Add some fluorescent lighting maybe 3 sets of quad units. Not very expensive and each tube is 40 watts x 12 = 360 watts per hour x 4 hrs per day. You should have some lights anyway so you get 12-14 hours per day. Put them on a timer 2 hrs in the a.m. and 2 in the early evening. I found a link for you re: hrs of sunlite in Abilene in December, you can input any month you like. Where I live on the 50 parallel (Winnipeg) and we only get 8 hours, 5 minutes, 22 seconds on Dec 21st. not enough lite to grow much of anything but moss in a heated greenhouse. You get 10 hrs + in Dec and Jan. a lot of it twilite and dawn.

Here is a link that might be useful: hours of sunlight in Abilene TX

I think it will depend on the size (N-S direction) of the GH and height of the attached shed. Basically it comes down to how much sun the GH will get when. You can do the calculations, or just go out to the spot in question and see where the shadows fall now (and if you remember during the other times of the year too).

I am guessing that you are choosing the N side of this shed because the door is on the S side or something else there? If it is something like that, might want to consider re-arranging the shed (door or whatever) and using the S side for the GH.