Week 7 State of charge estimation
Coulomb counting is a technique used to track the State of Charge of a battery pack. The name “coulomb” was given in honor of Charles-Augustin de Coulomb (1736–1806) who is best known for developing Coulomb’s law. It works by integrating the active flowing current (measured in amps) over time to derive the total sum of energy entering or leaving the battery pack. This produces a capacity that is typically measured in Amp-hours.
The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. The unit is the amount of electric charge (symbol: Q or q) transported by a constant electric current of one ampere in one second
Figure 1: Principle of a fuel gauge based on coulomb counting.
A circuit measures the in-and-out flowing energy; the stored energy represents state-of-charge. One coulomb per second is one ampere (1A).
The Coulomb counting method measures the discharging current of a battery and integrates the discharging current over time in order to estimate SOC, which is estimated from the discharging current. SOC is calculated by the following equation:
But there are several factors that affect the accuracy of Coulomb counting method including temperature, battery history, discharge current, and cycle life.
To improve the Coulomb counting method, a new technique called modified Coulomb counting method is proposed. The modified Coulomb counting method uses the corrected current to improve the accuracy of estimation.
The corrected current is the function of discharging current. There is a quadratic relationship between the corrected current and discharging current of battery. By practice of experimental data, corrected current is calculated by the following form:
where , K1 and K2 are constant values obtained from the practice experimental data.
In modified Coulomb counting method, SOC is calculated by the following equation:
The experimental results show that the accuracy of the modified Coulomb counting method is superior to the conventional Coulomb counting method.
Battery SoC & their Estimation
SoC(t) =Battery State of Charge at time instant ‘t’ in (%)
i(t) = Battery current at time instant
µn = Nominal capacity of the battery in ( Ah)
∆t = time step time
Example Calculation
If a 12v battery capacity of 500Ah (initial full charge) that is supplying a load of 0.6 ohm. The State of Charge of the battery after 3 hours is calculated as following;
Given; V = 12v, µn = 500Ah, time (∆t )= 3 hours
Battery is initially full charge = SoC(t-1) = 100%
Load current = i(t) = V/R = 12/0.6 = 20A
= 100 +( -20/500) x 3 x 100
= 100 – 6000/500
= 100 – 12 = 88%
The graph shows measuring the cell voltage during "rest periods"can improve the accuracy of the estimates of the SOC in Lithium batteries. Cell discharging capacity 100Ah after 15 hours at constant current.