# Transformer Efficiency: Definition, Determination, Maximum Efficiency

It is a well-established fact that the transmission of electrical power over extended distances results in a certain degree of energy loss. The aforementioned phenomenon leads to the emergence of the notion of transmission efficiency. Similar to other scenarios, transmission efficiency provides an indication of the proportion of useful energy that arrives at the receiving end relative to the amount of energy that was initially supplied at the transmitting end. The following discussion seeks to clarify the definition and calculation of electrical transmission efficiency.

## Definition of Transformer Efficiency

The efficiency of a Transformer(η) is defined as the ratio of useful power output to the input power, the two being measured in the 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

cos Φ = 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.

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

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.

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 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 the 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,