Modern home security systems are well equipped to deal with power outages, as they usually include a backup battery that allows the system to function up to 24 hours after losing their power source. Therefore, your alarm system should still sound and alert the authorities of a break-in as long as your battery works. Back-up batteries typically last 3-5 years, and you can replace them yourself. When your battery does begin to run low, your alarm should send a signal to the monitoring center and a representative will inform you that it needs to be changed.
For more information, ask your system provider for details on how your alarm works during a power outage.