 WAZIPOINT Engineering Science & Technology: Condition for Maximum Efficiency of Transformer

## Sunday, May 21, 2023

### 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.

Cosϕ2= Power factor of the load.

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

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,

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)