DC Vs AC Transmission Line

When and why is DC used instead of AC for long-distance electric power lines? Is DC becoming more common now? What are its advantages and disadvantages?

The largest losses in long distance electrical power transmission come from energy lost in the resistance of the power line.
If P is the power transmitted, and R is the resistance of the line:
P=IV$P=IV$
Ploss=I2R=P2R/V2$P_{loss}=I^{2}R=P^{2}R/V^2$
If P is fixed by community demand, then you can reduce lost power dramatically by increasing the transmission voltage. As a result, all long-distance power transmission, AC or DC, is done at high voltage.

The advantage of AC has always been that it is easy to change the voltage up and down with a transformer; DC requires more equipment and some losses to convert.

That being said, transferring AC power between separate grids requires making sure the phase of the power transmitted matches from the two grids (so that the power from the two grids doesn't cancel or ring), which is difficult and expensive. This is not a problem for DC, so DC lines are used in cases such as where power is transferred from another grid to increase the capacity of an existing grid, or between countries that use different frequency power.

Capacitance between the AC phases (usually 3 phases are transmitted at once over a line) or between the line and the surrounding soil or water causes losses that are not a problem with DC. Therefore, undersea high voltage lines tend to be DC.

Overall line loss is also lower per 1,000 km, so very long distance transmission lines sometimes use DC.