Efficiency Comparison of 2-Level SiC Inverter and Soft Switching-Snubber SiC Inverter for Electric Motor Drives

This paper focuses on the investigation and implementation of a high-performance power conversion system to reduce the overvoltage phenomenon in variable speed electric drive applications. Particularly, the pros and cons of using Silicon Carbide power MOSFETs in the power converter when a long power cable is employed in electric motor drive systems has been addressed. The three-phase two level inverter with the addition of snubber circuits that consist of capacitors and diodes has been investigated, designed and tested in order to mitigate the overvoltage problems without sacrificing the conversion efficiency. Given that the snubber circuit added to the switches can increase losses, an additional circuit is used to recover the energy from the snubber circuit. The proposed analysis has been then validated through an experimental campaign performed on the converter prototype. The experimental results show that the proposed converter can reduce the overvoltage at the electric motor terminals with excellent conversion efficiency compared to the classical solution like the three-phase two level inverter.


Introduction
Nowadays, thanks to continuous improvement of power electronics technologies, Wide-Band-Gap (WBG) switching devices are now reaching a satisfactory level of maturity and their performance and capabilities are very useful and promising for very high efficiency applications [1,2]. Among WBG devices, the most technologically mature are Silicon Carbide (SiC) based switches [3]. Using the SiC power semiconductors allows the switching rate to increase so that small power losses can be achieved. Alternatively, keeping constant the power losses, it is possible to increase the switching frequency leading to a reduction of volume and weight of passive energy-storage components. For this reason, being able to integrate components like inductors and capacitors, it is now possible to maximize the power density of the power conversion system. Furthermore, SiC power semiconductors present higher voltage-blocking capability and lower on-state resistance compared to silicon based power semiconductors, as well as several benefits related to thermal management, so they are perfect for high temperature applications [4][5][6]. Particularly, given that the SiC power semiconductors can operate at extremely high junction temperatures, it is either possible to increase the power density of the whole converter system by decreasing the size of the heatsink, or to reach higher voltage applications without the need to enlarge the heatsink. However, in some cases, the high-power density and the high efficiency can be achieved using sophisticated power conversion topologies, avoiding SiC power semiconductors [7][8][9][10]. In these cases, the complexity of the conversion system control strategy increases, due to the large number of power devices [11,12]. The SiC power Metal-Oxide-Semiconductor Field-effect Transistors (MOSFETs) will outshine Insulated Gate Bipolar Transistors (IGBTs) in all drives applications where the use of long cables and short circuit capability is not needed [13]. For example, in the automotive In [32] a design procedure for a passive electromagnetic interference filter based on the parallel connection of the inductors and the resistors has been proposed for reducing the overvoltage at the motor terminals. In [33] the mitigation of the overvoltage for an openend winding motor configuration has been presented using two parallel power converters without employing passive filters, whereas in [34] the overvoltage is reduced thanks to the active reflected wave canceller circuit. In [35] a modular multilevel converter (MMC) with a filter capacitor and the arm inductors has been proposed to reduce the overvoltage at motor terminal. A soft-switching circuit, entitled the auxiliary resonant soft-edge pole (ARSEP), has been proposed in [36] to mitigate the dV/dt.
The goals of this paper are to investigate, to analyze, and to implement a possible solution to reduce the overvoltage across the electrical motor when a long power cable and fast dynamic power semiconductors are used in variable speed electric drives, avoiding the presence of passive filters between the motor and the converter. To this purpose, a snubber two-level inverter (S2L Inverter) already present in the literature which makes use of SiC power MOSFETs has been designed and used to reduce the dV/dt of the SiC devices and to limit the overvoltage on the electric motor side. Furthermore, the performance of the S2L inverter is compared to the classical three-phase two level (2L) inverter. In the paper, following the introduction, the pros and cons of the SiC power MOSFETs in the motor drive application are presented in Section 2. Then the overvoltage phenomenon in motor drive application using SiC power MOSFETs is experimentally shown in Section 3. A case study of a power conversion system called S2L Inverter which is able to limit the overvoltage issue in motor drive application is discussed in Section 4. The experimental results from a S2L laboratory prototype are illustrated in Section 5. Conclusions are finally presented in Section 6.

SiC Power MOSFETs in Motor Drive Applications: Pros and Cons
In several industrial drive applications, the inverter and the electric motor are located in different places. Consequently, the use of long length feeding cable is necessary. Due to the presence of the long cable and motor, the inverter load is not anymore only resistive and inductive, but the high value of parasitic capacitance of the entire system changes the load in an inductive, resistive and capacitive load.
SiC MOSFETs can be excellent candidates in motor drive application. Compared to Si IGBTs they have better performance at low load conditions, lower switching losses, an intrinsic body diode with low recovery energy and the possibility to work in synchronous rectification helps a lot to reduce the total amount of power losses. These advantages of the SiC MOSFET over the IGBT have been supported by experimental tests. Figure 1 shows the experimental setup used to test the switching commutation of the power semiconductors when a long cable is connected to the electric motor. Looking at the figure, it is possible to recognize a 7.5 kW induction motor (part number: M2QA132S2B), the power cables of 2.5 m and 15 m with a section area equal to 4 mm 2 (Igus, part number: CF38.60.04) and the inverter. The inverter has been equipped with different switching components and the characteristics and operating parameters of each power semiconductor used as Device Under Test (DUT) are listed in Table 1.  To evaluate the thermal response of the different power switches, the case temperature of the device under test was checked every 10 s with a Negative Temperature Coefficient (NTC) sensor directly placed on the case. The power switches in all tests have been turned on and turned off every 60 s, as shown in Figure 2.
The thermal behavior demonstrates a huge improvement in terms of temperature performance of the SiC MOSFET (IMW120R045T1) compared to the IGBTs. This result shows that using the SiC MOSFET is possible to obtain one of these improvements: (1) higher efficiency of the power conversion system at the same switching frequency; (2) keeping constant the efficiency is possible to increase the switching frequency; (3) heatsink lower volume.
The loss reduction of power semiconductors is the key point to increase the power density of the conversion system. Increasing the power density, it is possible either to shrink the system physical dimensions with the same power rating or to maintain constant the physical dimension constant and increase the power rating of the converter. The less effort in power dissipation is also an important sales point, given that less power losses of SiC MOSFETs can lead to a reduction of both the cooling effort per power unit and the cooling cost per power. Naturally, there are also drawbacks of using SiC MOSFETs in motor drives applications. The first one is related to the overload condition requested in this kind of application. Typical overload values are: (1) 150% to 180% of the rated current  To evaluate the thermal response of the different power switches, the case temperature of the device under test was checked every 10 s with a Negative Temperature Coefficient (NTC) sensor directly placed on the case. The power switches in all tests have been turned on and turned off every 60 s, as shown in Figure 2.
The thermal behavior demonstrates a huge improvement in terms of temperature performance of the SiC MOSFET (IMW120R045T1) compared to the IGBTs. This result shows that using the SiC MOSFET is possible to obtain one of these improvements: (1) higher efficiency of the power conversion system at the same switching frequency; (2) keeping constant the efficiency is possible to increase the switching frequency; (3) heatsink lower volume. drives. At heavy loads, IGBTs have a better conduction performance compared to SiC MOSFETs, as well as easier short circuit detection. The second big drawback is the short circuit capability required in industrial drives; a short circuit time withstand of 8 µ s to 10 µ s is mandatory. Up to now only the commercial SiC MOSFETs from Infineon Technologies (IMW120RxxxM1) have a short circuit capability, however the time is 3 µ s, which is far away from the requested ones. The last main drawback is high dV/dt when the SiC power MOSFETs are used in the VFD application.

Overvoltage Phenomenon in VFD Applications
In many industrial applications, the converter and the motor are at separate locations. Consequently, the use of long feeding power cables is needed. It has been demonstrated [20][21][22] that the voltage pulses travel with speed, which is approximately half the speed of light (150 m/µ s). If the pulse takes longer than half the rise time to travel from the inverter to the motor, a full reflection occurs at the motor terminals, and the pulse amplitude is approximately doubled. So, if tr ≤ 2td, where tr is the voltage rise time at the inverter output terminals and td is the cable propagation time, the line-to-line peak voltage Vm on the motor side is almost two times the DC-bus voltage VBUS. Thus, the voltage reflection is a function of both the inverter pulse rise time and the length of the motor cables, as well as of the impedance mismatch between motor, cables and inverter. It is easy to understand that using new fast dynamic devices, line-to-line voltage Vm across the motor side is almost two times the DC bus voltage VBUS. Furthermore, the fast switching produces complex transitions that highly stress the motor insulation; as a result, the machine winding can fail prematurely [37,38]. The influence of the length of power cables connected between the converter and the motor is shown in Figures 3 and 4.
The converter is composed of the SiC power module (Semikron, part number: 26ACM12V17), while two Igus power cables (part number: CF270.UL.60.04.D) with different lengths, 15 m and 30 m, are used to connect the converter to the motor. The figures shown illustrate the turn-off and turn-on of the DUT. The blue waveform is the voltage between the output of the phase A (middle point) and minus DC-bus VBOT,A (voltage across the bottom device of the phase A) and the red waveform is the line-to-line voltage at the motor terminal Vm when the length of the power cable is equal to 15 m. The orange waveform is the inverter voltage VBOT,A and the violet waveform is the line-to-line voltage Vm across the motor when the length of the cable is equal to 30 m. As it can be seen, the voltage Vm is almost two times VBUS in both the figures and the ringing expiration time (RET) in- The loss reduction of power semiconductors is the key point to increase the power density of the conversion system. Increasing the power density, it is possible either to shrink the system physical dimensions with the same power rating or to maintain constant the physical dimension constant and increase the power rating of the converter. The less effort in power dissipation is also an important sales point, given that less power losses of SiC MOSFETs can lead to a reduction of both the cooling effort per power unit and the cooling cost per power. Naturally, there are also drawbacks of using SiC MOSFETs in motor drives applications. The first one is related to the overload condition requested in this kind of application. Typical overload values are: (1) 150% to 180% of the rated current per 60 s for the standard drives, (2) 200% to 300% of the rated current per 3 s for the servo drives. At heavy loads, IGBTs have a better conduction performance compared to SiC MOSFETs, as well as easier short circuit detection. The second big drawback is the short circuit capability required in industrial drives; a short circuit time withstand of 8 µs to 10 µs is mandatory. Up to now only the commercial SiC MOSFETs from Infineon Technologies (IMW120RxxxM1) have a short circuit capability, however the time is 3 µs, which is far away from the requested ones. The last main drawback is high dV/dt when the SiC power MOSFETs are used in the VFD application.

Overvoltage Phenomenon in VFD Applications
In many industrial applications, the converter and the motor are at separate locations. Consequently, the use of long feeding power cables is needed. It has been demonstrated [20][21][22] that the voltage pulses travel with speed, which is approximately half the speed of light (150 m/µs). If the pulse takes longer than half the rise time to travel from the inverter to the motor, a full reflection occurs at the motor terminals, and the pulse amplitude is approximately doubled. So, if t r ≤ 2t d , where t r is the voltage rise time at the inverter output terminals and t d is the cable propagation time, the line-to-line peak voltage V m on the motor side is almost two times the DC-bus voltage V BUS . Thus, the voltage reflection is a function of both the inverter pulse rise time and the length of the motor cables, as well as of the impedance mismatch between motor, cables and inverter. It is easy to understand that using new fast dynamic devices, line-to-line voltage V m across the motor side is almost two times the DC bus voltage V BUS . Furthermore, the fast switching produces complex transitions that highly stress the motor insulation; as a result, the machine winding can fail prematurely [37,38]. The influence of the length of power cables connected between the converter and the motor is shown in Figures 3 and 4. creases when the length of the power cable increases too. If the RET is too long, the switching frequency fsw is limited due to the overlap of the peaks, which can lead to an overvoltage higher than two times the DC-bus voltage VBUS.

Case Study: Design of the Snubber 2-Level Inverter
A topology solution used to reduce the overvoltage issue at the motor side when the SiC MOSFETs power switches are used in the inverter is addressed in this section. Figure  5 shows the electrical circuit of the S2L inverter. The S2L Inverter is composed of four parts: (1) DC-bus capacitor, (2) recovery circuit, 3) three-phase inverter and 4) snubber circuit. Each switch has a snubber circuit that consists of one capacitor Csx,t (or Csx,b) and one diode Dsx,t (or Dsx,b), with x ∈ {A, B, C}. Since the snubber circuit added to the switches can increase the losses, an additional circuit is used to recovery energy from the snubber circuit. The energy recovery circuit, connected between the snubber circuits and the DC-bus capacitor, is composed by the capacitor CR, creases when the length of the power cable increases too. If the RET is too long, the switching frequency fsw is limited due to the overlap of the peaks, which can lead to an overvoltage higher than two times the DC-bus voltage VBUS.

Case Study: Design of the Snubber 2-Level Inverter
A topology solution used to reduce the overvoltage issue at the motor side when the SiC MOSFETs power switches are used in the inverter is addressed in this section. Figure  5 shows the electrical circuit of the S2L inverter. The S2L Inverter is composed of four parts: (1) DC-bus capacitor, (2) recovery circuit, 3) three-phase inverter and 4) snubber circuit. Each switch has a snubber circuit that consists of one capacitor Csx,t (or Csx,b) and one diode Dsx,t (or Dsx,b), with x ∈ {A, B, C}. Since the snubber circuit added to the switches can increase the losses, an additional circuit is used to recovery energy from the snubber circuit. The energy recovery circuit, connected between the snubber circuits and the DC-bus capacitor, is composed by the capacitor CR, The converter is composed of the SiC power module (Semikron, part number: 26ACM12V17), while two Igus power cables (part number: CF270.UL.60.04.D) with different lengths, 15 m and 30 m, are used to connect the converter to the motor. The figures shown illustrate the turn-off and turn-on of the DUT. The blue waveform is the voltage between the output of the phase A (middle point) and minus DC-bus V BOT,A (voltage across the bottom device of the phase A) and the red waveform is the line-to-line voltage at the motor terminal V m when the length of the power cable is equal to 15 m. The orange waveform is the inverter voltage V BOT,A and the violet waveform is the line-to-line voltage V m across the motor when the length of the cable is equal to 30 m. As it can be seen, the voltage V m is almost two times V BUS in both the figures and the ringing expiration time (RET) increases when the length of the power cable increases too. If the RET is too long, the switching frequency f sw is limited due to the overlap of the peaks, which can lead to an overvoltage higher than two times the DC-bus voltage V BUS .

Case Study: Design of the Snubber 2-Level Inverter
A topology solution used to reduce the overvoltage issue at the motor side when the SiC MOSFETs power switches are used in the inverter is addressed in this section. Figure 5 shows the electrical circuit of the S2L inverter.

Case Study: Design of the Snubber 2-Level Inverter
A topology solution used to reduce the overvoltage issue at the motor side when the SiC MOSFETs power switches are used in the inverter is addressed in this section. Figure  5 shows the electrical circuit of the S2L inverter. The S2L Inverter is composed of four parts: (1) DC-bus capacitor, (2) recovery circuit, 3) three-phase inverter and 4) snubber circuit. Each switch has a snubber circuit that consists of one capacitor Csx,t (or Csx,b) and one diode Dsx,t (or Dsx,b), with x ∈ {A, B, C}. Since the snubber circuit added to the switches can increase the losses, an additional circuit is used to recovery energy from the snubber circuit. The energy recovery circuit, connected between the snubber circuits and the DC-bus capacitor, is composed by the capacitor CR, The S2L Inverter is composed of four parts: (1) DC-bus capacitor, (2) recovery circuit, (3) three-phase inverter and (4) snubber circuit. Each switch has a snubber circuit that consists of one capacitor C sx,t (or C sx,b ) and one diode D sx,t (or D sx,b ), with x ∈ {A, B, C}.
Since the snubber circuit added to the switches can increase the losses, an additional circuit is used to recovery energy from the snubber circuit. The energy recovery circuit, connected between the snubber circuits and the DC-bus capacitor, is composed by the capacitor C R , two diodes D R,t and D R,b , and the transformer T R with unitary turns ratio, in order to assure the same current value in both the windings. The operation mode of the S2L Inverter is clearly explained in [31]; in the following the hardware aspect design is discussed.

Inverter Power Semiconductor Selection
The power semiconductors of the three-phase inverter have been selected according to the voltage and current stresses. The voltage rating of the switches is a function of the DC-bus voltage V BUS and the overvoltage, as shown in (1).
In (1) V BL is the blocking voltage at steady state and ∆V is the switching overvoltage, function of different parameters such as the commutation inductance L ξ , the device current slope di sw /dt and the forward recovery voltage V FR of the complementary freewheeling diode. In the three-phase inverter the blocking voltage V BL is equal to the DC-bus voltage V BUS . Thus, considering 700 V as a nominal DC-bus voltage V BUS the power semiconductors must withstand at least 700 V. However, the overvoltage ∆V must also be considered, especially in motor drive applications in which, as seen in the previous section, the overvoltage can be almost two times the DC-bus voltage V BUS in case of long power cable. Thus, SiC power MOSFETs with at least 1200 V blocking voltage must be chosen. To select the current rating of the power semiconductors, the average (AVG) and Root Means Square (RMS) currents flowing into switches have been calculated according to Equation (2).
Energies 2021, 14, 1690 In (2), T 0 is the fundamental period, i x = I 0 sin(2πf 0 t − 2 / 3 kπ − ϕ) is the phase current, with ϕ being the phase displacement, k = 0, 1, 2, x ∈ {A, B, C}, and d sw is the duty cycles of the switch. Using the Sinusoidal Pulse-Width-Modulation (S-PWM), the duty cycle of the top and bottom devices (d x,t and d x,b ) can be derived from the Equation (3), where M 0 is the modulation depth and f 0 is the fundamental frequency. Substituting the (3) into (2), the RMS and AVG currents of the switch and diode can be written as in (4), where DT is the dead-time. According to this analysis the power semiconductors have been selected.

Snubber Circuit Design
The dV/dt is a function of the snubber capacitor values C sx,t and C sx,b , while the diodes D sx,t and D sx,b are used in order to block the current in one direction. During the turn-off of the switch S x,t and turn-on of the switch S x,b , the capacitor C sx,t is charged and the capacitor C sx,b is discharged; on the other hand, during the turn-on of the switch S x,t and turn-off of the switch S x,b the capacitor C sx,t is discharged and the capacitor C sx,b is charged. The recap of the turn-off of the switch S x,t is illustrated in Figure 6, where the commutation inductance L ξ is clearly highlighted. The turn-off of Sx,t occurs in four steps: after step 1, where the switch Sx,t is "on" and the current flows through it, the swich Sx,t is turned off, the snubber diode Dsx,t is "on" and the snubber capacitors Csx,t, Csx,b are respectively charged and discharged in step 2; in step 3, the snubber diode Dsx,b and the antiparallel diode Dx,b start to conduct the current; finally, in step 4, the current flows through the diode Dx,b and the switch Sx,b will be turned on under zero voltage. The turn-off of the bottom swich Sx,b will occur in a similar way. In state two the commutation inductance Lξ and snubber capacitor Csx,t form a resonant circuit, thus the second-order differential equation can be written in (5). The solution of the (5) is given in (6), where ωr = 1/ √ , is the resonant frequency, Zr = √ / , is the damping factor, VCsx,t,0 is the initial voltage of the capacitor Csx,t and IL0 is the initial current of the commutation inductance Lξ. From the Equation (6), the dV/dt across the power switch can be obtained as in (7).
It can be seen from (7) that the overvoltage is a function of the commutation induct- The turn-off of S x,t occurs in four steps: after step 1, where the switch S x,t is "on" and the current flows through it, the swich S x,t is turned off, the snubber diode D sx,t is "on" and the snubber capacitors C sx,t , C sx,b are respectively charged and discharged in step 2; in step 3, the snubber diode D sx,b and the antiparallel diode D x,b start to conduct the current; finally, in step 4, the current flows through the diode D x,b and the switch S x,b will be turned on under zero voltage. The turn-off of the bottom swich S x,b will occur in a similar way. In state two the commutation inductance L ξ and snubber capacitor C sx,t form a resonant circuit, thus the second-order differential equation can be written in (5). The solution of the (5) is given in (6), where ω r = 1/ L ξ C sx,t is the resonant frequency, Z r = L ξ /C sx,t is the damping factor, V Csx,t,0 is the initial voltage of the capacitor C sx,t and I L0 is the initial current of the commutation inductance L ξ . From the Equation (6), the dV/dt across the power switch can be obtained as in (7).
dV Csx,t dt = ω r (V BUS − V Csx,t,0 ) sin(ω r t) + ω r Z r I L,0 cos(ω r t) It can be seen from (7) that the overvoltage is a function of the commutation inductance L ξ , the snubber capacitance C sx,t and the initial current value I L0 . On one hand, high value of the inductance L ξ provides low value of the resonant frequency ω r and high value of the damping factor Z r ; consequently, the overvoltage will be high. The high initial current value also provides high overvoltage. On the other hand, the high value of the snubber capacitance C sx,t results in low resonant frequency ω r and damping factor Z r values; consequently the overvoltage during the commutation will be low. Finally, from (7) di/dt can be written as in (8). It can be noticed that di/dt is strictly dependent on the inductance L ξ and the initial current value I L0 .
The maximum value of dV/dt and di/dt occurs when the load current is equal to zero, that is when ω r t = π/2, V Csx,t,0 = 0, I L,0 = 0, and they are equal to (9).
From the obtained equations it is possible to select the snubber capacitors, considering that the commutation inductance L ξ depends on (1) the inductance L σ introduced by the Printed Circuit Board (PCB) tracks that connect the switching devices to the DC-bus capacitor, (2) the inductance L ESL related to the DC-bus capacitors and (3) the inductance L SW associated with the die and wire bond of the power semiconductors.

Recovery Energy Circuit Design
As it can be seen from Figure 5, the energy recovery circuit is created using two SiC diodes, the capacitor C R and the coupled inductor properly designed. The SiC diodes are used to have the unidirectional circulating current. The voltage stress of the diodes D sx,t , D sx,b , is equal to the DC-bus voltage V BUS plus the overvoltage, whereas the current stress is very low, since they are in on-state for a short time. The transferred average power as energy recovery is given in (10), where ∆I L,0 is the current ripple related to the DC-bus during each switching event.
According to the analysis presented in [39], using the S-PWM with 3rd harmonic injection and assuming three balanced loads, the DC-bus current ripple over the interval 0-π/3 is given in (11).
Replacing (11) into (10) and performing some algebraic manipulations, the average power is given in (12).
As it can be seen, the power managed by the energy recovery circuit is a function of switching frequency, load current, snubber capacitors and commutation inductance.

DC-bus Capacitor Design
The DC-bus capacitors are selected according to the DC-bus capacitor RMS current and DC-bus voltage ripple. It can be proven from [39] that the RMS current into DC-bus capacitor is given in (13).
This current is a function of the phase current I OUT , modulation depth M 0 , and phase displacement ϕ. Figure 7 shows the normalized RMS DC-bus current I Crms /I OUT as a function of the modulation depth M 0 when cosϕ = 1 and cosϕ = 0. As it can be seen, the maximum value of the RMS DC-bus current ICrms occurs when the cosφ is equal to 1 and the modulation depth M0 is between 0.55 and 0.6. The DC-bus capacitor must balance fluctuating instantaneous power on the DC-bus and its value can be selected according to the DC-bus voltage ripple. The required minimum DC-bus capacitor can be obtained from Equation (14), imposing the modulation depth M0 equal to 0.5.

Experimental Results
According to the previous analysis, the three-phase S2L prototype converter has been realized. Particularly, given that the DC-bus is set at 700 V and the output power is set at 18 kW, 1700V-45mΩ SiC MOSFETs (part number C2M0045170D) and freewheeling parallel 1200V-40A SiC diodes (part number IDW40G120C5B) are selected. The snubber circuit is realized with one SiC diode and two Multilayer Ceramic Capacitors (MLCC). The chosen value of the snubber circuit capacitors CSx,t and CSx,b have been selected considering (7) and (8). The energy recovery circuit has been built using two SiC diodes (part number FFSD10120A) and a 40µ F film capacitor (part number MKP1848). Based on (10), the coupled inductors have been designed in order to obtain 800 µ H at the nominal load. The core selection has been based on the Area Product (AP) method. In particular, the number of turns is set at 41 and the material and the shape of the selected core are ferrite and EE 40/20, respectively. According to (13) and (14), four 40 µ F film capacitors (part number MKP1848) are used as a DC-bus capacitor tank. All the components used to build up the S2L converter are listed in Table 2. To validate the proposed analysis and to obtain the overvoltage reduction at the motor side, using the SiC MOSFETs still keeping a high efficiency conversion, the experimental tests on the three-phase S2L inverter have been addressed. The experimental test setup is shown in Figure 8. It can be seen the three-phase As it can be seen, the maximum value of the RMS DC-bus current I Crms occurs when the cosϕ is equal to 1 and the modulation depth M 0 is between 0.55 and 0.6. The DC-bus capacitor must balance fluctuating instantaneous power on the DC-bus and its value can be selected according to the DC-bus voltage ripple. The required minimum DC-bus capacitor can be obtained from Equation (14), imposing the modulation depth M 0 equal to 0.5.

Experimental Results
According to the previous analysis, the three-phase S2L prototype converter has been realized. Particularly, given that the DC-bus is set at 700 V and the output power is set at 18 kW, 1700 V-45 mΩ SiC MOSFETs (part number C2M0045170D) and freewheeling parallel 1200 V-40 A SiC diodes (part number IDW40G120C5B) are selected. The snubber circuit is realized with one SiC diode and two Multilayer Ceramic Capacitors (MLCC). The chosen value of the snubber circuit capacitors C Sx,t and C Sx,b have been selected considering (7) and (8). The energy recovery circuit has been built using two SiC diodes (part number FFSD10120A) and a 40µF film capacitor (part number MKP1848). Based on (10), the coupled inductors have been designed in order to obtain 800 µH at the nominal load. The core selection has been based on the Area Product (AP) method. In particular, the number of turns is set at 41 and the material and the shape of the selected core are ferrite and EE 40/20, respectively. According to (13) and (14), four 40 µF film capacitors (part number MKP1848) are used as a DC-bus capacitor tank. All the components used to build up the S2L converter are listed in Table 2. To validate the proposed analysis and to obtain the overvoltage reduction at the motor side, using the SiC MOSFETs still keeping a high efficiency conversion, the experimental tests on the three-phase S2L inverter have been addressed. The experimental test setup is shown in Figure 8. It can be seen the three-phase S2L inverter, the synchronous machine, that is controlled by the S2L converter, mechanically coupled with an asynchronous machine can be controlled by an external test bench operating on 4-quadrants. Table 2. Component description used to build the three-phase S2L prototype.  The DC-bus voltage VBUS is kept at 400 V using the DC Power S laboratory. The achieved results from the three-phase S2L inverter to the three-phase 2L inverter with the same power devices. This la obtained by removing the snubber circuit and the energy recovery phase S2L prototype converter. Thus, the power semiconductors an tor Lξ are completely the same in both converters. Figure 9 shows the The DC-bus voltage V BUS is kept at 400 V using the DC Power Supply available in the laboratory. The achieved results from the three-phase S2L inverter have been compared to the three-phase 2L inverter with the same power devices. This latter inverter has been obtained by removing the snubber circuit and the energy recovery circuit form the threephase S2L prototype converter. Thus, the power semiconductors and the parasitic inductor L ξ are completely the same in both converters. Figure 9 shows the turn-off of S A,t located in the three-phase 2L inverter when the gate resistance R G = 4.7Ω, the dead-time DT = 1 µs, the switching frequency f sw = 10 kHz and the power cable length l C = 15 m. When the phase current is equal to 4.75 A as in Figure 9a, the dV/dt in turn-on is really slow due to the total parasitic capacitances. The value of the voltage V m at the motor side is only 1.285 times the V BUS . When the phase current increases from 4.75 A to 31.88 A the turn-off behavior is drastically changed, as illustrated in Figure 9b. Here, the commutation inductance shows the negative influences when the 2-level inverter is considered, since the dV/dt is fast (9.95 V/ns), and the voltage overshoot at the drain-source voltage is equal to 131 V (yellow track). This overshoot leads to a voltage at the motor terminals two times the V BUS (845 V). Figure 10 shows the turn-on and the turn-off of the S A,t located in the three-phase 2L inverter when the gate resistance R G = 22 Ω, dead-time DT = 1 µs, switching frequency f sw = 10 kHz and the power cable length l C = 15 m. Increasing the gate resistance from 4.7 Ω to 22 Ω for both turn-on and turn-off, the overvoltage at the motor terminals is slightly reduced. As it can be seen from Figure 10a the phase current IA is equal to 2.5 A, the dV/dt is equal to 4.5 V/ns and the voltage at the motor side Vm is equal to 785 V. Figure 10b shows the turn-off when the phase current IA is equal to 33A. Thanks to the greater values of the RG both the dV/dt and the voltage overshoot at the device side are reduced to 5.6 V/ns and 75 V, respectively. However, the over- Increasing the gate resistance from 4.7 Ω to 22 Ω for both turn-on and turn-off, the overvoltage at the motor terminals is slightly reduced. As it can be seen from Figure 10a the phase current IA is equal to 2.5 A, the dV/dt is equal to 4.5 V/ns and the voltage at the motor side Vm is equal to 785 V. Figure 10b shows the turn-off when the phase current IA is equal to 33A. Thanks to the greater values of the RG both the dV/dt and the voltage overshoot at the device side are reduced to 5.6 V/ns and 75 V, respectively. However, the over- Increasing the gate resistance from 4.7 Ω to 22 Ω for both turn-on and turn-off, the overvoltage at the motor terminals is slightly reduced. As it can be seen from Figure 10a the phase current I A is equal to 2.5 A, the dV/dt is equal to 4.5 V/ns and the voltage at the motor side V m is equal to 785 V. Figure 10b shows the turn-off when the phase current I A is equal to 33A. Thanks to the greater values of the R G both the dV/dt and the voltage overshoot at the device side are reduced to 5.6 V/ns and 75 V, respectively. However, the overvoltage V m is still more than double of the V BUS (811 V is 2.02 times the V BUS ). Figure 11 shows the turn-on of the S A,t located in the three-phase S2L inverter when the gate resistance R G = 4.7 Ω, snubber capacitors C Sx,t = 9.4 µF, dead-time DT = 1 µs, switching frequency f sw = 10 kHz and the power cable length l C = 15 m. It is possible to notice that the overvoltage at the motor side is smaller than the previous case when the 2-level inverter is used. The values of the overvoltage at the motor terminal are 664 V and 660 V when the phase current I A is 3.23 A and I A is 25.6 A, respectively (almost 1.66 times the V BUS ). The dV/dt is equal to 2.24 V/ns and 2.06 V/ns when the phase current is 3.23 A and 26.6 A, respectively.

Reference Part Number Description
It is possible to notice that the important parameter in the overvoltage issue is not the dV/dt but the rise time (fall time in turn-off) of the drain source voltage. If the two times of the travelling time (2t d ) of the voltage wave is greater than the rise/fall time (t f or t r ) of the drain source voltage, a double voltage appears at the motor terminals. It is possible to notice that the important parameter in the overvoltage issue is not the dV/dt but the rise time (fall time in turn-off) of the drain source voltage. If the two times of the travelling time (2td) of the voltage wave is greater than the rise/fall time (tf or tr) of the drain source voltage, a double voltage appears at the motor terminals. Figure 12 shows the turn-off of SA,t located in the three-phase S2L inverter when the phase current is equal to 5.7 A and 31.42 A. It is possible to recognize two different dV/dt (yellow line): the first one related to the snubber capacitor dynamic is equal to 0.3 V/ns and the second one is related to the turn-on of the bottom switch. The voltage at the motor terminals Vm is only 52 V higher than the VBUS. When the phase current is 31.42 A (Figure  12b), the dV/dt is a little bit faster than the previous case (1.47 V/ns), but still no voltage overshoot occurs at the VDS and the overvoltage value is equal to 562 V (1.4 times the VBUS). The turn-off commutations of the three-phase S2L inverter occur at zero current; this means that all the losses are shifted to the turn-on commutations. The experimental efficiency of the three-phase 2L inverter and the three-phase S2L inverter is experimentally evaluated controlling the speed of the Permanent Magnet Synchronous Generators (PMSM) at constant torque. Figure 13 shows the efficiency of the three-phase 2L inverter versus modulations depth M0 for different values of the switching frequency (10 kHz and 15 kHz) and gate resistance (4.7 Ω and 22 Ω) when the power cable length lC is equal to 15 m, the DC-bus voltage VBUS is equal to 400 V and the phase peak current Ix is equal to 30 A.  Figure 12 shows the turn-off of S A,t located in the three-phase S2L inverter when the phase current is equal to 5.7 A and 31.42 A. It is possible to recognize two different dV/dt (yellow line): the first one related to the snubber capacitor dynamic is equal to 0.3 V/ns and the second one is related to the turn-on of the bottom switch. The voltage at the motor terminals V m is only 52 V higher than the V BUS . When the phase current is 31.42 A (Figure 12b), the dV/dt is a little bit faster than the previous case (1.47 V/ns), but still no voltage overshoot occurs at the V DS and the overvoltage value is equal to 562 V (1.4 times the V BUS ). The turn-off commutations of the three-phase S2L inverter occur at zero current; this means that all the losses are shifted to the turn-on commutations. The experimental efficiency of the three-phase 2L inverter and the three-phase S2L inverter is experimentally evaluated controlling the speed of the Permanent Magnet Synchronous Generators (PMSM) at constant torque. Figure 13 shows the efficiency of the three-phase 2L inverter versus modulations depth M 0 for different values of the switching frequency (10 kHz and 15 kHz) and gate resistance (4.7 Ω and 22 Ω) when the power cable length l C is equal to 15 m, the DC-bus voltage V BUS is equal to 400 V and the phase peak current I x is equal to 30 A. ciency of the three-phase 2L inverter and the three-phase S2L inverter is experimentally evaluated controlling the speed of the Permanent Magnet Synchronous Generators (PMSM) at constant torque. Figure 13 shows the efficiency of the three-phase 2L inverter versus modulations depth M0 for different values of the switching frequency (10 kHz and 15 kHz) and gate resistance (4.7 Ω and 22 Ω) when the power cable length lC is equal to 15 m, the DC-bus voltage VBUS is equal to 400 V and the phase peak current Ix is equal to 30 A.  The efficiency shows the increasing trend when the modulation depth M0 increases. However, when the gate drive resistance changes from 4.7 Ω to 22 Ω, the efficiency decreases. The efficiency trend at fsw = 10 kHz, RG = 22 Ω is close to the efficiency curve at fsw = 15 kHz, RG = 4.7 Ω. Figure 14 shows the efficiency of the three-phase S2L inverter versus modulations depth M0 for different values of the switching frequency (10 kHz and 15 kHz), gate resistance (4.7 Ω and 22 Ω) and snubber capacitors (4.7 nF and 9.4 nF) when the power cable length lC is equal to 15 m, the DC-bus voltage VBUS is equal to 400 V and the phase peak current Ix is equal to 30 A. As it can be seen, the efficiency of the threephase S2L inverter is lower than the efficiency of the three-phase 2L inverter. This is due to the snubber circuit losses. Furthermore, the efficiency of the S2L inverter highly depends on the snubber capacitor values and the switching frequency. When a capacitor value of 4.7 nF is used, the drop of efficiency from switching frequency of 10 kHz to switching frequency of 15 kHz is less than 0.5% (orange line). On the other hand, when a 9.4 nF snubber value is used, the efficiency drop increase to 0.7%. This happens due to the high value of the inrush current into snubber capacitors during the turn on, which is a function of the snubber capacitor values. Higher value of snubber capacitor led to a higher inrush current. From the overvoltage mitigation point of view, the best S2L inverter setup happens when RG is equal to 4.7 Ω and the snubber capacitors CSx,t and Csx,b are equal to 9.4 nF. In this condition, the performance of the S2L inverter is slightly lower than the 2L The efficiency shows the increasing trend when the modulation depth M 0 increases. However, when the gate drive resistance changes from 4.7 Ω to 22 Ω, the efficiency decreases. The efficiency trend at f sw = 10 kHz, R G = 22 Ω is close to the efficiency curve at f sw = 15 kHz, R G = 4.7 Ω. Figure 14 shows the efficiency of the three-phase S2L inverter versus modulations depth M 0 for different values of the switching frequency (10 kHz and 15 kHz), gate resistance (4.7 Ω and 22 Ω) and snubber capacitors (4.7 nF and 9.4 nF) when the power cable length l C is equal to 15 m, the DC-bus voltage V BUS is equal to 400 V and the phase peak current I x is equal to 30 A. As it can be seen, the efficiency of the three-phase S2L inverter is lower than the efficiency of the three-phase 2L inverter. This is due to the snubber circuit losses. Furthermore, the efficiency of the S2L inverter highly depends on the snubber capacitor values and the switching frequency. When a capacitor value of 4.7 nF is used, the drop of efficiency from switching frequency of 10 kHz to switching frequency of 15 kHz is less than 0.5% (orange line). On the other hand, when a 9.4 nF snubber value is used, the efficiency drop increase to 0.7%. This happens due to the high value of the inrush current into snubber capacitors during the turn on, which is a function of the snubber capacitor values. Higher value of snubber capacitor led to a higher inrush current. From the overvoltage mitigation point of view, the best S2L inverter setup happens when R G is equal to 4.7 Ω and the snubber capacitors C Sx,t and C sx,b are equal to 9.4 nF. In this condition, the performance of the S2L inverter is slightly lower than the 2L inverter.

Conclusions
The benefits of using SiC MOSFETs in the motor drive applications have been discussed in the first part of this paper. The experimental tests performed on the power semiconductors in the first part of the paper show that SiC MOSFET (IMW120R045T1) allows a huge improvement in terms of temperature performance compared to the IGBTs. After that, the overvoltage issue when the electric drive is supplied by the converter with long power cables has been highlighted and supported by the experimental tests. The latter illustrate that the voltage at the motor terminal Vm is two times the DC bus voltage VBUS when the length of the power cable is equal to 15 m or 30 m. A case study of a three-phase two level inverter with the addition of snubber circuits has been discussed to solve the overvoltage problem in the motor drive application. Particularly, the prototype of the S2L inverter has been built according to the proposed design guidelines. Experimental results confirm the effectiveness of the proposed converters in significantly reducing the overvoltage at motor terminals and mitigating the windings insulation stress. When the 2L inverter is used the peak voltage at the motor side is equal to 845 V and the dV/dt is equal to 9.95 V/ns, while in the S2L inverter the peak voltage is equal to 562 V and the dV/dt is equal to 1.47 V/ns. However, the conversion efficiency is slightly reduced compared to the three-phase 2L inverter. Considering the same operating conditions, the peak efficiency of the three-phase 2L inverter is equal to 0.982%, whereas the peak efficiency of the threephase S2L inverter is equal to 0.976%. Consequently, the proposed analysis shows that by using the S2L inverter it is possible to find a good compromise between dV/dt, overvoltage and efficiency performance of the entire electric drive system.

Conclusions
The benefits of using SiC MOSFETs in the motor drive applications have been discussed in the first part of this paper. The experimental tests performed on the power semiconductors in the first part of the paper show that SiC MOSFET (IMW120R045T1) allows a huge improvement in terms of temperature performance compared to the IGBTs. After that, the overvoltage issue when the electric drive is supplied by the converter with long power cables has been highlighted and supported by the experimental tests. The latter illustrate that the voltage at the motor terminal V m is two times the DC bus voltage V BUS when the length of the power cable is equal to 15 m or 30 m. A case study of a three-phase two level inverter with the addition of snubber circuits has been discussed to solve the overvoltage problem in the motor drive application. Particularly, the prototype of the S2L inverter has been built according to the proposed design guidelines. Experimental results confirm the effectiveness of the proposed converters in significantly reducing the overvoltage at motor terminals and mitigating the windings insulation stress. When the 2L inverter is used the peak voltage at the motor side is equal to 845 V and the dV/dt is equal to 9.95 V/ns, while in the S2L inverter the peak voltage is equal to 562 V and the dV/dt is equal to 1.47 V/ns. However, the conversion efficiency is slightly reduced compared to the three-phase 2L inverter. Considering the same operating conditions, the peak efficiency of the three-phase 2L inverter is equal to 0.982%, whereas the peak efficiency of the three-phase S2L inverter is equal to 0.976%. Consequently, the proposed analysis shows that by using the S2L inverter it is possible to find a good compromise between dV/dt, overvoltage and efficiency performance of the entire electric drive system.