Introduction - Cable ampacity (how many amps a particular cable type can carry) is one of the most important design calculations. Oversizing cables leads to excessive cost, but undersizing cables can lead to overheating and potentially dangerous failures.
The National Electrical Code does an excellent job describing how ampacities of cables (and consequently cable sizes) can be determined in the middle of a circuit. The process, at a high level, is as follows:
Figure out the temperature rating of the cable, its maximum allowable steady-state operating temperature (e.g. 90 Celsius)
Figure out the routing conditions of the circuit (e.g. in isolated conduit in air, directly buried, etc.) and select the appropriate ampacity table
Use the table's column corresponding to the temperature rating, and apply derating factors for temperature, bundling, etc.
The middle of the circuit's ampacity isn't too difficult to figure our, even if there is some engineering judgment to be applied.
What is difficult, however, is figuring out the right way to size a cable to account for temperature limits at the point of termination (e.g. connection to a circuit breaker, switchgear bus bar, etc.).
The NEC in Article 110 provides prescriptive, although very confusing, guidance. Essentially, standard values from NEC 310.16 are to be used for ampacity at an LV termination point. For MV, the code allows engineers to use the 'applicable' table. Once again, implementing these rules isn't difficult but making sense of them is!
Low Voltage Terminations - First off, we need to understand that the LV requirement is based on UL listing criteria. Equipment is tested with cables of a minimum size that correspond to the sizes in 310.16. Theoretically we don't need to do any temperature or bundling derating of these cable sizes because equipment shouldn't be used outside of its maximum temperature range used during testing and cables aren't bundled at their point of termination.
Of course, nothing is really so simple. Consider the following: What if we had a set of cables with extreme derating just before entering an equipment enclosure, like a giant bundle? Are we sure that the minimum cable size prescribed by the NEC will be suitable in this case? Let's take a closer look.
Figure 1: A Big Bundle of Wires
Consider this example: 15 current-carrying XHHW-2 conductors are bundled together in a single conduit. The circuits each must carry 40A. The conductors terminate at a panel with terminations rated for 75 Celsius. What size of conductor is allowed based on the NEC?
Per the NEC we have to determine a cable size that is suitable for 40A at 75 Celsius for terminations (8 AWG CU per NEC 310.16).
Then, we compare this with the conditions of use. Derating for 15 current-carrying conductors is a factor of 0.5 and the 90 Celsius ampacity is allowable. This corresponds to a cable size of 4 AWG CU.
Since 4 AWG CU is the larger size, we're required to use that.
Figure 2: Example of Two Different Temperatures Leading to Conflicting Requirements
This example shown in Figure 2 illustrates the confusing part of the NEC: Why are we allowed to assume that the temperature of those cables at the point of termination will be so much less? Hypothetically, cables could be operating at 90 Celsius only a few inches before being lugged onto a 75 Celsius piece of equipment.
In the Canadian Electrical Code (CEC), this problem is handled in a much more physical way: Conductors must be sized to comply with their termination temperature limit based on the worst-case conditions within 5' of the point of termination. This means that the cables in the example above would have been sized for a 75 Celsius temperature even though XHHW-2 was used (because the conductors have no transition period without bundling before terminating).
The downside of the CEC method is that it will lead to larger cable sizes. The upside is that the odds of overheating equipment is much lower. Needless to say, using the CEC method in NEC territory can lead to some heated arguments over value engineering. I recommend cable sizing based on CEC methods for terminations, but ultimately this is something the responsible engineer for the project must assess.
Medium Voltage Terminations - NEC guidance on MV terminations is much less particular than low voltage. The requirements of Article 110 essentially say 'use engineering judgment for the right table'. This lax methodology leaves more to interpretation by the responsible engineer, which is of course a double-edged sword. The positive is that this allows for an engineer to make an educated assessment about the conditions of the cable as it approaches the point if termination. The downside is just that-there's no real direction.
In general, I recommend the same approaches used for LV terminations be used for MV (essentially derating for the worst-case conditions within 5' of the termination point).
Conclusion - Cable sizing is not nearly as simple as people often make it out to be. Everything is fun and games until you start to see things overheating and damaging equipment (or worse, catching fire). The NEC often has a reputation as a "conservative" document, meaning it should always provide exceptionally safe designs. However, I have found this is often not the case, and perhaps there is no situation where this is more present than terminations. Always make sure you understand what's going on at the ends of the cables before you size and install!