# SOH Estimation of Lithium-Ion Battery Pack Based on Integrated State Information from Cells
## 4 Prediction Result Analysis  
### Two-Cell Pack Prediction  
For a better analysis of the performance of the proposed method, the validation started from the most basic battery structure, a series and parallel pack. Figure 12 displays the samples and measurement circuit for a two-cell pack. To state the advantage of proposed method, we used a prediction result with only pack indicators for comparison. The abbreviations of two methods used for comparison are listed in Table 3.  
Figure 11: Correlation analysis between the deterioration rate and the temperature fluctuation.  
Figure 12: Two-cell pack measurement schematic diagram: (**a**) series; (**b**) parallel.  
For the simpler structure of series and parallel battery packs, the data fluctuations and rules are relatively stable. Therefore, the prediction performance is excellent in the entire life. The comparison results of the series and parallel pack are demonstrated in Figure 13. For accurate presentation, it only shows the SOH prediction results of different methods at 341-371 cycles except for the training and test data, and emphasizes the error in prediction phases. In addition, because of the disparity between the experiment times, the cycles of the series and parallel pack tests were slightly different.  
Figure 13a,b compare the SOH of series and parallel packs based on different methods, and same color lines symbolize the same method. As seen in Figure 13, in general, the SOH curves based on pack-prediction and cells-prediction methods are both closed to the real data. It means the both prediction methods have good performance. Furthermore, the cells-prediction always performs better than pack-prediction method. At the same time, the both curves are higher than real experiment data, which means prediction methods always give optimistic life expectation. It is caused by persistent negative impact between cells, which is getting worse during working. For the series pack in Figure 13a, the real data fluctuates apparently, which is captured by cells-prediction method better than the pack-prediction method. The pack-prediction curve is too flat to describe the dynamic degradation process. On the contrary, in the parallel pack, there are too many inaccurate fluctuations in pack-prediction at 345, 351, 359, 361 cycles, and so on. It makes the result of pack-prediction unreliable.  
For better comparison of the SOH prediction result, the relative error was adopted to be the indicator showing performances. The relative error was calculated as follows:  
\[\text{RE}=\frac{\hat{y}-y}{y}\times 100\% \tag{12}\]  
where RE represents the relative error, \(\hat{y}\) is the prediction value of the SOH, and \(y\) is the real value. The comparison result of the relative errors is shown in Figure 14.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviations** & **Input Data** & **Output Data** \\ \hline \multirow{2}{*}{Pack-Prediction} & Environment temperature & \multirow{2}{*}{SOH of pack} \\  & Cycles (time) label & \\ \hline \multirow{2}{*}{Cells-Prediction} & Environment temperature & \multirow{2}{*}{SOH of pack} \\  & Cycles (time) label & \\ \cline{1-1}  & SOH prediction data of cells & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Abbreviations of the SOH prediction methods.  
Figure 13: Comparison of the SOH prediction results: (a) series; (b) parallel.  
The comparison results in Figures 13 and 14 illustrate the fact that the two prediction methods could both achieve high accuracy in the case of a series and parallel structure. It can be seen visually that the cells-prediction method had a more precise and stable performance. However, because of the plain structure, the interaction between cells was limited, which led to the inconspicuous preponderance of the cells-prediction method.