Vraciu, have you tried the trick of draining the residual voltage in the detector like I described up thread by holding down the test button till it dies before putting the new batteries in?
Also is it chirping only when the power is out or does it keep doing it after power is restored? I can check in one of my rentals what it does when the power goes off, in my house the smokes don't complain when the power is off, they are pretty old, hardwired battery back up. 25 years old actually.