"Battery capacity" is a measure (typically in Amp-hr) of the charge stored by the battery, and is determined by the mass of active material contained in the battery. The battery capacity represents the maximum amount of energy that can be extracted from the battery under certain specified conditions. However, the actual energy storage capabilities of the battery can vary significantly from the "nominal" rated capacity, as the battery capacity depends strongly on the age and past history of the battery, the charging or discharging regimes of the battery and the temperature.
The energy stored in a battery, called the battery capacity, is measured in either watt-hours (Wh), kilowatt-hours (kWh), or ampere-hours (Ahr). The most common measure of battery capacity is Ah, defined as the number of hours for which a battery can provide a current equal to the discharge rate at the nominal voltage of the battery. The unit of Ah is commonly used when working with battery systems as the battery voltage will vary throughout the charging or discharging cycle. The Wh capcity can be approximated from the Ahr capacity by multiplying the AH capcity by the nominal (or, if known, time average) battery voltage. A more accurate approach takes into account the variation of voltage by integrating the AH capcity x V(t) over the the time of the charging cycle. For example, a 12 volt battery with a capacity of 500 Ah battery allows energy storage of approximately 100 Ah x 12 V = 1,200 Wh or 1.2 KWh. However, becasue of the large impact from cahrging rates or temperatures, for parcitcal or accurate analysis, addditional informataion about the variation of battery capcity are also provided by battery manufacturers.
(INSERT CALCULATOR AND EQUATION FOR BATTERY CAPACITY)
In many types of batteries, the full energy stored in the battery cannot be withdrawn (in other words, the battery cannot be fully discharged) without causing serious, and often irreparable damage to the battery. The Depth of Discharge (DOD) of a battery determines the fraction of power that can be withdrawn from the battery. For example, if the DOD of a battery is given by the manufacturer as 25%, then only 25% of the battery capacity can be used by the load.
(INSERT CALCULATOR AND EQUATION FOR useable BATTERY CAPACITY and DOD.)
In addition to an overall DOD below which the battery should not be discharged, many battery manufacturies will specify a daily DOD, which determines that maximum power that can be withdrawn from a battery in a single day.
(INSERT CALCULATOR AND EQUATION FOR daily BATTERY CAPACITY and daily DOD.)
The charging/discharging rates affect the rated battery capacity. If the battery is being discharged very quickly (i.e., the discharge current is high), then the amount of energy that can be extracted from the battery is reduced and the battery capacity is lower. This is due to the fact the necessary components for the reaction to occur do not necessarily have enought time to either move to their necessary positions. The only a fraction of the total reactants are converted to other forms, and therefore the energy available is reduced. Alternately, is the battery is discharged at a very slow rate using a low current, more energy can be extracted from the battery and the battery capacity is higher. Therefore, the battery of capacity should include the charging/discharging rate. A common way of specifying battery capacity is to provide the battery capacity as a function of the time in which it takes to fully disscharge the battery (note that in practice the battery often cannot be fully discharged). The notation to specify battery capacity in this way is written as Cx, where x is the time in hours that it takes to discharge the battery. In the above table, C10 = xxx (also written as C10 = xxx) means that the battery capacity is xxx when the battery is discharged in 10 hours.
The temperature of a battery will also affect the energy that can be extracted from it. At higher temperatures, the battery capacity is typically higher than at lower temperatures. However, intentionally elevating battery temperature is not an effective method to increase battery capacity as this also decreases battery lifetime.
The age and history of the battery have a major impact on the capacity of a battery. Even when following manufacturers specifications on DOD, the battery capacity will stay at or close to its rated capacity for a limited number of charge/discharge cycles. The history of the battery has an additional impact on capacity in that if the battery has been taken below its maximum DOD, then battery capacity may be prematurely reduced and the rated number of charge/discharge cycles may not be available.