## 2 Experiments and Methods
### Model Parameter Identification  
#### 2.3.1 Open Circuit Voltage  
The open circuit voltage (OCV) of the battery is the stable voltage value of the battery when the battery is left in the open circuit condition [11]. Regarding the battery after being charged, the battery terminal voltage will gradually decline to a stable value when it is left in the open circuit condition; regarding the battery after discharge, the battery terminal voltage will gradually rise to a stable value after the load is removed. The electromotive force of the battery is basically equal to the open circuit voltage of the battery, while the battery electromotive force is one of the metrics used to measure the amount of energy stored in the battery. Thus, there is a certain relationship between the battery OCV and the battery SOC [22]. There are a few ways to obtain OCV, in which the stationary method is a direct method and is relatively more accurate. To obtain the relationship between the battery OCV and SOC in the stationary method, the test procedures are performed as follows [30]:  
1. Calibrate the battery capacity. The battery is fully charged with the standard charging method, in which the battery is charged using a constant current phase of 2.35 A (1C) to 4.2 V followed by a constant voltage phase of 4.2 V until the current is reduced to 0.02 A. Then, the battery is discharged with a constant current phase of 2.35 A to its discharge cut-off voltage 2.7 V. The experiment is repeated until the difference between the discharge capacity of each measurement does not exceed 2%, and then the measured capacity is deemed to be the actual capacity of the battery.
2. The battery is fully charged with the standard charging method described by Step (1) and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium [9].
3. The battery is discharged with a constant current 2.35 A for 6 minutes (i.e., discharging by 10% of the capacity) and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium.
4. Step (3) is repeated eight times.
5. The battery is discharged with a constant current 2.35 A by 3 min (i.e., discharging by 10% of the capacity) and then the battery is left in the open-circuit condition for 4 h to achieve electrochemical and heat equilibrium.
6. Step (5) is repeated four times.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**BTS4000** & **BTS4000** & **BTS4000** & **Cell** & **Cell Maximum** & **Cell Limit** &
\begin{tabular}{c} **Sampling Frequency** \\ \end{tabular} \\
**Voltage** & **Current** & **Measuring** & **Nominal** & **Coninuous** & **Coninuous** \\
**Range (V)** & **Range (A)** & **Errors** & **Capacity** & **Discharging** & **Voltage** & **Current** & **HPPC** \\
**Current** & **Current** & **Current (A)** & **Current (V)** & **Discharge (Hz)** & **Test (Hz)** \\ \hline
0–10 & \(-6\) to 6 & 0.5\% & 2350 & 10 & 2.7–4.2 & 1 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The important parameters of the experimental scheme.  
In the tests, the measured voltages at the end of each standby stage are regarded as the final open-circuit voltage. The variation of OCV with SOC obtained by the experimental method above is shown in Figure 3.