## 1 Introduction  
Compared with direct-current (DC) motors and induction motors, permanent magnet synchronous motors (PMSMs) are preferred to power propulsion in the aviation and aerospace field for their high efficiency and high power-to-weight ratio. The efficiency performance is particularly important in the aviation and aerospace field since there is only limited energy. The efficiency of PMSMs will directly be related to the safe run time, battery size and effective load capacity. The motor losses of PMSMs consist of mechanical loss, copper loss, iron loss and stray loss. To achieve a higher efficiency of PMSMs, the electromagnetic structure is in the optimized design to reduce the copper loss and iron loss [1; 2; 3]. However, the high-performance PMSMs need not only the optimal design of the electromagnetic structure but also efficiency optimization control strategies. There are several vector control strategies for PMSMs such as \(i_{d}=0\) control, unity power factor (UPF) control, maximum torque per ampere (MTPA) control, maximum speed per voltage (MSPV) control and loss model control (LMC). The \(i_{d}=0\) control keeps the electromagnetic torque and \(q\)-axis current in a linear relationship by keeping the \(d\)-axis current at zero [4; 5]. The \(i_{d}=0\) control is widely used in surface-mounted PMSMs (SPMSMs) and will not damage the permanent magnet. The \(i_{d}=0\) control is the MTPA control in SPMSMs as the inductance in the \(d\)-axis is equal to that in the \(q\)-axis, and the torque is linearly related to the \(q\)-axis current. However, \(i_{d}=0\) control cannot maximize the electromagnetic torque in interior PMSMs (IPMSMs), and, therefore, MTPA control is presented to make the most use of the reluctance torque in IPMSMs [6; 7]. The MTPA control can achieve the minimum copper loss since the least armature current is required to obtain the same electromagnetic torque. The \(i_{d}=0\) control and MTPA control only optimize the copper loss and will not raise the maximum efficiency of PMSMs [8; 9; 10]. The MSPV control can minimize the winding terminal voltage and significantly decrease the iron loss. The MSPV control just affects the iron loss and cannot acquire the minimum loss of the PMSM. The UPF control could decrease the reactive power to zero and reduce the energy loss between power transmissions [11; 12]. However, the UPF control does not focus on the loss of the PMSM and will not achieve the maximum efficiency in each operation condition of the PMSM. The LMC takes into account both the copper loss and iron loss of the PMSM, and could optimize the motor loss in the whole operation range of the PMSM [13; 14]. However, the LMC only focuses on the optimization of the fundamental loss of the PMSM and ignores the harmonic loss of the PMSM. As the PMSM is fed by the pulse-width modulation (PWM) inverter, there must be a large number of harmonic components on the terminal voltage of the PMSM. The harmonic voltage will cause the harmonic current in the PMSM which can generate harmonic loss and have an influence on the efficiency of the PMSM. To acquire the minimum motor loss, the efficiency optimization control algorithm has to consider both the fundamental loss and harmonic loss. This paper proposes a novel analytic loss model of PMSMs, which is able to calculate fundamental loss (copper loss and iron loss) and harmonic loss (iron loss) together in either sine-wave pulse-width modulation (SPWM) or space vector pulse width modulation (SVPWM). The fundamental iron loss is estimated by the average flux density in the stator tooth and yoke. As the PMSM is fed by the PWM inverter, the harmonic content of the output voltage in the inverter is analyzed by the double Fourier integral analysis and the harmonic loss is obtained in the Bertotti iron loss formula by the harmonic voltages.