It is a DC circuit launches the relay when the power comes off using a capacitor charged when the power was on, so it is not needed any extra power for the relay.
You can increase the size of this C1 to increase the delay time, the power is 6v.

R1 and R2 must change to config it to be stable if you changed the DC power voltage.

I have a server computer connected to a UPS that give me 10 minutes backup time when the main power goes off, at this time i must shutdown the computer.
The problem my UPS doesn’t have any feature to send that signal to my computer, and any new UPS will be expensive.
Also my computer has no any COM port to accept the old type of UPS.

The circuit powered by a transformer connected directly to main power not to the UPS.

I will take two wires from the Power Button (on the mother board) and link it to this relay. When the main power off, my computer still on, and gets a signal to shutdown from that relay, as like if we press the Power button, we need to config our system (Windows 2003) to take this action.

Open RegEdit and add these keys

The  key will not ask there is users still using your server, it is shutdown immediately.

[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Windows]

[HKEY_USERS.DEFAULT\Control Panel\Desktop]

Also you must change in group policy in security options

“Shutdown: Allow system to be shut down without having to log on”

change it to Enabled
Also, I configured my bios to turn on when the AC comes back, so when the main power come, my computer will turn again.

This is my first circuit at my age, so do not trust with it 😀 , but it is worked fine for a week for me.

I discussed about this circuit in AllAboutCiruites forum and thanks to wayneh for help.