Begin by calculating the required load backup in Ah. The formulas are as follows:
• Load (A) x backup time (hours) = Ah
• Load (W/V) x backup time (hours) = Ah
Following are a couple of examples of how to calculate the load in Ah:
Example 1: 6A continuous load at 24VDC for 8 hours
6A x 8hours = 48Ah @ 24VDC
Example 2: 15W continuous load at 12VDC for 24 hours
15W/12V x 24hours = 30Ah @ 12VDC
Some other considerations for load calculations:
• Loads at non-system voltage to include inefficiencies (inverters, DC/DC converters)
• Intermittent loads should be averaged
• Future expansion considerations
• Factoring in uncertainty on run-time or power-draw (radios, pumps, lighting)
• Consider inrush current for AC loads, making sure inverter is properly sized to handle
The battery capacity calculations include derates for the battery.
Derates are factors that reduce the power rating of a device and are deducted from the total battery capacity. The most common battery derates are temperature and age. A common age derate is 20%. For temperature derate, refer to the manufacturer. The below temperature derate chart is for Deka Gel batteries.
Example:
100Ah at 25°C. Operating temperature 0°C, with age derate of 20%.
From the chart, the temperature derate is ~18%. The calculation looks like this: 100Ah x 0.8 x 0.82 = 65.6Ah. This is the new derated battery capacity to be used in the system sizing. The battery capacity is reduced with higher discharge rates. It is important to use the correct capacity based on the backup time. The below chart shows various battery capacities based on the discharge rate.
The formula for determining the required battery capacity is as follows:
[Load (Ah) / (Battery DOD [%])] * (1+Battery Derates [%]) = Required Battery Capacity
Following are a couple of examples of how to calculate the required battery capacity:
Example 1: 6A continuous load at 24VDC for 8 hours
6A x 8hours = 48Ah @ 24VDC
(48Ah / 80% DOD) * (1+20% [temperature derate]) = 72Ah
8G27 is rated 78.4Ah @ 8 hour rate
Example 2: 15W continuous load at 12VDC for 24 hours
15W/12V x 24hours = 30Ah @ 12VDC
(30Ah / 50% DOD) * (1+40% [temperature derate]) = 84Ah
8G27 is rated 88.1Ah @ 24 hour rate
To calculate the desired current charge, you must start with the battery recharge time.
The formula for determining the battery recharge time is as follows:
Battery Discharged Capacity (Ah) / (Charger Output [A] – Load [A]) = Estimated Recharge Time (hours)
Following are a couple of examples of how to calculate the battery recharge time:
Example 1: 6A continuous load at 24VDC for 8 hours
6A x 8hours = 48Ah @ 24VDC
(48Ah / 80% DOD) * (1+20% [temperature derate]) = 72Ah
8G27 is rated 78.4Ah @ 8 hour rate
78.4Ah * 80% DOD = 62.7Ah / (15A [Battery Charger Output] – 6A) = 7 hours
Example 2: 15W continuous load at 12VDC for 24 hours
15W/12V x 24hours = 30Ah @ 12VDC
(30Ah / 50% DOD) * (1+40% [temperature derate]) = 84Ah
8G27 is rated 88.1Ah @ 24 hour rate
88.1Ah * 50% DOD = 44.1Ah / (15A [Battery Charger Output] – 1.25A) = 3.2 hours
Alternate:
88.1Ah * 50% DOD = 44.1Ah / (5A [Battery Charger Output] – 1.25A) = 12 hours
Considerations:
• Should be no quicker than 3 hours. Anything faster than a 3 hour recharge rate could damage lead acid batteries, consult with the battery manufacturer.
• Typically 8-24 hours, but could be longer.
• Remember to subtract the load from the charger output.
• Should also check the recharge rate without the load.
