## 3 Materials and Methods
### Variable-Speed Motor Drive-Variable-Displacement Hydraulic Pump Energy Consumption Model  
In analyzing a three-phase asynchronous motor, the leakage inductance between the rotor and stator sides is neglected, while the mutual inductance between these two components is considered. A motor loss model is developed within a two-phase rotating coordinate system. The primary contributors to motor losses include copper losses and iron losses. Additionally, this comprehensive assessment considers stray and frictional losses during load variations to be relatively minor, and these are thus disregarded. Consequently, the overall motor loss can be expressed as  
\[P_{loss}=P_{Cur}+P_{Fe}+P_{Cus}=aT_{e}\omega_{m}+(b_{1}+b_{2}\omega_{m}{}^{2} )\psi_{rd}{}^{2}+c\frac{T_{e}{}^{2}}{\psi_{rd}{}^{2}} \tag{10}\]  
of which  
\[a=\frac{2(R_{r}+R_{m})}{R_{m}{}^{2}}(R_{s}+\frac{R_{r}R_{m}}{R_{r}+R_{m}}) \tag{11}\]  
\[b_{1}=\frac{R_{s}}{L_{m}{}^{2}},b_{2}=P_{m}{}^{2}(\frac{R_{s}}{R_{m}{}^{2}}+ \frac{1}{R_{m}}) \tag{12}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Item** & **Quantity Value** \\ \hline \multirow{3}{*}{three-phase power meter} & voltage & 10.0–500.0 V \\  & current & 0.03–40 A \\  & voltage & 10.0–500.0 V \\ \hline \multirow{3}{*}{three-phase induction motor} & rated power & 110 kW \\  & rated voltage & 380 V \\ \hline \multirow{3}{*}{frequency changer} & input capacitance & 160 kVA \\  & speed stability accuracy & \(\pm\)0.5\% \\  & torque control accuracy & \(\pm\)5\% \\  & input capacitance & 160 kVA \\ \hline \multirow{3}{*}{hydraulic pump} & maximum displacement & 85 mL/r \\  & speed range & 500–3000 r/min \\  & maximum pressure & 35 MPa \\ \hline \multirow{3}{*}{overflow valve} & diameter & 30 mm \\  & maximum working pressure & 31.5 MPa \\  & maximum flow rate & 650 L/min \\ \hline \multirow{3}{*}{torque-speed sensor} & power source & \(\pm\)24 V \\  & torque signal & 5–15 khz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main parameters of the experimental platform. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Power (kW)** & **Optimum Speed (r/min)** & **Efficiency (\%)** \\ \hline
11.56 & 1325 & 61.05 \\ \hline
14.45 & 1375 & 68.12 \\ \hline
17.34 & 1425 & 69.78 \\ \hline
20.23 & 1475 & 70.51 \\ \hline
23.12 & 1525 & 73.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal speed rule for different load powers. \[c=(R_{s}+\frac{R_{m}R_{r}}{R_{m}+R_{r}})\frac{(R_{m}+R_{r})^{2}}{{p_{m}}^{2}{R_{m}}^ {2}} \tag{13}\]  
where \(T_{e}\) is the rated torque of the motor, \(\omega_{m}\) is the angular speed of the motor, \(\psi_{rd}\) is the \(d\) axis to the \(P\) particle flux-linkage component, \(\omega_{r}\) is the rotor angular frequency, \(P_{m}\) is the polar logarithm, \(R_{s}\) is the stator resistance, \(R_{m}\) is the equivalent resistance of stator iron loss, and \(L_{m}\) is the viscous damping of the stator rotor mutual inductance load. Variable-displacement hydraulic pump energy consumption model  
The energy consumption of a variable piston pump is mainly the mechanical friction loss caused by the mutual movement of each friction pair and the volume loss caused by oil leakage and oil compressibility in the hydraulic pump, where the volume efficiency and mechanical efficiency are, respectively,  
\[\eta_{v}=1-C_{s}\frac{60\Delta p}{\mu n}.\frac{1}{\beta} \tag{14}\]  
\[\eta_{m}=[1+C_{v}(\frac{\mu n}{60\Delta p\beta})+\frac{C_{f}}{\beta}+\frac{2 \pi T_{s}}{\Delta pq_{i}\beta}]^{-1} \tag{15}\]  
where \(T_{s}\) is the input torque of the plunger pump, \(T\) is the actual torque of the pump, \(\Delta T\) is the torque loss of the piston pump due to mechanical friction, \(C_{f}\) is the oil friction coefficient under the laminar-flow state in the hydraulic pump, and \(C_{v}\) is the mechanical friction coefficient between the friction pairs in the pump.