## 2 System Dynamics Modeling
### Battery Model
#### 2.3.1 Energy Loss Model  
An accurate battery model is conducive to better battery management which allows full use to be made of the battery's performance. In accordance with the model mechanism, battery models can be divided into: electrochemical models, equivalent circuit models, neural network models and so on [34]. The model established according to the chemical reaction mechanism of the battery is called the electrochemical model, and this can accurately simulate the main characteristics of the battery. However, this model is complicated and has too many parameters, meaning it is difficult to calculate and is not suitable for control design [35]. The neural network model simulates the state change of the battery through the training and self-learning of the internal parameter data, but it requires a large volume of calculations and a long processing time [36]. The equivalent circuit model simplifies the reaction mechanism of the battery, reduces the number of calculations required for the model, and can reflect the battery mechanism. It is the current mainstream battery model [37]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters (Unit)** & **Value** & **Parameters (Unit)** & **Value** \\ \hline \(m\) (kg) & 775 & g & 9.8 \\ \(A\) (m\({}^{2}\)) & 2.04 & \(f\) & 0.0112 \\ \(r\) (m) & 0.252 & \(\mathcal{C}_{D}\) & 0.25 \\ \(\delta\) & 1 & \(\rho\) & 1.18 \\ \(\eta\) & 0.95 & \(i\) & 6.515 \\ \(\eta_{\text{m}}\) & 0.95 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 1: Efficiency map of the electrical machine. In summary, to meet control requirements, an equivalent circuit model is adopted in this article. In references [11; 38], the Rint model is used to account for the dynamic energy consumption of the batteries, and the verification results show that the model is accurate [4]. The Rint model has few parameters, which allows for faster controller calculations, as shown in Figure 2.  
According to the Rint circuit model, the output power and output voltage of the battery are expressed as Formula (3):  
\[\left\{ \begin{array}{l}P_{bat}=I_{bat}\cdot U_{t}\\ U_{t}=OCV-I_{bat}R_{0}\end{array} \right. \tag{3}\]  
where \(P_{bat}\) is the power of the battery; \(I_{bat}\) is the output current of the battery; \(U_{t}\) is the output voltage of the battery; \(OCV\) is the open circuit voltage of the battery, which changes with the SOC of the battery; and \(R_{0}\) is the ohmic resistance of the battery. In this study, the Lishen 20 AH lithium iron phosphate battery produced by a company was selected as the experimental object, and some of its specific parameters are shown in Table 2. The experimental equipment was a 5 V-20 A range battery test cabinet from Ningbo Baite Measurement and Control Co., Ltd. (Ningbo, China), a LW-150 high- and low-temperature test box from Shanghai Haixiang Instrument and Equipment Co., Ltd. (Shanghai, China), and a host computer. The battery test system shown in Figure 3 consisted of a thermostat used to set the test environment temperature for the battery, an upper computer used to design the test conditions for the battery and record the charge and discharge data of the battery, and a battery testing box used to test the battery according to the set charging and discharging conditions. The experimental results show that the OCV-SOC data of the battery can be fitted to a curve, as shown in Figure 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters (Unit)** & **Value** & **Parameters (Unit)** & **Value** \\ \hline Rated voltage \(V_{cell}\) (\(V\)) & 3.2 & Charging voltage (\(V\)) & 3.65 \(\pm\) 0.05 \\ Rated Capacity \(Q_{ini}\) (\(A\hbar\)) & 20 & Cut-off resistance \(R_{0,EOL}\) (\(\Omega\)) & 0.0107 \\ Initial resistance \(R_{0,new}\) (\(\Omega\)) & 0.0063 & Operating temperature (\({}^{\circ}\)C) & \(-\)20\(-\)45 \\ Number of batteries in series & 45 & Number of parallel batteries & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Battery parameters. Figure 2: Rint circuit model.