Open the project in CC 2015. Make an HD comp for each SD comp. Nest the old comps inside the new ones. Apply the Detail Preservbing Upscale effect to the nested comps, scale them up to taste.
Depending on where essential visual information is located in the old comps, theis may or may not work well. But it IS easy.
This is one way and what I would try first.
If that doesn't quite do it for you, there's also a comp resize script that comes with AE. That way, you can get a bit more involved and adjust things.
I would use the resize script. This will keep allow you to have more flexibility converting them to HD. You will have to resize or replace any pixel based assets like photos and videos or add the detail preserving upscale to those layers to help with the quality issues you run into when resizing video.