should i add another string of batteries

We typically run with 1-3 days of storage, with 50% maximum discharge (under normal usage) for longer battery life. For various reasons, with Lead Acid batteries, 2 days of storage and 50% maximum discharge usually works out as an "optimum choice".

So a 415 AH @ 48 volt battery bank would be optimum for cloudy day / overnight discharge of:

• 415 AH * 48 volts * 0.85 inverter eff * 1/2 days of storage * 0.50 maximum discharge = 4,233 Watt*Hours (storage per day)

Now--If a lot of your energy us used during the day (i.e., supplied directly by the solar panels)--And you can cut back to much less usage during bad weather--Then you may be OK with what you have. If you really want to use 8.4 kWH per day even during bad weather, and you want 2 days of storage--Then you could double the string.

Charging wise, we suggest 5% to 13% rate of charge, with 10% or more if you are full time off grid. You can go higher rate of charge (especially with AGM, but you tend to fill up the bank pretty quickly--And should use remote battery temperature sensor to help prevent battery over heating, especially if >13% rate of charge).

If you double the battery bank to 830 AH @ 48 volts with a 5% to 13% rate of charge from solar panels:

• 830 AH * 59 volt charging * 1/0.77 panel+controller derating * 0.05 rate of charge = 3,180 Watt array minimum
  
• 830 AH * 59 volt charging * 1/0.77 panel+controller derating * 0.10 rate of charge = 6,360 Watt array nominal
  
• 830 AH * 59 volt charging * 1/0.77 panel+controller derating * 0.13 rate of charge = 8,268 Watt array "cost effective" maximum

And then there is your energy usage and hours of sun per day (by season). Guessing at:
http://solarelectricityhandbook.com/solar-irradiance.html
\Your November through January sun is not great--So, if you wanted to (in average weather) to size the array for "break even" month of December, and wanted 8.4 kWH per day:

North Providence Rhode Island
Average Solar Insolation figures

Measured in kWh/m2/day onto a solar panel set at a 48° angle from Vertical:
(For best year-round performance)

Jan	Feb	Mar	Apr	May	Jun
3.33	3.97	4.61	4.67	4.93	5.04
Jul	Aug	Sep	Oct	Nov	Dec
5.04	5.01	4.76	4.31	3.24	2.98

If you want 8.4 kWH in deep winter:

• 8,400 WH per day * 1/0.52 off grid system eff * 1/2.98 hours of sun per day (ave December) = 5,421 Watt array minimum (December "break even" month)

So--If you double the battery bank, I would suggest a 6,360 Watt array (assuming you are full time off grid) with 10% rate of charge...

And if you look at the 9 month minimum (non-winter), it would produce:

• 6,360 Watt array * 0.52 off grid AC system eff * 3.97 Hours of Sun (February) = 13,130 Watt*Hours per day (~9 months of the year)

Because you have AGM batteries, your system may produce ~10-15% more energy (AGM batteries run >90% efficiency vs flooded cell at ~80% efficiency--The numbers I used above for 52% end to end efficiency with flooded cell batteries--just to be on the conservative side).

Anyway--That is how I rough out the math. Questions/corrections to my guesses?

-Bill