By default WOL doesn’t work over the internet AFAIK. The wikipedia page mentions it a bit en.wikipedia.org/wiki/Wake-on-LAN#Subnet_directed…

Like others said you may be able to get that going with a VPN or anything VPN-like that allows broadcasts between connected systems. Or if your motherboard supports IPMI / IMM you should be able to connect to the system & perform power functions that way.

In my case my motherboard doesn’t have those sort of management functions so in the end I settled on logging into my router remotely & initiated WOL through there. That could be another option for you if your network router is capable of sending WOL packets to the LAN.