I have a 260 ft run from my main 225A panel to a 100A subpanel in a steel shop out in my yard. I have a #4 bare copper wire grounded to the rebar in the foundation of the shop. Not knowing what I needed I was advised that I would need three strands of 1/0 THHN stranded copper wire and that that would fit in 1 1/4 pvc conduit. I bought the wire, buried the conduit, and then learned that that size wire was overkill even for the power drop for that distance. I also learned that in addition to grounding the subpanel to the rebar I need to run a 4th wire between the main panel to the subpanel. So at this point (if it's even possible to fit it in the conduit) what is the smallest size wire I can use for this ground wire and can it be bare wire? In either case does it have to run through the same conduit or would it be acceptable to run outside the conduit or in a separate conduit parallel to the original conduit. Just looking to reduce the damage caused by me trusting the advice of someone evidently unfamiliar with code and common sense. I could probably cram a #6 or #4 bare wire in there but if it has to be 1/0 or even #2 I will probably have to just dig up the conduit and bury new 2 in. conduit and deal with the added 250 bucks of conduit and trencher rental. Any advice would be greatly appreciated...I am a homeowner trying to minimize costs and ending up spending an unnecessary amount on wire and extra work because of it. You get what you pay for
So here's the deal, and here's how your friend "helped" you. There's a rule of "thumb" floating out there that we shouldn't let voltage drop exceed 3% when calculating a long run. This rule of "thumb" was invented by cable manufacturers, I'm fairly sure. There's no requirement whatsoever in the electrical code for this. It's just not there. They do comment that you shouldn't engineer for a 7%+ voltage drop, but nothing says 3%.
Even so, this should be based on your actual, expected load on the circuit, not the number written on the breaker handle. And when sizing a circuit, you shouldn't design it with >80% expected load, so if your actual load is 48A, you should run a 60-70A circuit not a 50A circuit. Follow? So your actual expected load probably doesn't exceed 80A and may be only 40-50A.
And third, anytime you're at #6 wire or larger, you should seriously consider aluminum conductors. Even the old alloy was reliable at these large sizes, and after all, the lugs are aluminum because Al lugs are compatible with both Cu and Al... so why create a dissimilar-metal problem when you don't have to?
So let's see how far off they threw you. Looking at 310.15b16, your absolute minimum legal wire size is #3Cu or #1Al @ 75 degrees C. (cost: $780 or $405)
If you are forced to use the 60C table, then #2Cu or #1/0Al. (cost $1006 or $460)
(Note that #2Cu@60C says 95, but they don't sell 95A breakers so you get to round up).
Now we look at voltage drop. Over your distance at 100A, #1Cu ($1287) is going to give you 3.3% voltage drop @100A, or alternately #2/0Al ($538) would give 3.5% voltage drop.
But hey!!! By bumping up to #1/0Cu ($1474), we get down to 2.7% voltage drop, and similarly #3/0Al ($663) would give 2.8% voltage drop.
What went wrong? Some fool decided that 3.00% was an absolute absolute when spending your money, so he disqualified #1Cu at 3.3%. Wasn't his money. And of course, it's stupid because you don't foresee drawing that circuit anywhere near 100A for very long, so really, your voltage drop will be proportionately lower, e.g. half at 50A.
Given the crazy expensive wire that is now in the ground, you could actually up-breaker that to 125A @ 60C (3.3% drop) or even 150A @ 75C (4% drop).
Or alternately, you can yank that copper outta there, sell it on eBay, and go with #1/0Al ($460), and just lump the 3.5% voltage drop @ 80 amps. That'll pay for the new ground wire, and still leave you with a stack of twenties.
Sizing the ground wire
I assume you picked Schedule 40 PVC conduit, because nobody ever swerves out of their way to buy Schedule 80 unless they've done a lot of research. That is nearly at the 40% conduit fill limit. There's just enough room for a #6 insulated wire (diameter 0.249) or the equivalent uninsulated wire (#3Cu, almost #2Cu bare). Bare wires must be Cu.
Here's the problem. When you upsize for voltage drop, you also need to upsize the ground wire in proportion. Normally a #8Cu or #6Al wire would suffice, but you need to bump it. AWG is based on proportion. You bumped 3 AWG sizes for voltage drop, so you bump 3 AWG sizes for the ground. Done! #5Cu isn't made, so you need #4Cu bare. I did run the numbers on this and it worked out the same.
I also like a rule of thumb: Consider the maximum breaker that would be allowed on the circuit if voltage drop were ignored, and size the ground wire for that. As discussed, you could bump to 150A based on 75C, so figure the ground that's called out for a 150A circuit. That would be a #6Cu. (#4Al is not possible because you don't have room for an insulated #4, and Al can't be bare.)
So if you keep the 100A breaker you need a #4Cu bare wire, but if you up-breaker to 150A you only need a #6Cu. Funny how that works out.
If you have Schedule 40 conduit, you will be at the absolute limit with a #6Cu insulated ground wire or a #3Cu bare (or possibly #2Cu, very close call).
If you have Schedule 80 conduit, that has thicker walls and thus a smaller inside diameter (pipe trade size is defined by outside diameter). You already exceeded fill when you selected 1/0 for the three conductors, so you are already out of compliance and you can't recover. Your only hope would be to yank the neutral and replace it with #2 Cu, and that would leave you just enough room for a #6 bare ground. You would need to look at your loads and see if it is legal to shrink neutral.
In any case, we are kissing 40% fill, which means this will be a bugbear of a pull. It's really easy for a DIYer to paint himsefl into a corner, when pushing fill limits on conduit. So we would have violently recommended that you use 2" PVC from the outset. I don't know if you have access to 260' of fishing tape, but you might have to pull the 3 conductors out in order to get the ground wire to fish.