http://jgdarden.com/batteryfaq/carfaq7.htm#backup
7.9. How Do I Size The Components For Backup AC Power?
For AC backup power, here are the basic steps for sizing the deep cycle battery bank, inverter, AC battery bank charger and generator based on your AC power requirements. Deep Cycle battery bank capacity sizing is based on power requirements, inverter efficiency, wiring power loss, discharge rate (or Peukert Effect), electrolyte temperature, and desired average Depth-of-Discharge. DC to AC Power Inverters has a simple and easy to use battery capacity calculator at
http://www.dcacpowerinverters.com/faq.htm#22. Please note that microwave ovens can have very large loads and might not be suitable for inverter or battery operation.
7.9.1. Calculate the cumulative daily AC load in amps hours (AH) at 120 VAC. This will require determining how much current an appliance uses and for how long times the "duty cycle" (the amount of time the appliance is on during that time period). The label of the electrical appliance will have the amount of power and the voltage that the appliance uses. Power is expressed either in watts or in amps. If wattage is given, divide it by the voltage to convert to the number of amps.
For example:
a. Two 60 watt lights that you use continuously for four hours, the calculation would be 60 watts/120 volts = .5 amps and .5 amps x 4 hours x 2 lights = 4 Amp Hours @ 120 VAC.
b. A 200 watt refrigerator that is on for 24 hours with a 25% duty cycle, the calculation would be 200 watts / 120 volts = 1.67 amps and 1.67 amps x 24 hours x 25% duty cycle = 10 Amp Hours @ 120 VAC.
c. A five amp power drill that you use 15 seconds at a time for 25 times, the calculation would be 5 amps x 15 seconds/60 seconds/60 minutes x 25 times = .52 Amp Hours @ 120 VAC.
d. A 10 amp sump pump that is on 24 hours and has a 50% duty cycle, the calculation would be 10 amps x 24 hours x 50% duty cycle = 120 Amp Hours @ 120 VAC.
The total daily usage of these four appliances would be 4 AH + 10 AH + .5 AH + 120 AH = 134.5 Amp Hours @ 120 VAC per day.
7.9.2. Depending on the efficiency of the inverter and the power loss in the wiring, it takes between 12 and 14 amps of 12 VDC power to produce one amp of 120 VAC power or 24 to 28 amps to produce one amp of 240 VAC. Using the above example in the worst case, the usage would be 14 x 134.5 AH = 1883.3 Amp Hours per day @ 12 VDC.
7.9.3. Depending on the average load on the battery bank, the total daily usage may have to be adjusted due to the Peukert Effect. Deep cycle batteries are normally rated by the fully charged capacity divided by the number of hours of discharge it take to drop to 10.5 VDC. A very common rate is over a 20 hour period and is expressed as "C/20". In the example above, 1883.3 AH are being consumed in a 24 hour period which is a slightly lower rate than over a twenty hour period, so we could probably decrease the daily usage by 10% or 1883.3 AH x .9 = 1695 AH per day. If all of this power were consumed over six hour period, you would probably need to increase the daily usage by approximately 25%.
7.9.4. Depending on the temperature of the battery electrolyte, the usage might also have to adjusted. The example above assumes 80 degrees F. If your battery bank was operating at 60 degrees F then you would have to increase the usage by 10% and at 32 degrees F, by 20%. Let us assume the batteries are in a heated area at 70 degrees, so you would increase the daily usage by 5% or 1695 AH x 105% = 1780 AH per day.
7.9.5. Depending how many discharge/charge cycles you want your battery bank to last, you will need to increase the usage. Let's assume that you are fully recharging the battery bank daily and using "low end" inexpensive deep cycle batteries that when fully discharged (or 100% average Depth-of-Discharge) will last 50 cycles, at 80% average DoD (or 20% State-of-Charge) will last 200 cycles and at 50% average DoD will last 500 cycles. In this example, for 100% average DoD, you would require a battery bank with a capacity of 1780 AH to provide for 1780 AH of daily usage, at 80% DoD (1780 AH / 80% = 2225 AH), and at 50% DoD (1780 AH / 50% = 3560 AH). However, you would have to replace the smaller, less expensive battery bank every 50 cycles.
You can determine the optimum battery bank size by multiplying the number of cycles time the total amp hour capacity divided into the cost. For a simple example, let's assume that a 225 Amp Hour (C/20) 12-volt deep cycle battery costs $85. At 100% DoD, 1750 AH / 225 AH per battery = 8 batteries x $85 per battery = $680 total cost and 50 cycles x 1780 AH = 89,000 total AH. So $680 / 89,000 = .764 cents per amp hour. At 80% DoD, the calculation would be 2225 AH / 225 AH per battery = 10 batteries x $85 per battery = $850 total cost and 200 cycles x 2225 AH = 445,000 total AH. So $850 / 445,000 = .191 cents per amp hour. At 50% DoD, the computation would be 3560 AH / 225 AH per battery = 16 batteries and 16 batteries x $85 per battery = $1360 total cost and 500 cycles x 3560 AH = 1,780,000 total AH. So $1360 / 1,780,000 = .076 cents per amp hour. In this example, a larger, more expensive battery bank with a lower average 50% DoD will cost approximately one tenth the cost of fully discharging the battery bank (100% DoD) every cycle. This example does not take into consideration the additional maintenance, cabling cost, cost of money, etc. that would be used in a Total Cost of Ownership determination.
7.9.6. Once you have determined your daily capacity, then you need to determine how many hours or days you want to run using your battery bank before you recharge your batteries and decrease or increase the size of the battery bank accordingly. Please see Section 9 for more information on charging.
7.9.7. To size the inverter (or inverter portion of an inverter charger using the example above, calculate the worst case load (with all the appliance on at once) which is (60 watts x 2 lights) + 200 watts + (5 amps x 120 volts) + (10 amps x 120 volts) = 2120 watts @ 120 VAC. Be sure to consider the start surge power requirement of up to five time the run current with large inductive starting loads, such as microwave ovens, motors and transformers. Some "square wave" or "modified" sine wave inverters are not capable of providing the power to run some motors, compressors or other electronic or electrical appliances. In these cases, a "true" sine wave inverter must be used. For more information on power inverters, please see Don Rows' Frequently Asked Questions about Power Inverters.
7.9.8. To size the battery charger (or charger portion of an inverter charger), you will need the output to be at least 12% of the battery capacity used to fully recharge the batteries within 24 hours. Using the example above, you would need at least a 214 amp charger to replace 1780 AH in 24 hours.
7.9.9. To size an AC generator, using the example above without recharging the battery bank, the worst case load (with all the appliance on at the same time) is (60 watts x 2 lights) + 200 watts + (5 amps x 120 volts) + (10 amps x 120 volts) = 2120 watts @ 120 VAC. You would also need to consider the surge power requirement up to five times the run load. If you are using motors, take into consideration their peak starting current. If the batteries need to recharged the batteries in addition to using the appliances, add 214 amps/12 DC amps per AC amp = 17.8 amps @ 120 VAC and 17.8 amps x 120 volts = 2140 watts @ 120 VAC to power the battery charger. So, to power both the load and recharge the batteries, a generator with a capacity of 8000 to 12000 watts @ 120 VAC in required depending on the surge of the pump motor and battery charger.
As can be seen from this example, using just battery backup for one day for AC power with a heavy load can become very expensive, so that is why most "grid" or commercial AC power backup systems is an AC generator, combination of batteries and AC generator, or combination of battery and solar power with AC generator backup.