## 3 Discussion on the Battery Modeling Methods
### Future Trends of Battery Modeling Methods  
As previously described, the accuracy of the battery model is critical for the model-based SOC estimation methods. Hybrid models utilizing the advantages of each modeling technology are proposed for the purpose of improving the modeling accuracy. In [66], the _Thevenin_ model represents the voltage corresponding to the current profile, while the nonlinear part of the model is represented by the _Shepherd_ model. Likewise, the _Nernst_ model can also replace the nonlinear  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Modeling Methods** & **Empirical Model** & \begin{tabular}{c} **Equivalent Circuit** \\ **Model** \\ \end{tabular} & \begin{tabular}{c} **Electrochemical** \\ **Model** \\ \end{tabular} & \begin{tabular}{c} **Data-Driven Model** \\ \end{tabular} \\ \hline \begin{tabular}{c} Modeling \\ expression \\ \end{tabular} & \(U_{t}=f(U_{cc},SOC,I)\) & \(U_{t}=f(U_{cc}(SOC),I,R,C)\) & \(U_{t}\) & \(U_{t}\) & \(=f(I,SOC,T)\) \\ \hline \multirow{3}{*}{Pros} & Simple expression, computational efficiency & \begin{tabular}{c} Easily understood, widely used in SOC \\ estimation \\ \end{tabular} & \begin{tabular}{c} High accuracy of \\ voltage calculation \\ \end{tabular} & \begin{tabular}{c} High accuracy of \\ calculation, do not need \\ prior knowledge of \\ the battery \\ \end{tabular} \\ \hline \multirow{3}{*}{Cons} & Limited capability of describing the terminal voltage & \begin{tabular}{c} Complex parameter \\ identification process \\ \end{tabular} & \
\begin{tabular}{c} Require prior \\ knowledge of the \\ battery, time \\ consuming \\ \end{tabular} &
\begin{tabular}{c} Laborious training dataset \\ collection process \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pros and cons of the modeling methods.  
Figure 4: The classifications of battery modeling methods.  
Figure 5: The connections of different modeling methods.  
of ECM for improving the modeling accuracy [67]. Since the kinetic battery model is capable of capturing the nonlinear capacity effects (such as the recovery effect and rate capacity effect), a hybrid battery model including ECM and a kinetic battery model is proposed for modeling batteries [68]. The electrochemical model can also be combined with the ECM by using the electrical analogy of the mass transport equations in electrodes and electrolytes [69]. In order to predict the variation of the parameters and the polarization voltage drop under the changing current, _Butler-Volmer_ equation is simplified and added to the _Thevenin_ model in [70].  
ECM has been extensively applied to SOC estimation area but the relationship between the numbers of RC pairs and the accuracy of the ECM still needs further explanation. Several publications have tried to explain the relationship between the numbers of the RC networks and the accuracy of ECM [44; 45; 71; 72]. However, the essential reason why some models are good for the specific battery is not fully known.  
Once the structures of the battery model are determined, how to find the optimal parameters for each model is becoming important for the accuracy of the model. However, the importance of the parameters is not the same for the SOC estimation results. The updating frequency of each parameter does not need to be the same, since the parameters vary with different time scales. For example, the capacity decreases slowly with the lifespan of the battery, while the RC parameters change in the discharging process [22; 73]. More work is still needed to find the key parameters in the battery models for SOC estimation and decide on a reasonable updating frequency for each parameter. Moreover, although temperature affects the performance of the Li-ion battery [74; 75], the battery models for most SOC estimation methods have not taken temperature into consideration.