Why do we use high voltage to transmit electrical power?

There are many advantages of using High Voltage to transmit power :

• Reduced Line current for a given amount of power

For the same amount of power to transfer , the line current will reduce and so does the current carrying capacity of conductors.
The reduced current capacity will result in the less volume of conductor for a given length.
Contrary to Distribution systems, there are no legal restrictions on voltage regulation in case of transmission of bulk power (in some cases voltage varies as much as 40%) ,the only criteria to transmit power is  the economy of conductors.

• Reduced I^2R Loss

With the reduction in line current comes the reduction in I^2R loss.

• Better Efficiency

With lesser Line losses due to reduced I^2*R loss , the efficiency of transmission increases.

• Improved Voltage Regulation

With the decreased Line current the voltage drop across line will decrease and this will improve the voltage regulation as the receiving end voltage will be more.
Voltage regulation is defined as (Vs-Vr/Vs)

• Better Efficiency due to improved voltage regulation

Regressing back to transmission efficiency , since the voltages are high the power transfer will increase which is substantiated by the fact
P=Vs*Vr*sin (8) /Xs

Now it makes sense to use  as High voltages as possible for Transmission be it AC or DC/HVDC but in practice the upper limit of voltage is decided by the economy of transmission which includes the cumulative cost of conductor, Towers , Length of cross arms , ground clearance , Insulation b/w tower and ground .

Power is transmitted at higher voltage to reduce power losses during transmission.

Power transmitted is the product of voltage and current.

P= V*I
I= P/V

So when same amount of power is transmitted at higher voltages, current in the conductors is lower. This leads to lesser power loss in the conductor(power-line) since power loss is proportional to the square of current.

P(loss) = (i^2) * R

So for the same value is R and power , power losses is less if current is less, this can be achieved by transmitting power at higher voltages.

if we transfer power in high voltage range
1.the current flow will decrease, so that the copper loss will decreased i.e I2*R
2. size of the conductor will be reduced.
3. we can reduce the theft in transmission lines.