EFFICIENCY OF A TRANSFORMER

Due to the losses in a transformer, its output power is less than the input power.

∴ Power output = Power input – Total losses

∴ Power input = Power output + Total losses = Power output + P_i + P_Cu

The ratio of power output to power input of any device is called its efficiency (η).

      

Output power of a transformer at full-load = V₂I_2ftcosθ, where cosθ is the power factor of the load, I_2ft is the secondary current at full load and V₂ is the rated secondary voltage of the transformer.

Full-load copper loss of the transformer = I_2ftR₀₂.

∴     Efficiency of the transformer at full load is given by

Now V₂I_2ft = VA rating of the transformer.

∴    

i.e.,    

Efficiency of the transformer at any load m is given by

where m= and P_Cuft is the Cu loss of the transformer at full load.

1.34 CONDITION FOR MAXIMUM EFFICIENCY

During working of a transformer at constant voltage and frequency, its efficiency varies with the load. Its efficiency increases as the load increases. At a certain load, its efficiency becomes maximum. If the transformer is further loaded, its efficiency starts decreasing. Figure 1.43 shows the plot of efficiency versus load current.

Figure 1.43 Comparison Efficiency and Current

To determine the condition of maximum efficiency, let us assume that the power factor of the load remains constant and the secondary terminal voltage (V₂) is constant. Therefore, efficiency becomes only a function of load current (I₂).

For maximum efficiency

Now,    

∴    

i.e.,  

i.e.,    V₂I₂cosθ+P_i+I₂²R₀₂–V₂I₂cosθ–2I₂²R₀₂=0

i.e.,    P_i=I₂²R₀₂    (1.66)

To achieve maximum efficiency, Iron loss = Cu loss

i.e.,     Constant loss = Variable loss

1.34.1 Load Current at Maximum Efficiency

Let I_2M be the load current at maximum efficiency.

∴    I_2M²R₀₂=P_i

i.e.,    

Let I_2ft be the full-load current.

∴    

i.e.,    

Equation (1.67) shows the load current in terms of full-load current at maximum efficiency.

1.34.2 kVA Supplied at Maximum Efficiency

For constant V₂ the kVA supplied is the function of load current only.

∴    

In general,

where