 WAZIPOINT Engineering Science & Technology: All-day Efficiency of Transformer

## Sunday, February 26, 2023

### All-day Efficiency of Transformer

The All-day Efficiency of the Transformer is computed on the basis of energy consumed during a period of 24 hours. It can be defined as the ratio of output to input in kWh for 24 hours.

## What is the all-day Efficiency of the Transformer?

If we go little more detail we know a transformer has two kinds of losses that we discussed in another article:

Core loss or Iron loss of a transformer: this kind of transformer loss takes place in the transformer's core that continues the whole day because the core is always energized. The transformer does not need to in loaded to cause the core loss, just in energization condition.

Variable or Copper loss of a transformer: this kind of transformer loss occurs in the copper winding of a transformer. Copper loss happens while the transformer is loaded condition.

### How do calculate the all-day efficiency of a transformer?

The power supplied to the load plus resistive, eddy current, hysteresis, and flux losses must equal the input power. The input power is always greater than the output power. The efficiency is actually the ratio of output and input power in percentage. The efficiencies of power transformers normally vary from 97 to 99 percent.

The maximum efficiency in such transformers occurs at about 60-70 % of the full load. So by proper design, high energy efficiencies can be achieved for distribution transformers. The transformer's all-day efficiency may calculate as below:

All Day Efficiency = Output (in kWh) in 24 hours/ Input (in kWh) in 24 hours

To know the exact value of all-day efficiency, we must know about the load cycle i.e. how much load is connected to the transformer and for how much time the load is connected (in 24 hours).

Please do not confuse the transformer efficiency and the transformer all-day efficiency. The transformer efficiency that we learned as-

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

### Why is transformer efficiency normally high?

Compared to other electrical machinery like an electric motor, or generator, the transformer efficiency is higher, normally 95 to 97%. The reason is that there is no rotating part in the transformer.

As the transformer operates on the magnetizing phenomenon and it has no rotating parts, its efficiency is very high. It usually stays above 95% but as the power flows across a transformer is very high even small changes in terms of efficiency percentage give significant energy savings.

### 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
Full 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)

If you are interested about to know anything regarding transformers the following article is enough for you: