Electric power loss over distance

Question

I am working on a project where I install an electric system by my property entrance, than I have to run a wire about at least 700 feet. I do want to deliver 240VAC and I know that voltage drop is a thing.

I've calculated aluminum wire 2AWG at 850' 200 amps over distance like if I want to power up a table saw for example at the end. Then I get voltage drop which leaves off 156 vac at the end.

My main question is, how can I convert 151vac to 120vac?

FYI, I will actually install an outlet at the end of 850' and power things over night. Generator won't be an option.

PS: I made major edits, I am not going to use copper wire, and I will supply 240 vac 200 amps instead of 120.

Answer 1

You've touched on the reason why electric utilities use high voltage for their distribution lines and also why you see transformers either on poles at your location or on the ground in a (usually) green box.

They do this to avoid power loss in the wires which increases with the square of the current. Mathematically, you have:

P = I^2 * R where P is power in Watts, I is current in Amps and R is resistance in Ohms.

Let's take two hypothetical examples that demonstrate this:

1. You want to transmit 1800W, which is 15A at 120V through a distance of 500' using a wire which has resistance of 1 Ohm. The power lost to heat in the wires in this case will be 15^2 * 1 = 225W. So you put 1800W in at the source but you only get 1575W at the load.

   2. Now say you bump up the voltage to 480V. Your 1800W only requires 3.75A at that voltage. So the power lost in the wires in this case is 3.75^2 * 1 = 14W. You save 211W of power by using the higher voltages.

Usually for consumers this doesn't play out all that often although that is one reason why high power consuming appliances like water heaters, HVAC systems, ovens and ranges almost always use 240V vs. 120V. The current requirements are 50% by using the higher voltage.

Consider that the power utilities are transporting megaWatts of power and often at very high voltages. The long distance towers you see may operate at 750K to 1,000,000 volts.

Now there are some other considerations. Transformers are not lossless, so you lose some power, again due to heat, when you step-up and then step-down the voltage. But the savings overall due to using smaller and cheaper wire and long term operating costs due to lower power losses may make it worthwhile.

As noted above, 2AWG Cu wire is quite expensive. Usually for longer distances Al wire is a much better value although you will usually need to go up a gauge or two in order to get the same performance.

By the way, you mentioned "AMP loss" in the wiring. That's not really a thing. Amps are not lost, for every Amp you put in one end of the wire, you get a corresponding Amp out the other end. You do lose Volts and that's where the power loss comes in.

Answer 2

Wow you need to do what I have done. I have a 240v to 600v transformer not quite as far 550’ running a 5 Hp motor and lights on 1 system then another lighter system With mostly lights and hand tools 5kva & 10 kva transformers.

Edit per note below I forgot the 2.5x reduction in current: Update:

You could use a pair of 5kva 240v to 600v transformers and run #14 for the 700’ for your load. This would have a 5% drop with # 14 wire at 20 amps 240v point of use

at 15 amps #14 wire would be 4.13% volts drop.

At 20 amps #12 wire 5% voltage drop.

I did not do any other calculations because you would be limited by the transformer size. But 20 amps of 240 is the same as 40 amps of 120v 5kva is a standard size, 14 awg UF is rated at 600v

So you can save a huge amount as I did and have more power available. If you like this idea we can give more details but a 240-600v pair of 5kva transformers would be needed (I got both my sets of 5kva and 10kva transformers used on e bay).

Ok I blew it I thought the drop was much higher than my 5kva with 14 awg I forgot the 2.5x reduction in current for the 600v. So this system is fed with a standard 20 amp double pole breaker this will be the best option as 240-600v transformers are out there used they don’t have to be the same brand.

Answer 3

I've calculated aluminum wire 2AWG at 850' 20(????) amps over distance like if I want to power up a table saw for example at the end. Then I get voltage drop which leaves off 156 vac at the end.

Voltage drop does not work that way

First, voltage drop is based on your actual load, being drawn at that instant - not breaker trip. (much as the wire salesman would like you to base it on that lol). So stop using the number on the breaker to compute voltage drop.

Voltage drop is variable based on current - here is the formula, with E being voltage drop and I being the instantaneous current you are using right now, and R being the (unchanging) resistance of the wire:

  E = I R 

R is constant, so as you can see, E (voltage drop) is proportional to I (current being drawn). So you spin up your table saw, your net voltage plunges to 74 volts then rises right back up to 227 volts. As you're moving work through the saw, it drops down to 156 volts. You hit a knot, and suddenly it blips down to 117 volts. It's all over the map.

So your whole idea of engineering for a fixed, static voltage drop is a non-starter.

Sometimes, you can fake it

If you have very specific loads that you understand, you can just lump the voltage drop. For instance if I knew you planned to run 200W of hardwired lighting, I would tell you to run 14 AWG @ 240V. And then use LED bulbs with switching power supplies, which accept anything between 100V (Japan) and 240V (UK). So it sags to 140V, nobody cares.

But usually, you can't "fake it" and accept a highly variable voltage drop like that.

Either use transformers or throw aluminum at the problem

Now you have to make a costing decision. You start by deciding how much ampacity you actually need to support due to your loads. First, you must breaker at least 125% of your planned load. If your max load is 16A you breaker for 20A. That means you only calculate voltage drop on 16A, not 20A. Second, if you have specific actual loads in mind (34A hot tub, say, and 125% of that is 42.5A so you must breaker for 50A), then you calculate voltage drop on actual 34A, not 50A breaker. Got that?

Second, as you correctly surmised, 3% is bullpuckey. (except in Canada, you must beat 3% on the number I discuss in the last paragraph; on the upside, Tim Hortons). In America, you are allowed any voltage drop you find acceptable, as long as it doesn't contradict equipment instructions (NEC 110.3(B)). I'm not going to lose any sleep over 5.5% @ max. But I'm not Canadian lol.

Once you've arrived at this, you can calculate it two ways.

First, you run the numbers with cubic aluminum. Punch your numbers into the voltage drop calc and play "what if?". And go hit a site like wireandcableyourway.com and price the called out wire/cable.

Second, see what Ed Beal has to say about transformers. Now there's one area I differ from Ed, who recommends 600V transformers. That makes sense if you're buying brand-new and large (50 KVA). But for small ones (2-5 KVA) or used transformers off Craigslist, 600V is enough of an odd duck that prices will be painful or availability will be scarce. Remember you need 2 of them. Your table saw will do fine with a 2-5 KVA 120/240--240/480V transformer, and I see those in the $100 ballpark on Craigslist often enough. Your "200A" requirement requires a 50 KVA transformer, which is a beast that probably sits on a concrete pad. Brace yourself, but remember, it's a costing game: this or stupid-fat wire.

If your wire needs are so stupid-fat that the voltage drop calc malfunctions, look for one with a "Parallels" option and put 2 there. You can also try 3 or 4. But paralleling requires very special equipment with a very special price tag, so transformers may start looking good again :)

Consider conduit, but not too hard.

The huge upside of conduit is that you can change or upgrade wires down the line (presuming you made the conduit large enough, which is a good idea given wires of this size).

The downside of conduit is it facilitates theft. It makes it easier for a wire thief to sneak in, slice the wires at the supply end, then at the remote end, hook a pickup truck to the wires and drive off with them. They slide right out of the conduit. Direct buried, they won't pull so well.