Is 3 AWG copper enough for 100 amps?

For ampacity yes, at 100 amperes in the 75 degrees C column of Table 310.16. Over 200 feet the voltage drop reaches about 4.1 percent.

Do I have to increase the ground wire when I upsize for voltage drop?

Yes. NEC 250.122(B) requires the equipment grounding conductor to be increased in proportion to the circular mil increase of the ungrounded conductors.

Is voltage drop enforceable in the NEC?

For ordinary feeders and branch circuits it appears only in Informational Notes, which 90.5(C) makes non enforceable. Some local amendments make it mandatory.

What size THHN do I need for a 100 amp run of 200 feet at 240 volts single phase?

Two calculations run in parallel here, and the longer run means voltage drop wins.

Step one: ampacity

Section 110.14(C)(1)(b) puts terminations on equipment rated over 100 amperes at the 75 degrees C column, and for equipment rated exactly 100 amperes or less you are in the 75 degrees C column as well under 110.14(C)(1)(a) when the conductors are rated 75 degrees C or higher. In the 75 degrees C column of Table 310.16, 3 AWG copper is 100 amperes and 1 AWG aluminum is 100 amperes. That is the ampacity minimum for a general feeder.

If this is the main power feeder to a dwelling unit or a dwelling service, 310.12 lets you use conductors rated at 83 percent of the service or feeder rating. At 100 amperes that is 83 amperes, which 4 AWG copper at 85 amperes and 2 AWG aluminum at 90 amperes both satisfy. That allowance only applies to a dwelling service or the single main power feeder that carries the entire dwelling load, not to an ordinary subpanel feeder.

Step two: voltage drop over 200 feet

The Informational Note to 215.2(A)(2) suggests 3 percent on a feeder and 5 percent total for feeder plus branch circuit. Three percent of 240 volts is 7.2 volts.

For a single phase circuit, voltage drop equals 2 times the one way distance times the current times the resistance per foot. Chapter 9 Table 8 gives stranded uncoated copper resistance in ohms per 1000 feet.

3 AWG copper at 0.245 ohms per 1000 feet: 2 times 200 times 100 times 0.000245 equals 9.8 volts, or 4.1 percent. Over the target.

2 AWG copper at 0.194: 7.76 volts, or 3.2 percent. Still over.

1 AWG copper at 0.154: 6.16 volts, or 2.6 percent. That works.

On the aluminum side, 1/0 at 0.201 ohms per 1000 feet gives 8.04 volts, or 3.35 percent, and 2/0 at 0.159 gives 6.36 volts, or 2.65 percent. So 2/0 aluminum is the equivalent answer.

Does voltage drop actually have to be met?

No. Every voltage drop reference in the NEC for normal branch circuits and feeders sits in an Informational Note, and Section 90.5(C) states that Informational Notes are explanatory and not enforceable as code requirements. Sensitive electronic equipment, fire pumps in 695.7, and elevators in 620.14 have their own mandatory limits, and some jurisdictions adopt voltage drop as a local amendment.

That said, at 200 feet and full load you are handing the customer 230 volts at the panel with 3 AWG. Motor and heating loads notice. Size for the drop.

Assembling the run

Pick 1 AWG copper THHN or THWN-2. Chapter 9 Table 5 lists 1 AWG THHN at 0.1562 square inches, so three of them plus a 6 AWG equipment grounding conductor fit comfortably in 1 1/4 inch EMT under the 40 percent column of Table 4. Section 250.122 sets the equipment grounding conductor at 8 AWG copper for a 100 ampere device, but 250.122(B) requires you to increase the equipment grounding conductor proportionally when the ungrounded conductors are upsized for voltage drop. 3 AWG to 1 AWG is a circular mil increase of roughly 1.59 times, so 8 AWG copper at 16,510 circular mils becomes about 26,250 circular mils, which lands on 6 AWG.

Field takeaway

1 AWG copper THHN with a 6 AWG copper equipment grounding conductor, or 2/0 aluminum with a 4 AWG aluminum equipment grounding conductor. Ampacity would have let you use 3 AWG. The 200 feet is what moved it.