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Maximum efficiency of Transformer:

Maximum efficiency of Transformer:

Condition for maximum efficiency of transformer can be obtained by differentiating the efficiency equation of the transformer with respect to the load factor (dη/dα).

where η is the efficiency of the transformer

α is the load factor = (operating load of transformer/ full load of transformer)

By solving the equations it will be obtained such that Maximum efficiency of transformer is at

**P**

_{core loss}= α^{2}x P_{copper loss}
From the above equation it can be defined as the

*maximum efficiency of the transformer occurs at a load factor (α) at which the iron losses is equal to copper losses.*
The efficiency of the transformer changes with the load ( load factor). The efficiency of the transformer will be maximum at certain load when the copper losses ( α

^{2}x P_{copper loss}) is equal to the core losses (P_{core loss}) i.e, maximum efficiency of the transformer will be attained when the copper losses at particular load should be equal to the no load losses (core losses are called no load losses and remain constant with the change in load).### Power and Distribution Transformer:

While designing transformer this average load factor (α) for a transformer is estimated from the load demand charts/curves.

*Power transformer*in power plants and in substations operate at full load, therefore the load factor for power transformer is designed at 0.8. Means the power transformer is designed to have*maximum efficiency at full load*. Load on*Distribution transformer*varies during the day, therefore the load factor of the distribution transformer is designed as 0.5. Thus distribution transformer will have*maximum efficiency at 50% of the full load*.
Thus maximum efficiencies of the transformer are determined based on the type of operation it perform.

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