Efficiency of a Transformer

The efficiency of a transformer is defined as the ratio of output power (in watts) to input power (in watts).

Thus, transformer efficiency formula is given by

where,

V₂ = load voltage

I₂ =  load current

Cos θ₂ = load power factor

P_C = transformer core loss

P_I =  transformer copper (ohmic) loss = I₂²R_e2

R_e2= equivalent transformer winding resistance referred to secondary or load side

Since transformers are almost always operated at rated voltage and rated frequency, therefore, making V₂ and P_c constant in above formula. Thus, transformer efficiency depends only on load power factor cos θ₂  and load current I₂ , as long as transformer is operated at rated voltage and rated frequency.

If load current I₂ is kept constant and power factor is varied, then, maximum efficiency would be obtained when load power factor is unity.

Variation of transformer efficiency with load power factor is shown as

Maximum Transformer Efficiency

If the load power factor cos θ₂ is kept constant but load current I₂  is varied , then , the condition for maximum efficiency is obtained as follows

we have,

i.e  Core loss = Copper loss

or,  constant loss = Variable loss , is the condition for maximum efficiency.

Load current I₂ at which maximum efficiency occurs is given by  

By putting  P_c = I₂²R_e2  in efficiency formula, we get transformer maximum efficiency as 

In practical situations, both load current and load power factor vary ( when we turn on and off domestic appliances etc ) , therefore, transformer efficiency variation with load power factor and load current together is shown below.

Related concepts :-

   Transformer construction- Core and Shell type transformer

    Open Circuit and Short Circuit test on Transformer
Transformer working Principle
Emf equation of transformer

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Voltage regulation of transformer