PhD Thesis - Cranfield University

Chapter 3
where 1Ah = 3600C. The Ah of a battery system which is sometimes denoted by the letter
‘C’ corresponding to the coulometric capacity, is specified under constant current discharge.
Ideally, the Ah rating for a specific battery would be the same for any discharge current.
However, in all practical battery systems, the actual capacity is dependent on the magnitude
of the discharge current. For example, a 20Ah battery could be rated to deliver 1A for 20
hours but instead would not be able to deliver 20A for a complete 1-hour duration. In
general, for most battery types, the higher the discharge current, the less the resultant Ah
measurement. This change is capacity is due to excess side reactions inside the battery cell.
To take the discharge current magnitude into account when specifying battery capacity, a
parameter termed as the ‘C rate’ is included when expressing of battery capacity. The
following equation provides a more complete definition of a battery capacity in relation to
the discharge current.
where,
I = kCn
( 3-4)
I is the charging or discharging current
C is the battery rated coulometric capacity in Ah
k is multiplication factor of C
n is the C rate (denoted as a subscript of the Capacity, C)
For instance, if a battery pack rated at 30Ah for 10hours is being discharged at a current of
15A, then following (3.4), this is expressed as 0.5C 10. Conversely, the C/10 rate of a battery
that is rated for 10Ah indicates that the discharging current is 1. If a 20Ah battery is
discharged at 4A, it is said to be discharging at 0.2C or at its C/5 or, “ C by five ” rate. Since
the value of C generally decreases as the C-rate increases, the constant discharge current
magnitude along with rated battery capacity must be stated together in order to accurately
describe the actual battery capacity and hence its usable energy.
3.7 Self Discharge
When left unused, batteries exhibit various levels of self-discharge over time. This
characteristic causes the energy stored in the battery to be wasted due to ion flow, which
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