Power stations send electricity over long distances through cables that have resistance. The cables heat up, and the power wasted as heat is given by P = I2R, where I is the current in amperes and R is the resistance of the cables in ohms. The wasted power depends on the current squared, so halving the current cuts the wasted power to a quarter.
The power delivered is P = I × V, so for a given power, a larger p.d. means a smaller current: I = P ÷ V. A step-up transformer raises the p.d. before transmission. For a transformer that is 100% efficient, VpIp = VsIs, so if the p.d. is stepped up by a factor of ten, the current falls by a factor of ten.
Example: 100 000 W is sent along cables of resistance 2 Ω. At 1000 V, I = 100 000 ÷ 1000 = 100 A and the wasted power is 1002 × 2 = 20 000 W, which is 20% of the power. At 10 000 V, I = 10 A and the wasted power is 102 × 2 = 200 W, only 0.2%. Ten times the p.d. means one hundred times less wasted power.
So high-voltage transmission wastes less energy as heat, which makes the national grid more efficient and cheaper to run. Transformers near homes step the p.d. back down for safe use.