Possible myth, current/voltage in relation to wire size

You are using the wrong formula. Try P=ExI (power equals voltage times current). For a given amount of power that you want to transmit, the higher the voltage, the lower the current. The calculation of how much power a transmission line can transmit is a little more complicated, but that formula holds true enough to answer your question.

Charles Perry P.E.

Thanks Charles for clarifying my formula usage. I can accept that formula, but my brain wants to know why. I guess what I'm looking for is an analogy or something to help me visualize. A lot of my learning recently has been through analogies, because I can't see EM fields yet and I tend to be a visual learner. I also don't like the old fashioned response of "because I said so." Just because a formula says it, I still want to know why. :-) Thanks.

A better relation to consider is

P = I * V

so, for a given amount of power that is required to be sent down a transmission line, higher voltage allows a lower current. Some transmission lines are thick, some are thin. Skin effect is taken into account in large transmission lines. Often lines are ACSR (Aluminum Conductor Steel Reinforced) and the center is steel, which is relatively high resistance compared to aluminum, but not much current wants to travel in the center anyways, due to skin effect.

| Thanks Charles for clarifying my formula usage. | I can accept that formula, but my brain wants to know why. I guess what I'm | looking for is an analogy or something to help me visualize. A lot of my | learning recently has been through analogies, because I can't see EM fields | yet and I tend to be a visual learner. I also don't like the old fashioned | response of "because I said so." Just because a formula says it, I still | want to know why. :-)

Suppose I have a 20 ohm resistor connected to 240 volts. That will draw a current of 12 amps and dissipate 2880 watts of power in the form of heat.

Upstream from me is a transformer that has a 240 volt secondary and a

Note that although the transformer ratio is 30:1, the impedance ratio is 900:1.

Adding 1 ohm of wire to a circuit with a 20 ohm load is going to do two things. It will reduce the current somewhat to 11.4285714 amps. And it will divide the voltage drop of 240 volts between the 20 ohm load and the

To get the same effective drop in power on the 7200 distribution line, which is operating into a load of 18000 ohms (not 20 ohms), that would involve 900 ohms being added. For the same size wire, that would mean the circuit could be run 900 times the distance.

According to table 8 of NEC chapter 9, 1000 feet of AWG 4/0 aluminum wire has 1/10 ohm. That means I can run almost a mile of 2 conductors of wire to power that heater within an acceptable 5% voltage drop. But for 900 ohms of added wire resistance (to the 18,000 ohm load), that would be 852 miles for the same ratio of voltage drop.

There are a LOT of other factors involved in engineering power distribution. But the above, I hope, gives a clearer picture of why a higher voltage is so much better for longer distances. The key point you may have missed was that the impedance at the higher voltage is increased in proportion to the square of the voltage increase. So as the voltage goes up 30 times, the impedance goes up 30^2 times.

Of course in reality, electrical distribution does deal with much more power than my 2880 watt heater. But they use even higher voltages and larger wires over such greater distances. And they have the option to boost generator voltage or change transformer taps to tweak the voltage to compensate for varying losses due to varying loads.

If you were expecting the 7200 volts to see 20 ohms directly, then you would be seeing 360 amps and 2.592 million watts. All the magic smoke would be released in a rather spectacular boom as the resistor vaporizes and the current flows as a terrific arc. Don't do this at home ... or anywhere else.

When was studying we were given analogy of water pipes. Voltage is same as the height of a water reservoir would be. Current obvously is the amount of water going through the pipes. Hence if you raise the level of water reservoir the energy of the flowing water to i.e. turbine will be increased.

I hope this analogy is what you sere looking for...

Reagrds, Petri Vatilo

I was told by a l Electrical properties: minimize resistance( so mimimize voltage drop and minimize heat build up)

Plus

Physical Properties: Strength ( so to span further distances, so to have a longer working life, so to stand up to high winds and rough weather).

Now was I snowed?

later,

tom @

I like where you're going with this analogy. However, I'm stumped on something. Let's say we have two water towers like this:

I think I answered my own problem in my head just now. Given the two water towers, with paddle wheels at the bottom, we should keep in mind the formula P=IxE which means we keep the paddle wheels spinning at the same rate. To do this, we need to slow the flow of water down the higher tower, because it is hitting the wheel with more force/pressure/potential (whatever you wish to call it). So as the pressure goes up, the current needs to slow down to keep the power constant. That sound about rigth?

Don't forget that at extra high voltages an important factor is reduction of corona discharge. Since the conductor size required for the current is usually too small to reduce the voltage gradient around the conductor to a value low enough to provide acceptable corona loss, EHV (365 kV and up) lines use bundled conductors to provide a larger effective conductor diameter.

According to one reference I have, the annual average corona loss on a

Bill

A previous poster got this mixed up with "skin effect", which only occurs at much higher frequencies. Many HV lines are made hollow to increase the diameter without increasing the weight.

I wonder when the economics will mandate DC lines. Maybe even buried super-conductive! It's only a matter of time.

Skin effect occurs at all frequencies - but at 60 Hz the skin depth (where the current density drops to 1/e of the value at the surface) is about 8 mm, so only large conductors are much affected. Bus tubes for arc furnaces, which have to carry 50,000 amperes, are hollow because of the skin effect - a solid 8 inch (200 mm) conductor wouldn't effectively carry much more 60 Hz current than a hollow conductor with a wall thickness of 16 mm.

The skin effect is also important even in distribution-size conductors for accurate calculation of the impedance of a circuit - such as for estimating fault levels, etc.

DC wins when the cost of the terminal equipment is offset by the lower cost of the conductors and transmission right-of-way - this can make a very short DC link economically preferable in situations such as urban construction, or for buried cables or underwater cables. Drawbacks to DC are the relative difficulty and expense of controlling multi-terminal networks and lack of a good HVDC circuit breaker.

Superconducting transmission cables are still laboratory experiments, from what I've read - maybe someday, but I don't think superconducting cables will be a big factor in energy transmission for many years.

Bill

| I think I answered my own problem in my head just now. | Given the two water towers, with paddle wheels at the bottom, we should keep | in mind the formula P=IxE which means we keep the paddle wheels spinning at | the same rate. To do this, we need to slow the flow of water down the | higher tower, because it is hitting the wheel with more | force/pressure/potential (whatever you wish to call it). So as the pressure | goes up, the current needs to slow down to keep the power constant. That | sound about rigth?

Yes. As in the post I made earlier, 2880 watts is 12 amps at 240 volts, but is only 0.4 amps at 7200 volts.

The efficiency goes up rather fast as the voltage goes up. For the same power and the same wire size, just doubling the voltage from 240 volts to

| I wonder when the economics will mandate DC lines. Maybe even buried | super-conductive! It's only a matter of time.

And all the fun lightning induced arcing faults to ground.

Nope. Your analogy is missing a component. When pressure goes up, current ALWAYS goes up, ALL OTHER CONDITIONS BEING EQUAL.

With power distribution at high voltage, we CHANGE THE CONDITIONS with a transformer.

Your water example does not have a device analogous to the transformer. If you add some gears to your fast moving paddle wheel, then you'll have a good analogy. The gears will transform the high speed, low torque rotation of the paddle wheel to a low speed high torque rotation on the output shaft driven by the gears, just as the electrical transformer transforms the high voltage low current to low voltage high current.

Ed

And now you have my gears turning. :-) I'll see if I can find some websites with visuals of this. If you know of any, please post. Thanks.