Math for why voltage is stepped-up in power lines?

In summary, this explanation of voltage and power loss in transmission lines says that increasing voltage decreases power loss. This is because you need less current to transfer the same amount of power.
  • #1
HydroGuy
29
0
I've long understood that voltage is stepped-up in power t-lines to decrease losses, however, I've never really understood the math reasoning behind it.

Isn't P = V^2/R the same as P = I^2*R? If so, it seems that either increasing V or increasing I would invoke the same losses... Could someone explain?

Thanks
 
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  • #2
When you are talking about the power lost over the transmission line, it's the voltage difference between the start and the end of the line, not between operating voltage and earth. This voltage is dependent on current and impedance of the line only.
 
  • #3
OK, thanks but that isn't really answering my question. Why does increasing the voltage decrease the power loss in the line?
 
  • #4
Snoogans said:
When you are talking about the power lost over the transmission line, it's the voltage difference between the start and the end of the line, not between operating voltage and earth.
Good answer - this is the thing most students misunderstand when first seeing this
 
  • #5
Another good reason for stepping up the voltage is that you need less current to get the same amount of energy transfer. Hence you can use a smaller gauge wire to carry the load saving wire cost.
 
  • #6
Yes that's the point - but it confuses people who think of power = V^2/r and v as the powerline voltage rather than the voltage drop.
 
  • #7
There are losses due to corona discharge also when the line to ground voltage gets very high. Not trying to confuse the issue; just noting.
 
  • #8
It helps if you draw a circuit with a load and consider that you have two voltages, the voltage at the generator and a lowered voltage at the load due to line resistance.

Generator:============Load
(= is wire pair across which we measure voltage).

You have V at the power source and V' at the load with voltage drop: V-V' = RI.
Where R is the line resistance (...for both legs. You can put the load anywhere in the current loop and get the same numbers.)

The load power is V'I and of course current is constant.
(We're doing this in DC for simplicity but you can see the reasoning will apply to AC as well.)

Efficiency is power received at load over power leaving the source:
P at source = VI
P at load = V'I
Efficiency is V'I/VI =V'/V= (V-RI)/V = 1-RI/V. So the less current and more voltage, the close to 100% efficiency.
 

Related to Math for why voltage is stepped-up in power lines?

1. Why is voltage stepped-up in power lines?

Voltage is stepped-up in power lines to reduce the amount of energy lost during transmission. Higher voltage means lower current, and lower current results in less energy being lost as heat due to resistance in the wires.

2. How does stepping-up voltage increase power transmission?

Stepping-up voltage increases power transmission by allowing more power to be transmitted over longer distances with less energy loss. This is because higher voltage results in lower current, which reduces the amount of energy lost as heat due to resistance in the wires.

3. What is the typical voltage used in power lines?

The typical voltage used in power lines is between 110 and 765 kilovolts (kV) in North America, and between 220 and 750 kV in Europe. However, some countries may use higher or lower voltages depending on their specific power grid infrastructure.

4. How is voltage stepped-up in power lines?

Voltage is stepped-up in power lines using a device called a transformer. A transformer works by using electromagnetic induction to increase or decrease the voltage of an alternating current (AC). In power lines, step-up transformers are used to increase the voltage for transmission and step-down transformers are used to decrease the voltage for distribution.

5. Are there any disadvantages to stepping-up voltage in power lines?

One potential disadvantage of stepping-up voltage in power lines is the increased risk of electric shock. Higher voltages can be more dangerous to humans and animals, so proper safety measures must be in place to prevent accidents. Additionally, the use of transformers adds complexity and cost to the power grid infrastructure.

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