See if you can locate something with a gauge at 18 or lower, according to length, to go from the wall to the power supply. This absolutely does matter. It is a direct correlation between power hungry computers and such as using power tools on a long cord. You cannot run a circular saw on the same thin gauge wire that Christmas lights would be fine on.
In my own case I not only upgraded the outlet that my main battery backup is plugged into, but due to the layout constraints I selected large gauge wire plug strips and/or extension cords. I also upgraded the breaker for that one outlet. My home has a basement/crawl and quite opportune that the AC unit had to be replaced, and a new circuit ran where the old one was left in place and able to be repurposed.