*2.2. Definition of Key Terms*

There is no standard definition that defines SoC and SoH for battery cells and may be defined differently depending on the battery application system. Therefore, it is necessary to clarify the terms defined in this paper before discussing cell state estimation.

• Definition of C-rate

In general, C-rate is used to indicate the rate of charge and discharge of a battery cell. The relationship shown in Equation (4) is given between the cell nominal capacity CN and the operating current *i*.

$$
\mathbf{h} = \mathbb{C}\_{\text{N}} / i \tag{4}
$$

where h is the time (hour) taken to completely discharge the battery cell, *i* is the current at which the cell operates, and CN is the nominal capacity of the battery (Ah). Here, the reciprocal of the h value is defined as the C-rate.

• Definition of SoC

In this paper, the cell SoC is set through the following three steps:

(1) Full charge of the battery cell. The constant-current (CC) charging procedure at 1C and the constant-voltage (CV) charging procedure at 4.2 V are followed in sequence, where 4.2 V is the upper cut-off voltage specified by the cell manufacturer. This first step is complete when the charging current drops below C/10. Subsequently, each cell is given 90 min of relaxation time.

(2) Discharge the cell at 1C until it reaches a lower cut-off voltage. From this step, the actual cell capacity Ccell is obtained.

(3) Set the cell to the target SoC. To fully charge the cell, Stage 1 is performed again, and then the charge of the cell is consumed until the target SoC is reached. Since different cell relaxation times can introduce errors, the same relaxation times must be observed [46,47]. Each cell is given 90 min of relaxation time after the target SoC is set and before it is used in the experiment.

The SoC is then defined as Equation (5).

$$\text{SoC} = \text{C}\_{\text{residual}} / \text{C}\_{\text{cell}} \times 100 \, (\%) \tag{5}$$

The SoC of a cell is the ratio of the residual capacity (Cresidual) to the total available capacity when the battery cell is fully charged (Ccell). The Ccell can be obtained from the second step of the procedure for setting up the cell SoC mentioned above. Depth of discharge (DoD) has the exact opposite definition of SoC, i.e., a cell of 80% SoC has the same meaning as a cell of 20% DoD.

• Definition of SoH

Battery cell SoH is defined as the ratio of the cell actual total available capacity Ccell to the cell initial total available capacity Cinit and expressed by Equation (6).

$$\text{SoH} = \text{C}\_{\text{cell}} / \text{C}\_{\text{init}} \times 100 \, (\%) \tag{6}$$

In this paper, cell impedances from 100% to 80% SoH of cells are measured and compared. The EoL of a battery is reached when the energy content or power capacity is no longer sufficient for the application. This can vary depending on battery application; thus, there is no universal definition of how many cell SoHs have reached EoL. Nonetheless, publications assume that EoL is reached when the battery cell SoH is less than 80% [48–50].
