What is the condition for maximum efficiency of a transformer at full load?

Losses in Transformers are1)Eddycurrent Loss,and Hysteresis Loss2)CopperLoss

Efficiency = output / input

Eddy current loss and hysteresis loss depend upon the magnetic properties of the material used for the construction of core. Hence these losses are also known as core losses or iron losses. Hysteresis loss in transformer Hysteresis loss is due to reversal of magnetization in the transformer core. This loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value of flux density. Eddy current loss in transformer In transformer, AC current is supplied to the primary winding which sets up alternating magnetizing flux. When this flux links with secondary winding, it produces induced emf in it. But some part of this flux also gets linked with other conducting parts like steel core or iron body or the transformer, which will result in induced emf in those parts, causing small circulating current in them. This current is called as eddy current. Due to these eddy currents, some energy will be dissipated in the form of heat. Copper loss is due to ohmic resistance of the transformer windings. It is clear that Cu loss is proportional to square of the current, and current depends on the load. Hence copper loss in transformer varies with the load. Efficiency of a transformer can be defined as the output power divided by the input power. That is  efficiency = output / input .Transformers are the most highly efficient electrical devices. Most of the transformers have full load efficiency between% to.5% . As a transformer being highly efficient, output and input are having nearly same value, and hence it is impractical to measure the efficiency of transformer by using output / input. A better method to find efficiency of a transformer is using, efficiency = (input - losses) / input =1 - (losses / input).

If the power factor which is a factor of active to reactive power, is close to 1.0, which is practically not possible in a system where you have so many rotating machinery and other local factors like losses within the transformer, capacitive and inductive losses etc, then the efficiency can be close to maximum. In power systems this can be also be achieved by using  Reactors or capacitor banks.

if iron losses are equal to the copper losses then efficiency will be maximum.

By reducing Losses in Transformers. Losses such as 1)Eddy current Loss, and Hysteresis Loss 2)Copper Loss

Efficiency = output / input

copper loss(Primary +secondary winding) i.e. I^2R = Core/Iron Loss( Hystersis loss due to reversal of magnetic flux+ eddy current loss due to induction in core laminant) 

condition for maximum efficiency of a transformer  i.e  Copper losses = Iron losses

Constant losses=variable losses is the condition for maximum efficiency