# Design and Multi-Objective Optimization of a 12-Slot/10-Pole Integrated OBC Using Magnetic Equivalent Circuit Approach

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## Abstract

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## 1. Introduction

- Multi-objective genetic algorithm (MOGA) optimization of the employed integrated OBC considering average output torque, torque ripple under propulsion, core losses under propulsion, torque ripple under charging, and core losses under charging.
- Sensitivity analysis to identify the influence of each design parameter on the various optimization performances of the SPM machine.
- Response surface (RS) methodology to illustrate the relationship between the optimization objectives and high-sensitive design parameters.
- Improved electromagnetic performances, namely, torque profile and core losses, under both operational modes were obtained and validated using finite element analysis (FEA).

## 2. Design Requirements and Integrated EV Charging Application

## 3. Parametric MEC Model

## 4. Motor Topology and Optimization Model

#### 4.1. Motor Topology

#### 4.2. Optimization Model

## 5. Overview of the Overall Design Optimization Process

#### 5.1. Comprehensive Sensitivity Analysis

#### 5.2. Flowchart of the Design Optimization Approach

## 6. Multi-Objective Optimization Approach

#### 6.1. Box–Behnken Response Surface Method

#### 6.2. Multi-Objective Genetic Algorithm (MOGA)

## 7. Finite Element Validation

^{TM}Designer 2D transient module. The two machines were assessed under both motoring and charging operational modes using the design parameters outlined in Table 2 considering the optimized values of the key design parameters listed in Table 5. Moreover, the results of the FE model were compared to the results obtained from the MEC model. Simulations of the two motors were carried out at the same speed of 1200 rpm.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Asymmetrical six-phase integrated battery charger schematic and phasor diagrams: (

**a**) configuration; (

**b**) phasor diagram under propulsion; (

**c**) phasor diagram under charging.

**Figure 7.**Response surface results of various optimization objectives versus ${t}_{so}/{\tau}_{so}$ and ${\alpha}_{PM}$: (

**a**) average torque under propulsion; (

**b**) torque ripple under propulsion. (

**c**) core losses under propulsion; (

**d**) torque ripple under charging; (

**e**) core losses under charging.

**Figure 8.**Response surface results of various optimization objectives versus ${t}_{so}/{\tau}_{so}$; and ${Y}_{m}$: (

**a**) average torque under propulsion; (

**b**) torque ripple under propulsion; (

**c**) core losses under propulsion; (

**d**) torque ripple under charging; (

**e**) core losses under charging.

**Figure 9.**MOGA-based optimization results of the five optimization objectives under various operational modes: (

**a**) propulsion; (

**b**) charging.

e-Golf Requirements | |
---|---|

Rated power (kW) | 5 |

Rated speed (rpm) | 1200 |

Maximum speed (rpm) | 10,500 |

Rated torque (Nm) | 39.8 |

Line current peak value (A) | 5.9 |

DC link voltage (V) | 600 |

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

Stator outer diameter (mm) | ${D}_{so}$ | 231.4 |

Stator inner diameter (mm) | ${D}_{si}$ | 155 |

Stack length (mm) | ${L}_{eff}$ | 84 |

Air gap length (mm) | $g$ | 1 |

Depth of stator slot (mm) | ${d}_{ss}$ | 22.5 |

Slot-opening width (mm) | ${t}_{so}$ | 9.06 |

Rotor outer diameter (mm) | ${D}_{ro}$ | 153 |

Shaft diameter (mm) | ${D}_{shaft}$ | 111.8 |

Rotor disc thickness (mm) | ${Y}_{r}$ | 15.4 |

Gap between magnets (mm) | ${d}_{pm}$ | 5.59 |

No. of turns per coil | ${N}_{t}$ | 80 |

Rated RMS current (A) | ${I}_{a}$ | 4.1676 |

Phase resistance (Ω) | $\mathcal{R}$ | 0.03988 |

Parameter | Symbol | Initial | Range |
---|---|---|---|

Magnet thickness (mm) | ${Y}_{m}$ | 4 | 2.5–5.5 |

Tooth-tang depth (mm) | ${d}_{1}$ | 6.7 | 5.5–7.9 |

Core back width (mm) | ${Y}_{sb}$ | 14.3 | 13–16 |

Tooth width (mm) | ${W}_{t}$ | 26.51 | 21.17–31.78 |

Slot-opening ratio | ${t}_{so}/{\tau}_{so}$ | 0.15 | 0.05–0.44 |

PM width to pole pitch ratio | ${\alpha}_{PM}$ | 0.95 | 0.5–0.95 |

Item | ${\mathit{H}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ | ${\mathit{H}}_{\mathit{r}\mathit{i}\mathit{p}\mathit{p}\mathit{l}\mathit{e}}^{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | ${\mathit{H}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{e}}^{\mathit{p}\mathit{r}\mathit{o}\mathit{p}}$ | ${\mathit{H}}_{\mathit{r}\mathit{i}\mathit{p}\mathit{p}\mathit{l}\mathit{e}}^{\mathit{c}\mathit{h}\mathit{a}\mathit{r}\mathit{g}}$ | ${\mathit{H}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{e}}^{\mathit{c}\mathit{h}\mathit{a}\mathit{r}\mathit{g}}$ | $\mathit{G}({\mathit{X}}_{\mathit{i}})$ |
---|---|---|---|---|---|---|

${Y}_{m}$ | 0.1627 | 0.0372 | 0.1003 | 0.0134 | 0.6168 | 0.3269 |

${d}_{1}$ | 0.0160 | −0.0046 | −0.0044 | 0.0072 | 0.0259 | 0.0207 |

${Y}_{sb}$ | 0.0183 | −0.0020 | 0.0171 | 0.0145 | 0.0284 | 0.0280 |

${W}_{t}$ | 0.0107 | −0.0040 | 0.0916 | 0.0052 | 0.0263 | 0.0440 |

${t}_{so}/{\tau}_{so}$ | −0.1932 | 0.2932 | 0.2636 | 0.1579 | 0.0409 | 0.3139 |

${\alpha}_{PM}$ | 0.7379 | 0.4595 | 0.5943 | 0.0364 | 0.1651 | 0.6818 |

Variable/Objective | Initial | Optimal |
---|---|---|

${Y}_{m}$ | 4 | 5.2 |

${d}_{1}$ | 6.7 | 6.8 |

${Y}_{sb}$ | 14.3 | 15.7 |

${W}_{t}$ | 26.51 | 29.23 |

${t}_{so}/{\tau}_{so}$ | 0.15 | 0.21 |

${\alpha}_{PM}$ | 0.95 | 0.88 |

${T}_{mean}$ | 42.7 Nm | 42.73 Nm |

${T}_{ripple}^{prop}$ | 10.9 Nm | 1.59 Nm |

${P}_{core}^{prop}$ | 64.77 W | 56 W |

${T}_{ripple}^{charg}$ | 2.56 Nm | 0.78 Nm |

${P}_{core}^{charg}$ | 2.53 W | 1.99 W |

Initial Machine | Optimal Machine | ||||||||
---|---|---|---|---|---|---|---|---|---|

Output | Propulsion | Charging | Output | Propulsion | Charging | ||||

JMAG | MEC | JMAG | MEC | JMAG | MEC | JMAG | MEC | ||

${T}_{avg}\left(Nm\right)$ | 43 | 42.7 | 0 | 0 | ${T}_{avg}\left(Nm\right)$ | 42.77 | 42.73 | 0 | 0 |

${T}_{ripple}\left(Nm\right)$ | 12.2 | 10.9 | 2.64 | 2.56 | ${T}_{ripple}\left(Nm\right)$ | 1.89 | 1.59 | 1 | 0.78 |

$rms{V}_{ph}\left(V\right)$ | 219.5 | 218 | 11.57 | 12.62 | $rms{V}_{ph}\left(V\right)$ | 223 | 222 | 10.95 | 11.64 |

${P}_{core}\left(W\right)$ | 65.3 | 64.77 | 2.31 | 2.53 | ${P}_{core}\left(W\right)$ | 54.5 | 56 | 2.35 | 1.99 |

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**MDPI and ACS Style**

Metwly, M.Y.; Hemeida, A.; Abdel-Khalik, A.S.; Hamad, M.S.; Ahmed, S. Design and Multi-Objective Optimization of a 12-Slot/10-Pole Integrated OBC Using Magnetic Equivalent Circuit Approach. *Machines* **2021**, *9*, 329.
https://doi.org/10.3390/machines9120329

**AMA Style**

Metwly MY, Hemeida A, Abdel-Khalik AS, Hamad MS, Ahmed S. Design and Multi-Objective Optimization of a 12-Slot/10-Pole Integrated OBC Using Magnetic Equivalent Circuit Approach. *Machines*. 2021; 9(12):329.
https://doi.org/10.3390/machines9120329

**Chicago/Turabian Style**

Metwly, Mohamed Y., Ahmed Hemeida, Ayman S. Abdel-Khalik, Mostafa S. Hamad, and Shehab Ahmed. 2021. "Design and Multi-Objective Optimization of a 12-Slot/10-Pole Integrated OBC Using Magnetic Equivalent Circuit Approach" *Machines* 9, no. 12: 329.
https://doi.org/10.3390/machines9120329