Portal Stories: Mel is a mod for Portal 2 that has been three years in the making. With a whole new story, new gear and new missions, it will hopefully feel like a whole new Portal, only it's one you don't need to pay for.
Well, kinda. You'll need a copy of Portal 2 already, since this is a mod. But if you've got that - and really, who doesn't by now? - you're good to go.
The story does the old "same place/sequence of events from a different person's perspective", as you take control of Mel, a survivor of the "Aperture: Science Innovators Short-Term Relaxation Vault". There will be over 20 maps, custom dialogue and visuals and even a prototype portal gun from the 1970s.
It will (hopefully) be out in early 2015.
Note that the character of Mel was originally supposed to not just be in Valve's own Portal 2, but be the main character. She ended up being scrapped entirely, but hey, an appearance here is better than nothing!
Portal Stories: Mel [Steam Greenlight]