I am hoping that that device works on an existing wireless LAN?
J0hn answered your question, but just to add a little bit more. I also have a HS100 (freebie from TPlink to several members of this forum who beta tested them before they were publicly available in the UK).
Yes they work over wifi and as J0hn mentioned, they work seamlessly with Alexa. I didn't want to confuse you in my earlier post, but if I am home I can simply say "Alexa - Turn off router". Outside of home (eg if I'm at my daughters house) I can use the Kasa app on my phone to control it.
In total, I have 4 of these plugs controlling various electrical items, 2 of which are TP-link. The TP-links are more expensive but IMHO they are far more reliable. The other 2 I have were cheaper but were slightly more of a pain to set up, and both of them tend to lose connectivity every couple of months or so. I've had the TP-links for several years and not once has either of them lost connectivity. I also have about 8 Hives which control lighting that I've had no issues with, but I don't have any Hive plugs to rate their performance. If I were to get another plug, then I personally would get another tp-link- despite them being a bit more expensive as they are more reliable and the Kasa app is better.
It would be very very simple to configure it to toggle power on/off with a single push button on your IOS device of choice with the IFTTT app for the purpose of powering on/off your modems.
@ Weaver. You could even use a 4 way adapter so that just one device would control all four modems. In the kitchen I use one of the other (non tplink) plugs in a 4-way to control a few electrical items. You can even group devices - which I have done with my lighting, but nothing stopping you grouping plugs either.
Grouping plugs and lighting with Alexa/echo is brilliant for me especially when I'm having a bad day as it allows me to set up custom commands.
eg I can simply say " Alexa - Goodnight" and she responds "Night night sleep well I have turned off all the lights." At which point it will ensure all the lights in my group are off and also 2 of the plugs. I can also do the reverse and ask her to turn things on in the morning without even leaving my bed, so it's ideal for anyone with disabilities.
Custom grouping and custom commands is limitless. For eg I have 3 lights in the study (Study1, Study2, Study3) which I can control individually. These are grouped as "Study lights". Then they are in another group "Upstairs" and finally in group "All lights". By using groups I can control an individual bulb, or all 3 in the study at once, or as part of any of the other 2 groups. It gives you an idea of what you could achieve by grouping your modems.
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PS you don't need an Echo/Alexa. You could do it all via the app on your phone/ipad. Alexa just gives you the ability to issue the commands by voice which is quicker than opening up the app on your phone... and allows you to group devices from different manufactures. Without Alexa you can only group devices by the same manufacturer.