If you check the status on your alarm panel and you have an "AC power failure" it means that the panel is unplugged or there is a problem with the power connections. Here are some things to check if you have a GE Simon panel.
(If you are experiencing a power outage and simply want the panel to stop beeping while you wait for it to come back on you can turn off the trouble beeps.)
First make sure the power supply is plugged in. If it is, unplug it for a minute and plug a lamp or other device into the outlet to make sure that the outlet is working properly and that your circuit breaker hasn't blown.
If you are still not getting AC power to the panel you will need to check the power wire connections, make sure the wire is securely attached to the two screws on the back of the power plug. Also check in the back of the panel that the wire is attached to screws 4 and 5 (the ones labeled 9 VAC). Don't worry if you get the wires switched, it does not matter which one is on 4 and which one is on 5.
If all else fails the last step would be to replace the wire if you have any similar 18-20 gauge wire (speaker wire works well). Or if you own a multimeter you can check the transformer and make sure you get 9 volts AC power, then check the panel as well to make sure the wire is good.