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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 + Pi + PCu
The ratio of power output to power input of any device is called its efficiency (η).
      images
Output power of a transformer at full-load = V2I2ftcosθ, where cosθ is the power factor of the load, I2ft is the secondary current at full load and V2 is the rated secondary voltage of the transformer.
Full-load copper loss of the transformer = I2ftR02.
∴     Efficiency of the transformer at full load is given by
images
Now V2I2ft = VA rating of the transformer.
∴    images
i.e.,    images
Efficiency of the transformer at any load m is given by
images
where m=images and PCuft 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.
images
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
images
Now,    images
∴    images
i.e.,  images
i.e.,    V2I2cosθ+Pi+I22R02–V2I2cosθ–2I22R02=0
i.e.,    Pi=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 I2M be the load current at maximum efficiency.
∴    I2M2R02=Pi
i.e.,    images
Let I2ft be the full-load current.
∴    images
i.e.,    images
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.
∴    images
images
In general,
images
where    images
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