I can only related to you using my line of thinking.
What you do, is entirely up to you.
"How to find the size of the battery ie., based on load or based on the solar insolation?"
Based on load.
"If I have a load requirement of 15 kWh's then what can be the size of the battery?"
Lets assume the battery bank to be at 48 volts nominal.
15,000 / 48 = 312 amphours absolute bare minimum.
But if it were me and I was living off grid, I would multiply that by a factor of no less than 5 for a total of 1,562 amphours at the 20 hour rate.
Lets also assume that the PV array is to be 48 volts nominal and it is to be fixed at an angle equal to latitude facing solar south in the southern half of Arizona where it might see 6 to 7 hours of equivalent full rated power output averaged out annually.
15,000 / 6 = 2,500 watt PV array absolute bare minimum if you want to completely recharge the batteries as soon as possible. You may want to add more.
All of this is based on 15 kWh's per 24 hours.
It would all change if it were based on 15 kWh's over 30 days.
Simply divide 15,000 by 30 days and follow the solution above. Or you own solution. Its up to you of course.
If the PV array is to be mounted in a different place than Arizona, it might be listed here -
http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/atlas/- if it is just recompute.
Of course you know, all of this really depends on uh, how tall a stack o jack you got. No what I mean?
Like the saying goes, "money talks and horsepucky walks."
Wow, I never though about it until I saw it in writting but thats a really funny saying. Walking horsepucky?
That reminds me of the time I was visiting the Smithsonian Institute in Washington DC and there happen to be a display of paintings, I don't remember the artists name, but they were of a western theme and one in particular was of a group of people riding horses early on a cold morning and, would you believe the artist actually painted steam rising from what could only be a fresh pile of horsepucky? Talk about realism. I thought to myself, "now if that painting wasn't roped off so people couldn't get to it, I bet some would actually touch it and smell their fingers just to satisfy their curiosty." I would have. That reminds me of another time when I was still in high school and it was the first day of the 10th grade. I was late for home room and there was this fella standing in the door way, uh, maybe I should save that one for another time. Anyway, I hope at least some of this helps you out. About the math I mean.