# Optimal Design of High-Speed Electric Machines for Electric Vehicles: A Case Study of 100 kW V-Shaped Interior PMSM

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## Abstract

**:**

## 1. Introduction

## 2. Definitions of High-Speed Machines

## 3. Methodology of Design and Optimization of High-Speed Machines

#### 3.1. Design Methodology of High-Speed Machines

#### 3.1.1. Electromagnetic and Mechanical Modelling

^{®}integrated into Matlab

^{®}. The electromagnetic performances of the machine are performed using magneto-static evaluations at each angular position of the rotor, which reduces computation time. The latter can be reduced further by using mechanical and electrical symmetries of the machine, which makes it possible to launch the simulations on only one pole of the machine and 1⁄6 of the electrical period. Electromagnetic quantities are reconstructed based on these symmetries, as detailed in [24]. The machine has three phases and is supplied with sinusoidal current using an ABC model. Two variables are defined for each operating point: current density and control angle. The former allows defining ampere-turns based on the required fill factor and slot area. Hence, the number of winding turns is not previously known but is determined downstream of the simulations according to the evaluated induced voltage and maximum DC voltage [24].

#### 3.1.2. Losses Modeling

- Iron losses:

- PM Losses:

- Mechanical Losses:

- Winding losses:

#### 3.2. Optimization Methodology of High-Speed Machines

- The distance between the strands must be guaranteed in order to take into account the thickness of the insulation,
- The slot must be uniformly and completely filled,
- The required fill factor must be verified.

- Objective 1: Mass of the machine,
- Objective 2: Total losses at Point ${P}_{1}$,
- Objective 3: Total losses at Point ${P}_{2}$.

## 4. Specifications

## 5. Results

- -
- ${P}_{vol}$: Power density (kW/L);
- -
- $PM/P$: Quantity of magnets per power (g/kW);
- -
- $Copp/P$: Quantity of copper per power (g/kW);
- -
- ${R}_{out-s}$: Outer radii of stator (mm);
- -
- ${L}_{act}$: Active length of the machine (mm);
- -
- DSW: Distributed stranded winding;
- -
- DHW: Distributed hairpin winding;
- -
- ${I}_{1},{I}_{2}$: RMS value of current per phase at points 1 and 2 (Arms);
- -
- ${J}_{1},{J}_{2}$: Current density at points 1 and 2 (Arms/mm²);
- -
- ${N}_{turns}$: Number of turns per coil;
- -
- ${R}_{ph}$: Resistance per phase ($m\mathsf{\Omega}$);
- -
- $nsh$: Number of strands in hand;
- -
- ${d}_{sh}$: diameter of strand (mm);
- -
- ${\eta}_{1},{\eta}_{2}$: Efficiency at points 1 and 2 (%);
- -
- ${P}_{J-1},{P}_{J-2}$: Joules losses at points 1 and 2 (W);
- -
- ${P}_{I-1},{P}_{I-2}$: Iron losses at points 1 and 2 (W);
- -
- ${P}_{AC-1},{P}_{AC-2}$: AC losses at points 1 and 2 (W);
- -
- ${P}_{M-1},{P}_{M-2}$: Mechanical losses at points 1 and 2 (W);
- -
- $CT$: Classic technologies;
- -
- $NT$: New technologies;
- -
- ${M}_{{\mathsf{\Omega}}_{max}\left(k.tr/min\right)-p-CT}$: Optimized electric machines using classic technologies with p pole pairs and operating at maximum speed ${\mathsf{\Omega}}_{max}\left(k.rpm\right)$;
- -
- ${M}_{{\mathsf{\Omega}}_{max}\left(k.tr/min\right)-p-NT}$: Optimized electric machines using new technologies with p pole pairs and operating at maximum speed ${\mathsf{\Omega}}_{max}\left(k.rpm\right)$;
- -
- ${M}_{{\mathsf{\Omega}}_{max}\left(k.tr/min\right)-p-CT}^{*}$: Electric machine with highest power density using classic technologies with p pole pairs and operating at maximum speed ${\mathsf{\Omega}}_{max}\left(k.tr/min\right)$;
- -
- ${M}_{{\mathsf{\Omega}}_{max}\left(k.tr/min\right)-p-NT}^{*}$: Electric machine with highest power density using new technologies with p pole pairs and operating at maximum speed ${\mathsf{\Omega}}_{max}\left(k.tr/min\right)$.

^{®}Xeon

^{®}X5690 3.47 GHz processor with 160 cores and AMD Ryzen™ Threadripper™ 3970X processor with 32 cores. All of these optimizations lasted 6 months.

#### 5.1. Maximum Rotation Speed ${\Omega}_{max}=\mathrm{15,000}$ rpm

#### 5.2. Maximum Rotation Speed ${\Omega}_{max}=\mathrm{20,000}$ rpm

#### 5.3. Maximum Rotation Speed ${\Omega}_{max}=\mathrm{30,000}$ rpm

#### 5.4. Maximum Rotation Speed ${\Omega}_{max}=\mathrm{40,000}$ rpm

^{2}and increases the slot’s surface thanks to the high outer radii of the stator. Furthermore, a higher number of turns means a higher resistance per phase and, therefore, higher joule losses (2.8 kW at point 1). The latter being dominant at low speed, total losses at point 1 of the machine with p = 3 are therefore high.

#### 5.5. Comparisons and Conclusions

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Li, S.; Li, Y.; Choi, W.; Sarlioglu, B. High-Speed electric machines: Challenges and design considerations. IEEE Trans. Transp. Electrific.
**2016**, 2, 2–13. [Google Scholar] [CrossRef] - Schubert, E.; Li, S.; Sarlioglu, B. High-speed surface permanent magnet machines—Rotor design analysis, considerations, and challenges. In Proceedings of the 2016 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, USA, 27–29 June 2016; pp. 1–6. [Google Scholar] [CrossRef]
- Gallicchio, G.; Di Nardo, M.; Palmieri, M.; Marfoli, A.; Degano, M.; Gerada, C.; Cupertino, F. High speed synchronous reluctance machines: Modeling, design and limits. IEEE Trans. Energy Convers.
**2022**, 37, 585–597. [Google Scholar] [CrossRef] - Shen, J.; Qin, X.; Wang, Y. High-speed permanent magnet electrical machines—Applications, key issues and challenges. CES Trans. Electr. Mach. Syst.
**2018**, 2, 23–33. [Google Scholar] [CrossRef] - Belahcen, A.; Martin, F.; El-Hadi Zaim, M.; Dlala, E.; Kolondzovski, Z. Combined FE and Particle Swarm algorithm for optimi-zation of high speed PM synchronous machine. COMPEL Int. J. Comput. Math. Electr. Electron. Eng.
**2015**, 34, 475–484. [Google Scholar] [CrossRef] - Belahcen, A.; Martin, F.; El-Hadi Zaim, M.; Dlala, E.; Kolondzovski, Z. Particle swarm optimization of the stator of a high speed PM synchronous machine. In Proceedings of the Digests of the 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation, Chicago, IL, USA, 9–12 May 2010; p. 1. [Google Scholar] [CrossRef]
- Benlamine, R.; Hamiti, T.; Vangraefschepe, F. Design of 60 kW–35,000 rpm interior PM machine for automotive application. In Proceedings of the International Conference on Optimization of Electrical and Electronic Equipment (OPTIM) & Intl Aegean Conference on Electrical Machines and Power Electronics (ACEMP), Brasov, Romania, 25–27 May 2017; pp. 311–316. [Google Scholar] [CrossRef]
- Gao, P.; Sun, X.; Gerada, D.; Gerada, C.; Wang, X. Improved V-shaped interior permanent magnet rotor topology with inward-extended bridges for reduced torque ripple. IET Electr. Power Appl.
**2020**, 14, 2404–2411. [Google Scholar] [CrossRef] - Zhang, G.; Yu, W.; Hua, W.; Cao, R.; Qiu, H.; Guo, A. The Design and Optimization of an Interior, Permanent Magnet Synchronous Machine Applied in an Electric Traction Vehicle Requiring a Low Torque Ripple. Appl. Sci.
**2019**, 9, 3634. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.; Castano, S.M.; Yang, R.; Kasprzak, M.; Bilgin, B.; Sathyan, A.; Dadkhah, H.; Emadi, A. Design and Comparison of Interior Permanent Magnet Motor Topologies for Traction Applications. IEEE Trans. Transp. Electrific.
**2017**, 3, 86–97. [Google Scholar] [CrossRef] - Tang, N.; Brown, I.P. Comparison of Candidate Designs and Performance Optimization for an Electric Traction Motor Targeting 50 kW/L Power Density. In Proceedings of the IEEE Energy Conversion Congress and Exposition (ECCE), Vancouver, BC, Canada, 10–14 October 2021; pp. 3675–3682. [Google Scholar] [CrossRef]
- Kim, S.-E.; You, Y.-M. Optimization of a Permanent Magnet Synchronous Motor for e-Mobility Using Metamodels. Appl. Sci.
**2022**, 12, 1625. [Google Scholar] [CrossRef] - Bernard, N.; Dang, L.; Olivier, J.-C.; Bracikowski, N.; Wasselynck, G.; Berthiau, G. Design optimization of high-speed PMSM for electric vehicles. In Proceedings of the 2015 IEEE Vehicle Power and Propulsion Conference (VPPC), Montreal, QC, Canada, 19–22 October 2015. [Google Scholar] [CrossRef]
- Soltani, M.; Nuzzo, S.; Barater, D.; Franceschini, G. A Multi-Objective Design Optimization for a Permanent Magnet Synchronous Machine with Hairpin Winding Intended for Transport Applications. Electronics
**2021**, 10, 3162. [Google Scholar] [CrossRef] - Reddy, P.B.; Jahns, T.M.; Bohn, T.P. Transposition effects on bundle proximity losses in high-speed PM machines. In Proceedings of the 2009 IEEE Energy Conversion Congress and Exposition, San Jose, CA, USA, 20–24 September 2009; pp. 1919–1926. [Google Scholar] [CrossRef]
- Reddy, P.B.; Jahns, T.M. Analysis of bundle losses in high speed machines. In Proceedings of the The 2010 International Power Electronics Conference—ECCE ASIA, Sapporo, Japan, 21–24 June 2010; pp. 2181–2188. [Google Scholar] [CrossRef]
- Mellor, P.H.; Wrobel, R.; McNeill, N. Investigation of proximity losses in a high speed brushless permanent magnet motor. In Proceedings of the Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting, Tampa, FL, USA, 8–12 October 2006; pp. 1514–1518. [Google Scholar] [CrossRef] [Green Version]
- Fatemi, A.; Ionel, D.M.; Demerdash, N.A.; Staton, D.A.; Wrobel, R.; Chong, Y.C. A computationally efficient method for calculation of strand eddy current losses in electric machines. In Proceedings of the 2016 IEEE Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, USA, 18–22 September 2016; pp. 1–8. [Google Scholar] [CrossRef] [Green Version]
- El Hajji, T.; Hlioui, S.; Louf, F.; Gabsi, M.; Mermaz-Rollet, G.; Belhadi, M. Hybrid model for AC Losses in High Speed PMSM for arbitrary flux density waveforms. In Proceedings of the International Conference on Electrical Machines (ICEM), Virtual, 23–15 August 2020; pp. 2426–2432. [Google Scholar] [CrossRef]
- Leuning, N.; Jaeger, M.; Schauerte, B.; Stöcker, A.; Kawalla, R.; Wei, X.; Hirt, G.; Heller, M.; KorteKerzel, S.; Böhm, L.; et al. Material Design for Low-Loss Non-Oriented Electrical Steel for Energy Efficient Drives. Materials
**2021**, 14, 6588. [Google Scholar] [CrossRef] [PubMed] - Mohamed, A.H.; Vansompel, H.; Sergeant, P. An Integrated Modular Motor Drive with Shared Cooling for Axial Flux Motor Drives. IEEE Trans. Ind. Electron.
**2021**, 68, 10467–10476. [Google Scholar] [CrossRef] - Salameh, M.; Spillman, T.; Krishnamurthy, M.; Brown, I.P.; Ludois, D.C. Wound field synchronous machine with segmented rotor laminations and die compressed field winding. In Proceedings of the 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA, 29 September–3 October 2019; pp. 1739–1746. [Google Scholar] [CrossRef]
- Deiml, M.; Eriksson, T.; Schneck, M.; Tan-Kim, A. High-speed Electric Drive Unit for the Next Generation of Vehicles. ATZ Worldw.
**2019**, 121, 42–47. [Google Scholar] [CrossRef] - Cisse, K.M.; Hlioui, S.; Belhadi, M.; Mermaz Rollet, G.; Gabsi, M.; Cheng, Y. Design Optimization of Multi-Layer Permanent Magnet Synchronous Machines for Electric Vehicle Applications. Energies
**2021**, 14, 7116. [Google Scholar] [CrossRef] - Van Millingen, R.D.; van Millingen, J.D. Phase shift torquemeters for gas turbine development and monitoring. In Proceedings of the ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, USA, 3–6 June 1991; pp. 1–10. [Google Scholar] [CrossRef] [Green Version]
- Kurvinen, E. Design and simulation of high-speed rotating electrical machinery. Ph.D. Thesis, Lappeenranta University of Technology, Lappeenranta, Finland, 2016. [Google Scholar]
- Benlamine, R.; Hamiti, T.; Vangraefschepe, F.; Lhotellier, D. Electromagnetic, Structural and Thermal Analyses of High-Speed PM Machines for Aircraft Application. In Proceedings of the XIII International Conference on Electrical Machines (ICEM), Alexandroupoli, Greece, 3–6 September 2018; pp. 212–217. [Google Scholar] [CrossRef]
- Rezzoug, A.; El-Hadi Zaïm, M.E. High-Speed Electric Machines. In Non-Conventional Electrical Machines; John Wiley and Sons: Hoboken, NJ, USA, 2013; pp. 117–189. [Google Scholar]
- Binder, A.; Schneider, T. High-speed inverter-fed AC drives. In Proceedings of the International Aegean Conference on Electrical Machines and Power Electronics (ACEMP), Bodrum, Turkey, 10–12 September 2007; pp. 9–16. [Google Scholar] [CrossRef]
- Bertotti, G. Physical interpretation of eddy current losses in ferromagnetic materials, I. theoretical considerations. J. Appl. Phys.
**1985**, 57, 2110–2117. [Google Scholar] [CrossRef] - Ishak, D.; Zhu, Z.Q.; Howe, D. Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole. IEEE Trans. Magn.
**2005**, 41, 2462–2469. [Google Scholar] [CrossRef] [Green Version] - Pyrhonen, J.; Jokinen, T.A.; Hrabovcova, V.A. Losses and Heat Transfer. In Design of Rotating Electrical Machines, 2nd ed.; John Wiley & Sons Ltd.: West Sussex, UK, 2014; pp. 527–529. [Google Scholar]
- Ramo, S.; Whinnery, J.R. Fields and Waves in Modern Radio; Wiley: New York, NY, USA, 1944. [Google Scholar]
- Sullivan, C.R. Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry. IEEE Trans. Power Electron.
**2001**, 16, 142–150. [Google Scholar] [CrossRef] - Taran, N.; Rallabandi, V.; Ionel, D.M.; Heins, G.; Patterson, D. A Comparative Study of Methods for Calculating AC Winding Losses in Permanent Magnet Machines. In Proceedings of the 2019 IEEE International Electric Machines & Drives Conference (IEMDC), San Diego, CA, USA, 12–15 May 2019; pp. 2265–2271. [Google Scholar] [CrossRef]
- Gyselinck, J.; Sabariego, R.V.; Dular, P. Time-Domain Homogenization of Windings in 2-D Finite Element Models. IEEE Trans. Magn.
**2007**, 43, 1297–1300. [Google Scholar] [CrossRef] [Green Version] - Volpe, G.; Popescu, M.; Marignetti, F.; Goss, J. Modelling AC Winding Losses in a PMSM with High Frequency and Torque Density. In Proceedings of the 2018 IEEE Energy Conversion Congress and Exposition (ECCE), Portland, OR, USA, 23–27 September 2018; pp. 2300–2305. [Google Scholar] [CrossRef]
- Ferreira, J.A. Appropriate modelling of conductive losses in the design of magnetic components. In Proceedings of the 21st Annual IEEE Conference on Power Electronics Specialists, San Antonio, TX, USA, June 1990; pp. 780–785. [Google Scholar] [CrossRef]
- Sato, Y.; Ishikawa, S.; Okubo, T.; Abe, M.; Tamai, K. Development of High Response Motor and Inverter System for the Nissan LEAF Electric Vehicle. In Proceedings of the SAE 2011 World Congress & Exhibition, Detroit, MI, USA, 11–14 April 2011; pp. 1–8. [Google Scholar] [CrossRef]
- Gu, W.; Zhu, X.; Quan, L.; Du, Y. Design and Optimization of Permanent Magnet Brushless Machines for Electric Vehicle Applications. Energies
**2015**, 8, 13996–14008. [Google Scholar] [CrossRef] [Green Version] - Bobba, S.; Carrara, S.; Huisman, J.; Mathieux, F.; Pavel, C. Critical Raw Materials for Strategic Technologies and Sectors in the EU—A Foresight Study; European Commission: Brussels, Belgium, 2020. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) Slot filled with real conductors used for DFEA model; (

**b**) equivalent slot uniformly filled with conductor material and virtually placed conductors used for SFEA model.

**Figure 8.**Pareto front of all electric machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{15,000}\text{}\mathrm{rpm}$.

**Figure 9.**(

**a**) ${M}_{15-2-CT}^{*}$, (

**b**) ${M}_{15-3-CT}^{*}$, (

**c**) ${M}_{15-4-CT}^{*}$, (

**d**) ${M}_{15-2-NT}^{*}$, (

**e**) ${M}_{15-3-NT}^{*}$, (

**f**) ${M}_{15-4-NT}^{*}$, (

**g**) Machine used in Peugeot e208.

**Figure 10.**Pareto front of all electric machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{20,000}\mathrm{rpm}$.

**Figure 11.**(

**a**) ${M}_{20-2-CT}^{*}$, (

**b**) ${M}_{20-3-CT}^{*}$, (

**c**) ${M}_{20-4-CT}^{*}$, (

**d**) ${M}_{20-2-NT}^{*}$, (

**e**) ${M}_{20-3-NT}^{*}$, (

**f**) ${M}_{20-4-NT}^{*}$, (

**g**) Machine used in Tesla Model 3.

**Figure 12.**Pareto front of all electric machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{30,000}\mathrm{rpm}$.

**Figure 13.**(

**a**) ${M}_{30-2-CT}^{*}$, (

**b**) ${M}_{30-3-CT}^{*}$, (

**c**) ${M}_{30-4-CT}^{*}$, (

**d**) ${M}_{30-2-NT}^{*}$, (

**e**) ${M}_{30-3-NT}^{*}$, (

**f**) ${M}_{30-4-NT}^{*}$.

**Figure 14.**Pareto front of all electric machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{40,000}\mathrm{rpm}$.

**Figure 15.**(

**a**) ${M}_{40-2-CT}^{*}$, (

**b**) ${M}_{40-3-CT}^{*}$, (

**c**) ${M}_{40-4-CT}^{*}$, (

**d**) ${M}_{40-2-NT}^{*}$, (

**e**) ${M}_{40-3-NT}^{*}$, (

**f**) ${M}_{40-4-NT}^{*}$.

**Figure 16.**Characteristics of optimal CT-based machines: (

**a-1**) Power density, (

**b-1**) efficiency at points 1 and 2, (

**c-1**) quantity of magnets, (

**d-1**) quantity of copper; and Characteristics of optimal NT-based machines: (

**a-2**) Power density, (

**b-2**) efficiency at points 1 and 2, (

**c-2**) quantity of magnets, (

**d-2**) quantity of copper.

**Figure 17.**Maximum rotational speed vs. power density for optimal machines and other machines used in hybrid electric vehicles (HEV).

**Figure 18.**Maximum rotational speed vs. quantity of magnets per power for optimal machines and other machines used in hybrid electric vehicles (HEV).

Definition | Reference | |
---|---|---|

Definition 1 | “Every time rotational speed occurs as a major constraint, either directly or indirectly, in the conception and design of the electric machine, we are referring to a high-speed machine” | [28] |

Definition 2 | $150\text{}\mathrm{m}/\mathrm{s}{\mathrm{V}}_{\mathrm{p}}$ | [26] |

Definition 3 | $100\text{}\mathrm{m}/\mathrm{s}{\mathrm{V}}_{\mathrm{p}}250\text{}\mathrm{m}/\mathrm{s}$ | [29] |

Definition 4 | $\mathsf{\Omega}>\mathrm{10,000}\text{}\mathrm{rpm}$ & ${\mathrm{D}}_{\mathsf{\Omega}}>{10}^{5}$ | [25] |

Electric Machine | Parameters | |
---|---|---|

Stator | Slot | 5 parameters * |

Outer radius | ${R}_{out,s}$ | |

Inner radius | ${R}_{inn,s}$ | |

Rotor | PM | 5 parameters * |

Air holes (near PM) | 5 parameters * | |

Air gap length | $\delta $ | |

Outer radius | ${R}_{out,r}={R}_{inn,s}-\delta $ | |

Inner radius | ${R}_{inn,r}$ | |

Active Length | ${l}_{act}$ | |

Operating Point ${P}_{i}$ | Current density | ${J}_{i}$ |

Control angle | ${\psi}_{i}$ |

Quantity | Value |
---|---|

Maximum Power: ${P}_{max}\left(\mathrm{kW}\right)$ | $100$ |

Flux Weakening Ratio: ${\mathrm{k}}_{\mathsf{\Omega}}$ | $4$ |

Maximum Rotational Speed: ${\mathsf{\Omega}}_{max}\left(rpm\right)$ | $\mathrm{15,000}$ |

$\mathrm{20,000}$ | |

$\mathrm{30,000}$ | |

$\mathrm{40,000}$ | |

Torque at Point 1: ${T}_{P1}\left(N.m\right)$ | - |

Torque at Point 2: ${T}_{P2}\left(N.m\right)$ | - |

Maximum Torque Ripple at Point 1 (%) | 30 |

Maximum Torque Ripple at Point 2 (%) | 50 |

Number of Pole Pair: $p$ | 2 3 4 |

Fill Factor ${K}_{fill}$(%) | 45 65 |

Lamination Thickness $T{h}_{lam}\left(mm\right)$ | 0.35 0.25 |

Remanent Flux Density of PM: ${B}_{r}\left(T\right)$ | 1.2 |

Maximum Current Density: ${J}_{max}\left(Arms/mm\xb2\right)$ | 15 33 |

Number of Slots per Pole per Phase: spp | 2 |

Air Gap Length (mm) | 0.7 |

$\mathrm{DC}\text{}\mathrm{Voltage}:\text{}{V}_{DC}\left(V\right)$ | 500 |

Maximum Current per Phase: ${I}_{ph-max}\left(Arms\right)$ | 445 |

Windings | Distributed—Series |

Yield Strength (MPa) | 400 |

Parameter | Type of Technology | |
---|---|---|

Classic Technologies | New Technologies | |

Fill Factor | 45% | 65% |

Maximum Current Density | 15 Arms/mm² | 33 Arms/mm² |

Lamination Thickness | 0.35 mm | 0.25 mm |

**Table 5.**Performances and characteristics of optimal machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{15,000}\mathrm{rpm}$ and machine used in Peugeot e208.

${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{15}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | Peugeot e208 | |
---|---|---|---|---|---|---|---|

$\mathbf{p}$ | 2 | 3 | 4 | 2 | 3 | 4 | 4 |

${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{\right)}$ | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

${\mathsf{\Omega}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{r}\mathbf{p}\mathbf{m}\mathbf{\right)}$ | 15,000 | 15,000 | 15,000 | 15,000 | 15 000 | 15,000 | 14,000 |

${\mathbf{P}}_{\mathbf{v}\mathbf{o}\mathbf{l}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{/}\mathbf{L}\mathbf{\right)}$ | 15.5 | 16.3 | 18.9 | 24.4 | 32.7 | 28.8 | 18 |

PM/P | 28.9 | 26.8 | 31 | 19.8 | 24.6 | 16.8 | 18 |

Copp/P | 92 | 79.8 | 68.6 | 42.2 | 33.2 | 30.4 | - |

${\mathbf{R}}_{\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{-}\mathbf{s}}$ | 95.3 | 97.6 | 89.2 | 79.3 | 74.3 | 82.2 | 95 |

${\mathbf{L}}_{\mathbf{a}\mathbf{c}\mathbf{t}}$ | 189 | 176.8 | 190.4 | 182.7 | 162.2 | 152.9 | 175 |

$\mathbf{T}{\mathbf{h}}_{\mathbf{l}\mathbf{a}\mathbf{m}}$ | 0.35 | 0.35 | 0.35 | 0.25 | 0.25 | 0.25 | 0.35 |

${\mathbf{K}}_{\mathbf{f}\mathbf{i}\mathbf{l}\mathbf{l}}$ | 45 | 45 | 45 | 65 | 65 | 65 | ~65 |

${\mathbf{J}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 15 | 15 | 15 | 33 | 33 | 33 | 16 |

${\mathbf{I}}_{\mathbf{p}\mathbf{h}\mathbf{-}\mathbf{m}\mathbf{a}\mathbf{x}}$ | 445 | 445 | 445 | 445 | 445 | 445 | 370 |

${\mathbf{V}}_{\mathbf{D}\mathbf{C}}$ | 500 | 500 | 500 | 500 | 500 | 500 | 350 |

Type of winding | DSW | DSW | DSW | DSW | DSW | DSW | DHW |

${\mathbf{I}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{2}}$ | 380/199 | 407/234 | 435/257 | 407/195 | 428/229 | 429/215 | - |

${\mathbf{J}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{J}}_{\mathbf{2}}$ | 14.3/7.5 | 14/8.1 | 14/8.3 | 31.7/15.2 | 31/16.6 | 27.2/13.9 | - |

${\mathbf{N}}_{\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{n}\mathbf{s}}$ | 5 | 3 | 2 | 5 | 3 | 2 | 4 |

${\mathbf{R}}_{\mathbf{p}\mathbf{h}}$ | 13 | 8.6 | 6.7 | 22.3 | 15.1 | 11.1 | |

$\mathbf{n}\mathbf{s}\mathbf{h}$ | 39 | 50 | 47 | 52 | 65 | 70 | 1 |

${\mathbf{d}}_{\mathbf{s}\mathbf{h}}$ | 0.9 | 0.85 | 0.9 | 0.56 | 0.52 | 0.53 | - |

${\mathsf{\eta}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathsf{\eta}}_{\mathbf{2}}$ | 94.4/95.2 | 95.5/95.9 | 95.9/96 | 89.9/96.7 | 92.2/96.6 | 94.3/96.8 | - |

${\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{2}}$ | 5655/1559 | 4294/1421 | 3801/1332 | 11,109/2552 | 8345/2392 | 5845/1537 | - |

${\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{2}}$ | 270/2758 | 344/1627 | 435/1978 | 159/545 | 193/686 | 263/1074 | - |

${\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{2}}$ | 27/85 | 25/140 | 55/372 | 9/40 | 9/44 | 12/41 | - |

${\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{2}}$ | 35/637 | 45.6/862 | 34/610 | 18/300 | 23/390 | 38/727 | - |

**Table 6.**Performances and characteristics of optimal machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{20,000}\mathrm{rpm}$ and machine used in Tesla Model 3.

${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{20}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | Tesla Model 3 | |
---|---|---|---|---|---|---|---|

$\mathbf{p}$ | 2 | 3 | 4 | 2 | 3 | 4 | 3 |

${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{\right)}$ | 100 | 100 | 100 | 100 | 100 | 100 | 202 |

${\mathsf{\Omega}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{r}\mathbf{p}\mathbf{m}\mathbf{\right)}$ | 20,000 | 20,000 | 20,000 | 20,000 | 20,000 | 20,000 | 18,000 |

${\mathbf{P}}_{\mathbf{v}\mathbf{o}\mathbf{l}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{/}\mathbf{L}\mathbf{\right)}$ | 15.7 | 21 | 19.8 | 29 | 42.1 | 36.5 | 37.5 |

PM/P | 21.1 | 25.4 | 20.1 | 16.5 | 21.5 | 12.3 | 18 |

Copp/P | 86.9 | 53.3 | 60.7 | 39 | 27.7 | 32.9 | - |

${\mathbf{R}}_{\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{-}\mathbf{s}}$ | 96.8 | 83.2 | 88.1 | 71.2 | 63.7 | 68.8 | 110.3 |

${\mathbf{L}}_{\mathbf{a}\mathbf{c}\mathbf{t}}$ | 178.2 | 197.7 | 187.4 | 194.2 | 173.8 | 173.2 | 131 |

$\mathbf{T}{\mathbf{h}}_{\mathbf{l}\mathbf{a}\mathbf{m}}$ | 0.35 | 0.35 | 0.35 | 0.25 | 0.25 | 0.25 | 0.25 |

${\mathbf{K}}_{\mathbf{f}\mathbf{i}\mathbf{l}\mathbf{l}}$ | 45 | 45 | 45 | 65 | 65 | 65 | 45 |

${\mathbf{J}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 15 | 15 | 15 | 33 | 33 | 33 | 33.7 |

${\mathbf{I}}_{\mathbf{p}\mathbf{h}\mathbf{-}\mathbf{m}\mathbf{a}\mathbf{x}}$ | 445 | 445 | 445 | 445 | 445 | 445 | 850 |

${\mathbf{V}}_{\mathbf{D}\mathbf{C}}$ | 500 | 500 | 500 | 500 | 500 | 500 | 350 |

Type of winding | DSW | DSW | DSW | DSW | DSW | DSW | DSW |

${\mathbf{I}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{2}}$ | 392/205 | 442/235 | 415/219 | 412/205 | 378/256 | 419/219 | - |

${\mathbf{J}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{J}}_{\mathbf{2}}$ | 12/6.3 | 15/8 | 12.8/6.7 | 27.9/13.8 | 33/22.3 | 25.9/13.5 | - |

${\mathbf{N}}_{\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{n}\mathbf{s}}$ | 4 | 2 | 2 | 4 | 3 | 2 | 15 |

${\mathbf{R}}_{\mathbf{p}\mathbf{h}}$ | 7.8 | 5.8 | 5.7 | 15.5 | 18 | 10.9 | - |

$\mathbf{n}\mathbf{s}\mathbf{h}$ | 49 | 50 | 48 | 67 | 54 | 89 | 19 |

${\mathbf{d}}_{\mathbf{s}\mathbf{h}}$ | 1 | 0.85 | 1 | 0.53 | 0.52 | 0.48 | 0.75 |

${\mathsf{\eta}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathsf{\eta}}_{\mathbf{2}}$ | 96.1/96.4 | 96.3/96 | 96.5/95.2 | 92.5/96.9 | 92.6/95.2 | 94.3/96.3 | - |

${\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{2}}$ | 3610/989 | 3378/959 | 2936/819 | 7921/1956 | 7828/3591 | 5791/1583 | - |

${\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{2}}$ | 438/1887 | 468/2176 | 584/3000 | 215/807 | 211/837 | 289/1591 | - |

${\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{2}}$ | 31/150 | 29/133 | 91/452 | 12/45 | 12/95 | 18/77 | - |

${\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{2}}$ | 39/742 | 51/1010 | 44/849 | 26/474 | 30/568 | 43/835 | - |

**Table 7.**Performances and characteristics of optimal machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{30,000}\mathrm{rpm}$ and machines designed by AVL [23].

${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{30}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | AVL [23] | |
---|---|---|---|---|---|---|---|

$\mathbf{p}$ | 2 | 3 | 4 | 2 | 3 | 4 | 3 |

${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{\right)}$ | 100 | 100 | 100 | 100 | 100 | 100 | 150 |

${\mathsf{\Omega}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{r}\mathbf{p}\mathbf{m}\mathbf{\right)}$ | 30,000 | 30,000 | 30,000 | 30,000 | 30,000 | 30,000 | 30,000 |

${\mathbf{P}}_{\mathbf{v}\mathbf{o}\mathbf{l}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{/}\mathbf{L}\mathbf{\right)}$ | 25.2 | 27.8 | 24.8 | 53.4 | 48.1 | 57.7 | 45.5 |

PM/P | 18.9 | 12.9 | 15.6 | 10.6 | 7.9 | 12.5 | - |

Copp/P | 60.1 | 48.5 | 57.1 | 30.1 | 34 | 22.3 | - |

${\mathbf{R}}_{\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{-}\mathbf{s}}$ | 74.7 | 72.5 | 87.2 | 54 | 63.6 | 54.4 | 75 |

${\mathbf{L}}_{\mathbf{a}\mathbf{c}\mathbf{t}}$ | 196 | 197 | 146.6 | 188 | 151.2 | 179.2 | 175 |

$\mathbf{T}{\mathbf{h}}_{\mathbf{l}\mathbf{a}\mathbf{m}}$ | 0.35 | 0.35 | 0.35 | 0.25 | 0.25 | 0.25 | 0.2 |

${\mathbf{K}}_{\mathbf{f}\mathbf{i}\mathbf{l}\mathbf{l}}$ | 45 | 45 | 45 | 65 | 65 | 65 | - |

${\mathbf{J}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 15 | 15 | 15 | 33 | 33 | 33 | >15 |

${\mathbf{I}}_{\mathbf{p}\mathbf{h}\mathbf{-}\mathbf{m}\mathbf{a}\mathbf{x}}$ $\mathbf{\left(}\mathbf{A}\mathbf{r}\mathbf{m}\mathbf{s}\mathbf{\right)}$ | 445 | 445 | 445 | 445 | 445 | 445 | 525 |

${\mathbf{V}}_{\mathbf{D}\mathbf{C}}\mathbf{\left(}\mathbf{V}\mathbf{\right)}$ | 500 | 500 | 500 | 500 | 500 | 500 | 800 |

Type of winding | DSW | DSW | DSW | DSW | DSW | DSW | DSW |

${\mathbf{I}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{2}}$ | 444/212 | 421/209 | 439/214 | 414/196 | 423/193 | 371/217 | - |

${\mathbf{J}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{J}}_{\mathbf{2}}$ | 14.5/6.9 | 15/7.4 | 13.6/6.6 | 32.1/15.2 | 26.2/12 | 32/18.7 | - |

${\mathbf{N}}_{\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{n}\mathbf{s}}$ | 3 | 2 | 2 | 4 | 3 | 2 | - |

${\mathbf{R}}_{\mathbf{p}\mathbf{h}}$ | 5.88 | 5.72 | 5.35 | 16.2 | 11.47 | 14.6 | - |

$\mathbf{n}\mathbf{s}\mathbf{h}$ | 47 | 48 | 48 | 60 | 89 | 59 | - |

${\mathbf{d}}_{\mathbf{s}\mathbf{h}}$ | 0.9 | 0.85 | 0.9 | 0.52 | 0.48 | 0.5 | - |

${\mathsf{\eta}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathsf{\eta}}_{\mathbf{2}}$ | 96.2/96.1 | 96.4/94.4 | 96/94.3 | 92.2/96.6 | 94/96.8 | 94.1/96.1 | 92/93 |

${\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{J}\mathbf{-}\mathbf{2}}$ | 3480/792 | 3053/751 | 3100/734 | 8333/1874 | 6168/1286 | 6040/2073 | - |

${\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{I}\mathbf{-}\mathbf{2}}$ | 447/1989 | 613/3619 | 874/3182 | 186/1111 | 288/1156 | 288/1092 | - |

${\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{A}\mathbf{C}\mathbf{-}\mathbf{2}}$ | 33/120 | 75/263 | 171/756 | 16/51 | 26/95 | 38/224 | - |

${\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{P}}_{\mathbf{M}\mathbf{-}\mathbf{2}}$ | 56/1150 | 70/1487 | 70/1571 | 32/605 | 39/792 | 41/829 | - |

**Table 8.**Performances and characteristics of optimal machines operating at ${\mathsf{\Omega}}_{max}=\mathrm{40,000}\mathrm{rpm}$.

${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{C}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{2}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{3}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | ${\mathbf{M}}_{\mathbf{40}\mathbf{-}\mathbf{4}\mathbf{-}\mathbf{N}\mathbf{T}}^{\mathbf{*}}$ | |
---|---|---|---|---|---|---|

$\mathbf{p}$ | 2 | 3 | 4 | 2 | 3 | 4 |

${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{\left(}\mathbf{k}\mathbf{W}\mathbf{\right)}$ | 100 | 100 | 100 | 100 | 100 | 100 |

40,000 | 40,000 | 40,000 | 40,000 | 40,000 | 40,000 | |

30.3 | 25 | 25.5 | 52 | 63.9 | 68.2 | |

PM/P | 13.4 | 11.6 | 12.7 | 8.9 | 9.4 | 6 |

Copp/P | 42.6 | 43.3 | 32.4 | 21.7 | 21.8 | 23 |

${\mathbf{R}}_{\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{-}\mathbf{s}}$ | 74.5 | 80 | 75 | 58.5 | 50 | 52.2 |

${\mathbf{L}}_{\mathbf{a}\mathbf{c}\mathbf{t}}$ | 158.6 | 183.6 | 210 | 162.8 | 188.3 | 163.5 |

$\mathbf{T}{\mathbf{h}}_{\mathbf{l}\mathbf{a}\mathbf{m}}$ | 0.35 | 0.35 | 0.35 | 0.25 | 0.25 | 0.25 |

${\mathbf{K}}_{\mathbf{f}\mathbf{i}\mathbf{l}\mathbf{l}}$ | 45 | 45 | 45 | 65 | 65 | 65 |

${\mathbf{J}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 15 | 15 | 15 | 33 | 33 | 33 |

${\mathbf{I}}_{\mathbf{p}\mathbf{h}\mathbf{-}\mathbf{m}\mathbf{a}\mathbf{x}}$ | 445 | 445 | 445 | 445 | 445 | 445 |

${\mathbf{V}}_{\mathbf{D}\mathbf{C}}\mathbf{\left(}\mathbf{V}\mathbf{\right)}$ | 500 | 500 | 500 | 500 | 500 | 500 |

Type of winding | DSW | DSW | DSW | DSW | DSW | DSW |

${\mathbf{I}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{I}}_{\mathbf{2}}$ | 370/256 | 423/215 | 443/224 | 429/208 | 445/194 | 423/195 |

${\mathbf{J}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathbf{J}}_{\mathbf{2}}$ | 14/9.7 | 14.4/7.3 | 14.2/7.2 | 32/15.5 | 31.7/13.9 | 32.4/15 |

${\mathbf{N}}_{\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{n}\mathbf{s}}$ | 3 | 2 | 1 | 3 | 2 | 2 |

${\mathbf{R}}_{\mathbf{p}\mathbf{h}}$ | 6.4 | 5.3 | 3.4 | 10.6 | 9.8 | 11.9 |

$\mathbf{n}\mathbf{s}\mathbf{h}$ | 38 | 47 | 45 | 74 | 77 | 72 |

${\mathbf{d}}_{\mathbf{s}\mathbf{h}}$ | 0.9 | 0.85 | 0.9 | 0.48 | 0.48 | 0.48 |

${\mathsf{\eta}}_{\mathbf{1}}\mathbf{,}\mathbf{}{\mathsf{\eta}}_{\mathbf{2}}$ | 96.9/92.6 | 96.3/95.3 | 96.8/93 | 94.2/96.6 | 94.2/96.8 | 93.6/95.7 |

2620/1256 | 2880/743 | 2026/518 | 5858/1376 | 5802/1112 | 6394/1361 | |

520/5156 | 895/2758 | 1072/4668 | 303/1076 | 364/1036 | 449/1788 | |

54/462 | 121/590 | 123/572 | 17/65 | 36/135 | 80/341 | |

77/1768 | 58/1248 | 89/2000 | 49/1067 | 49/1028 | 49/1062 |

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## Share and Cite

**MDPI and ACS Style**

El Hajji, T.; Hlioui, S.; Louf, F.; Gabsi, M.; Mermaz-Rollet, G.; Belhadi, M.
Optimal Design of High-Speed Electric Machines for Electric Vehicles: A Case Study of 100 kW V-Shaped Interior PMSM. *Machines* **2023**, *11*, 57.
https://doi.org/10.3390/machines11010057

**AMA Style**

El Hajji T, Hlioui S, Louf F, Gabsi M, Mermaz-Rollet G, Belhadi M.
Optimal Design of High-Speed Electric Machines for Electric Vehicles: A Case Study of 100 kW V-Shaped Interior PMSM. *Machines*. 2023; 11(1):57.
https://doi.org/10.3390/machines11010057

**Chicago/Turabian Style**

El Hajji, Taha, Sami Hlioui, François Louf, Mohamed Gabsi, Guillaume Mermaz-Rollet, and M’Hamed Belhadi.
2023. "Optimal Design of High-Speed Electric Machines for Electric Vehicles: A Case Study of 100 kW V-Shaped Interior PMSM" *Machines* 11, no. 1: 57.
https://doi.org/10.3390/machines11010057