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There are certain basic battery terminology that tends to be misunderstood in practice. These terms commonly refers to the condition of the battery as well as capacity of the battery:
State of Charge (SOC) %
SOC defines the present battery capacity as a percentage of maximum capacity. SOC is generally calculated using current integration to determine the change in battery capacity over time.
Depth of Discharge (DOD) %
This expresses the percentage of battery capacity that has been discharged expressed as a percentage of maximum capacity. A discharge to at least 80 % DOD is referred to as a deep discharge.
Terminal Voltage (V)
This is the voltage between the battery terminals with load applied. Terminal voltage varies with SOC and discharge/charge current.
Open Circuit Voltage (V)
This is the voltage between the battery terminals with no load applied. The open-circuit voltage depends on the battery state of charge (SOC), increasing with state of charge.
Internal Resistance
This is the resistance within the battery, generally different for charging and discharging, also dependent on the battery state of charge. As internal resistance increases, the battery efficiency decreases and thermal stability is reduced as more of the charging energy is converted into heat.
Consider the battery circuit above, where E is the open circuit voltage, I is the load current flowing in amps, V is the terminal voltage across a load resistance $R_L$, r is the battery internal resistance
Power input to battery is given by:
$$P_i = IE$$
$$E = I (R+r)$$
$$P_i = I *I(R+r) = I^2(R+r)$$
power output:
$$P_o = IV = I*IR = I^2R$$
Battery Efficiency $$Eff = {\frac{P_o}{P_i}} = {\frac{I^2R}{ I^2(R+r)}} = {\frac{R}{(R+r)}}$$
As can be seen, the more the internal resistance of the battery, the less efficient the battery becomes due to increasing conversion of useful battery energy to heat.
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C and E – Rates
In describing batteries, discharge current is often expressed as a C-rate in order to normalize against battery capacity, which is often very different between batteries. A C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity.
C – Rate can be expressed as:
$$I = M * C_n $$
Where:
I = Discharge current in Amps
C = Numerical value of rated capacity of the battery in ampere – hours (AH)
n = Time in hours for which rated capacity of battery is declared
M = Multiple or fraction of C
Consider a battery rated at 200AH with a discharge current of 10Amps, the C rate is calculated as:
M = I/Cn = 10/200 = 1/20 = 0.05C or C/20 rate
E’’ Rate
An E-rate describes the discharge power. A 1E rate is the discharge power to discharge the entire battery in 1 hour. Just like the C rate, the E rate can be expressed as:
$$P = M * E_n $$
Where:
I = Discharge current in Amps
E = Numerical value of rated power of the battery in watt – hours (Wh)
n = Time in hours at which the battery was rated
M = Multiple or fraction of C
Consider a battery with rated at 1200mWh with rated power of 600mW, the E rate is calculated as :
M = P/En = 600mW/1200mW = 0.5E or E/2 rate
