"I was able to test each 250w panel. They were producing at 37V and 9.1amps. Seemed very healthy. I'm curious if anyone can comment on the likely output of these to the batteries from the MPPT controller after the controller converts it to be used on my 12v system... Is there a simple equation for this?"
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if the panels are aimed at the sun at high noon, your 500w loses 10% from panel heating, so now at 450w. Line loss from panels to controller using proper wire should be under 3%, so call it 2% off the 450, so now at 439w input watts to controller. Say controller is 95% efficient doing 24-12, so lose 5% of 439 = 22w so output watts = 417w
Amps to battery (assuming no other loads) = output watts / batt v, so
it depends on batt v at the time what amps are. (there might be some more loss on the wires from controller to battery too, but we are pretending that is no loss for this example)
417/13v = 32 amps
417/13.5 = 31 amps
417/14 = 29.8 amps
With 500w of PWM aimed at high sun for full Isc (you get about the same amps to battery as the Isc and no loss for panel heating since Isc does not drop with heat (it goes up a bit)--expect about 31 amps
31 = 31. but as previously mentioned that is with panels aimed at high noon on 21 June in say, Texas.
You need another calculation for say, 9am with flat on roof panels on 21 Sep in, say Seattle, and another for 21 Dec.
All you can do is stick those panels up there and you get what the weatherman will allow that day for your latitude and calendar date. Looks like you got a very good deal on those 250s!