# Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy
## 3 System-Scale Optimization of Drive Systems
### Optimization Model for Control Level  
The response current of the motor under different operating conditions is related to the control strategy and the limits of the inverter bus voltage. A full-speed domain vector controller is adapted to meet the requirements of low-speed starting and high-speed cruising for the proposed IPMSM driving motor. In order to optimize the performance of the motor under different operating conditions, MTPA and flux-weakening control are used in this paper to meet the requirements of EVs. The control block is shown in Figure 6.  
When the load is given and the motor terminal voltage does not reach the limit with the speed below base speed, the IPMSM adopts the MTPA control strategy and runs at the MTPA trajectory. As shown in Figure 6, in this MTPA mode, by comparing the real speed \(n\) with the speed demand \(n^{*}\), the torque demand \(T^{*}\) could be obtained from the speed controller and input into the MTPA control part. And then, the current demand \(i_{\text{dq}}{}^{*}\) can be solved from torque Equations (6) and (9). If the motor operates in MTPA mode, d-axis and q-axis current demand \(i_{\text{d}}{}^{*}\), \(i_{\text{q}}{}^{*}\) are decoupled from \(i_{\text{dq}}{}^{*}\) and sent directly to the d-axis current controller and the q-axis current controller, respectively. Subsequently, the voltage demands \(u_{\text{d}}{}^{*}\), \(u_{\text{q}}{}^{*}\) are obtained, and through the \(2r/2\)s transformation and SVPWM module, they are finally turned into the switching signal to control the IGBT inverter. \[\frac{\partial(T/i_{\text{s}})}{\partial i_{\text{d}}}=\frac{\partial(T/i_{ \text{s}})}{\partial i_{\text{q}}}=0. \tag{9}\]  
When the speed demand is higher, the motor provides more torque to accelerate the rotor. At the early stage of speed regulation, the motor does not reach the base speed. However, as the motor voltage reaches its limit shown in (10), the motor speed approaches the base speed, and the speed loop saturates with the maximum given current. Therefore, the flux-weakening control strategy is adopted to redistribute the current in the dq axis through the leading angle so that the speed loop exits the saturation state and the motor torque meets the load. As shown in Figure 6, in this flux weakening mode, the leading angle \(\delta\) is calculated from the angle controller by comparing the bus voltage \(U_{\text{dc}}\) with the motor voltage. And the d-axis and q-axis current demand \(i_{\text{d}}{}^{*}\), \(i_{\text{q}}{}^{*}\) are redistributed by the current decoupling module according to \(\delta\) as (11). It can be found that the flux-weakening control can increase the motor torque and expand the operating range in comparison with the MTPA control at the same motor speed. \[u_{\text{s}}^{2}=p\Omega\sqrt{\left(L_{\text{q}}i_{\text{q}}\right)^{2}+\left( L_{\text{d}}i_{\text{d}}+\lambda_{\text{pm}}\right)}\leq u_{\text{lim}}^{2}, \tag{10}\]  
Figure 6: Control block diagram of the full-speed domain vector controller. where the motor stator resistance is neglected, and \(u_{\text{lim}}\) is the limited value of motor phase voltage. \[\left\{ \begin{array}{l}i_{\text{d}}^{*}=i_{\text{s}}\cos(\delta+\Delta\delta) \\ i_{\text{q}}^{*}=i_{\text{s}}\sin(\delta+\Delta\delta)\end{array} \right.. \tag{11}\]  
As described above, the speed demand is converted into torque demand by the speed controller, and the current demand is converted into voltage demand by two current controllers. In the implementation, the three PI controllers shown in Figure 6 have the form  
\[\left\{ \begin{array}{l}K_{\text{sp}}=\frac{\alpha+1}{\alpha}\frac{\pi l}{360T _{\text{s}}\lambda_{\text{APm}}};K_{\text{si}}=\frac{1}{\alpha}\frac{K_{\text{ sp}}}{4T_{\text{s}}}\\ K_{\text{ip\_d}}=\beta L_{\text{d}};K_{\text{ip\_q}}=\beta L_{\text{d}};K_{\text {ii\_d}}=K_{\text{ii\_q}}=\beta R_{\text{s}}\end{array}