Need Help With System Design

At this point, 4,000 Watt*Hours per year. A full size energy star fridge, LED Lighting, a "solar friendly well pump", LED TV, Laptop, Cell phone charging, clothes washer (during good sun or with backup genset).

The well pump--Standard well pumps with induction motors (Franklin, etc.) are not very efficient, and (usually) have high starting surge current.
 
Solar "Friendly" well pumps are typically Permanent Magnet 3 phase motors with a "variable frequency drive" (a.k.a. a variable frequency inverter). The PM motors are much more efficient and the VFDs are "soft start" and can vary pump RPM based on water needs and available energy (some pumps can be connected directly to a solar array without any batteries or generators--The VFD takes available solar energy and modulates the pump RPM base on available solar power).

These solar friendly pumps are not cheap--But make designing and running a solar power system much easier. Grundfos pumps is a high end pump mfg. And their SQF Series are the most flexible in-well pumps. Reliable, lots of options, and no surge current over running Watts. The SQF is solar panel, DC, and AC power compatible. From our host, NAZ (Northern Arizona Wind & Solar):

Product Documents

There are other alternatives. A "slow pump" (lower power) to cistern, then use a pressure pump from cistern to house (can even be an RV style pump for cabins and outbuildings). In some areas, off grid homes may have building regulations that require water storage tank(s) and fire pumps (some areas in California require fire water/pumps).

OK... The math & modeling. The battery bank assume that you have 2 days of "no sun" and discharge to 50% of capacity (longer battery life). This is usually the sizing for Lead Acid/AGM batteries. If you use Li Ion, smaller AH battery bank can make sense.

For cold climates, Lead Acid are nice... They work down to 0F pretty nicely (temporary loss of capacity when cold--Can heat/insulated box to keep warm). Li Ion batteries really need to be around 50F or warmer to cycle. Cold Li Ion batteries cannot charge without being damaged.

• 4,000 Watt*Hours per day * 1/0.85 AC inverter eff * 2 days storage * 1/0.50 max planned discharge * 1/48 volt bank = 392 AH @ 48 VDC minimum suggested
  

The minimum suggested Lead Acid battery for an AC inverter is 100 AH @ 48 volts per 1,000 Watts of inverter. Your 4,400 Watt inverter, would suggest 440 AH @ 48 VDC minimum (2x larger bank is not bad if you have heavier loads or ~880 AH @ 48 volts).

Now sizing the solar array... Firs based on battery bank capacity and recommended charging. 10-13% minimum rate of charge works well for Lead Acid when used for full time off grid homes. Li Ion batteries can take much higher rates (charge faster/more efficiently/less time than Lead Acid).

• 440 AH * 58 volts charging * 1/0.77 panel+controller deratings * 0.10 rate of charge = 3,314 Watt array minimum off grid array
• 440 AH * 58 volts charging * 1/0.77 panel+controller deratings * 0.13 rate of charge = 4,308 Watt array nominal off grid array

Of course, if you choose a 2x larger AC inverter with a 2x larger AH battery bank, then need more solar panels. Or spend money on a "solar friendly" well pump and don't go with the larger inverter and/or battery bank.

Next is sizing the array for the amount of sun you get... Fixed array facing south:
http://www.solarelectricityhandbook.com/solar-irradiance.html

Coeur d'Alene Idaho
Average Solar Insolation figures

Measured in kWh/m2/day onto a solar panel set at a 42° angle:
(For best year-round performance)

Jan	Feb	Mar	Apr	May	Jun
2.12	3.30	4.37	5.04	5.24	5.53
Jul	Aug	Sep	Oct	Nov	Dec
6.07	5.88	5.11	3.71	2.33	1.88

For the three months of winter--It appears you may not have a lot of sun... If we design for 9 months of sun, and assume less power/more generator runtime in winter... Pick February at 3.30 hours of sun per day as "break even":

• 4,000 WH per day * 1/0.52 off grid system eff * 1/3.30 hours of sun per day (Feb) =  2,331 Watt array "Feb break even" array

If you assume that you only use 50% to 65% of predicted harvested solar power:

• 2,331 Watt array (Feb break even) * 1/0.50 "solar fudge factor" = 4,661 Watt array (to carry better through winter, support additional loads when need, and reduce genset runtime).

So it looks like you can "justify" a 4,308 to 4,661 Watt array if you are living full time in the house.

Note that I am using 4,661 numbers to avoid round off errors and so you can follow the math. In reality, solar "math" is only accurate to about 10% (i.e., 4,661 +/- 466 Watt array). Don't feel like you have to use a 440 AH battery bank if you are using 415 AH batteries...

In general, batteries are expensive and have a (relatively) short life (5-7 years maybe for "good quality" Lead Acid. 15+ years for "forklift" batteries, etc.). Batteries are also the easiest to "murder" (typically through under charging, over discharging, poor maintenance).

Generally, the #1 place to put "extra money" is the solar array. Solar panels are "cheap" and last 20+ years. And a well charged battery bank is a "happy" battery bank.

The next place to put your money is, possibly, Lithium Ion batteries (LiFePO4 typically). More efficient, charge faster (large array in short periods of sunlight). However they tend to be more expensive and you are a bit more on the "bleeding edge" of technology. Li Ion batteries need a BMS (battery monitor system) to ensure your expensive batteries are operating withing voltage/state of charge/temperature/current specifications. Lead Acid batteries tend to be cheap(er) and more forgiving. Li Ion batteries, done right, have made for many happy users.

Nothing above is "written in stone"... Just a starting point to see how well this will work for you and figure out where your money is going.

The idea is to get the requirements documented and everything planned out.

-Bill