Those interested in seeing some of the other ways that people have approached these issues ( and in particular, those seeking a solution which doesn’t require your smart phone to be present) can go to the community – created wiki, look on the quick browse lists, go down towards the bottom of that page for the “project reports“ section and then choose the “power“ list.
Or just jump straight to the following thread, which I think is typical. Although the thread itself is a couple of years old, the basic approach is still solid, although you might end up picking different devices. But essentially it combines a UPS power brick, a router with fallover, and a cellular modem with a low-cost pay as you go plan.
This is very similar to how many lower-cost security systems work. If the power goes out or the Internet goes out, you automatically fall over to a battery operated cellular-based system.
This is the approach that most people with boats or remote vacation homes will take. It’s not intended to run for very long, but long enough to get you all the notifications that there’s a problem and, if necessary have someone physically go to the location.
It’s also a good approach for people who live where they have frequent but short service loss from their regular Internet service. 