How many solar panels

I believe you are in the Deoghar, JH, India area?

For 20 amp MPPT charge controller, the largest "cost effective" solar array would be around:

• 20 amps * 59 volts charging 1/0.77 panel+controller efficiency = 1,532 Watt array "cost effective" maximum

Next, the battery bank--We suggest 5% to 13% rate of charge--For a weekend/emergency/seasonal system, 5% can work OK. If daily use, look at 10% or greater rate of charge. With a 20 Amp charge controller:

• 20 amps * 1/0.05 rate of charge = 400 AH @ 48 volts largest suggested battery bank
  
• 20 amps * 1/0.10 rate of charge = 200 AH @ 48 volts nominal bank
  
• 20 amps * 1/0.13 rate of charge = 154 AH @ 48 volts smallest battery bank
  

Now, you need to look at the Vmp of the solar panel... For a 48 volt lead acid battery bank, you need ~72 volt minimum solar array Vmp voltage for proper charging. A typical 250 Watt solar array, they tend to run around Vmp~30 volts. So you would need a minimum of 3x panels in series (Vmp-array ~ 90 volts). And your array would be:

• 1,532 Watt array / 250 Watts per panel = 6.1 panels ~ 6 panels

So, you would need two strings of 3 panels in series, then connect those two strings in parallel.

Note--You need to read the specifications of the MPPT charge controller, they have both a minimum and maximum Vmp-array voltages. In the US, our "higher end" MPPT controllers typically have a working Vmp-array maximum of around 100 VDC (Vmp rises as temperatures fall, so cold climates you have to "adjust" the maximum Voc voltage open circuit up) for a MPPT controller with a Voc input rating of ~140-150 VDC maximum input voltage.

-Bill

Remember that "12 volt panels" in our case usually have Vmp in the range of 17.5 to 19.0 volts (36 cell panels):

• 59 volts charging * 42 AH * 1/0.77 panel+controller eff * 0.05 rate of charge = 161 Watt minimum
  
• 59 volts charging * 42 AH * 1/0.77 panel+controller eff * 0.10 rate of charge = 322 Watt nominal
  
• 59 volts charging * 42 AH * 1/0.77 panel+controller eff * 0.13 rate of charge =418 Watt "cost effective" maximum

You would need a minimum of 4x "12 volt" panels in series:

• 150 Watt * 4 panels in series = 600 Watt array

That is a bit large for your battery bank... With some types/brands of charge controllers, too high of charging current can cause the battery bank to "over voltage". Monitor your charging to make sure you charge controller + battery bank stay withing proper charging voltages.

Do you really need 48 volt battery bank? For a smaller system, a 12 or 24 volt battery bank may be a better choice. Instead of 4x 42 AH 12 volt batteries, you could use 2x 6 volt @ ~200 AH golf cart batteries. May be less expensive and golf cart (flooded cell) batteries are pretty forgiving (and fewer cells to check water levels, less wiring, but heavier copper wiring). Plus you can find more inverter and charge controller options.

-Bill