For example. If you have 3 sets of 350. By sets I mean 3 conduits with blk, red, blu and white in each conduit is a set.
Say from Transformer to switchgear one set is 4 ft shorter then the other two.
How likely are the short ones to get hotter?
This is an interesting, but frustrating, code issue. Because no matter how careful you are in your attempt to get your parallel sets the same length, there will always be a slight difference. One conduit path will end up having the inside track around bends, and therefore unintentionally be shorter. To comply with the rule, you are supposed to add slack in the shorter wire to curtail the difference. The NEC does not specify a tolerance on just how different the lengths can be, before it is objectively wrong.
When you have parallel paths in a circuit, each path gets an equal voltage difference across it. As a result, the current through each path is inversely proportional to the path's resistance. Given identical wire cross sections, the path's resistance is proportional to its length, and therefore the current through each parallel set is inversely proportional to the length.
Suppose sets 1 and 2 are each 40 ft long, and set 3 is therefore 36 ft long.
The fraction of the current though each set should be 1/3. But instead, here are the fractions of the current which really flow:
Set 1: (1/40)/(1/40 + 1/40 + 1/36) = 32%
Set 2: (1/40)/(1/40 + 1/40 + 1/36) = 32%
Set 3: (1/36)/(1/40 + 1/40 + 1/36) = 36%
3 sets of 350 kcmil copper have a combined 75C ampacity of 930A, if they are all identical. But if they are different in length per the above, one would expect safe performance up to 868A, in order to keep the shorter set below 310A. The NEC does not prescribe this calculation, so even if you just had 1A flowing through this entire set of wires, it is still technically a violation.
