## 4 System Loss Optimized Control for PMSM Drive System
By substituting Equations (5), (15) and (22) into Equation (57), the \(P_{Motor\_affect\_loss}\) can be simplified as:  
\[P_{Motor\_affect\_loss}=P_{conduction\_inverter}+P_{motor\_f}=f(i_{od},T_{e}, \omega_{r}) \tag{58}\]  
Equation (58) shows that the loss \(P_{Motor\_affect\_loss}\) is a function of \(d\)-axis magnetizing current \(i_{od}\), electromagnetic torque \(T_{e}\) and motor speed \(\omega_{r}\). Therefore, for each certain operation point, there must be an optimal \(d\)-axis magnetizing current \(i_{od}\)*, which can minimize the loss affected by motor state. The optimal \(d\)-axis magnetizing current \(i_{od}\)* can be expressed as:  
\[\frac{\partial P_{Motor\_affect\_loss}}{\partial i_{od}}\bigg{|}_{i_{od}=i_{od }^{*}}^{T_{e}=const,\omega_{r}=const}=0 \tag{59}\]  
By keeping the \(d\)-axis magnetizing current \(i_{od}\) at the optimal value, the proposed system efficiency improvement control can minimize the loss affected by motor operation condition at each working point of the PMSM system in EVs. There are two constraints for the optimal \(d\)-axis magnetizing current \(i_{od}\)*. One is that, in order to protect permanent magnet, the optimal \(d\)-axis magnetizing current should smaller than the maximum flux-weakening current, which can be shown as:  
\[|i_{od}^{*}|\leq\left|i_{d\_fluxeoakening\_max}\right| \tag{60}\]  
where \(i_{d\_fluxeoakening\_max}\) is the max flux-weakening current. When the \(d\)-axis current is larger than the maximum flux weakening current, the magnetic performance of the permanent magnet will be damaged beyond retrieval. Therefore, to maintain the system stability of PMSM drive system, the \(d\)-axis current should not exceed the max flux-weakening current. The other one is the total motor current should smaller than the maximum value of inverter current, which can be expressed as:  
\[i_{d}^{2}+i_{q}^{2}\leq I_{s\_max}^{2} \tag{61}\]  
where \(I_{s\_max}\) is the maximum allowable current of inverter. When the \(d\)-axis magnetizing current \(i_{od}\) is controlled at \(i_{od}\)*, the motor operation state is determined. Therefore, the second part of system loss \(P_{Double\_affect\_loss}\) will be only affected by the PWM frequency \(f_{sw}\) of the power converter, which is shown as:  
\[P_{Double\_affect\_loss}=P_{switch\_inverter}+P_{motor\_h}=f(f_{sw}) \tag{62}\]  
The PWM frequency \(f_{sw}\) impacts on the switching loss of the inverter and harmonics of motor loss. The high carrier to noise ratio (CTNR) in the higher PWM frequency will decrease the harmonics of the motor current, which will reduce the harmonic motor loss. However, an increasing switch loss will be caused by the higher PWM frequency. Therefore, it is significant to obtain the optimum PWM frequency \(f_{sw}\)* which can achieve the minimum value of switching loss and harmonic motor loss. However, the PWM frequency \(f_{sw}\) not only has an important influence on the loss affected by the motor and inverter operation state, but also affects the system stability of the PMSM system in EVs. As mentioned above, the PWM output voltage of the inverter must cause the harmonic current in the PMSM and the harmonic current will be greater in the low CTNR with small PWM frequency, which  
magnetizing _d_-axis current and PWM frequency at the optimum value over the whole operation range. The proposed control strategy can increase the efficiency of the PMSM drive system and reduce the energy consumption of EVs, by which the endurance mileage of EVs in one charge will be significantly improved. The structure diagram of the proposed system loss optimized control system is shown in Figure 8.