## 4 The Experimental Results  
To test the SoC estimation algorithm for LiBP, in this study we use LiBP with seven cell modules connected in series; each cell module consists of nine cells connected in parallel. Cells used in the LiBP are Lithium-SAMSUNG with parameters (supplied by manufacturer): ICR18650-22P 2200 mAh, Vmax = 4.25 V, Vmin =2.75 V, nominal voltage 3.62 V. The test temperature limit is considered from \(-5\)\({}^{\circ}\)C to 45 \({}^{\circ}\)C.  
By experimental testing, the dynamic parameters of the cell are given in Table 1. Instead of forming a plot of the relationship between the OCV and SoC at many temperatures, we only form the relationship between the OCV and SoC at reference temperature 20 \({}^{\circ}\)C and the change amount of OCV with respect to the SoC when the temperature changes 1 \({}^{\circ}\)C at reference temperature 20 \({}^{\circ}\)C, so the relationship between OCV and SOC at any temperature can be calculated easily. The relationship between OCV and SoC at 20 \({}^{\circ}\)C and the change amount of OCV with respect to the SoC when the temperature changes 1 \({}^{\circ}\)C at reference temperature 20 \({}^{\circ}\)C are given in Figures 6 and 7, respectively. Figure 6 shows that the relationship OCV and SoC is strong, nonlinear relationship, and the OCV-SOC characteristic curve is greatly influenced by the temperature change and has a great influence on the accuracy of battery state estimation. The LiBP power is 480 W; the voltage at both ends of the LiBP is 24 V. The initial parameters of the LiBP assumed at 25 \({}^{\circ}\)C include \(\textbf{SOC}_{0}\in R^{(N_{y}\times N_{p})}\), \(\textbf{R}_{0}\in R^{(N_{y}\times N_{p})}\)(see Tables 1 and 2 in the Appendix A). The covariance matrices of the state vector estimation errors of the current noise and the voltage noise are listed as follows, respectively. \[\sigma_{\overline{x},0}^{+}=\left[ \begin{array}{ccccc}0.001&0&0&0&0\\ 0&0.0001&0&0&0\\ 0&0&0.01&0&0\\ 0&0&0&0.01&0\\ 0&0&0&0&0.01\end{array} \right],\sigma_{\overline{w}}=\left[ \begin{array}{ ccc}0.001&0\\ 0&0.001\end{array} \right],\sigma_{\overline{\zeta}}=0.001, \tag{11}\]  
The bias current is 0.5 A (\(b_{k}=0.5A\)); the charge and discharge scenarios with current through the LiBP and the voltages measured on seven cell modules over a period of 3900 s are shown in Figures 8 and 9, respectively. In order to show the capability of describing more the cell dynamic more exactly, the SoC estimation is experimented on for the LiBP, charged and discharged; with amplitude varying suddenly (see Figure 8), the maximum charged and discharged amplitudes of current are 5 A and 23 A, respectively. We suppose that the measured current through LiPB drifts with the bias current 0.5 A.  
Figure 8: The current through the LiBP in the charge and discharge scenarios. Figure 9: The voltages measured on seven cell modules. This experimental charged and discharged scenario is similar to the charged and discharged situation of LiBP using for EVs in practice. The measured voltages of seven cell modules are influenced by the noise; the varying of those voltages depends on the charged and discharged amplitude of current through LiPB, as shown in the Figure 9.  
The average SoC estimations for cell modules in LiBP are shown in Figure 10; the SoC estimation errors of the cell modules are plotted in Figure 11. From the SoC estimation results, we see that after about 0.1 h, the SoC estimations of the cell modules are close to the actual average SoC of the cell modules. The SoC estimation errors for the cell modules 1-7 at the end point of the experiment are: 0.17%, 0.4%, 0.15%, 0.5%, 0.17%, 0.02% and 0.17%, respectively  
Figure 12 plots the estimation of current bias of the current through the LiBP; after a period of time 0.05 h, the estimated value is distributed around the true value of 0.5 A. The error of this estimation is quite large; the largest error is approximately 0.1 A, but the mean of this error calculated over the experimental period of time is about 4%.