# Research on Constant Power Control Strategy of Pure Electric Excavator
## 3 Constant Power Control Based on Discharge Characteristics of the Power Battery  
As can be seen in Figure 3 which is provided by the battery manufacturer, the maximum discharge power of a cell monomer varies with the SOC at different ambient temperatures. Therefore, during the working process, the maximum discharge power of the battery should be limited according to the current environmental temperature and the SOC, so as to ensure that the battery will not over discharge and the battery life will not be shortened, and the system will run reliably due to the limitation of the discharge power. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Rated Power** & **Rated Torque** & **Rated Speed** & **Maximum Torque** & **Maxim Speed** \\ \hline PMSM & 49 (kW) & 260 (N-m) & 1800 (rpm) & 450 (N-m) & 3000 (rpm) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the EM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Normal** & **Normal** & **Maximum** & **Maximum Pulse** \\  & **Energy** & **Capacity** & **Discharge Current** & **Discharge Current** & **Voltage Range** \\ \hline LFP & 117 (kW-h) & 202 (A-h) & 202 (A) & 300 (A) & 450–675 (V) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the power battery. Figure 3: Maximum discharge power of the battery unit with SOC at different ambient temperatures. The discharge capacity of the battery pack varies from different SOC. The larger the SOC, the stronger the discharge capacity and the larger the discharge power. The maximum allowable discharge power of the power li-ion battery can be measured through an experimental platform for different SOC and is given in Figure 4.  
In the traditional electric excavator, by calculating the power required by the hydraulic pump, the output power of the battery is controlled. However, the discharge capacity of the power battery pack is also an important factor that should be taken into consideration. To avoid the over discharge of the battery pack and ensure control performance, the operating power of the power train system should be less than the maximum allowable discharge power of the battery pack. Therefore, during the control process, the current status information of the battery pack, such as SOC and temperature, should also be considered. The power of the control system should be not greater than the maximum allowable discharge power of the battery pack. The output power of the power train system can be described as:  
\[P_{p}\leq P_{bmax}\cdot\eta_{b}\cdot\eta_{mc}\cdot\eta_{m}\cdot\eta_{p}, \tag{1}\]  
where \(P_{bmax}\) is the maximum allowable discharge power of the current power lithium battery pack. \(\eta_{b}\) is the efficiency of the battery. \(\eta_{mc}\) is the efficiency of the EM driver. \(\eta_{m}\) is the efficiency of the EM. \(\eta_{p}\) is the efficiency of the hydraulic pump. The total efficiency after converting to the output power of the hydraulic pump can be calculated according to:  
\[\eta=\eta_{b}\cdot\eta_{mc}\cdot\eta_{m}\cdot\eta_{p}, \tag{2}\]  
where, \(\eta\) is the total efficiency from the battery to the hydraulic pump. As shown in Figure 5, the discharge efficiency of the power battery, which varies with different SOC, can be measured through an experimental platform and obtained according to the relationship between the discharge efficiency and the residual capacity of the battery measured during the discharge process at 23 \({}^{\circ}\)C from 100% to 10%. Figure 4: Maximum permissible discharge power of Li-ion batteries with different SOC 23 \({}^{\circ}\)C.  
Considering the high efficiency of the EM inverter, the loss of the EM inverter can be neglected. According to Figure 5, the maximum allowable discharge power of the li-ion battery pack at 23 \({}^{\circ}\)C can be described as:  
\[P_{\mathit{lmax}}=\left\{ \begin{array}{ccc}11\ \,&0\leq SOC\leq 10\%\\ 38\ \,&10\%<SOC\leq 30\%.\\ 63\ \,&30\%<SOC\end{array} \right.