Battery Efficiency

Battery efficiency can be used as an indicator of the current usage time compared to the initial time. A battery efficiency equation was proposed to express the relationship between the capacity and voltage of the battery model. Because the internal resistance of a battery affects the battery output, the battery's internal resistance must be accurately calculated.

The internal resistance of a battery is the key indicator of its state. The internal resistance of a battery increases with an increase in the heat generated during the chargedischarge of the battery.

Figure 6 illustrates the current capacity of the ESS with aging.

As the battery aged, its internal resistance increased and the current capacity decreased, which significantly affected the performance of the ESS when the capacity was large. Furthermore, the use of a battery with reduced performance causes overcharging and overdischarging, which limits battery safety.

The current battery capacity is the amount of current that a fully charged battery can discharge for one hour. Compared to a battery in the birth of life (BOL) state, an aging battery, upon discharge, reaches the terminal voltage limit faster because of its reduced current capacity.

The efficiency of a battery decreases when it is used. As a battery shows the maximum efficiency at the initial state, its efficiency can only decrease when it is in operation.

Equation (1) defines the efficiency of a battery. The efficiency of a battery *ηbat* can be expressed by subtracting the battery loss *ηloss* from the initial battery efficiency, 100%.

As the decrease in the efficiency can be expressed as the increase in the internal resistance, *ηloss* can be calculated based on the charging and discharging powers, as shown in Equation (2).

*Ibat* is the charge-discharge current, R is the battery's internal resistance, and *Vbat* is the battery voltage.

$$
\eta\_{\text{bat}} = 100 - \eta\_{\text{loss}} \tag{1}
$$

$$\eta\_{loss} = \frac{I\_{bat}^2 \times R}{V\_{bat} \times I\_{bat}} \tag{2}$$

In this case, the charge-discharge current of the battery can be represented by Equation (3).

During the charge-discharge of a battery, the current can be calculated as the amount of charge (battery capacity) and the C-rates at which the battery has been charged or discharged over time. *Qbat* is the battery capacity, while *t* is the charge-discharge time of the battery. Equation (3) uses the electric charge equation.

Equations (2) and (3) give the total loss in battery efficiency, as represented in Equation (4). Using Equation (4), the battery loss equation, as well as Equation (1), the battery

efficiency can be calculated. Equation (4) can be used to determine the internal resistance of a battery. Equation (5) gives the internal resistance of the battery. In this paper, as the charge-discharge process progressed, the battery efficiency decreased.

$$I\_{bat} = \frac{Q\_{bat}}{t} \tag{3}$$

$$\eta\_{loss} = \frac{\left(\frac{Q\_{\text{bat}}}{l}\right) \times R}{V\_{\text{bat}}} \tag{4}$$

$$R = \frac{\eta\_{loss} \times V\_{bat} \times t}{Q\_{bat}} \tag{5}$$
