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Underestimating the size of the solar system to run what they want to run.  They don't do the math....
This example happens all the time:   
A customer wants to run a small window air conditioner, plus some lights and a refrigerator.
To do this they think they can buy a 2 panel (235 watts ea), 2 battery (105 ahr ea), 3000 watt inverter system.   They reason to themselves that a 3000 watt inverter will run their 1500 watt AC unit plus lights and a refrigerator. 
Unfortunately, it won’t work.
Here is the math....
  • The very small AC unit takes 1500 watts of electricity per hour and they want to run it 24 hours a day....for a total of 36,000 watts per day...not counting the lights and refrigerator.  
  • The inverter would run the AC unit, BUT... it doesn't produce the power.  
  • The solar panels produce a total of 470 watts per hour of direct sun.  The sun only shines directly on the solar panels (direct sun) approximately 6-7 hours a day during the summer (3-4 hrs avg per day during the winter)...producing a total  of  2,800 watts of energy per day during the summer.  
    • We won't mention that ALL solar panels actually produce only about 85% of their rated power, due to electrical loss and the way the solar panel manufacturers calculate the wattage of the panels.  And then there is dust, bird poop, pollution particles, cloudy days, etc. which also affect the actual electrical production of the solar panels.  
    • Additionally, the inverter, along with the charge controller(s), use energy themselves. Usually about 2%--5% of the rated power of the device.     
  • The batteries hold approximately 1000 watts of electricity each for a combined 2000 watts of electricity.  You can use the electricity out of the batteries fast or slow... but, there is only so much electricity in them.  So, the batteries would last approximately 1 hour before being depleted.  (And then there is the 50% rule on using AGM or lead acid batteries... if you use/deplete 50% or more of the energy in the battery... you shorten the life of the battery.)
Bottom line... the system they want would not run their AC unit.  They actually would need a much larger system, one that produces not only enough energy to run the AC during the day, but enough energy to charge up the batteries as well.        
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