So there are a couple of things that are good to know.
One.
Land Line systems have thier own power supply. The system is on a large battery bank and the generators are required, by FCC mandate, to have several days worth of fuel to support.
Two.
Most cell sites, now, have six hours of battery back up but sometime this won’t go six hours due to extremly large loads at the cell.
Three.
Here is the stupid part. Some cell sites have fiber to them instead of T1s. While the FCC mandated that the cell sites has 6 hours of battery back up the fiber converter that translate DS0s only has two hours. So the site could keep going except its backhaul has dropped off. Mean while… Like I said earlier cell sites that are connected via T1s should remain up for the duration of the cell sites batteries.
Four.
VOIP systems will fail because you do not have a local power supply. IDCs will have power, the same way that local land line switchs do, and the connection is still there but the local reciever (modem) will not have power.
Five.
Diaster Recovery. All carriers have a diaster recovery plan. It covers all highways, police, fire, and other first responders, including hospitals. Those sites will be restored first and sometimes maintianed by generator if possible. If you live under a site that is low traffic and low priority it could be sometime before you service is restored.
Lastly, If you have to communicate to your love ones that you are ok it is best to try to send a text rather than a voice call. In a text format some handset will retry continually to get the message out. Once that message is out… It will be on the local switch SMS… Where it will be queued to get out. So long after the cell site fails, due to power, the message will still get out because the SMS at the switch will still be on an active system. It may get out hours later due to congestions but better late than never.