When electrical power passes through a conductor a part of it is lost as heat in the conductor due to the resistance of the conductor. The power transmitted through a resistor is dependent on the current that is passing through it as well as the voltage across the conductor. P = V*I where P is power transmitted, V is the voltage across the conductor and I is the current flowing through the conductor. The voltage and current are related to each other by the resistance of the conductor: V = I/R. The heat produced in the conductor is given by I^2*R. To transmit the same power if the voltage is raised, there is a corresponding decrease in the current and the heat produced is decreased by a factor that is equal to the square of the factor by which the voltage is raised.
In electrical power transmission over long distances around 7% of energy is wasted as heat produced in the cables due to the inherent resistance of the cables. To reduce this loss, the voltage is increased, this decreases the current and the power loss by a substantially larger extent
The conductors,through which AC power is transmitted have some resistance per meter length.Over long distance it becomes significantly high.At high current power transmission a power loss of (I^2.R) in form of heat would happen.To reduce it, AC power is transmitted at high voltage and low current .In this way power loss as heat can be minimised.
One hundred year ago, the advantage to AC power lay in the fact that the voltage of AC power could be increased easily by use of a transformer. With higher voltage, the amount of power lost due to resistance in the power line would be less.
Improvements in technology have removed that advantage. The voltage of DC power can be increased, so that the advantage now probably lies with DC power over AC power.
DC power probably now has the advantage because it only requires two lines to transmit the power whereas AC normally has three lines. That should make the construction costs cheaper for DC lines. Also, the average voltage on a DC line can be greater because the average voltage can approach the peak voltage. That should mean that the DC line can transmit more power, or maybe the insulators might be less expensive.