#### BMS Battery Management System Principle（2）-Battery Monitoring

As mentioned in the previous article (1), the main purpose of IBS is to monitor battery status and transmit status variables to BCM or other ECUs as needed. Use the measured battery current, battery voltage and temperature sampling values as battery monitoring inputs. Battery monitoring outputs are SoC, SoH and SOF.

##### 1. State of charge (SoC)

The definition of SoC is very intuitive and is usually expressed as a percentage. A fully charged battery has an SOC of 100% and a fully discharged battery has an SOC of 0%. The SoC value changes as the battery charges and discharges.

This leads to formula (l), where Cr is the remaining (dischargeable) capacity of the battery and Ca is the total available battery capacity:

However, there is often a problem where the available battery power is different from the battery’s nominal capacity (usually marked on the battery casing). For a new battery, it may be higher than the nominal capacity, and for a battery that has been used for a while, the available charge will be lower. Another problem is that the actual available power is difficult to determine based on the input value of the IBS。

Therefore, SoCs are usually rated by the nominal capacity Cn, which has several advantages:

The available charge capacity of a battery for a particular SoC is known, including older batteries; C is measured at a determined current (I=Cn/20h) and temperature (27C).

There are 2 commonly used SOC calculation methods: bank counting, also known as current integration or ampere-hour balancing, and open circuit voltage (OCV) measurement.

Coulomb counting is the best algorithm for tracking rapid changes in SoCs. It is based on integrating the current flowing into and out of the cell and adjusting the calculated cell SC accordingly. Formula (2) is used for SOC calculation, where (t0) represents the initial charge of the battery, a represents the efficiency factor, i() represents the current (forward or reverse), and C represents the nominal capacity of the battery.

Except for the a factor, the parameters in the formula are very intuitive. This is a factor used to describe efficiency, also known as Peukert’s law. It expresses the capacity of a lead-acid battery at different discharge rates. As the discharge rate increases, the battery’s available power decreases. Another parameter that affects the available power is temperature. The higher the temperature, the higher the available power. Both efficiencies are used (description, so the a value needs to take a 2-dimensional array (temperature and discharge rate). Based on the measured temperature and discharge rate, the corresponding values are used for each integration step separately. The a value is very large The extent depends on the design and chemistry of the battery, and often the values will vary even between different models of batteries from the same manufacturer. They are usually obtained through charge and discharge tests in the laboratory.

Although Peukert’s law only applies to the discharge case, there is also an efficiency factor similar to the a value that is used for the charge cycle. In addition to temperature and charge rate, the actual SoC also needs to be taken into account, because the charge efficiency at higher SOC is higher. Less charging efficiency than mid-range SoC.

Due to the integration of current and a values, errors arising from changing battery conditions and current measurement and quantification errors will become larger over time. Therefore, the parameter Ot0) (the starting point of the current integration) is usually obtained by a different method that provides higher accuracy: the OCV method. OCV is the voltage between the terminals of a battery when no electrical devices are drawing current from the battery.

Lead-acid batteries show a good linear relationship between OCV and SoC. Therefore, by measuring OCV, SoC can be calculated directly. The exact factor between OCV and SoC must be characterized.

The only flaw of this method is that the OCV can only be measured after parking, that is, after (almost) all electrical devices are turned off, and it must be measured dozens of minutes or even hours after the car is turned off.

Therefore, the OCV method is often used to recalibrate the library count, while the library counting method is run continuously. This combination provides a good method of calculating the SoC and can make the calculation more accurate by correcting the SOC with the self-discharge rate during longer shutdown times.

##### 2. State of health (SOH)

Various aging effects of lead-acid batteries will have different effects on the battery. Since it is difficult to monitor and quantify these aging effects individually through IBS, SoH is usually not rated directly based on these aging effects. Instead, SoH is rated by the reduction in battery capacity over its lifetime, which is the primary result of aging. Another very important parameter related to battery aging is starting performance, but it is usually expressed in terms of the state of function (SoF) of starting capability.

From this, SoH can be estimated by formula (3), where Caged represents the aged battery capacity and Cn represents the nominal capacity as a reference according to the calculation of SOC.

Since Cn is known, the key task in calculating SoH is to find Caged. One possible approach is to track the maximum charge (or SOC) achieved throughout the battery’s lifetime. If after several subsequent full charges, the maximum charge level of the battery is lower than the previously calculated aging capacity, it means that the aging capacity has become smaller. Accordingly, Caged and SOH must be adjusted based on the capacity determined by coulomb counting and OCV methods. Full charge status can be monitored when the charge current drops below a specific reading.

Another way to determine SOH is to track charge and discharge cycles and evaluate the cycle stability provided by the battery manufacturer. Typically, manufacturers will guarantee a total number of charge and discharge cycles at a specified temperature for a certain depth, for example, 500 cycles at 27C and 25% discharge depth. By evaluating all cycles with these numbers and applying temperature and state-of-charge correction factors, tracking of the Caged mentioned above is provided. These correction factors must be determined by characterizing the battery characteristics.

However, both methods are also often combined with other specialized algorithms that are tightly coupled to multiple battery parameters over battery life. These battery parameters are determined through extensive battery characterization in the laboratory, and they usually only apply to a specific battery model.

##### 3. Functional state (SoF)

Starting a car’s engine is an important, if not the most important function for a lead-acid battery. Therefore, a very important task of BMS is to predict whether the car can start under actual conditions. The launch prediction is represented by the SoF parameter.

In addition to the “traditional” stop-and-start, predictive start functions are becoming even more important through the introduction of start-stop systems in micro-hybrids. The BMS must decide whether the engine can be started again after shutdown and whether it is safe to enter stop mode and communicate with the BCM.

A very good way to obtain SoF parameters is to analyze the remaining charge (as a function of SoC and SOH) and actual temperature from the most recent engine start. During starting, the internal battery resistance Ri (calculated from voltage drop and current) needs to be recorded. Because Ri is relatively consistent over the life of the battery and only rises significantly toward the end of the battery’s life, the average Ri needs to be below a certain value to ensure safe starting. Another effect of aging batteries is that during the starting phase, the Ri values calculated from voltage and current samples tend to be nonlinear, that is, there will be different current values for the same voltage sample value. For new batteries, Ri is linear. See Figures 3 and 4 for common voltage and current trends during cranking.

Combining Ri (calculated from voltage drop and current), remaining battery capacity and actual temperature provides a good representation of starting capability. In addition, these thresholds must also be determined through battery characterization.

In order to determine the linearity or nonlinearity of Ri with the necessary accuracy, all voltage and current values sampled during the starting phase need to be filtered using a linear filter, preferably a bandpass filter.