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# Transformer Losses and Efficiency Calculation

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## Transformer Efficiency Definition

The efficiency of the transformer is defined as the ratio of the power output Poutput and power input Pinput, both expressed in watts.

Thus,

$\begin{matrix} \eta =\frac{{{P}_{out}}}{{{P}_{in}}} & {} & \left( 1 \right) \\\end{matrix}$

Or since the input is the output plus losses,

\begin{matrix} \begin{align} & \eta =\frac{{{P}_{in}}-{{P}_{loss}}}{{{P}_{in}}}=1-\frac{{{P}_{loss}}}{{{P}_{in}}} \\ & \eta =1-\frac{{{P}_{loss}}}{{{P}_{out}}+{{P}_{loss}}} \\\end{align} & {} & \left( 2 \right) \\\end{matrix}

The transformer losses consist of copper losses and core losses.

$\sum{(losses)=Core\text{ }Loss+Copper\text{ }Loss}$

$\sum{(losses)={{P}_{core}}+(I_{1}^{2}{{R}_{1}}+I_{2}^{2}{{R}_{2}})}$

The copper loss represents the energy dissipated in the resistance of the windings, while the copper loss is composed of the hysteresis and eddy current losses in the ferromagnetic core of the transformer.

## Transformer Core Losses

Core losses are a function of the voltage applied to the transformer since the voltage determines the magnitude of the core flux. Normally the voltage applied to the primary of a transformer does not change much, so the core losses are considered to be constant.

## Transformer Copper Losses

Copper losses are a function of the current in the windings. If the voltage is fairly constant, the current is essentially proportional to the load, so copper losses vary with the square of the load on the transformer.

$Copper\text{ }Loss\text{ }\alpha \text{ }I_{s}^{2}$

Depending on what is known, efficiency may be calculated in several ways as shown by equations (1) and (2).

Regardless of which form is used, only the real power should be used to calculate efficiency.

## Maximum Efficiency of a Transformer

At full-load current, the losses are essentially constant no matter what the power factor, but the output power will vary with the power factor. If the power factor drops, the output power will also drop for a given KVA rating and thus the efficiency of the transformer also decreases.

The maximum efficiency of a transformer at a given power factor occurs when the copper losses are equal to the core losses.

Obviously, the absolute maximum efficiency occurs when the power factor of the load is unity.

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