A year ago I asked the question how you replace a router... I have (had) an ER605v1 and I wanted to upgrade to an ER7602.

The majority of the responses were "plug it in and forget the old one... all your configuration is stored on the controller!"

I'm leaving this here as a cautionary note -

Depending on your setup, plugging the new device blindly into your network may make you want to run the router through an industrial shredder. I'm sure it works like magic if you've never done anything except use the router defaults.  Life would be much easier if TP-Link didn't start a DHCP server by default.

My advice/sequence of steps that works without screwing up all your devices (which I already did once.) -

1. Make sure you have a static IP set on the controller and plug the controller and a laptop into the new router.  Do not plug in the rest of your LAN.  
2. Configure your laptop IP to be on the same subnet as the controller.
3. Open the controller webpage on your laptop.
4. Open the WAN settings and make sure the right model of router is set. (It will complain if the new model doesn't match the old one.)
5. NOW adopt the new router. This seems to take longer than it should... for me, it was 5-10 minutes. 
6. Once the new router shows as adopted, check its IP through the controller interface and make sure it shows the IP of your old router. 
7. If the IP address of the router doesn't match what it should be, force a provision (select new router from devices, click the config tab, expand the "manage" section, and click Force Provision).
8. Wait for it to reboot or go brain dead for a few minutes, then check the IP again.  It should eventually be correct.
9. Unplug power from the router and controller and plug them back into your network, then power them back up.
10.  Wait 10 minutes while things sort themselves out.  Hopefully you're done.

Take it or leave it, that's the process I'm going to follow from now on.  The mistakes made along the way were painful.

Best wishes,

John