For a 100 ampere circuit, the conductors will likely be required to be 3 AWG copper or 1 AWG aluminum. However, if you care about power quality, you're going to want to increase the size of the conductors to reduce voltage drop.
It's recommended to reduce voltage drop to below 3% of the supply voltage. So for a 240 volts supply, you'll want the drop less than 7.2 volts. When I calculate voltage drop for panel feeders, I always use the maximum ampere rating of the circuit. This is a worst case calculation, if you're pulling the maximum capacity of the circuit. Calculating it this way, means that I don't have to do a load calculation (which is usually impossible over the internet). It also reduces the chances of having power quality issues, if you get up near the maximum current limit of the circuit.
3 AWG copper and 1 AWG aluminum conductors, have a resistance of about 0.254 ohms per thousand feet. If I plug that into a voltage drop formula, I can figure out what the voltage drop across the conductors will be.
Voltage drop (VD) = length (L) * 2 * ohms/ft. * current (A)
VD = 200 ft. * 2 * 0.000254 ohms/ft. * 100 amperes
VD = 400 * 0.000254 ohms/ft. * 100 amperes
VD = 40000 * 0.000254 ohms/ft.
VD = 10.16 Volts
Since this is greater than 7.2 volts, I'll try the next larger size conductors (#2 cu. 1/0 al.).
VD = 40000 * 0.000200 ohms/ft.
VD = 8 volts
Getting closer, but the voltage drop is still too high. Once again with the next larger size (#1 cu. 2/0 al).
VD = 40000 * 0.000157 ohms/ft.
VD = 6.28 volts
6.28 volts is less than 3% of 240 volts, so I found the size conductors to use.
tl;dr
To feed a 100 ampere secondary panel 200 ft. from the main panel, you'll want to use 1 AWG copper or 2/0 aluminum conductors. This is large enough to safely carry 100 amperes, and to maintain power quality over the distance.
NOTES:
- You'll want to feed the panel using 4 conductors (hot, hot, neutral, ground).
- You'll have to isolate the grounded (neutral) conductors and bus bar in the secondary panel.
- You'll have to install an adequate grounding electrode system at the outbuilding, and bond the grounding conductor to it.
Conductor resistance values are from Table 8 Conductor Properties, from chapter 9 of the 2014 National Electrical Code