## 2 Experiments and Methods
### Model Parameter Identification
#### 2.3.2 Ohmic Resistance  
In general, the methods used to measure the battery resistance are the power-off method, the step method, and the electrochemical impedance spectroscopy (EIS) method. With the EIS method, the battery is excited by a series of alternating current (AC) signals of different frequency and then through analyzing the relation between the input excitation signal and the battery voltage output response, and the battery impedance characteristic can be obtained. The principle of the power-off method and the step method is similar, in which the difference between Ohm polarization response time and other polarization response time is utilized to identify the different impedance. When the current has a sudden change, the voltage drop part caused by ohmic polarization changes instantaneously and then the voltage drop part by other polarization completes the transient process with the approximation exponential until the voltage returns to a steady-state voltage value. Assuming that the voltage before the current changes is U\({}_{0}\) and the voltage after the moment the current changes is U\({}_{1}\), the formula for calculating the ohmic resistance is as follows:  
\[\mathrm{R}_{0}(\mathrm{SOC})=\frac{\mathrm{U}_{1}-\mathrm{U}_{0}}{\Delta \mathrm{I}} \tag{1}\]  
Referring to the \"Freedom CAR Battery Test Manual\" hybrid pulse power characterization test (HPPC test) [31], this paper adopts the step method to obtain the ohmic resistance, the polarization resistance, and polarization capacitance from the different SOCs. The hybrid pulse power characterization test profile is shown in Figure 4.  
To obtain the battery ohmic resistance, polarization resistance, and polarization capacitance at the different SOCs, tests are performed as follows:  
1. Calibrate the battery capacity as described in Section 2.3.1.
2. Charge the battery fully with the standard charging method the same as described in Section 2.2.
3. The HPPC test is performed and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium [9].
4. The battery is discharged with a constant current 2.35 A for 6 minutes and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium.
5. Steps (3) and (4) are respectively repeated eight times alternately.
6. The battery is discharged with a constant current 2.35 A for 3 min and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium.  
Figure 3: The varying curve of open circuit voltage (OCV) with state-of-charge (SOC).  
The HPPC test is performed and then the battery is left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium.
* Steps (6) and (7) are respectively repeated four times alternately.  
From the above experimental steps, it can be seen that the HPPC test can be implemented along with the open circuit voltage test described by Section 2.3.1. According to the above experimental procedures, the voltage response curves of lithium-ion battery excited by HPPC test at different SOC can be obtained. The results are shown in Figure 5. Then, the ohmic resistance at different SOCs can be obtained by calculating Equation (1). The results are shown in Figure 6.  
Figure 4: Hybrid pulse power characterization (HPPC) test current profile.  
Figure 5: Voltage response curves by HPPC test at different SOC.