Ok some 120V with battery back up will beep when they are operating on battery alone. Check your circuit breakers. Also some smoke detectors require a particular battery, The actual voltage on a new 9 volt battery is someplace around 10.5 and 11 volts. So if you tried a new/old battery try a good high output battery like a duracell or the like.Your detector may be sensitive to even the smallest amount of voltage drop. Good Luck and hope you get some rest, I know I have one in a pile on my closet floor from a temper tantrum and a thrown shoe.
In the last house we were in there were three interconnected smoke alarms with battery backups and they didn't care for power outages at all. One of these units was also a gas detector with voice annunciation. During any power outage it would trip the other two alarms and go through it's whole repertoire of voice warnings. The only way to reset it was to pull the battery, switch off the circuit breaker and wait 10 seconds.
Smoke detectors are self testing. Since it is beeping, it is related to the internal function of the smoke detector. If it were related to smoke or carbon monoxide, the alarm would be activated. Most likely cause is a poor battery. If you are sure the battery is good, consider replacing the smoke detector.
It might need a new battery, it might be a faulty detector or do you have a candle burning or incense? I had a candle burning the other day and didnt even think that could make one go off, and it did!
all modern smoke detectors have a built in alert system when the battery is low and needs to be changed. if you rent, just tell your landlord or manager. they will be happy to change it for you. if not just tell the handyman of the family! requires 1 9volt battery.