## 5 Drive System Simulation
### Simulation Results  
To validate to proposed control methods, we ran a simulation of the OW-PMSM drive system on Matlab/Simulink platform. The basic parameters of the drive system circuit are shown in Table 2 and the controller parameters are shown in Table 3. It is important to note that an extra motor speed controller, which is actual a PI controller, was used to generate the desired torque \(T_{e}^{*}\) inputted to the torque regulator mentioned above to make the motor speed follow the preset value. This motor speed controller is not necessary in an electric vehicle and not shown in Figure 10.  
Figure 10: Overall configuration of the proposed system. This simulation's duration was 0.9 s. The expected motor speed linearly increased from 0 to 6000 r/min in 0-0.3 s and stayed at 6000 r/min till 0.6 s. Then the speed linearly dropped to 0 in 0.6-0.9 s. The load torque jumped from 0 to 60 N\(\cdot\)m at 0.05 s and remained until simulation finished. Curves of motor's expected and actual rotational speed are shown in Figure 11a, curves of motor's desired torque, electromagnetic torque, and load torque are shown in Figure 11b. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modules** & **Items** & **Parameters** \\ \hline \multirow{2}{*}{Solver} & Solve type & Discrete \\ \cline{2-3}  & Time step \(T_{s}\)/s & \(5\times 10^{-7}\) \\ \hline \multirow{6}{*}{OW-PMSM} & Motor type & Interior open-end winding PMSM \\ \cline{2-3}  & Number of pole pairs \(p_{0}\) & 4 \\ \cline{2-3}  & Stator resistance \(R_{s}\)/\(\Omega\) & 0.1 \\ \cline{2-3}  & Fundamental amplitude and third harmonic amplitude & [0.2, 0.01] \\ \cline{2-3}  & of permanent magnet flux linkage [\(\psi_{f}\), \(\psi_{\gamma 3}\)]/Wb & [0.2, 0.01] \\ \cline{2-3}  & d-axis and q-axis inductance [\(I_{d}\),\(I_{q}\)]/F & [0.0012, 0.0015] \\ \cline{2-3}  & Zero sequence inductance \(I_{0}\)/F & 0.0003 \\ \cline{2-3}  & Rotational inertia of rotor \(J_{m}\)/kg m\({}^{-2}\) & 0.011 \\ \cline{2-3}  & Cullen and viscous resistance coefficient & [0.001, 0.0005] \\ \hline \multirow{6}{*}{Inverter devices} & On-resistance \(R_{m}\)/\(\Omega\) & 0.01 \\ \cline{2-3}  & Forward voltage drop \(V_{f}\)/V & 0.8 \\ \cline{2-3}  & Current fall time and tailing time [\(T_{f}\),\(T_{1}\)]/s & [1, 1.5] \(\times 10^{-6}\) \\ \cline{2-3}  & Current capacity of each phase \(i_{\text{max}}\)/A & 160 \\ \hline \multirow{2}{*}{Power Sources} & DC-bus voltages of primary and secondary power & [300, 200] \\ \cline{2-3}  & source [\(V_{d\text{+}1}\),\(V_{d\text{+}2}\)]/V & [300, 200] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the drive system circuit. OW-PMSM: open-end winding permanent magnet synchronous motor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modules** & **Items** & **Parameters** \\ \hline \multirow{3}{*}{Motor speed controller} & Sampling time \(T_{s\_SC}\)/s & \(1\times 10^{-4}\) \\  & Proportionality coefficient \(P_{SC}\) & 0.2 \\  & Integral coefficient \(I_{SC}\) & 2 \\ \hline \multirow{2}{*}{Torque regulator} & Sampling time \(T_{s\_TR}\)/s & \(1\times 10^{-4}\) \\  & Voltage saturation coefficient \(k_{u}\) & 0.95 \\ \hline \multirow{3}{*}{Current regulator} & Sampling time \(T_{s\_CR}\)/s & \(1\times 10^{-4}\) \\  & Proportionality coefficient \(P_{CR}\) & 2 \\  & Integral coefficient \(I_{CR}\) & 120 \\ \hline \multirow{3}{*}{Desired power calculator} & Sampling time \(T_{s\_PC}\)/s & \(1\times 10^{-4}\) \\  & Gain of the inertial element \(K_{PC}\) & 0.5 \\  & Time constant of the inertial element \(T_{PC}\)/s & 0.05 \\ \hline \multirow{2}{*}{Voltage vector distributor} & Sampling time \(T_{s\_VD}\)/s & \(1\times 10^{-4}\) \\  & Maximum power difference of inverter1 \(D_{pinv1\_max}\)/kW & 3 \\ \hline \multirow{2}{*}{SVPWM modulator} & Sampling time \(T_{s\_SVM}\)/s & \(1\times 10^{-4}\) \\  & Control period \(T_{c\_SVM}\)/s & \(1\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the drive system controller. SVPWM: space vector pulse width modulation.