I found a way to do it without any special clocks, although you need to do some investigation beforehand.
What you need is a Wi-Fi router and a smartphone with a good battery. I will use an Android phone in my explanation.
The Idea
As mentioned in How often does an Android system scan Wi-Fi?, Android phones regularly scan for Wi-Fi networks and try to connect to them, if you have Wi-Fi on but are not connected to any networks.
In the case of your home network, it should connect automatically once the network is detected. There are also apps that can help you confirm how often your phone tries to do this.
The idea is to leave your Wi-Fi router plugged in, and to leave your phone on and with Wi-Fi turned on. So, when the electricity is back, your phone will connect to the Wi-Fi. Then, there are ways to view logs or statistics to find out what time the power came, but you need to have experimented with it beforehand.
How to Check
You might be able to see at what time your phone connected to the Wi-Fi (see How can I see what specific times my phone has connected/disconnected to Wi-Fi?).
Alternatively, you might be able to connect to your router and find information about when the router went back up or what time your phone was connected to it.
Usually, you can connect to your router by typing its IP address in your browser. For example, in my case it is 192.168.100.1
. If you do not know the IP address of your router, you will usually be able to find the default IP address by searching for the model online. You will probably also need to log in, and you can also find default credentials for different models online.
Once you are connected, you might be able to find an event log which contains information on when the router went back up. Or you might be able to find a list of connected devices and for how long they have been connected.