## 2 Lithium-Ion Battery Modeling and Experimental Setup
### Method of Constructing Fusion OCV Curve
The fusion process is as follows:  
Take one DOD interval as an example, the two adjacent control points in set A constitute a semi-open closed DOD sub-interval \(A_{k}\), which can be described as \(\left[DOD_{k}^{(I)},DOD_{k+1}^{(I)}\right)\), \(1\leq k\leq N-1\). The corresponding OCV interval is \(\left[OCV_{k}^{(I)},OCV_{k+1}^{(I)}\right)\) because the OCV is monotonically decreasing during the discharge process. The corresponding DOD sub-interval \(B_{k}\) in set \(B\) can be determined by \(A_{k}\), and can be described as \(\left[DOD_{j}^{(L)},DOD_{j+s}^{(L)}\right]\). \(B_{k}\) needs to meet the following conditions:  
Figure 4: (**a**) Incremental test and low current test results. (**b**) Voltage difference between the two test control points. \[\left\{ \begin{array}{l}1\leq j\leq N\\ j+s\leq M\\ DOD_{j}^{(L)}\leq DOD_{k}^{(I)}<DOD_{j+1}^{(L)}\\ DOD_{j+s}^{(L)}<DOD_{k+1}^{(I)}\leq DOD_{j+s+1}^{(L)}\end{array} \right.. \tag{4}\]  
The fused dataset can be expressed as:  
\[F_{k}=\left\{\left(DOD_{k0}^{(F)},OCV_{k0}^{(F)}\right)\cdots,\left(DOD_{k,s}^{ (F)},OCV_{ks}^{(F)}\right)\right\}, \tag{5}\]  
where \(\left(DOD_{k0}^{(F)},OCV_{k0}^{(F)}\right)=\left(DOD_{k}^{(I)},OCV_{k}^{(I)}\right)\), \(\left\{\left(DOD_{k,i}^{(F)},OCV_{k,i}^{(F)}\right)|i=1,\cdots,s\right\}\) is obtained by recursion and interpolation, the calculation process is as follows:  
Step 1, \(i=1\). Linear interpolation at \(DOD_{k}^{(I)}\) between the point \(\left(DOD_{j}^{(L)},OCV_{j}^{(L)}\right)\) and \(\left(DOD_{j+1}^{(L)},OCV_{j+1}^{(L)}\right)\), and get the OCV value \(OCV_{k,i-1}^{(I)}\) corresponding to the incremental test control points. Step 2, Compute the fusion coefficient \(\alpha=\Delta OCV_{k,k+1}^{(I)}/\Delta OCV_{k,j+s}^{(L)}\), where \(\Delta OCV_{k,k+1}^{(I)}=OCV_{k}^{(I)}-OCV_{k+1}^{(I)}\), \(\Delta OCV_{k,j+s}^{(L)}=OCV_{k,0}^{(I)}-OCV_{j+s}^{(L)}\). Step 3, Compute the OCV increment \(\Delta OCV_{k,i}^{(I)}=OCV_{k,i-1}^{(I)}-OCV_{k,i}^{(I)}\). Step 4, Compute the fused OCV value, \(OCV_{k,i}^{(F)}=OCV_{k,i-1}^{(F)}+\alpha\times\Delta OCV_{k,i}^{(I)}\). Step 5, \(i=i+1\), repeat Step 3-5 until \(i=s\), where \(DOD_{k,i}^{(F)}=DOD_{k,i+i}^{(L)}\). \(F_{k}\) is the sub-interval fused by the above steps. The raw test data and fusion results are shown in Figure 5, where the green point set is the fused data. The fused data adjusts the low-current test results based on the control points of incremental test, retains the non-linear characteristic information, and dramatically reduces the polarization effect. The DOD needs to be converted to get the final OCV curve. The conversion formula is as follows:  
\[SOC_{k}=\left(1-\frac{DOD_{k}}{Q}\right)\times 100\%, \tag{6}\]  
where \(SOC_{k}\) is the SOC value in time \(k\). \(DOD_{k}\) is the DOD, and \(Q\) is the cell nominal capacity. The neural network has better non-linear mapping ability than polynomial fitting. The fusion results have enough data points to fit the OCV curve by using a neural network. The fitting curve is shown in Figure 6. The non-linearity of the OCV curve in the SOC range of 10% to 60% is strong, and the simple polynomial fitting cannot meet the precision requirement. For example, The SOC  
Figure 5: The OCV fusion results. estimation absolute error of order 5, order 8, order 10 polynomial, and neural network at 40% SOC is 4.016%, 3.062%, 2.221%, and 0.287%, respectively. The experimental results show that the neural network method has a smaller fitting error and is more suitable for fitting the fusion OCV data.