PG& needs to send 100 MW to Davis over transmission lines that are many miles lo
ID: 1619556 • Letter: P
Question
PG& needs to send 100 MW to Davis over transmission lines that are many miles long so-long that the resistance is not completely negligible (let's say 0.001 Ohm). Given that the product VI needs to be 100 MW, PG&E; could send this power at low voltage and high current, or at high voltage and low current. If you use V^2/R as the power dissipated in the lines, it seems like high voltage is bad-its leads to a lot of power wasted in the transmission lines-yet you probably know that transmission lines are indeed high-voltage. Explain how high-voltage lines actually lead to smaller losses in the lines.Explanation / Answer
Electric energy is transported with high-voltage lines because the line losses are much smaller than with low-voltage lines.
All wires currently used have some resistance (the development of high-temperature superconductors will probably change this some day). Let's call the total resistance of the transmission line leading from a power station to your local substation R. Let's also say the local community demands a power P=IV from that substation. This means the current drawn by the substation is I=P/V and the higher the transmission line voltage, the smaller the current. The line loss is given by Ploss=I²R, or, substituting for I,
Ploss = P²R/V²
Since P is fixed by community demand, and R is as small as you can make it (using big fat copper cable, for example), line loss decreases strongly with increasing voltage. The reason is simply that you want the smallest amount of current that you can use to deliver the power P. Another important note: the loss fraction
Ploss/P = PR/V²
increases with increasing load P: power transmission is less efficient at times of higher demand. Again, this is because power is proportional to current but line loss is proportional to current squared. Line loss can be quite large over long distances, up to 30% or so. By the way, line loss power goes into heating the transmission line cable which, per meter length, isn't very much heat.
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