# Transformer Efficiency

## Definition:

The efficiency of Transformer(η) is defined as the ratio of useful power output to the input power,the two being measured in same units(either in watts or kilowatts).

i.e Transformer efficiency,

Now power output=V2I2cosΦ

where,

V2=secondary terminal voltage on load

I2=secondary current at load and

cosΦ=power factor of the load.

**Iron loss**,**Pi**=**Hysteresis loss+eddy current loss**

## Determination of Transformer Efficiency

The other ordinary transformer has a very high efficiency(96-99%).Transformer efficiency cannot be determined with high precision by direct measurement of output and input,since the losses are of the order of only 1-4%.The difference between the readings of output and input instruments is then so small that an instrument error as low as 0.5% would cause an error of the order of 15% in the losses.

The best way of determining the transformer efficiency is to compute losses from open-circuit and short-circuit tests and determine the efficiency as follows:

**Iron loss**,Pi=Wo or Po,determined from open circuit test.

**copper loss at full load**,

Pc=Ws or Ps,determined from short-circuit test

**copper loss at a load x times full load**=

where x is the ratio of load current I2 to full-load secondary current,

Transformer efficiency=η

The advantage of this method is that it is not necessary for the transformer to be loaded to its full-load rating during testing,and the kW rating of the test plant need be equal to the value of the individual transformer losses.

## Efficiency versus Load

With the constant voltage the mutual flux of the transformer is practically constant from no load to full load .The core or iron loss is considered as constant regardless of load.copper loss varies as the square of the load current or kVA output.From the efficiency load curve it is clear that the efficiency is very high even at light load,as low as 10% of rated load.The efficiency is practically constant from about 20% rated load to about 20% overload.At the light load the efficiency is poor because of constant iron loss whereas at high loads the efficiency falls off due to increase in copper loss as the square of load.The transformer efficiency is maximum at the point of intersection of copper loss and iron loss curves i.e when copper loss equals to iron loss.

## Condition for maximum efficiency

From the transformer efficiency we get,

where p is equal to the full load(rated output in volt-amperes or kVA) *load power factor(cosΦ),Pi is the iron loss,Pc is the full-load copper loss and x is the fraction of full-load kVA at which efficiency is maximum.

Now differentiating the both side of equation(i),we get,

Efficiency η will be maximum if

Hence the efficiency will be maximum when variable loss(copper loss) is equal to constant loss(iron loss).

output kVA corresponding to maximum efficiency,

output current I2 corresponding to maximum efficiency is,

copper loss at given load at which efficiency is maximum=

and since for maximum efficiency to occur it is necessary that copper loss equals Pi,

or current corresponding to maximum efficiency,

**Note:**

- power transformer used for bulk power transmission are operated continuously near about full load and designed to have maximum efficiency.
- Distribution transformer are designed to have maximum efficiency at about three-fourths the full load.
- copper loss depends on current and the iron loss depends on the voltage.
- Total loss in the transformer depends upon volt-ampere product,and not on the phase angle between voltage and current i.e independent of the load power factor.
**Hence the transformer is rated in kilovolt amperes(kVA) and not in kilowatts.**

## Efficiency versus power factor

Transformer efficiency is given by,

* fig:variation of efficiency with power factor at different loadings for a typical transformer*

**Questions:**

**1.Is the efficiency of a transformer same at the same load at 0.8 pf lag and 0.8 pf lead?**

Ans:Yes ,the efficiency of a transformer remains the same for a given load at a given power factor irrespective of the fact whether the Power factor is lagging or leading.

**2.What is meant by all day efficiency of a power transformer and why is it lower than commercial efficiency?**

Ans:The all day efficiency also known as energy efficiency or operational efficiency is defined as the ratio of energy(kWh) output over 24 hours to the energy input over the same period.

**i.e** **All day efficiency=output in kWh/Input in kWh**

There are certain type of transformer such as distribution transformers which remains energized for 24 hours but they supply very light loads for major portion of the day.Thus the iron or core loss occurs for the whole day but the copper loss occurs only when the transformer is loaded and so the all-day efficiency of transformer is lower than its commercial efficiency.

**For more notes on electrical engineering:**

https://engineeringnotesonline.com/transformer-design/