How is the minimum conductor size (of some type) for a certain run determined?

I have a 200A service in a garage. I would like to run cable from this to a 100A service in a house. I would also like to run from this to a separate 50A service in the house which will supply generator-backed-up power. Both runs will be single-phase 240V. The run lengths are no greater than 160'. The cables will run through buried PVC conduit.

How do I determine a suitable conductor size for these cables?

Considering ampacity alone, I would expect to be able to use #3 copper (SER or THHN) or #1 aluminum (SE) or #2 aluminum (THHN) for the 100A run.

By the same logic, for the 50A run, #6 copper (NM) or #8 copper (SE or THHN) or #6 aluminum (SE or THHN) or #8 aluminum (NM).

However, considering the voltage drop over 160', large conductors seem indicated.

To achieve a less than a 3% voltage drop for the 100A run, it seems like #2 copper (Vdrop 2.6%) or 1/0 aluminum (Vdrop 2.7%) will be required. For the 50A run, #6 NM copper (Vdrop 3%) or #3 SE aluminum (Vdrop 2.7%).

Another factor I know matters but that I don't know how to evaluate is the temperature at the breaker terminals. For example, will #2 copper in the 100A run remain below the required 60C or 75C when actual load approaches 100A?

I'm also not sure whether 3% is the right magic number to select for Vdrop. It seems allowed (encouraged?) to accept a 5% Vdrop in situations like this one. Yet allowing even 3% loss on a 100A line seems like a lot of wasted power. Have I understood this part of the decision properly?

And, not being a professional, I wonder if there are further questions I should be asking that I'm not even aware of.

So, what are the proper conductors for this scenario and why? I am interested in both code compliance as well as good performance of the resulting system (should those two not necessarily be the same).

Thanks.

Temperature at the terminals is handled for you

The NEC's ampacity charts handle temperature at the terminals for you, simply by way of you selecting the appropriate column from the chart for the temperature limit of your terminals.

3% for feeders is a good voltage drop rule of thumb

The reason 3% is used for feeder voltage drop is because we want overall voltage drop to be no more than 5% at max ampacity (some stuff can take more, but it's not particularly kind to certain loads, esp. motors), and the other 2% needs to be left for voltage drop across the branch circuit to the load in question. Varying this is possible, depending on the load, though -- a water heater might be OK with a bit of extra voltage drop, while your air conditioner would be better off with the full 240V at its terminals.

Of course, if you wish to analyze load diversity and come up with a more realistic design point than maximum load for the feeder to be at design voltage drop, that's your prerogative -- as long as the wire meets Code minima, it'll be able to handle the current safely.

Will it fit?

There are two final things you need to check:

1. Is your conduit big enough for your wires? An overstuffed conduit may overheat, in addition to making the pull far harder than it needs to be -- in fact, it's wise to oversize the conduit to keep pulling difficulty down and provide room for future expansion.

2. Will your wires fit in the breaker lugs? Most lugs accept a wide variety of wire, but it's good to double-check before you have everything pulled.

P.S. TORQUE MATTERS

Section 110.14(D) in the 2017 NEC requires that connections be torqued to manufacturer specifications; in practice, you'll need a torque screwdriver and/or torque wrench, both reading in inch-pounds, for this.

• I'd rather run 8 AWG down the 30A branch circuit than 'ought wire down the main run... That is i'll take the entire 5% hit on the expensive wire, and upspend on the cheap wire here and there for the odd load that matters (like, NOT the water heater). Commented Sep 21, 2017 at 1:25

The key is that a 100A line isn't 100A all the time

... Or, ever.

Go read the brochure website on any power plant, particularly a nuke or solar installation, it will say something like "this 1.5 gigawatt plant serves 1.5 million homes". Um. So they are saying the average home takes 1kw (about 4.1 amps at 240V). Seriously?

Yeah, seriously. They are saying your house spends most of its time asleep, drawing even less than 1 amp because everything's off. The dryer pulls 23A but only 90 minutes a week. Averaged through the year the A/C draws only 2 hours a day.

Your electric bill proves it. 1KW is 1KWH per hour or 720 KWH per month. At 12 cents a KWH, with fees, that amounts to about a \$100 power bill. If your house drew 100A all the time, your monthly power bill would be \$10,000. It's clearly not.

So you have to pause and think about your realistic load - the level of load you care about. It really helps to have experience with a whole-house power monitor. Then, in those odd moments, those excessive peaks when the dryer is running while someone is cooking and the A/C is kicking -- how much voltage drop can you live with?

There isn't anything wrong with heating a little wire in those 1-in-1000 moments. As long as you follow the specs in those charts (NEC 310.16) it guarantees the wire cannot get too warm, no matter how much length or voltage drop you have.

Those voltage drop calcs are a menace...

... because they don't think about that. One guy had a calc tell him to run #6 for a 20A circuit of only 135'. Datz kray. I showed him for realistic loads, #12 would be fine and #10 would be overkill.

It's pretty much my "hat" here to have someone coming in complaining that the calc told to use 600kcmil for his 2000' run to a 100W pole light... And then I show him how to do it with 14AWG wire, the smallest size you can use on mains wiring.

So to start with, set your amp values to the realistic common number. Put "acceptable percentage" to 5% just so it's not bumping you up a size just because the smaller size would be 3.06% (that happened in the 20A case).

Try a couple other numbers and up the permissible percentage.

Then do punch in the nameplate amp number, but put 99% for permissible voltage drop. And see just how bad the worst case is. If it gives you a gory number like 19%, then back the number off to 18% to force it to go one size larger at a time.

That said, why not provision for 200A?

I seriously doubt you plan to use 50-100A in the garage. So why not go ahead and plan for 150-200A wire for the "main" circuit to the house? That will certainly remove any concern of voltage drop at 100A usage levels, and give you the headroom to use your entire 200A panel capacity. That would be 250KCmil aluminum for 2.64% drop at 200A and 1.32% drop at 100A and you never have to give it another thought.

By the way, a person wouldn't even think of using copper at these large sizes, unless they were tragically misinformed. Aluminum has 12 times the conductivity of copper, when measuring by dollar of raw metal. (and twice the conductivity when measuring by weight.)

I take it the generator will be in the garage? Normally you're not allowed to run two parallel services between buildings, but a special usage like a generator is permitted. On that, #4 aluminum will give you 3.06% voltage drop at 50A. **

** remember what I was saying about how those calculators getcha? When you did it, you got #3 aluminum because you told the calculator to limit drop to 3%, which 3.06% failed. Passes in my book. That's why I started by telling the calc 99% was acceptable, to see what it would say.

Oh and it's coincidence that it was 3.06% in my earlier example. This last was an edit. I just did the calc now. This happens a lot.