Editing Electric power transmission (section)

== Advantage of high-voltage transmission ==
{{See also|Ideal transformer}}{{Unreferenced section|date=November 2022}}
High-voltage power transmission allows for lesser resistive losses over long distances. This efficiency delivers a larger proportion of the generated power to the loads.

[[File:Power split two resistances.svg|thumb|Electrical grid without a transformer]]
[[File:Transformer power split.svg|thumb|Electrical grid with a transformer]]
In a simplified model, the grid delivers electricity from an [[ideal voltage source]] with voltage <math>V</math>, delivering a power <math>P_V</math>) to a single point of consumption, modelled by a resistance <math>R</math>, when the wires are long enough to have a significant resistance <math>R_C</math>.

If the resistances are [[in series]] with no intervening transformer, the circuit acts as a [[voltage divider]], because the same current <math>I=\frac{V}{R+R_C}</math> runs through the wire resistance and the powered device. As a consequence, the useful power (at the point of consumption) is:
:<math>P_R= V_2\times I = V\frac{R}{R+R_C}\times\frac{V}{R+R_C} = \frac{R}{R+R_C}\times\frac{V^2}{R+R_C} = \frac{R}{R+R_C} P_V</math>
Should an [[ideal transformer]] convert high-voltage, low-current electricity into low-voltage, high-current electricity with a voltage ratio of <math>a</math> (i.e., the voltage is divided by <math>a</math> and the current is multiplied by <math>a</math> in the secondary branch, compared to the primary branch), then the circuit is again equivalent to a voltage divider, but the wires now have apparent resistance of only <math>R_C/a^2</math>. The useful power is then:
:<math>P_R= V_2\times I_2 = \frac{a^2R\times V^2}{(a^2 R+R_C)^2} = \frac{a^2 R}{a^2 R+R_C} P_V = \frac{R}{R+R_C/a^2} P_V</math>

For <math>a>1</math> (i.e. conversion of high voltage to low voltage near the consumption point), a larger fraction of the generator's power is transmitted to the consumption point and a lesser fraction is lost to [[Joule heating]].