Mike,
WOW! Thanks so, so much for taking the time to help me. Your information is immensely valuable to this novice.
I read it is either: (1) a (cheap) faulty breaker, or (2) something in my system causing a surge of power in the cable from the solar charge controller to the batteries.
The breaker is possibly the problem, as it is a who-knows-what brand, probably Chinese, from Amazon.com. I didn't know any better. I looked again online and found a Blue Sea Systems 50 amp breaker, and since I used that brand a lot in past years on various boats, I am under the impression it is a higher quality product (and more expensive, of course). Is there a different, higher quality breaker I should consider?
The breaker has not flipped off again since the first two incidents (now for about 2 weeks, I'm guessing). So, possibly it was an anomaly?
I don't know whether it matters, but recently I read an article that basically argued "a larger sized wire/cable is ALWAYS better, and does no harm," So, I actually installed the breaker because I was changing the output-side +/- wire/cable from the solar charge controller to the batteries from 10 AWG to 6 AWG, because I had extra 6 AWG wire and figured it would do no harm. (The input wire from my solar panels is 10 AWH, per the panel's specs.) I assume this is not a factor in the breaker flipping.
FYI, my solar controller and my inverter are wired into my system via a busbar using 2/0 AWG wire (3 12-volt LiFePO4 150 Ah batteries). Per one spec I read, I put a 100 amp fuse on the battery-end of the short cable from the busbar to the batteries. Unless that's the wrong size fuse, I'm guessing I kinda' got that correct, per your suggestions.
I've been in the process of installing (plus rewiring, repairs, replacements) my DIY solar system for nearly 6 months. Every week there seems to be another, new issue of some sort. Or, I learn of something I could do better, such as rewiring my solar panels (8 - 100W panels) from all-parallel to a series-to-parallel configuration and installing a breaker on both +/- incoming solar cables so both can be easily turned on/off simultaneously.
Thank you, thank you, once again for your most gracious guidance.
If there is something obviously (to you) very wrong with my info above, and you have a moment for a brief response, it will again be appreciated. But, you have already done a lot to help me, so please do not feel obligated.
You have my enduring heartfelt thanks.
Jim S.