# Robust Explorative Particle Swarm Optimization for Optimal Design of EV Traction Motor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Robust Explorative Particle Swarm Optimization

#### 2.1. Conventional PSO

_{1}and c

_{2}are acceleration coefficients; rand

_{1}and rand

_{2}are two uniformly distributed random numbers generated within [0, 1]; pBest is the personal best point for the i-th particle; and gBest is the global best point.

#### 2.2. Explorative PSO

_{k}and p

^{k}denote the mesh and frame in the k-th iteration, respectively; D is a positive spanning set; N

^{nD}is the number of search directions; S

_{k}is the set of points where the cost function is evaluated at the k-th iteration; d is the frame direction in the k-th positive spanning set D

_{k}; ${\Delta}_{k}^{m}$ is the mesh size parameter, which scales D to expand or contract depending on the success or failure of previous searches [13]. Examples of MADS reference frames are shown in Figure 2.

#### 2.3. Proposed Algorithm for Searching Robust Optimum

_{i}is the cost value of i-th iteration.

## 3. Numerical Validation of the Proposed Algorithm

## 4. Derivation of Performance Specifications

_{r}and C

_{d}are the coefficients of rolling resistance and aero-drag resistance, respectively; g is the acceleration due to gravity; θ is the climbing angle; ρ is the air density; A is the frontal area of the vehicle; and v

_{e}is the vehicle velocity. [15,16]. If the calculated drive shaft torque and speed of the vehicle are greater than the sum of all the driving loads, the vehicle is able to be driven.

## 5. Design of the Base Model

## 6. Optimal Design Using RePSO

_{ripple}+ νT

_{cogging}

## 7. Manufacturing and Experiment

## 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 6.**Comparison of change rate at global optimum and robust optimum: (

**a**) change rate of the cost function at global optimum; (

**b**) change rate of the cost function at robust optimum.

**Figure 11.**Design result of the base model in no-load condition: (

**a**) back-EMF waveform; (

**b**) cogging torque waveform.

**Figure 12.**Design result of the base model in load condition: (

**a**) torque waveform; (

**b**) magnetic flux density and flux line plot.

**Figure 14.**The flowchart of optimal design with optimization algorithm and FEM: (

**a**) flow chart of optimization with optimization algorithm; (

**b**) flow chart of traction motor optimization with FEM.

**Figure 16.**Optimal design result in no-load condition: (

**a**) back-EMF waveform; (

**b**) cogging torque waveform.

**Figure 17.**Optimal design result in load condition: (

**a**) torque waveform; (

**b**) magnetic flux density and flux line.

**Figure 20.**Optimal design result in load condition: (

**a**) torque waveform; (

**b**) magnetic flux density and flux line.

Variables | Value |
---|---|

The number of particles | 60 |

The inertia weight (ω) | 0.8 |

Acceleration co-efficienct 1 (c_{1}) | 2 |

Acceleration co-efficienct 2 (c_{2}) | 2 |

Iteration | RPSO | ePSO | RePSO | |||
---|---|---|---|---|---|---|

Function Call | Location | Function Call | Location | Function Call | Location | |

1 | 3528 | (3, 1) | 1692 | (3, 1) | 735 | (3, 1) |

2 | 3924 | (3, 1) | 504 | (3, 4) | 553 | (3, 4) |

3 | 4212 | (3, 2) | 1080 | (3, 1) | 687 | (3, 1) |

4 | 5364 | (3, 1) | 1188 | (3, 1) | 693 | (3, 1) |

5 | 5940 | (3, 2) | 576 | (3, 4) | 1384 | (3, 1) |

6 | 3096 | (3, 1) | 900 | (3, 4) | 675 | (3, 1) |

7 | 3528 | (3, 1) | 540 | (3, 4) | 729 | (3, 1) |

8 | 4896 | (3, 1) | 288 | (3, 0) | 1012 | (3, 1) |

9 | 1872 | (3, 1) | 612 | (3, 4) | 831 | (3, 1) |

10 | 5364 | (3, 1) | 252 | (3, 4) | 663 | (3, 1) |

Average | 4172.4 | - | 763.2 | - | 796.2 | - |

Parameters | Unit | Value |
---|---|---|

GVW | [kg] | 1595 |

Frontal Area | [m^{2}] | 2.6845 |

Aerodynamic Drag Co-efficient | [N/A] | 0.285 |

Rolling Resistance Co-efficient | [N/A] | 0.02 |

Gear Ratio | [N/A] | 7.41 |

Reduction Gear Efficiency | [%] | 97.0 |

Tire Radius | [m] | 0.31595 |

Parameters | Unit | Value |
---|---|---|

Maximum Speed | [kph] | 160 |

Climbing Performance | [%] | 40 |

Acceleration Performance (0 to 100 kph) | [sec] | 10 |

Parameters | Unit | Value |
---|---|---|

Motor Type | [N/A] | IPMSM |

The number of poles and slots | [EA] | 8 poles 72 slots |

Stator outer diameter | [mm] | 200 |

Airgap Length | [mm] | 0.8 |

Slot Fill Factor (Copper only) | [%] | 45 |

The Area of Slot | [mm^{2}] | 4787.04 |

Depth of Electric Steel Sheet | [mm] | 0.27 |

Residual Flux Density of Magnet | [T] | 1.31~1.35 |

The Area of Magnet | [mm^{2}] | 1598.3 |

The Maximum Current Density | [A_{rms}/mm^{2}] | 23 at 88 kW, 5 s |

Target Stack Length | [mm] | Under 140 |

Target Torque | [Nm] | 294.8 |

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**MDPI and ACS Style**

Lee, J.-H.; Kim, W.-J.; Jung, S.-Y.
Robust Explorative Particle Swarm Optimization for Optimal Design of EV Traction Motor. *Processes* **2021**, *9*, 2000.
https://doi.org/10.3390/pr9112000

**AMA Style**

Lee J-H, Kim W-J, Jung S-Y.
Robust Explorative Particle Swarm Optimization for Optimal Design of EV Traction Motor. *Processes*. 2021; 9(11):2000.
https://doi.org/10.3390/pr9112000

**Chicago/Turabian Style**

Lee, Jin-Hwan, Woo-Jung Kim, and Sang-Yong Jung.
2021. "Robust Explorative Particle Swarm Optimization for Optimal Design of EV Traction Motor" *Processes* 9, no. 11: 2000.
https://doi.org/10.3390/pr9112000