)/(400,000 + 2500 + 7500)] x 100

 

= 97.56% (Ans)

 

Maximum Efficiency of Transformer

 

For maximum efficiency, Copper loss (Pc) = Iron losses (Pi) = 2500 W

 

= [(output power)/(output power + Pi +Pc)] x 100

 

Therefore, maximum efficiency = [(400,000)/(400,000 + 2500 + 2500)] x 100

 

= 98.76% (Ans),

Output KVA Corresponding to Maximum Efficiency
 

= full load KVA x √(Pi/Pc)

 

= 500 x √(2500/7500)

= 500 x √0.333 = 166.5 KVA (Ans)

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.