# Design and Finite-Element-Based Optimization for a 12-Slot/10-Pole IPM Motor with Integrated Onboard Battery Charger for Electric Vehicle Applications

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

## 3. Machine Design

#### 3.1. Selecting Base Machine

#### 3.2. Sizing Equation

^{2}), f is the frequency in hertz (Hz), and p is the number of pole pairs. The ratio between effective length and air gap diameter is defined as the aspect ratio ${K}_{l}$, whereas the ratio between the air gap diameter and stator outer diameter is defined as the split ratio $\lambda $. The winding factor can be obtained through a series of equations presented in [26], or simply from tables given in [31]. The rest of the motor geometrical parameters can be derived analytically as starting parameters to initiate the optimization process [29].

#### 3.3. Design Flow Chart

#### 3.4. Rotor Design

## 4. Sensitivity Analysis and Optimization

#### 4.1. Variance-Based Sensitivity Analysis

#### 4.2. Finite Element (FE) Based Optimization

## 5. Optimal Machine Versus Initial Machine

## 6. Experimental Validation

- The Park’s transformation is utilized to transform motor currents into measured ${i}_{d}$ and ${i}_{q}$. ${i}_{d}$ is aligned with the rotor magnetic field, and ${i}_{q}$ is $\pi /2$ ahead of ${i}_{d}$. ${i}_{q}$ reference is controlled by a PI closed-loop speed controller, while ${i}_{d}$ reference is nullified to obtain maximum allowable torque.
- The d-axis and q-axis current controllers generate the voltage references. The inverse Park’s transformation is employed to calculate the actual voltage values that are fed to the sinusoidal pulse width modulated (SPWM) inverter to feed the motor in propulsion mode.

- The grid current components are controlled in a way that maximizes the reference direct component ${i}_{d}^{\mathrm{*}}$, thereby maintaining maximum charging level, canceling out the reference quadrature component ${i}_{q}^{\mathrm{*}}$, and assuring the grid-side operation with a unity power factor. The reference sequence current components are regulated based on the reference grid current components.
- The inverse Park’s transformation is employed to calculate the $\mathrm{x}\mathrm{y}$ reference currents, ${i}_{xy}^{\mathrm{*}}$ and the reference $\mathsf{\alpha}\mathsf{\beta}$ grid current, ${i}_{\alpha \beta}^{\mathrm{*}}$, which have the same value, with the grid being synchronized with the inverter using a phase-locked loop (PLL).
- A zero-average torque is generated by setting the stator $\mathsf{\alpha}\mathsf{\beta}$ currents, ${\mathrm{i}}_{\mathsf{\alpha}\mathsf{\beta}}$, and the zero sequence current components, ${\mathrm{i}}_{{0}^{+}{0}^{-}}$, to zero.

#### 6.1. Propulsion Mode of Operation

#### 6.2. Charging Mode of Operation

^{®®}). The vibration level is shown in Figure 21. ISO 10816-3 standards provide guidance for evaluating vibration severity in machines [53]. This machine is considered a machine of class II (from 15 kW up to 300 kW). For class II, vibration is good in the range of (0–1.4 mm/s rms) and satisfactory in the range of (1.4–2.8 mm/s rms). The vibration level recorded during charging under full-load current is 2.7 mm/s rms, which is considered satisfactory and can maintain operation without vibrational issues.

## 7. Conclusions

- For the propulsion mode, average torque is directly proportional to magnet width, magnet thickness, and V-angle. On the contrary, it is inversely proportional to the bridge value and magnet clearance.
- For the propulsion mode, torque ripple is inversely proportional to the bridge value. On the other hand, regarding the variations in magnet width, magnet thickness, V-angle, and magnet clearance, some ranges show an increase in torque ripples while others show a decrease in torque ripples.
- In the charging mode, torque ripple is directly proportional to the bridge value and magnet clearance. Conversely, it is inversely proportional to V-angle, magnet width, and magnet thickness.
- In the propulsion mode, core losses are inversely proportional to the bridge value and magnet clearance. On the other hand, they are directly proportional to magnet thickness and magnet width. Additionally, they show variations in the changing V-angles.
- For the charging mode, core losses are directly proportional to the bridge value and magnet clearance. In contrast, they are inversely proportional to V-angle, magnet width, and magnet thickness.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclatures

${W}_{m}$ | Magnet Width (mm) |

${T}_{m}$ | Magnet thickness (mm) |

${M}_{2}$ | Clearance between the two magnets (mm) |

$Bri$ | The bridge between the magnet and rotor surface (mm) |

$V$ | $\mathrm{V}\text{-}\mathrm{angle}\text{}\mathrm{between}\text{}\mathrm{the}\text{}\mathrm{two}\text{}\mathrm{magnets}\text{}$ (°) |

${W}_{FBi}$ | $\mathrm{Flux}\text{}\mathrm{barrier}\text{}\mathrm{width},\text{}{W}_{FBi}$$,\text{}\mathrm{where}\text{}i$ takes on a value of 1 or 2, 1 indicates the upper flux barrier, and 2 indicates the lower flux barrier. (mm) |

${F}_{Bij}$ | $\mathrm{The}\text{}\mathrm{flux}\text{}\mathrm{barrier}\text{\u2019}\mathrm{s}\text{}\mathrm{two}\text{}\mathrm{angles},\text{}{FB}_{ij}$$,\text{}\mathrm{where}\text{}j$$\text{}\mathrm{takes}\text{}\mathrm{a}\text{}\mathrm{value}\text{}\mathrm{of}\text{}1\text{}\mathrm{or}\text{}2,\text{}\mathrm{representing}\text{}\mathrm{the}\text{}\mathrm{two}\text{}\mathrm{base}\text{}\mathrm{angles},\text{}\mathrm{which}\text{}\mathrm{are}\text{}\mathrm{kept}\text{}\mathrm{constant}\text{}(\xb0)$ |

${P}_{n}$ | Rated power (W) |

${K}_{w}$ | Winding factor |

${K}_{l}$ | Aspect ratio “Stack length to air gap diameter ratio” |

$\eta $ | Efficiency (%) |

${B}_{g}$ | Air gap flux density (T) |

${A}_{s}$ | Stator’s electrical loading (A/mm) |

$f$ | Frequency (Hz) |

$p$ | Number of pole pairs |

${D}_{g}$ | Stator’s outer diameter (mm) |

${D}_{so}$ | Stator’s inner diameter (mm) |

${L}_{eff}$ | Stack length (mm) |

$\lambda $ | Split ratio “Stator’s inner diameter to outer diameter ratio” |

${h}_{bi}$ | Back iron thickness (mm) |

${B}_{bi}$ | Back iron flux density (T) |

${h}_{t}$ | Tooth height (mm) |

${w}_{t}$ | Tooth width (mm) |

${B}_{t}$ | Tooth flux density (T) |

$Q$ | Number of the stator’s slots |

${V}_{peak}$ | Rated peak voltage (V) |

${m}_{i}$ | Modulation index |

${V}_{DC}$ | DC bus voltage (V) |

$m$ | Number of phases |

${I}_{peak}$ | Rated peak current (A) |

$\mathrm{cos}\theta $ | Power factor |

${K}_{e}$ | EMF factor |

${N}_{t}$ | Number of turns |

${K}_{Cu}$ | Copper fill factor |

$J$ | $\mathrm{Current}\text{}\mathrm{density}\text{}(A/{mm}^{2})$ |

## References

- Austmann, L.M. Drivers of the electric vehicle market: A systematic literature review of empirical studies. Financ. Res. Lett.
**2021**, 41, 101846. [Google Scholar] [CrossRef] - Paoli, L.; Gül, T. Electric Cars Fend off Supply Challenges to More Than Double Global Sales; IEA: Paris, France, 2022. [Google Scholar]
- Alshahrani, S.; Khalid, M.; Almuhaini, M.J. Electric vehicles beyond energy storage and modern power networks: Challenges and applications. IEEE Access
**2019**, 7, 99031–99064. [Google Scholar] [CrossRef] - Sreeram, K.; Surendran, S.; Preetha, P.J. A Review on Single-Phase Integrated Battery Chargers for Electric Vehicles. In Information and Communication Technology for Competitive Strategies (ICTCS 2021); Springer: Singapore, 2023; pp. 751–765. [Google Scholar]
- Valente, M.; Wijekoon, T.; Freijedo, F.; Pescetto, P.; Pellegrino, G.; Bojoi, R. Integrated on-board ev battery chargers: New perspectives and challenges for safety improvement. In Proceedings of the 2021 IEEE Workshop on Electrical Machines Design, Control and Diagnosis (WEMDCD), Modena, Italy, 8–9 April 2021; pp. 349–356. [Google Scholar]
- Gundogdu, T.; Zhu, Z.-Q.; Chan, C.C. Comparative Study of Permanent Magnet, Conventional, and Advanced Induction Machines for Traction Applications. World Electr. Veh. J.
**2022**, 13, 137. [Google Scholar] [CrossRef] - Yang, Z.; Shang, F.; Brown, I.P.; Krishnamurthy, M.J. Comparative study of interior permanent magnet, induction, and switched reluctance motor drives for EV and HEV applications. IEEE Trans. Transp. Electrif.
**2015**, 1, 245–254. [Google Scholar] [CrossRef] - Huynh, T.-A.; Chen, P.-H.; Hsieh, M.-F. Analysis and Comparison of Operational Characteristics of EV Traction Units Combining Two Different Types of Motors. IEEE Trans. Veh. Technol.
**2022**, 71, 5727–5742. [Google Scholar] [CrossRef] - Pellegrino, G.; Vagati, A.; Boazzo, B.; Guglielmi, P.J. Comparison of induction and PM synchronous motor drives for EV application including design examples. IEEE Trans. Ind. Appl.
**2012**, 48, 2322–2332. [Google Scholar] [CrossRef] [Green Version] - Salem, A.; Narimani, M.J. A review on multiphase drives for automotive traction applications. IEEE Trans. Transp. Electrif.
**2019**, 5, 1329–1348. [Google Scholar] [CrossRef] - Subotic, I.; Bodo, N.; Levi, E.; Jones, M.J. Onboard integrated battery charger for EVs using an asymmetrical nine-phase machine. IEEE Trans. Ind. Electron.
**2014**, 62, 3285–3295. [Google Scholar] [CrossRef] - Haghbin, S.; Lundmark, S.; Alakula, M.; Carlson, O.J. Grid-connected integrated battery chargers in vehicle applications: Review and new solution. IEEE Trans. Ind. Electron.
**2012**, 60, 459–473. [Google Scholar] [CrossRef] - Subotic, I.; Levi, E.; Bodo, N. A fast on-board integrated battery charger for EVs using an asymmetrical six-phase machine. In Proceedings of the 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal, 27–30 October 2014; pp. 1–6. [Google Scholar]
- Subotic, I.; Bodo, N.; Levi, E.J. An EV drive-train with integrated fast charging capability. IEEE Trans. Power Electron.
**2015**, 31, 1461–1471. [Google Scholar] [CrossRef] [Green Version] - Zhou, C.; Huang, X.; Li, Z.; Cao, W.J. Design consideration of fractional slot concentrated winding interior permanent magnet synchronous motor for EV and HEV applications. IEEE Access
**2021**, 9, 64116–64126. [Google Scholar] [CrossRef] - Fan, X.; Zhang, B.; Qu, R.; Li, D.; Li, J.; Huo, Y.J. Comparative thermal analysis of IPMSMs with integral-slot distributed-winding (ISDW) and fractional-slot concentrated-winding (FSCW) for electric vehicle application. IEEE Trans. Ind. Appl.
**2019**, 55, 3577–3588. [Google Scholar] [CrossRef] - Tessarolo, A.J. A quadratic-programming approach to the design optimization of fractional-slot concentrated windings for surface permanent-magnet machines. IEEE Trans. Energy Convers.
**2017**, 33, 442–452. [Google Scholar] [CrossRef] - Dajaku, G.; Spas, S.; Gerling, D.J. Advanced optimization methods for fractional slot concentrated windings. Electr. Eng.
**2019**, 101, 103–120. [Google Scholar] [CrossRef] - Gundogdu, T.; Komurgoz, G.J.S.; Optimization, M. A systematic design optimization approach for interior permanent magnet machines equipped with novel semi-overlapping windings. Struct. Multidiscip. Optim.
**2021**, 63, 1491–1512. [Google Scholar] [CrossRef] - Vidanalage, B.D.S.G.; Toulabi, M.S.; Filizadeh, S.J. Multimodal design optimization of V-shaped magnet IPM synchronous machines. IEEE Trans. Energy Convers.
**2018**, 33, 1547–1556. [Google Scholar] [CrossRef] - Ma, Q.; Ayman, E.-R. Finite Element-based Multi-objective Design Optimization of IPM Considering Saturation Effects for Constant Power Region of Operation. In Proceedings of the 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 11–15 October 2020; pp. 1411–1417. [Google Scholar]
- Lee, J.H.; Song, J.-Y.; Kim, D.-W.; Kim, J.-W.; Kim, Y.-J.; Jung, S.-Y.J. Particle swarm optimization algorithm with intelligent particle number control for optimal design of electric machines. IEEE Trans. Ind. Electron.
**2017**, 65, 1791–1798. [Google Scholar] [CrossRef] - Sasaki, H.; Igarashi, H. Topology optimization of IPM motor with aid of deep learning. Int. J. Appl. Electromagn. Mech.
**2019**, 59, 87–96. [Google Scholar] [CrossRef] [Green Version] - Metwly, M.Y.; Ahmed, M.; Hemeida, A.; Abdel-Khalik, A.S.; Hamad, M.S.; Belahcen, A.; Ahmed, S.; Elmalhy, N.A.J. Investigation of Six-Phase Surface Permanent Magnet Machine with Typical Slot/Pole Combinations for Integrated Onboard Chargers Through Methodical Design Optimization. IEEE Trans. Transp. Electrif.
**2022**, 9, 866–885. [Google Scholar] [CrossRef] - Huang, S.; Luo, J.; Leonardi, F.; Lipo, T.A.J. A general approach to sizing and power density equations for comparison of electrical machines. IEEE Trans. Ind. Appl.
**1998**, 34, 92–97. [Google Scholar] [CrossRef] [Green Version] - Bianchi, N.; Bolognani, S.; Frare, P.J. Design criteria for high-efficiency SPM synchronous motors. IEEE Trans. Energy Convers.
**2006**, 21, 396–404. [Google Scholar] [CrossRef] - Hemeida, A.; Metwly, M.Y.; Abdel-Khalik, A.S.; Ahmed, S.J.E. Optimal Design of A 12-Slot/10-Pole Six-Phase SPM Machine with Different Winding Layouts for Integrated On-Board EV Battery Charging. Energies
**2021**, 14, 1848. [Google Scholar] [CrossRef] - Yang, Y.; Castano, S.M.; Yang, R.; Kasprzak, M.; Bilgin, B.; Sathyan, A.; Dadkhah, H.; Emadi, A.J. Design and comparison of interior permanent magnet motor topologies for traction applications. IEEE Trans. Transp. Electrif.
**2016**, 3, 86–97. [Google Scholar] [CrossRef] - Pyrhonen, J.; Jokinen, T.; Hrabovcova, V. Design of Rotating Electrical Machines; John Wiley & Sons, Ltd.: Chichester, UK, 2014; ISBN 978-1-118-58157-5. [Google Scholar]
- Hemeida, A. Electromagnetic and Thermal Design of Axial Flux Permanent Magnet Synchronous Machines. Ph.D. Thesis, Ghent University, Ghent, Belgium, 2017. [Google Scholar]
- Yokoi, Y.; Higuchi, T.; Miyamoto, Y.J. General formulation of winding factor for fractional-slot concentrated winding design. IET Electr. Power Appl.
**2016**, 10, 231–239. [Google Scholar] [CrossRef] [Green Version] - Murali, N.; Ushakumari, S. Performance comparison between different rotor configurations of PMSM for EV application. In Proceedings of the 2020 IEEE Region 10 Conference (TENCON), Osaka, Japan, 16–19 November 2020; pp. 1334–1339. [Google Scholar]
- Wang, A.; Jia, Y.; Soong, W.J. Comparison of five topologies for an interior permanent-magnet machine for a hybrid electric vehicle. IEEE Trans. Magn.
**2011**, 47, 3606–3609. [Google Scholar] [CrossRef] - Hu, Y.; Zhu, S.; Liu, C.; Wang, K.J. Electromagnetic performance analysis of interior PM machines for electric vehicle applications. IEEE Trans. Energy Convers.
**2017**, 33, 199–208. [Google Scholar] [CrossRef] - Liu, X.; Chen, H.; Zhao, J.; Belahcen, A.J. Research on the performances and parameters of interior PMSM used for electric vehicles. IEEE Trans. Ind. Electron.
**2016**, 63, 3533–3545. [Google Scholar] [CrossRef] - Krishnan, R. Permanent Magnet Synchronous and Brushless DC Motor Drives; CRC Press: Boca Raton, FL, USA, 2010. [Google Scholar]
- Bunting-e-Magnets. Available online: https://e-magnetsuk.com/wp-content/uploads/2020/11/Neodymium-Material-Data-Sheet.pdf (accessed on 18 February 2023).
- Carlier, A.; Geris, L. Sensitivity analysis by design of experiments. In Uncertainty in Biology; Springer: Cham, Switzerland, 2016. [Google Scholar]
- Rodriguez-Fernandez, M.; Banga, J.R.; Doyle, F.J., III. Novel global sensitivity analysis methodology accounting for the crucial role of the distribution of input parameters: Application to systems biology models. Int. J. Robust Nonlinear Control
**2012**, 22, 1082–1102. [Google Scholar] [CrossRef] [Green Version] - Cao, D.; Zhao, W.; Ji, J.; Wang, Y. Parametric equivalent magnetic network modeling approach for multiobjective optimization of PM machine. IEEE Trans. Ind. Electron.
**2020**, 68, 6619–6629. [Google Scholar] [CrossRef] - Bianchi, N.; Bolognani, S. Design optimisation of electric motors by genetic algorithms. IEE Proc. Electr. Power Appl.
**1998**, 145, 475–483. [Google Scholar] [CrossRef] - Cho, D.-H.; Jung, H.-K.; Lee, C.-G.J. Induction motor design for electric vehicle using a niching genetic algorithm. IEEE Trans. Ind. Appl.
**2001**, 37, 994–999. [Google Scholar] - Çunkaş, M.; Akkaya, R.J. Design optimization of induction motor by genetic algorithm and comparison with existing motor. Math. Comput. Appl.
**2006**, 11, 193–203. [Google Scholar] [CrossRef] - Desai, C.; Williamson, S.S. Optimal design of a parallel hybrid electric vehicle using multi-objective genetic algorithms. In Proceedings of the 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA, 7–10 September 2009; pp. 871–876. [Google Scholar]
- Hamiti, T.; Gerada, C.; Rottach, M. Weight optimisation of a surface mount permanent magnet synchronous motor using genetic algorithms and a combined electromagnetic-thermal co-simulation environment. In Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, USA, 17–22 September 2011; pp. 1536–1540. [Google Scholar]
- Jannot, X.; Vannier, J.-C.; Marchand, C.; Gabsi, M.; Saint-Michel, J.; Sadarnac, D.J. Multiphysic modeling of a high-speed interior permanent-magnet synchronous machine for a multiobjective optimal design. IEEE Trans. Energy Convers.
**2010**, 26, 457–467. [Google Scholar] [CrossRef] - Mahmoudi, A.; Kahourzade, S.; Abd Rahim, N.; Hew, W.P.J. Design, analysis, and prototyping of an axial-flux permanent magnet motor based on genetic algorithm and finite-element analysis. IEEE Trans. Magn.
**2012**, 49, 1479–1492. [Google Scholar] [CrossRef] - Rahideh, A.; Korakianitis, T.; Ruiz, P.; Keeble, T.; Rothman, M.J. Optimal brushless DC motor design using genetic algorithms. J. Magn. Magn. Mater.
**2010**, 322, 3680–3687. [Google Scholar] [CrossRef] - Metwly, M.Y.; Abdel-Majeed, M.S.; Abdel-Khalik, A.S.; Hamdy, R.A.; Hamad, M.S.; Ahmed, S.J. A review of integrated on-board EV battery chargers: Advanced topologies, recent developments and optimal selection of FSCW slot/pole combination. IEEE Access
**2020**, 8, 85216–85242. [Google Scholar] [CrossRef] - Wang, Z.; Chen, J.; Cheng, M.; Chau, K.J. Field-oriented control and direct torque control for paralleled VSIs fed PMSM drives with variable switching frequencies. IEEE Trans. Power Electron.
**2015**, 31, 2417–2428. [Google Scholar] [CrossRef] - Abdel-Majeed, M.S.; Shawier, A.; Abdel-Khalik, A.S.; Hamad, M.S.; Sedky, M.M.; Elmalhy, N.A.J. General current control of six-phase-based non-isolated integrated on-board charger with low order harmonic compensation. Sustainability
**2022**, 14, 1088. [Google Scholar] [CrossRef] - Shawier, A.; Habib, A.; Mamdouh, M.; Abdel-Khalik, A.S.; Ahmed, K.H.J. Assessment of predictive current control of six-phase induction motor with different winding configurations. IEEE Access
**2021**, 9, 81125–81138. [Google Scholar] [CrossRef] - Romahadi, D.; Xiong, H.; Pranoto, H. Intelligent system for gearbox fault detection & diagnosis based on vibration analysis using bayesian networks. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 694, 012001. [Google Scholar]

**Figure 1.**Six-phase integrated OBC’s scheme and operation modes’ phasor diagram. (

**a**) Asymmetrical six-phase topology, (

**b**) Propulsion mode current phasor diagram, and (

**c**) Charging mode current phasor diagram.

**Figure 6.**Optimization results of the six objectives under the two modes of operation: (

**a**) propulsion mode and (

**b**) charging mode.

**Figure 8.**Torque curves under the two modes of operation: (

**a**) propulsion mode and (

**b**) charging mode.

**Figure 9.**Phase voltage curves under the two modes of operation: (

**a**) propulsion mode and (

**b**) charging mode.

**Figure 13.**Test bench setup. (

**a**) Propulsion subsystem: (i) 12/10 IPM synchronous machine, (ii) Load motor, (iii) Torque sensor, (iv) 20 kW Dynamo system, and (v) Data acquisition “DAQ” box. (

**b**) Grid and battery emulator and (

**c**) Driving controller and visualization: (i) dSpace microlab box 1200, and (ii) Oscilloscope, and (

**d**) Inverter subsystem: (i) 40 kW six-phase inverter, (ii) Measurement board, and (iii) Interface board.

Rated power (kW) | 15 |

Rated speed (rpm) | 1500 |

Peak line current (A) | 17.54 |

Inputs | |

Number of phases | 6 |

Number of slots | 12 |

Number of poles | 10 |

Air gap flux density (T) | 0.8 |

Aspect ratio “Stack length to air gap diameter ratio” | 0.822 |

Stator electrical loading (A/mm) | 15 |

Constraints | |

Required flux density (T) | 1.5 |

DC bus voltage (V) | 600 |

$\mathrm{Current}\text{}\mathrm{density}\text{}(A/m{m}^{2})$ | 5 |

Copper fill factor | 0.5 |

Design Variable | Range | Initial Value |
---|---|---|

$V-angle$ ($\text{}\xb0$) | 80–160 | 145 |

${W}_{M}$ (mm) | 18–22 | 21 |

${T}_{M}$ (mm) | 1–3 | 2.2 |

${W}_{Bri}$ (mm) | 1–4.5 | 3 |

${M}_{2}$ (mm) | 2–4 | 3 |

${W}_{FB1}$ | 1–7 | 1.5 |

${W}_{FB2}$ | 1–3.5 | 1 |

Parameter/Objective | ${\mathit{\rho}}_{{\mathit{T}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}}^{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | ${\mathit{\rho}}_{{\mathit{T}}_{\mathit{r}\mathit{i}\mathit{p}\mathit{p}\mathit{l}\mathit{e}}}^{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | ${\mathit{\rho}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{e}}^{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | ${\mathit{\rho}}_{\mathit{T}\mathit{r}\mathit{i}\mathit{p}\mathit{p}\mathit{l}\mathit{e}}^{\mathit{c}\mathit{h}\mathit{a}\mathit{r}}$ | ${\mathit{\rho}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{e}}^{\mathit{c}\mathit{h}\mathit{a}\mathit{r}}$ | $\mathit{H}\left({\mathit{x}}_{\mathit{i}}\right)$ |
---|---|---|---|---|---|---|

${W}_{Bri}$ | −0.312 | −0.479 | −0.085 | 0.19 | 0.052 | 0.224 |

$V-angle$ | 0.18 | −0.199 | −0.216 | −0.112 | −0.12 | 0.215 |

${M}_{2}$ | −0.218 | −0.375 | −0.057 | 0.14 | 0.462 | 0.221 |

${T}_{M}$ | 0.412 | 0.067 | 0.093 | −0.252 | −0.111 | 0.187 |

${W}_{M}$ | 0.464 | −0.024 | 0.099 | 0.401 | −0.233 | 0.244 |

${W}_{FB1}$ | 0.284 | 0.272 | −0.01 | 0.049 | 0.288 | 0.141 |

${W}_{FB2}$ | 0.283 | 0.159 | −0.009 | 0.037 | 0.313 | 0.122 |

Parameter | Symbol | Value |
---|---|---|

Slot/Pole combination | ${N}_{s}$/$2p$ | 12-slot/10-pole |

Stator outer diameter $\left(mm\right)$ | ${D}_{so}$ | 279.4 |

$\mathrm{Stator}\text{}\mathrm{inner}\text{}\mathrm{diameter}\left(mm\right)$ | ${D}_{g}$ | 241.6 |

Stack length $\left(mm\right)$ | ${L}_{eff}$ | 147.7 |

$\mathrm{Air}\text{}\mathrm{gap}\text{}\mathrm{length}\text{}\left(mm\right)$ | $g$ | 1 |

Back iron width $\left(mm\right)$ | ${Y}_{sb}$ | 18.9 |

$\mathrm{Shaft}\text{}\mathrm{diameter}\text{}\left(mm\right)$ | ${D}_{shaft}$ | 50 |

Rotor outer diameter $\left(mm\right)$ | ${D}_{ro}$ | 178.6 |

$\mathrm{V}\text{-}\mathrm{angle}\text{}\left(deg\right)$ | $V-angle$ | 153 |

Magnet width $\left(mm\right)$ | ${W}_{M}$ | 20 |

$\mathrm{Magnet}\text{}\mathrm{depth}\text{}\left(mm\right)$ | ${T}_{M}$ | 2 |

Number of turns per coil | ${N}_{t}$ | 31 |

$\mathrm{Rated}\text{}\mathrm{rms}\text{}\mathrm{current}\text{}\left(A\right)$ | ${I}_{r}$ | 12.3 |

Winding layer/Coil pitch | $-$ | Double layer/single |

$\mathrm{Clearance}\text{}\mathrm{between}\text{}\mathrm{magnets}\text{}\left(mm\right)$ | ${M}_{2}$ | 2.8 |

Bridge spacing $\left(mm\right)$ | ${W}_{Bri}$ | 2.9 |

$\mathrm{Width}\text{}\mathrm{of}\text{}\mathrm{flux}\text{}\mathrm{barrier}\text{}1\text{}\left(mm\right)$ | ${W}_{FB1}$ | 5.9 |

Angle of flux barrier 1-1 $\left(deg\right)$ | ${F}_{B11}$ | 85 |

$\mathrm{Angle}\text{}\mathrm{of}\text{}\mathrm{flux}\text{}\mathrm{barrier}\text{}1\text{-}2\text{}\left(deg\right)$ | ${F}_{B12}$ | 85 |

Width of flux barrier 2 $\left(mm\right)$ | ${W}_{FB2}$ | 1.5 |

$\mathrm{Angle}\text{}\mathrm{of}\text{}\mathrm{flux}\text{}\mathrm{barrier}\text{}2\text{-}1\left(deg\right)$ | ${F}_{B21}$ | 80 |

Angle of flux barrier 2-2 $\left(deg\right)$ | ${F}_{B22}$ | 80 |

Parameters | ||

Parameter | Initial | Optimal |

Magnet Width | $21\text{}mm$ | $20\text{}mm$ |

Magnet Thickness | $2.2\text{}mm$ | $2\text{}mm$ |

Upper Flux Barrier Width | $1.5\text{}mm$ | $5.9\text{}mm$ |

Lower Flux Barrier Width | $1\text{}mm$ | $1.5\text{}mm$ |

Magnet Clearance | $3\text{}mm$ | $2.85\text{}mm$ |

Magnet Bridge | $3\text{}mm$ | $2.9\text{}mm$ |

V-angle | $145\xb0$ | $163\xb0$ |

Objectives | ||

Objective | Initial | Optimal |

${T}_{average}$ | $92.06\text{}N.m$ | $96.1\text{}N.m$ |

${P}_{core}^{propulsion}$ | $215.47\text{}W$ | $188.87\text{}W$ |

${T}_{ripple}^{propulsion}$ | $6.46\text{}N.m$ | $4.6\text{}N.m$ |

${P}_{core}^{charging}$ | $47.48\text{}W$ | $38.22\text{}W$ |

${T}_{ripple}^{charging}$ | $14.31\text{}N.m$ | $3.16\text{}N.m$ |

${M}_{size}$ | $6758\text{}{mm}^{3}$ | $5910\text{}{mm}^{3}$ |

${{V}_{ph}}_{rms}^{propulsion}$ | $215.9\text{}V$ | $225.6\text{}V$ |

${{V}_{ph}}_{rms}^{charging}$ | $14.4\text{}V$ | $11.27\text{}V$ |

Objective | Experimental | Simulated |
---|---|---|

${T}_{average}$ | $95.77\text{}N.m$ | $96.1\text{}N.m$ |

${T}_{ripple}^{propulsion}$ | $0.08\text{}N.m$ “Due to sensor limitations” | $4.6\text{}N.m$ |

${Back\text{}EMF}_{peak}$ | $230\text{}V$ | $236\text{}V$ |

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**MDPI and ACS Style**

Abdel-Wahed, A.T.; Ullah, Z.; Abdel-Khalik, A.S.; Hamad, M.S.; Ahmed, S.; Elmalhy, N.A.
Design and Finite-Element-Based Optimization for a 12-Slot/10-Pole IPM Motor with Integrated Onboard Battery Charger for Electric Vehicle Applications. *Machines* **2023**, *11*, 534.
https://doi.org/10.3390/machines11050534

**AMA Style**

Abdel-Wahed AT, Ullah Z, Abdel-Khalik AS, Hamad MS, Ahmed S, Elmalhy NA.
Design and Finite-Element-Based Optimization for a 12-Slot/10-Pole IPM Motor with Integrated Onboard Battery Charger for Electric Vehicle Applications. *Machines*. 2023; 11(5):534.
https://doi.org/10.3390/machines11050534

**Chicago/Turabian Style**

Abdel-Wahed, Ahmed T., Zia Ullah, Ayman S. Abdel-Khalik, Mostafa S. Hamad, Shehab Ahmed, and Noha A. Elmalhy.
2023. "Design and Finite-Element-Based Optimization for a 12-Slot/10-Pole IPM Motor with Integrated Onboard Battery Charger for Electric Vehicle Applications" *Machines* 11, no. 5: 534.
https://doi.org/10.3390/machines11050534