For the below I will assume 90C conductors and 75C terminations. I presume that the OCPD are not being subject to increased operating temperature, which would otherwise open up a whole other kettle of fish.
The steps that I will follow are:
1) Use article 310 to find the minimum suitable conductor that meets the requirements of 210.19(A)(1) first sentence.
2) Use article 310 to find the minimum suitable conductor that meets the requirements of 210.19(A)(1) second sentence.
3) Select the larger of the conductors selected in 1 and 2 above.
4) Use 210.20(A) to select the minimum OCPD required.
5) Use article 240 to determine if the conductor from step 3 is properly protected by the OCPD from step 4. If the conductor is not properly protected, then select a larger conductor.
1. 100a N-cont + 75 A Cont 30C
1) Per 210.19(A)(1) first sentence, an ampacity of 175A is required. Using the 75C column of table 310.16, with no adjustment or correction for current carrying conductors or ambient temperature, this requires a 2/0 Cu conductor.
2) Per 210.19(A)(1) second sentence, an ampacity of 194A is required. Using the 75C column of table 310.16, with no adjustment or correction for current carrying conductors or ambient temperature, this requires a 3/0 Cu conductor.
3) Select the 3/0 Cu conductor.
4) Per 210.20(A) the minimum OCPD required is 194A. Per article 240, this next larger standard breaker is a 200A breaker.
5) Under the specified operating conditions, a 3/0 conductor has an ampacity of 200A at the terminals(75C) and 225A along the run(90C), and is properly protected by a 200A OCPD.
The conductor size to use is 3/0 Cu.
2. 100a N-cont + 75 A Cont 42C
1) Per 210.19(A)(1) first sentence, an ampacity of 175A is required. We must examine both the 75C column without temperature correction (because of the device terminations) and the 90C column with temperature correction (for the thermal limit of the conductor). A 2/0 Cu 90C conductor in a 42C ambient has an ampacity of 170A; A 3/0 Cu conductor is required.
2) Per 210.19(A)(1) second sentence, an ampacity of 194A is required. Using the 75C column of table 310.16, with no adjustment or correction for current carrying conductors or ambient temperature, this requires a 3/0 Cu conductor.
3) Select the 3/0 Cu conductor.
4) Per 210.20(A) the minimum OCPD required is 194A. Per article 240, this next larger standard breaker is a 200A breaker.
5) Under the specified operating conditions, a 3/0 conductor has an ampacity of 200A at the terminals (75C) and 196A along the run (90C derating factor 0.87), and is properly protected by a 200A OCPD.
The conductor size to use is 3/0 Cu.
3. 100a N-cont + 75 A Cont 42C and 4 current carring conductors in conduit.
1) Per 210.19(A)(1) first sentence, an ampacity of 175A is required. We must examine both the 75C column without temperature correction (because of the device terminations) and the 90C column with temperature correction (for the thermal limit of the conductor). A 3/0 Cu 90C conductor in a 42C ambient with 4CCC has an ampacity of 157A; A 4/0 Cu conductor is required.
2) Per 210.19(A)(1) second sentence, an ampacity of 194A is required. Using the 75C column of table 310.16, with no adjustment or correction for current carrying conductors or ambient temperature, this requires a 3/0 Cu conductor.
3) Select the 4/0 Cu conductor.
4) Per 210.20(A) the minimum OCPD required is 194A. Per article 240, this next larger standard breaker is a 200A breaker.
5) Under the specified operating conditions, a 4/0 conductor has an ampacity of 230A at the terminals (75C) and 181A along the run (90C derating factor 0.87 adjustment for CCC 0.8), and is properly protected by a 200A OCPD.
The conductor size to use is 4/0 Cu.
New: 80a N-cont + 100A Cont 42C and 4 current carrying conductors in conduit.
1) Per 210.19(A)(1) first sentence, an ampacity of 180A is required. We must examine both the 75C column without temperature correction (because of the device terminations) and the 90C column with temperature correction (for the thermal limit of the conductor). A 3/0 Cu 90C conductor in a 42C ambient with 4CCC has an ampacity of 157A; A 4/0 Cu conductor is required.
2) Per 210.19(A)(1) second sentence, an ampacity of 205A is required. Using the 75C column of table 310.16, with no adjustment or correction for current carrying conductors or ambient temperature, this requires a 4/0 Cu conductor.
3) Select the 4/0 Cu conductor.
4) Per 210.20(A) the minimum OCPD required is 205A. Per article 240, this next larger standard breaker is a 225A breaker.
5) Under the specified operating conditions, a 4/0 conductor has an ampacity of 230A at the terminals (75C) and 181A along the run (90C derating factor 0.87 adjustment for CCC 0.8), and is _not_ properly protected by a 225A OCPD. A 250kcmil conductor has an ampacity of 202A along the run and _is_ properly protected by a 225A OCPD.
The conductor size to use is 250kcmil Cu.
-Jon