# Motor Vector Control Based on Speed-Torque-Current Map
## 3 Motor Vector Control Strategy Based on Speed-Torque-Current Map  
### Motor Model and Operation Constraints  
The motor MG1 is taken as an example for modeling. The PMSM with three-phase and four-pair poles is selected, whose parameters are shown in Table 3.  
There is always power loss in the working process of a motor, which leads to the fluctuation of speed and torque. The iron loss model can not only reflect the changes of motor voltage, current, flux, and torque, but can also express the changes of the controllable loss including copper loss and iron loss caused by the winding current, which is widely used in the PMSM loss modeling [17]. The equivalent circuit diagram of the PMSM dynamic model employed in this paper is shown in Figure 3. Considering the loss caused by the stator eddy current and hysteresis effect, an iron loss resistance \(R_{c}(\omega)\) is added to the equivalent circuit in parallel. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Quantity (Unit)** & **Value** \\ \hline \multirow{4}{*}{MG1} & Rated/peak power (kW) & 22/46.5 \\  & Rated/maximum speed (rpm) & 2880/5636 \\  & Rated/maximum torque (Nm) & 73/154 \\  & Rated/peak power (kW) & 10/20.5 \\ MG2 & Rated/maximum speed (rpm) & 3300/8338 \\  & Rated/maximum torque (Nm) & 29/59 \\ \multirow{2}{*}{Planetary gear} & Ratio k & 2.6 \\  & Ratio i\({}_{1}\) & 2.92 \\  & Gear 2 & Ratio i\({}_{2}\) & 1.2 \\  & Ratio i\({}_{0}\) & 4.05 \\  & Type & Li-ion \\ Battery pack & Rated voltage (V) & 333 \\  & Rated capacity (Ah) & 78 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters of the system. Figure 3: Equivalent circuit diagram of the permanent magnet synchronous motor (PMSM) dynamic model. (**a**) d-axis equivalent circuit, (**b**) q-axis equivalent circuit. The voltage equivalent equations of the dynamic model are as follows. \[\left[ \begin{array}{c}\mathrm{u_{d}}\\ \mathrm{u_{q}}\end{array} \right]=\mathrm{R_{s}}\left[ \begin{array}{c}\mathrm{i_{ od}}\\ \mathrm{i_{oq}}\end{array} \right]+\left(1+\frac{\mathrm{R_{s}}}{\mathrm{R_{c}}} \right]\left[ \begin{array}{c}\mathrm{u_{od}}\\ \mathrm{u_{oq}}\end{array} \right] \tag{1}\]  
\[\left[ \begin{array}{c}\mathrm{u_{od}}\\ \mathrm{u_{oq}}\end{array} \right]=\left[ \begin{array}{cc}0&-\omega\mathrm{p }\mathrm{L_{q}}\\ \omega\mathrm{L_{d}}&0\end{array} \right]\left[ \begin{array}{c}\mathrm{i_{ od}}\\ \mathrm{i_{oq}}\end{array} \right]+\left[ \begin{array}{c}0\\ \omega\mathrm{\varphi_{f}}\end{array} \right] \tag{2}\]  
\[\left\{ \begin{array}{c}\mathrm{i_{od}}=\mathrm{i_{d}}-\mathrm{i_{od}},\\ \mathrm{i_{oq}}=\mathrm{i_{q}}-\mathrm{i_{eq}}\end{array} \right. \tag{3}\]  
\[\left\{ \begin{array}{c}\mathrm{i_{cd}}=-\frac{\omega\mathrm{p}\mathrm{L_{d}} \mathrm{i_{eq}}}{\mathrm{R_{c}}},\\ \mathrm{i_{cq}}=\frac{\omega(\mathrm{\varphi_{f}}+\mathrm{i_{od}})}{\mathrm{R_{ c}}}\end{array} \right. \tag{4}\]  
The iron loss resistance \(\mathrm{R_{c}}\) is calculated by [18]:  
\[\mathrm{R_{c}}=\frac{1}{\mathrm{K_{f}}\frac{\mathrm{R_{h}}}{\omega}}. \tag{5}\]  
Due to the limits of battery voltage, temperature, the bearing capacity of components, and PWM (pulse width modulation) modulation methods, the current and voltage supply capacity of the inverter is limited respectively to \(\mathrm{i_{lim}}\) and \(\mathrm{U_{dc,lim}}\).