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Just to clarify, the inverter in the UPS isn't the big problem (although it's an inefficient way to power electronics that consume DC, like DC pumps). The big problem is that the batteries in UPSs are just too small.
The Duracell battery you showed in the video has a rated capacity of 35Ah, which at 12V is about 420W total. My Vortech MP10 uses about 7W on Reef Crest at 100%. At that load, the battery you showed will last up to 60 hours, give or take a few hours to account for battery DOD.
This $144 UPS from Amazon, by contrast, has a total of 15Ah (according to the replacement battery sizes). This equates to around 180W of power. This would only run one MP10 for 25 hours at the very most. Not bad, but that's a $150 UPS. A battery like the one you showed in the video is much cheaper, usually around $65.
UPSs will certainly work, but they're not my favorite solution. Hooking a battery up to the battery backup port of a DC pump will be much cheaper.
Interesting, I certainly don't claim to be an electrical engineer : )
We were working with a UPS supplier at one time and they shared one of the reasons we got shorter run times than anticipated for the battery size was the internal inverter consumes considerably more power than the ~7watt pumps we are using. They also suggested that the larger UPS's with bigger batteries also have larger inverters capable of producing higher wattage AC power but it also consumes more power so there are instances where a smaller UPS may actually last longer on a single ~7 watt pump. End of the day he said we should find a UPS with the highest efficiency inverter, likely with the lowest output rating coupled with the largest battery. The aquarium needs just ended up being pretty different than the higher wattage PC needs.
Now that said this is way outside my field so I can't claim that to be accurate, just what the manufacturer's rep shared with me and sounded plausible at the time. It was many years ago but we did run some tests of various sizes/outputs of the same UPS brand and while the larger sizes always lasted longer, double the Ah did not produce double the run time on the single Tunze ac pump we used. I can't remember the exact run times but the difference and how they scaled was notable.