20kwh battery used over 24hr period. = 833w/hr avg
if you remove the "5hrs" the sun shines 20kwh/19h = 1052w
20kwh recharged in 5hrs of sun is 4000 pv watts. charging the battery while useing 830w from above 4800w PV. 25% PV loss due to heat/dust etc 4800x1.25 = 6000w pv