*3.2. Improved SoC and SoH Prediction Method*

A battery protection system monitors the battery state and prevents it from overcharging and overdischarging, improving its safety and performance. The performance of a BMS is evaluated based on how accurately it predicts the SoC and SoH of the battery [34].

CCM is used to track the SoC with the value calculated by integrating the current during the charge-discharge of the battery to the initial value of the SoC; however, because the current is accumulated to the initial value of the CCM, errors are accumulated if the precise initial value is unknown [70,71]. Because errors gradually increase, the paper propose following the SoC with an improved method combining the OCV and CCM to improve the initial value.

Equation (6) expresses the voltage calculated using the open circuit voltage formula of the battery through Equation (5). The battery state can be more accurately predicted using the internal resistance obtained through Equation (5) and the OCV of the battery.

The final CCM is depicted in Equation (7). The accuracy of the prediction of the battery state can be improved by applying the internal resistance value derived from the battery efficiency equation to the conventional CCM. *SoC*(*t*) is the SoC at time t, *SoC*(*t*−1) is the initial SoC, *C<sup>n</sup>* is the battery capacity, and *Vocv* is the battery voltage in the open state [72,73].

$$So\mathbb{C}(t-1) = V\_{ocv} + \left(I\_{bat} \times \frac{\eta\_{loss} \times V\_{bat} \times t}{Q\_{bat}}\right) \tag{6}$$

$$\text{SoC}(t) = \text{SoC}(t-1) + \int\_0^t \frac{I(t)}{\mathbb{C}\_n} dt \tag{7}$$

SoH, which is an indicator of the battery life time, is essential for managing the battery charge-discharge process. Various models for predicting SoH have been proposed to improve the battery safety and performance. The standard method predicts the life time of a battery by analyzing it according to the chemical principle of the battery and through mathematical or physical modeling [74–76]; however, these methods do not consider the internal resistance of a battery, which significantly affects its life time.

Figure 7 illustrates the constant current–constant voltage (CC–CV) charging curve of a battery.

**Figure 7.** Voltage and SoH of a battery during charging.

A battery is typically charged through the CC–CV [77]. Whenever the battery is charged, its CC charging time decreases, while the CV charging time increases. As the battery charging proceeds, the battery temperature increases and internal resistance increases, resulting in a decrease in its SoH.

Figure 8 shows the discharge characteristics of a battery.

**Figure 8.** Voltage and SoH of a battery during discharging.

As in the charging cycle, the time to reach the cut-off voltage is also reduced during charging because the SoH decreases as the temperature and internal resistance of the battery increase, as shown in the charging curve.

This paper considered the internal resistance of a battery, which significantly affects the SoH, to propose a method for predicting the battery SoH based on the charging time after the charge-discharge process. Although previous studies [62,64] did not accurately predict the internal resistance value, they numerically derived and applied the internal resistance value based on the battery efficiency.

To calculate a battery's SoH, the equation should be rearranged by *t* using the SoC derived from Equations (6) and (7) after the SoC charge-discharge process, resulting in Equation (8). By applying the internal resistance equation derived from the battery efficiency equation, the charge-discharge time is compared based on the charge-discharge cycle of the battery. Here, *tafter* is the time after the charge-discharge process, which can be used to predict the battery SoH using the battery characteristics by comparing the values after the charge-discharge process (Equations (8) and (9)). *SoHafter* is the SoH of the battery compared to the time after charging and discharging. The SoH of the battery can be predicted using the charge-discharge time of the battery. Here, *tbefore* is the battery charge-discharge time before *tafter*.

$$t\_{after} = \frac{C\_{\text{ll}} \times \left(SoC(t) - V\_{ocv} - \eta\_{loss} \times V\_{bat}\right)}{I\_{bat}} \tag{8}$$

$$SoH\_{after} = \frac{t\_{after}}{t\_{before}} \times 100\% \tag{9}$$
