Breaker Failure

Yes,

1. Loose connection.

2. Breaker pole may heat UP from inside the breaker connection

While I do think that Tornado has already identified the likely problem, I just wanted to point out that you don't have a lot of a surge margin there. A brief 25% over draw from your measured value will be at your circuit breaker limit. Try measuring the current load when one of the larger air-conditioners starts. I'm certain you'll find more current drawn. Will this be sufficient to trip this breaker, only an on site evaluation can tell.

Your 225Amp breaker is supposed to be under only an eighty percent load at its max. 225 x .80 = 180. Make sure that your hot legs are balanced per phase, if one of the phases is carrying too much of the load it can cause you problems. The loose connection is the most likely problem as already suggested. Oh, if some of your individual breakers are also running at their maximum, they will add to the heating problem by cascading the heat up to the main breaker. Remember that the breaker has a bi-metallic strip that when heated causes the breaker to trip.

Many breakers don't have many cycles in their life. If you have had frequent trips the breaker may need replacing.

Use a peak detecting meter and measure the current for several days to catch your peak demand.

You may have a couple air conditioners trying to start about the same time. If the cable runs to the air conditioners have an excessive voltage drop they may be struggling to start, drawing too many amps for too long.

Check this link effect of harmonic currents http://www.nalanda.nitc.ac.in/nitcresources/ee/lectures/Effect.pdf

crm

All good posts; follow these and you will likely find the cause. Loose connection(s!) and unbalanced load are the most probably causes. Also, if this building was built during the Aluminum wiring days, or if the main is aluminum, or both, then each time any connections warmed up, they swell, then shrink, thus making a semi-loose connection, much looser over time. If you have several A/C units on the line, one of them may be pulling a heavy intermittent load as it cycles, so check your amperage over a period of time looking for spikes that last for more than a jiff. Also, if the breaker is older, after many trips your going to get residue on the contacts from arcing and sparking, and the contacts will become severely pitted from the intense heat, causing further high resistance. I would replace the breaker as a matter of good policy and safety, as well as try to isolate the cause of the trip.

what to do if theres an unbalanced load?

Check the line and load side connections for tightness. I have seen cross threaded screws on the load side causing heat. Where is the discoloration? If it gets as hot as you say, the insulation will show it. A 225A main should not trip at 180 unless there are real issues present. Testing by the UL is performed with a single breaker mounted in the panel (both sides are open) and the air is allowed to cool the breaker on all sides. The NEC does an automatic derate when it only allows branch circuits to be loaded to 80%. Most service panels in the US have a main breaker that is separated from the branch circuit breakers. If you have access to a thermal imaging camera, use it. The results will indicate clearly where the issue is. I have serious doubts it is a harmonics issue. generally if harmonics are present it will heat up the neutral, not the phase conductors. If this has been subjected to the heat you indicated the breaker should be replaced anyway. When the breaker is removed it will probably be obvious where the problem is. One last thing to keep in mind, every time you reset a breaker that "gets so hot" you get one step closer to the breaker not opening as designed. I have seen breakers that are blown apart, swollen to the point where they will never open, and practically melted in place. Continuous resets of a breaker because of "nuisance tripping" can be disastrous

if the cable overheats near the terminal of the breaker, then most likely the problem is loose connections or the breaker is defective. However, if the entire cable is overheating, then further investigation would be required. Also, check and make sure that the cable is not substandard.

Limit the THD to 15%

I'm sorry, what's a THD?

Total Harmonic Distortion (THD) is most likely the undefined acronym. The effect a single phase or three phase power grid experiences when it drives many non-linear loads, like uncompensated switching supplies. This type of distortion can produce a false low current reading depending on how your current measurement is done, but still cause a breaker trip.

But one could easily assemble some completely silly acronyms like Trigonometric Hyper-Drive, Time variant Heated Damper, Taco Heavy Diaper. (Ewww )