# Comparative Evaluation of Two-Level Inverters and a Disruptive Multi-Level Solution: Impact of Switch Technology

Rémi Jardot, Anas Lahlou, Guillaume Krebs, Francis Roy, Claude Marchand

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Rémi Jardot, Anas Lahlou, Guillaume Krebs, Francis Roy, Claude Marchand. Comparative Evaluation of Two-Level Inverters and a Disruptive Multi-Level Solution: Impact of Switch Technology. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0245. hal-05088316

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# Comparative Evaluation of Two-Level Inverters and a Disruptive Multi-Level Solution: Impact of Switch Technology

Rémi Jardot¹,², Anas Lahlou³, Guillaume Krebs¹, Francis Roy², and Claude Marchand¹

¹ GeePs, CentraleSupelec, Université Paris-Saclay,
91192 Gif-sur-Yvette, France

² Centre Technique de Carrières-sous-Poissy,
78955 Carrières-sous-Poissy, France

³ SAFT, 111-113 Boulevard Alfred Daney,
33074 Bordeaux, France

Tel.: (+33)6 02 16 85 30

E-Mail: remi.jardot@centralesupelec.fr

*Index Terms*—PMSM, SiC IGBT, IBIS traction chain, FEA modeling, iron loss, copper loss

*Abstract*—This study investigates the performance of electric vehicle drivetrains using various modeling techniques. A comprehensive approach combining Matlab Simulink and finite element analysis assesses electrical and mechanical outputs, efficiency, and losses in different components. The findings aim to compare drivetrain architectures (CHB like and SiC three-phase inverter architectures) and identify opportunities for performance optimization.

## I. INTRODUCTION

The involvement of automotive industry stakeholders in combating climate change and developing more sustainable products continues to grow. Many manufacturers, encouraged and supported by public authorities, choose to fully or partially electrify their vehicle ranges [1]. On the user and customer side, enthusiasm for electrification is heavily dependent on government financial incentives [2]. As proof, the market share of internal combustion engine vehicles in passenger car sales is steadily declining. [3], [4]. Figure 1 illustrates this trend. According to these estimates, electrified vehicle sales are expected to surpass combustion vehicles within the next two decades, which is already the case in the chinese market.

<figure><img src="image_2.png" /><figcaption>Figure 1. Worldwide Market share of electrified vehicles and ICE vehicles [5]</figcaption></figure>

Therefore, the electric automotive sector requires increasingly substantial new research activity. Also, it seems essential to explore new powertrain structures that have the potential to revolutionize this domain of the industry in order to reduce the cost of vehicle fabrication. Figure 2 is a scheme of a classic electric vehicle powertrain. This type of powertrain involve an inverter, which convert the current of the battery in a sinusoidal current, used in the electrical machine.
### A. SiC 800V traction chain

Silicon Carbide (SiC) is a wide-band gap semiconductor material that offers superior electrical properties compared to traditional silicon. SiC inverters leverage these properties to achieve higher efficiency, faster switching speeds, and increased power density. Using SiC enables EVs to operate more efficiently, extend driving range, and reduce overall energy consumption [18]. This material is advantageous because SiC has a higher critical field. This characteristic allows a thinner and highly doped drift region for the same breakdown voltage or a higher breakdown voltage for the same characteristics. Furthermore, these chemical properties allow a higher melting temperature and a better resistance to erosive and corrosive environments.

Apart from the switching devices, the cost of these two inverters is almost identical [19], [20]. Now, it remains to consider the price of the basic component. Unfortunately, for SiC, it remains significantly more expensive than its counterpart at the moment. New electric vehicle traction chain begin to appear with this SiC Mosfet technology and a rise in battery voltage, from 400V to possibly 800V.

A SiC three-phase inverter is schematized in the figure 3. The structure is the same as the classical three-phase inverter. The Si IGBTs are replaced with SiC Mosfets.

<figure><img src="image_3.png" /><figcaption>Figure 3. Scheme of the SiC three-phase inverter</figcaption></figure>

### B. IBIS traction chain

A sine wave voltage can also be generated by connecting several switching cells in series. By doing so, a multilevel output voltage is created, which resembles the effect of an analog-to-digital conversion of a sine wave signal. Many structures of this type are discussed in the literature [13], [17]. They offer the advantage of reduced harmonic content compared to more conventional high-voltage inverter structures, great modularity, and a higher output voltage for the same number of

<figure><img src="image_4.png" /><figcaption>Figure 2. Electric vehicle scheme</figcaption></figure>

The primary motivation behind this work is to support this trend by proposing a methodology and a modeling tool to characterize, quantify, and compare different electric vehicle technologies and architectures currently popular in the automotive industry. The first application considered in this study focuses on a permanent magnet synchronous machine (PMSM), the most used machine type in the world [6], [7]. This type of machine is typically characterized by its compact design and higher efficiency compared to asynchronous machines. The rotor of the PMSM is composed of permanent magnets. When mapping the losses in this type of machine, it becomes evident that it achieves higher efficiency at low speeds than other machines.

One of the strong trends in this industry is the use of Silicon Carbide (SiC) converters instead of conventional Silicon (Si) converters. Offering several advantages over its competitor [8]–[10], SiC technology allows for higher switching frequencies in three-phase inverters and increases the output voltage level from the battery, up to 800 V for the most well-known architectures [11], [12]. Conversely, another trend in research involves using low-voltage components in multi-level structures [13]–[15]. The IBIS project [16], [17], which will be examined here, falls into this category.

Ultimately, this work aims to compare these different technologies, particularly regarding their impact on machine losses. The overall system efficiency will also be discussed to create a tool for technological decision-making. To address these questions, this article presents the different technologies studied. Then, it highlights the modeling strategy, the simulation tool, and the various loss models. Finally, it presents the results concerning losses, efficiency, and range over driving cycles.
cells. However, the complexity of the wiring and the number of components required for their construction still present significant challenges for their large-scale industrial application.

The IBIS architecture, developed by Stellantis, serves a purpose similar to that of a multilevel inverter architecture. This multilevel configuration is depicted in Figure 4. The same machine will be connected in delta instead of star. This is because the voltage at the terminals of the new battery is greater, making this new connection possible.

<figure><img src="image_5.png" /><figcaption>Figure 4. Scheme of the IBIS battery concept</figcaption></figure>

This new structure consists of three distinct current lines, each connected to a different phase of the machine. Each line is made up of a defined number of clusters, which in turn contain a fixed number of battery cells and a low-voltage conversion board. An external control unit manages the battery operation and monitors the status of the clusters throughout their operation. The control of the IBIS battery is achieved using the Nearest Level Command (NLC) approach, which selects the nearest level to the desired value. Additionally, one could envision a control scheme combining NLC and PWM, enabling the attainment of any desired value. The output voltage of the battery is hence:

$$V_i = \pm \sum_{k=1}^{N_k} v_{k_i}(c=1), \quad i=1,2,3 \quad (1)$$

This design allows for achieving a higher output voltage than the voltage tolerance of each individual switch while using the same number of cells. In our application, the machine voltage seems more comparable to 800V than 400V. Hence, the electrical machine will be the same as in the 400V application but with a delta connection, as shown in the figure 4. Additionally, it provides enhanced modularity and more precise control compared to traditional inverter architectures. Advances in low-voltage switching components, along with the use of a specific patented structure, are partly responsible for enabling the potential for industrial application. As mentioned earlier, the IBIS structure allows the machine to be powered with minimal harmonic content. Figure 5 compares the currents within the machine for the different types of structures examined in this article. It clearly shows a lower harmonic content with the IBIS architecture, followed by the SiC 800V inverter structure.

<figure><img src="image_6.png" /><figcaption>Figure 5. Current comparison between the 800V SiC and IBIS architectures on the same operating point</figcaption></figure>

### III. MODELING STRATEGY

To effectively compare the different electric vehicle drivetrains presented in this study, a detailed protocol is outlined in this section. Figure 6 provides a schematic representation of the strategy adopted for this purpose.

The initial phase of the modeling is dedicated to determining the various electrical and mechanical parameters at the output of each component within the drivetrains. This phase will be implemented using Matlab Simulink, which will simulate the characteristics of the battery cells and the conversion boards. For the electric machine, its characteristics will be calculated using the finite element method (FEM) model of the machine. This
<figure><img src="image_7.png" /><figcaption>Figure 6. Traction chain modeling protocol</figcaption></figure>

approach allows for a detailed analysis of the behavior of each component, ensuring that the performance metrics are accurately captured.

The second phase of the modeling focuses on evaluating the efficiency of each individual component, as well as the overall efficiency of the entire powertrain. The relevant quantities required for the various loss calculations will be extracted from the results of the initial modeling phase, which provides the overall efficiency as an output. For the machine losses, the FEM model described earlier will be used to ensure a precise calculation. This comprehensive approach enables a thorough understanding of the powertrain's performance and helps identify areas for potential optimization.

### A. Battery modeling

The dynamic behavior of batteries is generally modeled with a serial RC network and a resistor. These models provide a reasonably accurate description of cell behavior. In the case of the conventional architecture of an electric powertrain, the cell is model by a constant voltage source, in series with a resistance. The dynamic behavior of the cell is not taken into account because in the conventional architecture the current flowing into the cell is a DC current. The cell voltage is given by the following equation:

$$V_{cell} = E_{0} + R_{0}i_{cell} \quad (2)$$

Where $V_{cell}$, $E_0$ and $R_0$ refers respectively to cell voltage in [V], open circuit voltage in [V], and internal resistance of the cell in [Ω]. The current $i_{cell}$ refers and the current flowing in the cell in [A], which takes a

positive value when the cell is in charge and a negative value when the cell is in discharge. The battery voltage $V_{bat}$ is given by:

$$V_{bat} = n_{s}V_{cell} \quad (3)$$

Where $n_s$ is the number of cells in series. In the case of IBIS powertrain architecture, the power conversion is performed by a Cascaded H Bridge Multi-Level Inverter (CHB MLI). Theliander et al. [21], [22] showed that considering dynamic behavior leads to improved efficiency in the case of CHB MLIs, due to the low-frequency component of the current. In this case, the cell voltage is given by the following equation:

$$V_{cell} = E_{0} + R_{0}i_{cell} + R_{1}i_{cell,R_{1}} \quad (4)$$

Where $R_1$ and $i_{cell,R_1}$ refers respectively to the resistance of the RC circuit in [Ω] and the current flowing in this resistance $R_1$ in [A]. The current $i_R$ is given by the following differential equation:

$$R_{1}C_{1}\frac{di_{cell,R_{1}}}{dt} + i_{cell,R_{1}} = i_{cell} \quad (5)$$

Where $C_1$ is the capacitance in [F] of the RC circuit capacitor. We note that $E_0$, $R$, $R_1$, and $C_1$ are functions of the state of charge and temperature, and are calculated at each time step, by linear interpolation in those maps.

### B. Inverter modeling

A conventional SiC inverter is composed of 6 SiC Mosfets [23], each one is controlled in a specific pattern to produce the desired voltage waveform. The SiC Mosfets, are modeled by their current-voltage characteristic of the p-n junction. The current-voltage characteristic is a map that associates both the gate-source voltage $V_{gs}$ and the drain-source voltage $V_{ds}$ to the drain-source current $i_{ds}$. This map is extracted from the Mosfet datasheet. We note here that the drain-source voltage $V_{ds}$ is equal to $V_{bat}$ when the mosfet is ‘on’ state, and 0 when the Mosfet is in ‘off’ state. The current $i_d$ through the body diode is described by an exponential law given by the following equation:

$$i_{d} = I_{s}\left[\exp\left(-\frac{V_{ds}}{\Phi_{T}}\right) - 1\right] \quad (6)$$

Where $I_s$ is the reverse saturation current, and $\Phi_T$ is the thermal voltage equal to $0.86 \times 10^{-4} \times T$, where $T$ is the Mosfet temperature in [K]. An H-bridge in a multi-level inverter is composed of 4 Mosfets [24]. The components in the CHB section can be modelled in the same way. Due to the computation load, we can choose
to model the Mosfets of a Cascaded H-bridge multilevel inverter by a resistive switch. Its resistance $R_{ds,on}$ represents the drain-source resistance of the Mosfet when the Mosfet is in an 'on' state.

### C. Electrical machine model

The application considered in this study focuses on a permanent magnet synchronous machine (PMSM). This type of machine is illustrated in Figure 7 and was already used in previous studies [17].

<figure><img src="image_8.png" /><figcaption>Figure 7. Used PMSM</figcaption></figure>

A modeling approach was implemented using a 2D finite element method (FEM) in MATLAB. This model can be meshed using FEMM for detailed representation of complex machine parts, or directly in MATLAB for a more simplified geometric approximation. The goal of this modeling is to obtain the full range of electrical and magnetic properties of the machine. A specialized meshing technique is applied to balance computational efficiency with the need for adequate accuracy, ensuring that calculation times are kept to a minimum.

A second 2D finite element modeling of a slot in the electric machine was carried out. This modeling aims to accurately calculate the copper losses (both AC and DC losses) that occur within the slot of the machine [25]–[28]. The purpose of this modeling is to obtain electrical and magnetic quantities within the slot with higher precision, allowing for the observation of the effects of the machine's supply frequencies and the accurate calculation of copper losses in these slots.

The two meshes illustrated in Figure 8 are connected by an interpolation technique at the boundary of the slot, known as the mortar method [29], [30]. This method enables a more detailed representation of the electromagnetic quantities by using a finer mesh, but only over a localized area where greater precision is needed. As a result, this technique reduces the computational resources

<figure><img src="image_9.png" /><figcaption>Figure 8. Used meshes with the MORTAR method</figcaption></figure>

required and shortens the overall calculation time, while still maintaining an accurate representation of the key electromagnetic phenomena within the targeted region.

## IV. LOSSES AND EFFICIENCY CALCULATION

### A. Battery losses

In the case of conventional powertrain, the cell model includes one resistance that corresponds physically to internal resistance. Hence, the instantaneous power loss $P_{bat,loss}$ can be expressed by the following equation:

$$P_{bat,loss} = \sum_{p=1}^{3} \sum_{k=1}^{n_{clusters}} n_{cell} (R_{0}i_{cell,k,p}^{2} + R_{1}i_{cell,R_{1},k,p}^{2}) \quad (7)$$

Where $n_{clusters}$ refers to the number of clusters in one phase of IBIS architecture, $n_{cell}$ refers to the number of cells by cluster, $i_{cell,k,p}$ and $i_{cell,R_{1},k,p}$ refers respectively to the $i_{cell}$ and $i_{cell,R_{1}}$ currents defined earlier in this paper, through the k-th cluster in the p-th phase.

### B. Converter losses

In the case of conventional architecture, the instantaneous power loss in the inverter is the sum of the conduction loss in the junction and the body diode and switching loss. It is given by the following equation:

$$P_{inv,loss} = 6 (i_{ds}V_{bat}u + i_{d}V_{bat} + E_{on}f_{sw,k,p}\delta_{on,k,p} + E_{off}f_{sw,k,p}\delta_{off,k,p}) \quad (8)$$

Where $u$ is the function that is equal to 1 when the Mosfet is turned on, and 0 when the Mosfet is off. $E_{on}$ (resp. $E_{off}$) is the switching energy loss in [Wh], when the Mosfet passes from off to on state, (resp. from off to
on state). $f_{sw}$ is the switching frequency. $\delta_{on,k,p}$ (resp. $\delta_{off,k,p}$) is the functions that take the value of 1 when the Mosfet changes its state from 'off' to 'on' (resp. 'on' to 'off') and takes 0 everywhere else. In the case of IBIS architecture, the instantaneous power loss in the multilevel inverter is equal to the sum of conduction losses and switching losses, which can be expressed by the following time-dependent equation:

$$P_{IBIS,loss} = \sum_{p=1}^{3} \sum_{k=1}^{n_{clusters}} (i_{ds}V_{k,p}u + i_{d}V_{k,p} + E_{on}f_{sw,k,p}\delta_{on,k,p} + E_{off}f_{sw,k,p}\delta_{off,k,p}) \quad (9)$$

$f_{sw,k,p}$ and $V_{k,p}$ refers to the switching frequency and the voltage of the Mosfet of the k-th cluster in p-th phase, and $\delta_{on,k,p}$ (resp. $\delta_{off,k,p}$) is the functions that take the value of 1 when Mosfet changes its state from 'off' to 'on' (resp. 'on' to 'off') and takes 0 everywhere else for each Mosfet from the k-th cluster in p-th phase.

### C. Machine losses

The losses in the machine can be categorized into several different groups: iron losses (losses in the machine's ferromagnetic materials), copper losses (losses in the machine's conductive materials), which can be further divided into AC and DC losses, losses in the magnets, and mechanical losses. In this article, the electrical losses are calculated using the presented model, while the mechanical losses will be estimated from tables derived from experimental characterizations. The magnets losses are neglected.

The calculation of iron losses is based on the finite element modeling (FEM) discussed earlier. To determine the total losses throughout the machine, an estimation of the volumetric losses is performed for each small-volume element discretized by the previous FEA. This estimation is based on the magnetic flux density computed for each time step of the simulation. Various models can be used to estimate the iron losses in the machine, some of which emphasize simplicity, while others are suitable for frequency-domain modeling. The method applied here, detailed in Equation 10, accounts for minor hysteresis loops in the magnetic induction, any DC bias present, and the mechanical stresses exerted on the machine's stator.

$$P_{tot}^{Fe} = \sum_{i=1}^{N_{Fe}} \left[ \frac{1}{T} \int_{0}^{T} k_{iGSE} \left| \frac{dB}{dt} \right|^{\alpha} |\Delta B|^{\beta-\alpha} dt \right] dV_{i} \quad (10)$$

In this equation, $k_{iGSE}$ is a factor calculated using the problem characteristics, $B$ is the magnetic flux, $T$ represents one electrical period of the machine, and finally, $\alpha$ and $\beta$ are factors calculated using experimental data. The copper losses within the machine slots are calculated by interpolating the magnetic vector potential from the machine's mesh onto the slot mesh. A finer mesh is required to capture the skin effect in the conductors accurately. Both AC and DC losses are directly considered by calculating the current density in the conductors based on the magnetic vector potential. Equation 11 provides the estimation of these losses in the machine's conductors.

$$P_{tot}^{Cu} = \sum_{i=1}^{N_{Cu}} \left[ \rho_{i} \left( \sigma \frac{\delta A}{\delta t} + \sigma U_{c} \right)^{2} \right] dV_{i} \quad (11)$$

Here the factors $\rho_i$ and $\sigma$ represent the characteristics of the materials. The two terms represent the AC copper loss, using $A$ the magnetic potential, and the DC copper loss, $U_c$ the voltage in the coil.

### V. COMPARISON BETWEEN THE TRACTION CHAINS

In this section, the various simulation and loss calculation models will be used to compare the efficiencies of different SiC MOSFET and IBIS powertrains. The comparison will be performed over an entire WLTC cycle, represented by five barycenters of the cycle. The reduction method used in the works [17], [25] is applied. Figure 9 shows the barycenter segmentation used in this study.

<figure><img src="image_10.png" /><figcaption>Figure 9. Barycenters of the WLTC cycle</figcaption></figure>

The black crosses represent the barycenters of the domains, points in different colors, calculated using a k-means clustering method. Energy recovery is taken into account here, which explains the presence of operating points with negative torque. The literature suggests a 5% error when representing the WLTC cycle using these five
barycenters in the torque-speed domain. The simulation is run for each barycenter, and the total loss results for all the traction chain components are calculated.

Specifically for losses in the electrical machine, the multi-level structure has lower losses than the three-phase SiC 800V inverter structure. This is also the case compared to a conventional inverter structure (Si 400V) due to the harmonic content of the current in the machine. Iron losses and copper losses in the machine depend on the frequency content of the current and tend to increase with it. The barycenters most affected by this gain are the barycenters where the current is smoother than the three-phase inverter, i.e. those with a lower speed. Table I compares the performance of the two technologies in the overall powertrain chain.

<table><caption>Table I
COMPARISON OF THE EFFICIENCY OF THE TWO TECHNOLOGIES</caption><thead><tr><th></th><th>SiC Mosfet<br>[η]</th><th>IBIS<br>[η]</th><th>Gain<br>[Δη]</th></tr></thead><tbody><tr><td>Cells efficiency</td><td>98.6</td><td>97.2</td><td>-1.4</td></tr><tr><td>Converter efficiency</td><td>96.9</td><td>98.5</td><td>1.5</td></tr><tr><td>Machine efficiency</td><td>90.2</td><td>93.4</td><td>3.2</td></tr><tr><td>Total efficiency</td><td>86.3</td><td>89.4</td><td>3.1</td></tr></tbody></table>

The IBIS structure outperforms the 800V SiC Mosfet structure by several efficiency points. Regarding the electric machine, the IBIS structure exhibits lower harmonic content in the machine currents than the SiC structure, leading to reduced losses. However, the storage stage in the IBIS structure experiences higher losses due to increased current through the cells. Lastly, the conversion stage shows higher losses for the SiC architecture than for the IBIS architecture. Nevertheless, the losses in the SiC converters are lower than those in a conventional conversion structure [17]. Table II presents the simulated characteristics of two electric vehicles: one equipped with SiC switch technology and an 800V three-phase inverter, and the other with IBIS technology. The comparison highlights the performance differences between these two configurations, particularly in terms of efficiency, electric consumption, and overall driving range, providing a clear view of how each technology impacts the vehicle's capabilities.

Overall, the gain of the IBIS technology over the entire WLTC cycle for a city car with a classic three-phase Si inverter and a range of 400 km is approximately 40 km. The SiC 800V structure, when modeled on a WLTC cycle, provides a driving range of 414 km, which is 25 km less than the range offered by the IBIS technology.

<table><caption>Table II
COMPARISON OF THE VEHICLE CHARACTERISTICS</caption><thead><tr><th></th><th>SiC Mosfet</th><th>IBIS</th><th>Gain</th></tr></thead><tbody><tr><td>Efficiency [η]</td><td>86.3</td><td>89.4</td><td>3.1</td></tr><tr><td>Consumption [kW/h]</td><td>11.3</td><td>10.7</td><td>0.6</td></tr><tr><td>Range [km]</td><td>400</td><td>424</td><td>24</td></tr></tbody></table>

## VI. CONCLUSION

In this study, a method for modeling and calculating losses in an electric vehicle powertrain was developed. This approach centers around a Simulink-based model of the entire vehicle, which simulates losses in both storage and conversion functions. It is coupled with a finite element analysis (FEA) of the electric machine to provide more accurate calculations of the machine's characteristics and losses. The examination of SiC converters and a new electric vehicle powertrain topology (IBIS) helped to enrich the simulation software with practical examples.

The relevance of this research lies in the comparison of two breakthrough powertrain topologies: the 800V SiC powertrain and the IBIS topology discussed earlier. The findings demonstrated that the IBIS powertrain has a higher efficiency than the other topologies, directly impacting the vehicle's range. Beyond being a practical research case, this study could guide industrial decision-making regarding the deployment of future electric vehicle technologies within automotive groups.

## REFERENCES

[1] C. Sulzberger, "An early road warrior: electric vehicles in the early years of the automobile," *IEEE Power and Energy Magazine*, vol. 2, no. 3, pp. 66-71, 2004.

[2] J. J. Gómez Vilchez, A. Smyth, L. Kelleher, H. Lu, C. Rohr, G. Harrison, and C. Thiel, "Electric car purchase price as a factor determining consumers' choice and their views on incentives in europe," *Sustainability*, vol. 11, no. 22, 2019. [Online]. Available: https://www.mdpi.com/2071-1050/11/22/6357

[3] C. Rudolph, "How may incentives for electric cars affect purchase decisions?" *Transport Policy*, vol. 52, pp. 113-120, 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0967070X16300877

[4] M. Dijk, P. Wells, and R. Kemp, "Will the momentum of the electric car last? testing an hypothesis on disruptive innovation," *Technological Forecasting and Social Change*, vol. 105, pp. 77-88, 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0040162516000147

[5] I. Cavalcante, A. Rodrigues da Silva, M. Zajc, I. Mendek, L. Calearo, A. Malkova, C. Ziras, P. Pediaditis, K. Michos, J. Mateus, S. Matias, M. Brito, A. Lekidis, C. P. Guzman, A. R. Nunes, and H. Morais, "Dataset on Electric Road Mobility: Historical and Evolution Scenarios until 2050,"
*Scientific Data*, vol. 11, no. 1, p. 1019, Sep. 2024. [Online].
Available: https://doi.org/10.1038/s41597-024-03801-3

[6] S. Singh, S. Singh, and A. Tiwari, *PMSM Drives and its Application: An Overview*. Bentham Science Publishers, 2022.

[7] Y. Dai, L. Song, and S. Cui, "Development of pmsm drives for hybrid electric car applications," *IEEE Transactions on Magnetics*, vol. 43, no. 1, pp. 434–437, 2007.

[8] K. Olejniczak, T. Flint, D. Simco, S. Storkov, B. McGee, R. Shaw, B. Passmore, K. George, A. Curbow, and T. McNutt, "A compact 110 kva, 140°c ambient, 105°c liquid cooled, all-sic inverter for electric vehicle traction drives," in *2017 IEEE Applied Power Electronics Conference and Exposition (APEC)*, 2017, pp. 735–742.

[9] A. Merkert, T. Krone, and A. Mertens, "Characterization and scalable modeling of power semiconductors for optimized design of traction inverters with si- and sic-devices," *Power Electronics, IEEE Transactions on*, vol. 29, pp. 2238–2245, 05 2014.

[10] J. Zhu, H. Kim, H. Chen, R. Erickson, and D. Maksimovic, "High efficiency sic traction inverter for electric vehicle applications," 03 2018, pp. 1428–1433.

[11] T. Ayalew, "Sic semiconductor devices technology, modeling and simulation," Ph.D. Dissertation, Technischen Universität Wien, 2004.

[12] G. Vacca, "Benefits and advantages of silicon carbide power devices over their silicon counterparts," *Semicond. Compd. Adv. Silicon*, vol. 12, pp. 72–75, 2007.

[13] A. Poorfakhraei, M. Narimani, and A. Emadi, "A review of modulation and control techniques for multilevel inverters in traction applications," *IEEE Access*, vol. 9, pp. 24187–24204, 2021.

[14] A. Choudhury, P. Pillay, and S. S. Williamson, "Comparative analysis between two-level and three-level dc/ac electric vehicle traction inverters using a novel dc-link voltage balancing algorithm," *IEEE Journal of Emerging and Selected Topics in Power Electronics*, vol. 2, no. 3, pp. 529–540, 2014.

[15] A. Poorfakhraei, M. Narimani, and A. Emadi, "A review of multilevel inverter topologies in electric vehicles: Current status and future trends," *IEEE Open Journal of Power Electronics*, vol. 2, pp. 155–170, 2021.

[16] G. Pongnot, A. Desreveaux, C. Mayet, and D. Labrousse, "Modelization and experimental validation of CHB inverters for EVs and efficiency comparison with IGBT and SiC inverters on realistic driving cycles," Feb. 2024, working paper or preprint. [Online]. Available: https://hal.science/hal-04505313

[17] R. Jardot, G. Krebs, A. Lahlou, F. Roy, and C. Marchand, "Calculation of losses in a motor fed by a conventional inverter and a battery distributed inverter," *Energies*, vol. 16, no. 24, 2023.

[18] J. J. Berzelius, "Untersuchungen über die flussspathsäure und deren merkwürdigsten verbindungen," *Annalen der Physik*, vol. 80, no. 5, pp. 1–22, 1825. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.18250800502

[19] S. Yu, J. Wang, X. Zhang, Y. Liu, N. Jiang, and W. Wang, "The potential impact of using traction inverters with sic mosfets for electric buses," *IEEE Access*, vol. 9, pp. 51561–51572, 2021.

[20] B. Ralph and J. Kolar, "Component cost models for multi-objective optimizations of switched-mode power converters," 09 2013, pp. 2139–2146.

[21] O. Theliander, A. Kersten, M. Kuder, W. Han, E. A. Grunditz, and T. Thiringer, "Battery modeling and parameter extraction for drive cycle loss evaluation of a modular battery system for vehicles based on a cascaded h-bridge multilevel inverter," *IEEE Transactions on Industry Applications*, vol. 56, no. 6, pp. 6968–6977, 2020.

[22] J. Wang, T. Zhao, J. Li, A. Q. Huang, R. Callanan, F. Husna, and A. Agarwal, "Characterization, modeling, and application of 10-kv sic mosfet," *IEEE Transactions on Electron Devices*, vol. 55, no. 8, pp. 1798–1806, 2008.

[23] *Automotive-grade ACEPACK DRIVE power module, sixpack topology 1200 V, 3.8 m typ. SiC MOSFET gen.3 based*, ST Microelectronics, 2022.

[24] *Automotive N-Channel 40 V (D-S) 175 °C MOSFET*, Vishay, 2020.

[25] G. Krebs, E. de Cecco, and C. Marchand, "Design approach of an axial flux motor for electrical powertrain vehicle," in *2012 XXth International Conference on Electrical Machines*, 2012, pp. 2812–2817.

[26] M. Al Eit, F. Bouillault, C. Marchand, and G. Krebs, "2-d reduced model for eddy currents calculation in litz wire and its application for switched reluctance machine," *IEEE Transactions on Magnetics*, vol. 52, no. 3, pp. 1–4, 2016.

[27] N. Taran, V. Rallabandi, D. M. Ionel, G. Heins, and D. Patterson, "A comparative study of methods for calculating ac winding losses in permanent magnet machines," in *2019 IEEE International Electric Machines Drives Conference (IEMDC)*, 2019, pp. 2265–2271.

[28] D. Winterborne, S. Jordan, L. Sjöberg, and G. Atkinson, "Estimation of ac copper loss in electrical machine windings with consideration of end effects," in *2020 International Conference on Electrical Machines (ICEM)*, vol. 1, 2020, pp. 847–853.

[29] F. B. C. M. Al Eit, P. Dular and G. Krebs, "Perturbation finite element method for efficient copper losses calculation in switched reluctance machines," *IEEE Trans. Magn.*, vol. 53, 2017.

[30] R. Jardot, G. Krebs, A. Lahlou, F. Roy, and C. Marchand, "Order Reduction of a Frequency Magneto-Dynamic Problem for the Calculation of Copper Losses," ICEM (International Conference on Electrical Machines), Symposium, Sep. 2024, poster.