## 3 Model Parameter Identification and Comparison  
### Experiments  
The experiments were performed using a commercial LIB with cathode of LiNi\({}_{x}\)Co\({}_{y}\)Mn\({}_{1-x-y}\) (NCM). To fully verify the effectiveness of the proposed model, two types of LIBs were selected for experiments. The basic parameters of two LIBs are listed in Table 2. As shown in Figure 3a, the experiments were conducted in a battery tester made by DIGATRON which has a current range of \(-100\) A to \(+100\) A and a voltage range of 0 V to 20 V. The voltage accuracy is 1 mV and the current accuracy is \(\pm 0.1\%\) full scale. A software (BTS-600, Digatron Power Electronics, Aachen, Germany) installed on PC is used to control the charging and discharging of the battery according to the given operating conditions, and record the terminal voltage and current of the battery at a frequency of 1 Hz. The acquired data was used for model parameter identification and SOC estimation. \begin{table}
\begin{tabular}{c c c} \hline
**Model Name** & **Discretization Equations (Discharge Is Negative)** & **Number of Parameters** \\ \hline
0 RC & \(U_{t}(k)=U_{\text{OCV}}\big{(}\text{SOC}_{\text{arg}}(k)\big{)}+IR_{0}\) & 2 \\ E0 RC & \(\left\{\begin{array}{l}U_{t}(k)=U_{\text{OCV}}\big{(}\text{SOC}_{\text{surf} }(k)\big{)}+IR_{0}\\ \text{SOC}_{\text{surf}}(k)=\text{SOC}_{\text{arg}}+\Delta\text{SOC}(k)\\ \Delta\text{SOC}(k)=\Delta\text{SOC}(k-1)e^{-\frac{T_{s}}{k_{\text{SD}}}}+K_ {\text{SD}}I\bigg{(}1-e^{-\frac{T_{s}}{k_{\text{SD}}}}\bigg{)}\end{array}\right.\) & 4 \\ \(n\)RC: 1 RC 2 RC 3 RC & \(\left\{\begin{array}{l}U_{t}(k)=U_{\text{OCV}}\big{(}\text{SOC}_{\text{arg} }\big{)}+I_{k}R_{0}+\sum\limits_{i=1}^{n}U_{i}(k)\quad(n=1,2,3)\\ \text{2 RC}:6\\ \text{3 RC}:8\end{array}\right.\) \\ E_nRC: 1 RC 2 RC 3 RC & \(\left\{\begin{array}{l}U_{t}(k)=U_{\text{OCV}}\big{(}\text{SOC}_{\text{ arg}}(k)\big{)}+I_{k}R_{0}+\sum\limits_{i=1}^{n}U_{i}(k)\quad(n=1,2,3)\\ \text{SOC}_{\text{surf}}(k)=\text{SOC}_{\text{avg}}+\Delta\text{SOC}(k)\\ \Delta\text{SOC}(k)=\Delta\text{SOC}(k-1)e^{-\frac{T_{s}}{k_{\text{SD}}}}+K_ {\text{SD}}I\bigg{(}1-e^{-\frac{T_{s}}{k_{\text{SD}}}}\bigg{)}\end{array}\right.\) & E1 RC: 6 \\ \hline \end{tabular}
\end{table} 
Table 1: Discretization equations of various resistance-capacitance (RC) models. Figure 2: Schematic of the proposed E_n_RC model. Capacity and hybrid pulse power characterization (HPPC) experiments [25] were first performed to determine the capacity and OCV of LIBs. The capacity test process is as follows: Place the test LIB in the temperature chamber at 25 \({}^{\circ}\)C for 3 h. Then, discharge the LIB at a constant discharge current 1/3 C to 2.5 V. After waiting for 1 h, fully charge the LIB using the constant current-constant voltage (CC-CV) method. In this method, the LIB is charged at a constant current (1/3 C) until the voltage reaches 4.15 V, and then, the LIB is charged at a constant voltage until the charging current falls to 1.6 A; then, charging is paused for 1 h. This process is repeated three times, and the mean value of the test capacity is chosen as the battery capacity. The HPPC test is designed to determine the open circuit voltage (OCV). In this test, a series of pulse power sequences are provided to the fully charged battery. Following one pulse power sequence, the battery is discharged to a SOC of 97.5% at 1/3 C and rested for 3 h before the next pulse power sequence is provided. The battery is tested at decrements of 2.5% SOC (10% when the SOC is less than 90%) until the cutoff voltage of 2.5 V is reached. Then, the two test LIBs were subsequently fully charged at 1/3 C. The discharge experiment was then performed, until the batteries were fully discharged at 1/3 C under the NEDC and DST working cycles until the cutoff voltage of 2.5 V is reached, respectively. It is noted that the charge and discharge currents are controlled by the program according to the cyclic working curve.