# A Novel Energy Optimization Control Strategy for Electric Drive System Based on Current Angle
## 2 Electric Drive System Loss Model
### Mathematical Motor Loss Model  
Generally, there are two modeling methods of motor: Finite element modeling and mathematical modeling. The finite element model of the motor can accurately reflect the internal loss in motor and other nonlinear phenomena, such as demagnetization and inductance change [29]. However, this kind of method takes up a lot of computing resources and is often used in the performance simulation of motor rather than the research of control strategy, so this paper used MATLAB/ Simulink (Version 2018 b) to complete the mathematical modeling. In this paper, a surface mounted permanent magnet synchronous motor is used for research. Its parameters are as Table 1.  
The controllable loss of motor includes copper loss and iron loss. The loss caused by resistance heating of the motor winding is called copper loss. Meanwhile, iron loss is caused by hysteresis effect and stator eddy current, among which the former is caused by the blocking effect of the iron core on the flux flow of the stator, and the latter is caused by the eddy current generated by the induced electromotive force on the cross section of the iron core. To consider the influence of iron loss, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Peak power & 46.5 KW \\ Rated speed & 2880 rpm \\ Peak torque & 154.2 Nm \\ Pole number & 4 \\ Rated voltage & 600 V \\ Peak current & 200 A \\ Rotor flux linkage & 0.0642 Wb \\ dq-axis inductance & \(7.0743\times 10^{-4}\) H \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Permanent magnet synchronous motor (PMSM) parameters in this paper. Figure 1: Schematic of general electric drive system. an iron loss resistance \(R_{c}\) is paralleled in the dynamic equivalent circuit diagram of permanent magnet synchronous motor, as shown in Figure 2. The equivalent equation of voltage in this model is [30]:  
\[\left[ \begin{array}{c}\begin{array}{c}\mathcal{U}_{d}\\ \mathcal{U}_{q}\end{array}\end{array} \right]=R_{s}\left[ \begin{array}{c}i_{ad} \\ i_{aq}\end{array} \right]+(1+\frac{R_{s}}{R_{c}})\left[ \begin{array}{c}U_{od}\\ U_{aq}\end{array} \right] \tag{1}\]  
\[\left[ \begin{array}{c}\mathcal{U}_{od}\\ \mathcal{U}_{aq}\end{array} \right]=\left[ \begin{array}{cc}0&-\omega pL_{q}\\ \omega L_{d}&0\end{array} \right]\left[ \begin{array}{c}i_{ad}\\ i_{aq}\end{array} \right]+\left[ \begin{array}{c}0\\ a\psi_{f}\end{array} \right] \tag{2}\]  
\[\left\{ \begin{array}{c}i_{ad}=i_{d}-i_{cd}\\ i_{aq}=i_{q}-i_{cq}\end{array} \right. \tag{3}\]  
\[\left\{ \begin{array}{c}i_{cd}=\frac{-\omega pL_{d}i_{aq}}{R_{c}}\\ i_{cq}=\frac{\omega(\phi_{f}+L_{d}i_{ad})}{R_{c}}\end{array} \right. \tag{4}\]  
where \(i_{d}\), \(i_{q}\) are the armature current vector of d-axis and q-axis, respectively. \(U_{d}\), \(U_{q}\) are the voltage vectors of d-axis and q-axis, respectively. \(i_{cd}\), \(i_{cq}\) are the iron loss current of d-axis and q-axis, respectively. \(i_{dd}\), \(i_{qq}\) are the effective current vectors of d-axis and q-axis, respectively. \(L_{d}\), \(L_{q}\) are the inductance of d-axis and q-axis, respectively. \(R_{s}\) is copper loss resistance; \(R_{c}\) is the core loss resistance; \(\psi_{f}\) is the flux linkage. \(\omega_{e}\) is the electric angular velocity. \(\rho\) is the salient rate. The iron loss resistance \(R_{c}\) can be calculated by the following formula [31]:  
\[R_{c}=\frac{1}{K_{f}\frac{K_{b}}{\omega e}} \tag{5}\]  
Copper loss is caused by the resistance heating when the stator armature passes through the stator winding, and its valve is related to the armature current and copper loss resistance. In the equivalent circuit of this paper, the expression is:  
\[P_{Cu}=R_{s}({i_{d}}^{2}+{i_{q}}^{2}) \tag{6}\]  
Substituting Equations (3), (4) and (6), copper loss can be derived to be:  
\[P_{Cu}=R_{s}\left\{(i_{od}-\frac{\omega pL_{d}i_{aq}}{R_{c}})^{2}+(i_{aq}+ \frac{\omega(\phi_{f}+L_{d}i_{od})}{R_{c}})\right\} \tag{7}\]  
Figure 2: Equivalent circuit schematic of PMSM: d-axis equivalent circuit (**a**); q-axis equivalent circuit (**b**).