Check your TV first before assuming, some provide power only on startup, some only in Firmware upgrade mode, and some all the time. Just plug a mobile external hard drive (2.5", with no external power supply) in and listen for it to spin up, and keep spinning for a minute or so. If the ports power is low, it would either click, spin then go off, or do nothing. If it provides no power it will not do anything.
If yours provides low or no power, just go on eBay or some other website and buy a cheap usb power adapter, the very cheap iPhone adapters (like $3 should work perfectly, they don't work on iPhone, but perfect for anything else). You may also be able to use something like the older Motorola adapters the use mini USB connectors, that way the cord is included and built-in.