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Distribution Transformers are used on distribution side not transmission side.

Core losses or Iron losses ( Hysteresis and eddy current losses ) are proportional to the square of the voltage.

Copper losses are proportional to the square of the current.

Distribution side voltage is less compared to the transmission side.

core losses are constant irrespective of the load, but copper losses varies with the load.

Transmission side transformers are not usually stopped from working by the operator frequently, they continued to work throughout the year until and unless if there is a problem and also they almost have constant load. So they are going to have more core losses. So their core is designed in order to get less core losses. Any way the copper losses will be less since the current is less because voltage is more.

Distribution side transformers are having more load fluctuations and more stoppages.Their voltage is low so they will have less core losses, no need to design a better core, but distribution side current is more so copper losses are more, so distribution side transformers are designed to have less winding resistance, so that the copper losses are low.

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