## 1 Introduction  
One of the major challenges currently faced in the transportation sector is how to decrease the dependency on fossil fuels and thus reduce the emission of greenhouse gases. As electric vehicles (EVs) have the advantage of eliminating the automobile exhaust and offer an ultimate solution for sustainable personal mobility [1; 2], EVs seem to be one of the best future alternatives for the automotive industry and transportation [3]. However, the limited operational range of EVs is a major drawback which is mostly affected by the battery management system and motor drive system. As the motor drive system is the main power source of EVs, the efficiency of the drive system will directly influence their mileage endurance. Compared with induction motors (IMs) and switched reluctance motors (SRMs) [4; 5], permanent magnet synchronous motors (PMSMs) with their advantage of high power density and high efficiency, can decrease the energy consumption and improve the operational mileage of EVs [6; 7; 8], therefore, the PMSM direct drive system has been widely applied in EVs for transportation. The optimization of the electromagnetic structure and control strategy of PMSMs has been widely discussed in recent years. There are several PMSM control strategies, such as \(i_{4}=0\) control, maximum torque per ampere (MTPA) control, maximum speed per voltage (MSPV) control, unity power factor (UPF) control, loss model control (LMC) and etc. [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. The \(i_{d}=0\) control is the most conventional vector control method used in PMSM drive systems. In [9; 10; 11], the finite element method (FEM) is used to calculate the motor loss, and the \(i_{d}=0\) control is used to drive the PMSM system to verify the performance of a PMSM. By keeping the motor current in the \(d\)-axis at zero, the \(i_{d}=0\) control can make the electromagnetic torque and \(q\)-axis motor current proportional, and will not damage the magnetic properties of the permanent magnet. However, in [12], the \(i_{d}=0\) control method could not minimize the stator current in the interior of a PMSM in which the \(d\)-axis magnetic inductance is not equal to \(q\)-axis magnetic inductance, and could not achieve minimum copper loss in IPMSMs. Compared with other control strategies, the MTPA control method can take advantage of the reluctance torque of the motor, by which the stator current is decreased [13; 14; 15; 16]. In [16], the improved MTPA control takes the core saturation and cross coupling of the \(d\)- and \(q\)-axis magnetic flux into account, and the motor performance was optimized with the consideration of the impact of various temperatures. The MTPA control can obtain the minimum stator current and achieve the least copper loss below the rated speed. Meanwhile, the MSPV control can optimize the stator voltage and obtain the optimal stator iron below rated torque [17]. However, as the losses of a PMSM are comprised of copper loss and iron loss, both the MTPA control method and MSPV control method only consider part of the total motor loss, and ignore the coupling relationship between copper loss and iron loss. Therefore, neither the MTPA control strategy nor the MSPV control strategy will achieve the maximum motor efficiency in PMSMs [18]. The UPF control can keep the power factor of PMSMs to one and decrease the energy consumption in the power transfer process [19; 20; 21]. In Ref. [21], a PMSM drive system with small DC-link capacitor applied UPF control to stabilize the motor driving and decrease the energy loss on the input side. As the UPF control does not take into consideration the power loss in PMSMs, the motor efficiency will not always achieve the maximum value under UPF control. The LMC can optimize both copper loss and iron loss by the PMSM loss model and improve the motor efficiency of the PMSM system [22; 23; 24]. In Ref. [23], the motor iron loss is calculated by the iron loss resistance, and both the iron loss and copper loss are optimized.