## 1 Introduction  
The permanent magnet synchronous motor (PMSM) is widely used in electric vehicles due to its high power density and excellent control performance [1; 2; 3], and it is usually driven with the pulse width modulation (PWM) inverters. The overall efficiency of the electric drive system is of vital significance for the operation reliability and the cost. Therefore, the power losses of different components for the drive system need to be investigated [4; 5]. In this paper, the conduction and switching losses are studied since the losses modeling can provide guidance for the improvement of the system efficiency and power density [6; 7]. Furthermore, it is regarded as an important input for the junction temperature prediction of semiconductor chips. In order to realize the accuracy of the junction temperature measurement and prevent the semiconductor chips from burning out, the real-time power losses calculation plays an important role [8; 9; 10]. Generally, the power losses of the converter chips can be divided into switching and conduction losses [7; 11]. The intrinsic switching delay accounts for the switching losses of the converters [12; 13]. In order to calculate the switching losses of the converter, it is essential to obtain the turn-on and turn-off energy losses of insulated-gate bipolar transistors (IGBT) and free-wheeling diodes (FWD) at every instance of turn-on and turn-off. The turn-on and turn-off energy losses data of IGBTs and FWDs are available in the device datasheet. However, they are given based on the specific test condition and not applicable in other operating points. Furthermore, the off-line measurement using the oscilloscope is an alternative to get the turn-on and turn-off energy loss data. However, it is not easy to measure at every operating point. Notably, the turn-on and turn-off energy losses are closely related to the collector-emitter drop and collector current, which change during the inverter operation. Thus, the empirical models are adopted to fit the experimental data, or look-up tables are utilized to estimate the IGBT switching losses based on different operating currents and voltages with the advantage of simplicity [12; 14]. The use of polynomials to fit switching loss characteristics can be found in ref. [15]. In ref. [16], an algebraic equation is derived to calculate the energy loss in one half of each switching transient. However, in order to obtain an accurate fitting waveform, too many measurements are required to obtain the voltage and current waveforms of the operating points. The on-state current and voltage drop across the IGBTs and FWDs account for the conduction losses in the power inverters. One common and traditional method is the measurement of the on-state current and the voltage drop based on every switching period [17]. Then these one-switching period losses are multiplied by the switching frequency for the total conduction losses. This method is independent of the modulation scheme. However, the computation demand is not ignored since the real-time calculation is required in every switching period. Considering that six switching tubes are operating symmetrically, the current-period-based method is adopted to calculate the power losses of IGBTs and FWDs. The modulation type and the machine topology determine the chips power losses in the inverter [18]. The conduction losses based on sinusoidal pulse width modulation (SPWM) are investigated [19; 20]. Since the space vector pulse width modulation (SVPWM) scheme has higher voltage utilization ratio than the SPWM-based algorithm, SVPWM-based modulation strategies have been widely used in automobile electric drives. Thus, the conduction losses model based on SVPWM is widely investigated [21; 22]. One of the difficulties is that the duty cycle is a complex piecewise function according to the power factor angle, which brings difficulties to practical application.