Week 7 State of charge estimation

What is Coulomb counting

The Coulomb counting method measures the discharging current of a battery and integrates the discharging current over time in order to estimate SOC. The SOC is expressed as  the ratio of available capacity to the nominal one. The common equation to calculate the SOC is given by Eq. (1), where the SOC0 represents the initial SOC, bat I  represents the current across the battery and, Qrated is the nominal capacity of the battery.

But there are several factors that affect the accuracy of Coulomb counting are the access to the initial SOC is not guaranteed. Secondly, selfdischarge may distort the real SOC value after a long storage period and finally the reference capacity Qrated must be updated in terms of battery ageing. Furthermore an SOC estimation is performed at varying ambient temperature which should be taken into account. method including temperature, battery history, discharge current, and cycle life.

Initial SOC determination

The OCV-SOC function that relates the open circuit voltage to its corresponding SOC value. 2. This curve is actually determined experimentally by the OCV test by applying a pulse load on the Li-ion battery, then the battery reach an equilibrium where the voltage is extracted in every 5% of Depth Of Discharge (DOD). SOC from measuring the initial OCV, for that we consider the inverse function noted SOC-OCV relationship of Li-ion battery which can be approximated to piecewise linear curve. 

                                                     SOC = f(OCV) = a*OCV - b.

Charge Mode

The typical charge procedure of a Li-ion battery consists of constant-current constant voltage (CC-CV) process .
The Coulomb counter is presented by Qgained which represents the quantity of charge accumulated during an operating period equal to τ.

                                               

Thus, the variation of the state of charge gained in this same operating period is obtained by the Eq.

                                               
By accumulating the previous state of charge indication and the obtained one, we can have the instantaneous value of SOC is obtained using below equation.
                                                 

    
The value of DOD is updated in every charging operation in order to get it back in every switching to discharging mode.
                                       

                                                SOC (t) + DOD (t)  = 100%. 

Discharge mode

When the current bat I is negative, then the battery is in the discharging mode. In this mode, the Coulomb counter is presented by Qlost, which represents the amount of charges losses in the operating period τ.

The value of DOD is calculated according to Eq below

Self-Discharge Mode

At the battery storage periods, considering that Li-ion batteries reach 5% rate of self-discharge per month, the amount of charge losses per hour is calculated; this amount is designed by the constant, q per hour. Then, the quantity of charge dissipated in this phase Qoc is calculated by Eq which representing the cumulative losses during the storage hours.

where h is the hour of storage 
This value will be added to the amount of charges lost Qlost during discharge mode and subtracted from the amount of charge accumulated Qgained in the charge mode as expressed

This compensation of self-discharging loss is made at each open circuit period and before switching to another operating battery’s mode.

Temperature Monitoring

Different studies have highlighted that the temperature has an important effect on the battery behavior & at low values the released capacity from the battery decreases dramatically. At the initial SOC determination phase, we are considering the effect of the temperature variation for temperature range 5 - 15 degC. 

How BMS implements coulomb counting for SOC estimation

The adopted Coulomb-counting algorithm for SOC estimation was implemented on a hardware platform. The monitoring functions include the measurement of battery voltage and the current flowing through it by the 10 bits Analog to Digital Converter MCU PIC18F.

The battery parameters detection is one of the most important issue in control and management of a BMS. It includes cell voltage measurement and current detection. Estimation of SOC and other battery states imposes high requirements on cell voltage precision.

In order to measure the voltage and the current with which the battery is charged or discharged, a sensing resistor Rsens is placed in series with the battery. The battery voltage Vbat is obtained by measuring the voltage across it. The difference between the voltages at the two terminals of the resistor will derive the current value bat I through the sensing resistance. This resistance, which allows the current sensing in the battery gauge, should not be too high in order to avoid power dissipation during the charging at a constant current of 1C-rate, but it should still be enough so that the analog/digital converter in the micro
controller can detect a voltage variation across it, which corresponds eventually to a 10 mA current, in order to detect the end of charging. In our case, a 10-bit converter is used to detect a voltage variation of 1mV. A 0.1 Ohms resistance can detect a current of 10 mA (for U = 1mV) and does not dissipate too much power while charging the maximum current value (P=100mW). The transmission of the battery
electrical parameters is ensured by a USB connection between the multimedia application and the MCU PIC18F. The ambient temperature is measured using a negative temperature coefficient resistor
RNTC. This thermistor is biased by IO of the MCU and connected close to the battery.