## 3 Design and Result Analysis of the Battery Cycle Life Test
### Experimental Results and Analysis  
The cycle life test and the OCV test continued until the available capacity of the aging battery is less than 80% of the nominal capacity. The experimental results of the No. 1 battery are shown in Figures 3-6. The relationship between the available capacity and the cycle number of the cycle life test is shown in Figure 3. It should be noted that the amount discharged under such a cycle life test is considered to be the available capacity of the battery. Figure 3: Cycle life vs. maximum available capacity. Figure 2: Flowchart of the procedure. Six OCV test for different cycle numbers are shown in Figure 4. The \(i\)th time indicates that the corresponding OCV data is obtained after the \(i\)th time of the cycle life test. Figure 5 showed the terminal voltage drop when the fully charged battery has a rest for 2 h and the terminal voltage drops when the discharged battery has a rest for 2 h for the six OCV test. The following can be inferred by analyzed the experiment results. Figure 4: Open circuit voltage (OCV) test data. Figure 5: Terminal voltage drop after it rests for two hours. Figure 6: Cycle life vs. voltage drop. (1) Figure 3 presented that with the increasing number of cycles, although the amount discharged (i.e., the available capacity of the battery) is not monotonically attenuated, the overall trend is decreasing. On the other hand, compared with the early life stage (for example, the 1-200 cycle), the capacity decreases rapidly at the later stage of life (for example, cycle > 400). (2) Figure 4 showed that the six OCV test is operated under the same working condition, the results are different. The battery has a rest for two hours after it reaches fully charged state in CV mode. The terminal voltage of the battery is gradually decreasing as the number of cycles increases. The charging process also has a similar regular pattern. (3) Figure 5 presented that during the discharging, even with the same discharging current, the same discharging time, when the battery is stopped charging and rests for the same time (i.e., two hours in this study), the terminal voltage drop of the battery is gradually increasing with the degradation of the battery. The value of the terminal voltage drop is relative to SOC value and the lower the SOC value, the greater the terminal voltage drop. Terminal voltage is no longer changing, it can be regarded as the OCV of the battery. Conversely, the decreasing battery capacity leads to the changes in the thermodynamic and kinetic characteristics of battery and the corresponding relationship between the available capacity and OCV is the direct external embodiment of thermodynamic characteristics of battery [43]. Thus, the capacity degradation causes a change in the OCV, that is, the value of the terminal voltage drop with the same rest time can reflect the degradation of the available capacity. (4) Figure 6 showed that with the increasing number of cycles, after the fully charged battery has rested for 30 min and compared with the initial terminal voltage at the moment when the battery is just fully charged, the terminal voltage drop does not increase monotonously but the overall trend is increasing. The terminal voltage drop is trending in the opposite direction to the change in the available capacity of the battery combined with Figure 3.  
In addition, the following must be taken into account:  
(1) It is difficult to get precise SOC values. Equation (5) is generally used to calculate the SOC of the battery:  
\[SOC=1-\frac{Q_{t}}{Q_{all}}=1-\frac{\int_{0}^{t}i(\tau)d\tau}{\int_{0}^{T}i( \tau)d\tau} \tag{5}\]  
The \(Q_{t}\) represents the amount discharged from the beginning of the discharging (the fully charged battery) to the moment t, \(Q_{all}\) represents the amount discharged from the fully charged battery to the cut-off voltage. T represents the whole discharging duration. In real application, we can get \(Q_{t}\) easily but the \(Q_{all}\) cannot be measured at the moment \(t\) if the battery is not out of power.