Week 7 State of charge estimation
QUESTION:- What is coulomb counting? How BMS implements coulomb counting for SOC estimation?
Coulomb Counting:-
Coulomb counting is a technique used to track the State of Charge of a battery pack. 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.
Perhaps the most important function of the Battery Management System (BMS) is to provide an estimate of the SoC & for that Coloumb Counting is necessary. In-vehicle applications, SoC acts as a constraint on how the energy management system optimizes the overall performance in terms of fuel economy and drivability. Knowing the SoC is very important in determining the best operating strategy of the vehicle.
To know the SOC, the following primary Coulomb Counting method is used for almost every battery.
Coulomb Counting Method:-
The Coulomb counting method measures the discharging current of a battery and integrates the discharging current over time in order to estimate SOC. Coulomb counting method is done to estimate the `SOC(t)`, which is estimated from the discharging current,`I(t)` , and previously estimated SOC values, `SOC(t-1)`. SOC is calculated by the following equation:
`SOC(t) = SOC(t-1) + ((I(t))/Q_n)*Deltat`
But the classic Coulomb counting method (current integration)requires an initial condition which, if given incorrectly, results in incorrect estimation by the same amount. The only time that the correct SoC is known is when the battery is fully charged or discharged. There are several more factors that affect the accuracy of the Coulomb counting method including temperature, battery history, discharge current, and cycle life.
Modified Coulomb Counting Method:-
To improve the Coulomb counting method, a new technique called the 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 the discharging current of the battery. By the practice of experimental data, the corrected current is calculated by the following form:
`I_c(t)=k_2I(t)^2 + k_1I(t) + k_0`
where, `k_2,k_1 and k_0` are constant values obtained from the practice experimental data.
In the modified Coulomb counting method, SOC is calculated by the following equation:
`SOC(t) = SOC(t-1) + ((I_c(t))/Q_n)*Deltat`
The experimental results show that the accuracy of the modified Coulomb counting method is superior to the conventional Coulomb counting method.
Implementation in BMS:-
Coulomb counting method can be implanted in BMS with a suitable algorithm. The following chart is giving a general idea, how SOC estimation is going to work. This algorithm can be implemented with the state machine in Simulink, which can be further uploaded in the flash memory of BMS hardware using the code generation option.
Below is the basic proposed flow chart for SOC estimation.
Fig:-Flowchart of the proposed algorithm
Flow chart Explain:
A. Charge Mode-
In this mode, the coulomb counter is presented by `Q_(gai n ed)` as expressed in the following, which represents the quantity of charges accumulated during `tau`.
So the variation of the state of charge gained in this same operating period is obtained by the following relation 
By cumulating the previous state of charge indication and the obtained one we can have the instantaneous value of SOC:
Knowing the relationship indicated in the following relation the value of depth of discharge DOD is updated in every charging operation in order to get it back every switching to discharging mode.
.....................(1)
B. Discharge Mode-
In the discharging mode, the coulomb counter is presented by `Q_(lost)` , which represents the amount of charges losses in the operating period `tau` by the following equation:
The depth of discharge variation is calculated according to the following first eq and used in the following 2nd eq to calculate the value of DOD.
The SOC indication then is done by applying the equation (1).
C. Self-Discharge Mode-
At the battery storage periods, the percentage of monthly self-discharge is converted to the amount discharged per hour; this amount is designed by the constant `q_((per)/(hour))`. Considering a 5% rate of self-discharge per month `q_((per)/(hour))` is approximated to 0.0016 Ah. So the quantity of charges dissipated in the open circuit period `Q_(oc)` is calculated by the following equation representing the accumulative losses during the storage hours.
Fig: Coulomb Counter
The only time that the correct SoC is known is when the battery is fully charged or discharged. In the operation of the vehicle, these two conditions are rarely encountered. Also, such methods require that the current measurement is perfect, but no current sensor is immune from noise, component-to-component variations, and other effects. Therefore small errors always exist in every measurement and these errors may cause the estimates to wander away from the true value. Thus, Coulomb counting is not a preferred method for SoC estimation when a battery must be operated for a long time without full charge or discharge. Nevertheless, if the initial condition is known and the battery is operated for a relatively short period of time, then this method does provide a reliable measurement. This is important because, in order to design any SoC estimator, a true measurement must exist for purposes of comparison.
Below is the table of comparison to measure the SOC with different methods.
