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A Master Electrician here to help. I am a double qualified; USA & UK electrician. Please give me a moment to formulate a reply.
Perhaps the biggest unknown here is the degree of insulation. Also is this just conventional electric heat ?.
Assume typical insulation and conventional electric heat.
The barn would have some activity in the winter such as a garage.
Where to hot air would escape.
OK, I will try to approach this a little differently. Just let me know if you cant answer this. I use 2200 gal of propane for heat, hot water and range top. I also use 11,000 kW-hr per year for lights etc. I would like to build a 30ft x 80ft gable end barn and heat it. I would like to size a solar PV array to eliminate all my anticipated energy needs. How many kW-hrs should this solar array produce? Give me a range. Your answer will not significantly affect my decision because I am oversizing the array. I would just like to bounce this off of an expert. Will you answer this? huh?
Thanks. The news is not so bad. I am building a 60kW system and I want to backup my claim that it is for personal use and not commercial. Using your high end estimate of 200 kW per day or (200 kW-hrs per day)(365 days) = 73,000 kW-hrs per year. This is approx what the 60kW array will produce in a year. The ROI is a different matter.
PS, I am using your 200kW per day as an annual average and not a winter avg. Is the 200kW a winter avg or anual avg?