Time machine backup is not completing--notification that computer was running on battery when it was actually connected to a power source the whole time

I just got a new MacBook Air to replace my five-year-old MacBook Air. The problem that I had with the previous computer and backup drive has persisted. I bought a new external hard drive from the Apple store online in case the problem was with my old Seagate external hard drive. Same problem. See screenshot of Time Machine alert. Is anyone else experiencing this, and if so, have you solved the problem?