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Battery capacity is the Amp-hr [Ah] rating of a battery. Amp-hr is the rating on a battery that describes how long a battery can provide a certain amount of Amps to the system. For example, a 100Ah battery can provide 100 Amps to a system for 1 hour (100A x 1hr = 100Ah), or a 50Ah battery can provide 10 Amps to a system for 5 hours (10A x 5hr = 50Ah). Systems that are larger or draw more amperage will require a larger battery capacity (100 Amps for 5 hrs = 500Ah). Similarly, a system that will need to draw a large amount of amperage for a short time will also need a larger capacity (200 Amps for 3 hours = 600Ah) than a system that will need to draw a small amperage for a shorter period of time (50 Amps for 1 hour = 50Ah). The required battery capacity for your specific system will depend on the characteristics of your system and how long you will need your system to function off the battery alone.

The battery capacity is affected by the temperature that your battery will be working in. Lower temperatures cause a battery's capacity to decline while higher temperatures allow a battery's capacity to be higher. To account for this discrepancy in battery capacity and temperature, a temperature multiplier should be used to acquire a more accurate battery capacity for your system. Table 1 (below) shows a range of temperature multipliers for different batteries at different temperatures that can be useful in determining the best temperature multiplier for your battery.

Battery Capacity Table

When calculating the capacity of a battery, you will need to account the operating temperature of the battery (the operating temperature of the battery will affect the battery capacity). To do this, divide the Ah demand of the battery by the battery's depth of discharge (a property of the specific battery chosen for your system that will be listed on the spec sheet of your battery). Then multiply this number by the temperature multiplier for your battery at the nominal operating temperature. This will give the working capacity for your battery at the temperature it will be operating in. Table 1 shows the temperature multipliers for several different batteries at different temperatures.

Table 1. Battery Capacity Temperature Multipliers
Temp (°C) Zinc-Chloride Portable Sealed NiMH (2C) Iron-Electrode (0.1C) low rate extended life design Rechargeable Zinc/Alkaline/Manganese Dioxide 50-100mA Lithium Ion (1.07C) Lithium Iron Phosphate (0.5C) Lead Acid (0.05C)
-30°C - - - - - - 0.52
-20°C - - - - 0.51 - 0.64
-10°C 0.60 0.50 0.50 0.55 0.70 0.75 0.76
0°C 0.80 0.80 0.70 0.75 0.82 0.91 0.85
10°C 0.97 0.85 0.90 0.85 0.89 0.97 0.92
20°C 1.00 0.90 1.00 0.95 0.93 1.01 0.98
25°C 1 1 1 1 1 1 1
30°C 1.10 1.00 1.00 1.00 1.00 1.02 1.02
40°C 1.15 1.00 1.00 1.00 1.00 1.02 1.04

Temperature multipliers are used when calculating the correct battery size of a solar photovoltaic system. The temperature multiplier for the battery is multiplied by the depth of discharge (DoD) and amp-hour (Ah) demand to obtain the needed battery storage of your system. These values were obtained from 3rd and 4th Edition of Thomas B. Reddy's Battery Handbooks, [1], and [2]; a study done by Technische Universität München,[1] a study by Dr. René Groiß,[2] battery specifications from batteryspace.[3]

References

1. https://mediatum.ub.tum.de/doc/1355829/file.pdf
2. Dr. René Groiß, "The influence of temperature on the operation of batteries and other electrochemical energy storage systems" https://basytec.de/Literatur/Temperature.pdf
3. https://www.batteryspace.com/prod-specs/9055.pdf

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