the maximum efficiency of a transformer is at which power factor?

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 = α2 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.