**3. Measurement Results**

The measurement system and parameters described in Section 2 are used for cell impedance measurements. The overall process of cell state estimation in this paper is shown in Figure 2 as a flow chart.

Table 2 shows the experimental conditions. Cell impedance is measured every second while discharging from 0% to 100% DoD for each cell with 100% to 80% SoH. A DC bias of 1C and an excitation amplitude of 130 mA are applied, i.e., an amplitude of 65 mA is given at each frequency of 1 Hz and 1 kHz. This amplitude is chosen for the cell output voltage amplitude to be less than 10 mV. The multi-sine test signal, the sum signal of the two frequencies, applies to the cell DC bias, and the impedance at each frequency is measured simultaneously.

**Figure 2.** Flow chart showing the cell state estimation process.



Figure 3 shows continuous 1 Hz and 1 kHz impedance during discharging of cells with different SoHs.

**Figure 3.** 1 Hz and 1 kHz cell impedance during discharge of cells with different SoHs. The solid lines represent the 1 Hz impedance, the dotted lines represent the 1 kHz impedance, and the different brightness of the line represents the different cell SoH.

As shown in Figure 3, the lower the cell SoH, the higher the cell impedance, and while 1 kHz impedance is relatively constant for DoD changes, 1 Hz impedance is more affected by cell DoD. While the cell is completely discharged, the increased rate of the highest value to the lowest value of 1 kHz impedance is 3.74%. At the same time, for 1 Hz impedance, the increased rate of the highest value to the lowest value between DoD 5% and 95% is 10.16%. The 1 kHz impedance shows a smaller increased rate, and it indicates less susceptibility to changes in cell DoD. Therefore, the 1 kHz impedance is more suitable to be used for

SoH estimation of cells for which the cell SoC is unknown. Contrastively, 1 Hz impedance shows larger increase rate, which means that it is more suitable for cell SoC estimation.

For the calculation of the increase rate, 1 Hz impedance between DoD 5% and 95% in Figure 3 are used (if the full range of DoD 0% to 100% is considered, the difference in impedance deviation at 1 Hz and 1 kHz will be more prominent.). The reason is that at the beginning and end of cell discharge, the 1 Hz impedance is not measured correctly and cannot be used for cell SoC estimation. The voltage response of an electrochemical cell is not only affected by the cell impedance. The cell discharge process causes an overpotential, which is the voltage loss described by polarization. Polarization refers to a phenomenon in which the electrode potential becomes excessive or insufficient in an equilibrium state. During the reaction process in a battery cell, the rate of charge transfer process occurring in each cell component is not the same. If this rate is relatively slow for a particular process, it becomes the rate-limiting process for the entire reaction of the cell. As the cell discharges, current flows between both terminals, causing the voltage to be measured below its equilibrium potential. In this case, the difference between the voltage at both terminals and the equilibrium voltage is called overpotential, indicating the degree of polarization. Figure 4 shows the three polarization regions appearing in the typical discharge curve of a Li-ion battery cell. In the cell discharge process, polarization can be classified into three categories: activation polarization, concentration polarization, and ohmic polarization [58].

**Figure 4.** Typical discharge curve of a battery cell, showing three different regions of polarization.

Ohmic polarization, also referred to as ohmic loss, is caused by the current flowing through the internal resistance of the battery cell. The greater the cell internal impedance, the greater the operating voltage drop as the ohmic losses increase proportional to the current density. Therefore, in this region, it has a slope related to the cell impedance and shows the most linearity when charging and discharging the cell. Due to this linearity, impedance can be measured accurately; hence, it is the most suitable region for cell state estimation through impedance measurement. Meanwhile, the cell output voltage in the activation and concentration polarization regions has nonlinearity. Activation polarization is due to various delay factors inherent in the dynamics of electrochemical reactions, such as the work function that ions must overcome at the junction between the electrode and the electrolyte. It has a dominant effect at the beginning of cell discharge. Concentration polarization takes into account the resistance that ions face in the process of mass transfer (e.g., diffusion) as they move across the electrolyte and from one electrode to another. This polarization has a dominant effect at high cell DoD. In conclusion, the cell voltage drops significantly non-linearly as the cell discharges in the region of activation and concentration polarization. Because this nonlinearity is based on slow response, especially in battery cells, the lower the frequency, the more difficult it is to obtain an accurate cell impedance. As shown in Figure 3, the effect of activation and concentration polarization at a frequency of 1 Hz is more pronounced than at 1 kHz, because slow transport processes are well represented at lower frequencies. On the other hand, slow transport reactions cannot be detected at higher frequencies, but the effects of fast kinetics can be revealed.
