# Design and Optimization of Permanent Magnet Brushless Machines for Electric Vehicle Applications

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## Abstract

**:**

## 1. Introduction

## 2. Machine Design Specifications

_{s}is the slot number, and p is the number of pole pairs. Machines applying a N

_{s}= 2p ± 1 combination have asymmetric stator and rotor structure [21], which may result in relatively high unbalanced magnetic force, excessive noise, and vibration, hence reducing the bearing life. Thus, an N

_{s}= 2p ± 2 combination is preferred, and a 12-slot/10-pole PM brushless machine is selected in this paper.

_{i1}is the inner diameter of stator, L is the stack length, P

_{c}is the continuous power, η is the efficiency, α

_{i}is the calculating pole-arc coefficient, k

_{B}is the waveform factor of air-gap flux, k

_{dp}is the winding factor, k

_{n}is the speed correction factor related to the maximum operating speed n

_{max}, A is the electrical load, and B

_{δ}is the maximum value of air-gap flux density.

Parameters | Values | |
---|---|---|

Design specifications | Continuous power P_{c} (kW) | 5 |

Continuous torque below and at base speed T_{c} (Nm) | 40 | |

Efficiency η (%) | 80–93 | |

Base speed ω_{b} (rpm) | 1200 | |

Maximum speed ω_{max} (rpm) | 5000 | |

Constant power speed range | 3–4 | |

Maximum phase voltage U_{lim} (V) | 74 | |

Maximum phase current I_{lim} (A) | 28 | |

Initial design | Number of slots N_{s} | 12 |

Number of pole pairs p | 5 | |

Stator outer diameter D_{1} (mm) | 200 | |

Stator inner diameter D_{i1} (mm) | 121 | |

Stack length L (mm) | 79.2 | |

Number of turns N | 20 |

## 3. Optimization of the Constant Power Speed Range

_{max_c}is the maximum speed in the constant power region, ω

_{b}is the base speed, ψ

_{f}is the PM flux linkage, I

_{lim}is the maximum phase current, and, L

_{q}and L

_{d}are q-axis and d-axis inductance, respectively, and, ψ

_{f}and L

_{d}are expressed as:

_{M}is the PM magnetic field intensity, b

_{M}is the effective width of the PM, L is the stack length, μ

_{0}is the air permeability, α

_{i}is the calculating pole-arc coefficient, τ is the pole pitch, δ is the air-gap length, k

_{δ}is the air-gap coefficient, and k

_{s}is the saturation coefficient of the magnetic circuit.

_{f}is not suitable to extend the constant power speed range. Thus, under the condition of maintaining constant ψ

_{f}, increasing L

_{d}is more effective. There are a variety of ways to increase the machine inductance [25,26,27], such as reducing the air-gap length or the PM thickness to increase the permeance. However, since permeability of NdFeB is quite close to air, the machine inductance will lack the sensitivity to variation of the air-gap length or the PM thickness. Reducing the slot opening width or increasing the tooth-tip height is also be an effective method in increasing the inductance. However, great flux leakage and high level saturation may occur in the tooth-tip region, resulting in increased iron loss. It can be concluded from Equations (5) and (6) that ψ

_{f}is proportional to N and L, whereas L

_{d}is proportional to the square of N and L. In order to increase the machine inductance with little effects on other performances, N should be increased, and L should be proportionally decreased to realize constant ψ

_{f}.

_{h}, k

_{e}, α and β are coefficients of the silicon steels, and G is the weight of the PM brushless machine. Due to the higher inductance, the flux-weakening capability is improved, hence reducing the flux density B. Meanwhile, the decreased L is contributed to lighter G. Thus, the higher the d-axis inductance is, the lower the iron loss will be.

_{D}, τ

_{y}, α

_{c}are parameters of the coils, s is the slot number, α

_{1}is the number of branches in parallel, N

_{t}is the number of wires in parallel, and q

_{a}is the cross section of the wire. Since N is increased and L is decreased proportionally, R is increased. In the region of low speed operation, due to the little-changed I, the copper loss is increased while, in the region of high speed operation, the increased d-inductance yields a lower d-axis current to weaken the PM flux field, hence, resulting in a much lower copper loss.

**Table 2.**Comparison of machine parameters of the initial and optimal permanent magnet (PM) brushless machines.

Design variants | Initial Values | Optimal Values |
---|---|---|

Number of turns N | 20 | 24 |

Stack length L (mm) | 79.2 | 66 |

d-axis inductance L_{d} (mH) | 4.26 | 5.11 |

Permanent magnet flux linkage ψ_{f} (wb) | 0.14 | 0.14 |

## 4. Performance Analysis

#### 4.1. Performance Analysis at the Rated Operating Point

**Figure 2.**PM flux linkage and d-axis inductance curves of the initial and optimal PM brushless machines. (

**a**) PM flux linkage; and (

**b**) d-axis inductance.

**Figure 3.**No-load back electromotive force (EMF) of the optimal PM brushless machine. (

**a**) Waveform; and (

**b**) harmonic spectrum.

**Figure 4.**Cogging torque and output torque curves of the initial and optimal PM brushless machines. (

**a**) Cogging torque; and (

**b**) output torque.

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

Torque (Nm) | 40.8 | 40.1 |

Torque density (kNm/m^{3}) | 18.47 | 21.78 |

Torque production per unit PM (kNm/mm^{3}) | 4.46 | 5.26 |

Power (kW) | 5.1 | 5.0 |

Iron loss (W) | 43.8 | 38.5 |

Eddy loss (W) | 13.9 | 17.0 |

Copper loss (W) | 163.2 | 175.2 |

Total loss (W) | 320.9 | 330.8 |

Efficiency (%) | 94.12 | 93.84 |

#### 4.2. Performances Analysis over the Speed Range

**Figure 5.**Power-speed and torque-speed curves of the initial and optimal PM brushless machines. (

**a**) Power-speed; and (

**b**) torque-speed.

**Figure 6.**Losses and efficiency curves of the initial and optimal PM brushless machines. (

**a**) Iron loss; (

**b**) copper loss; (

**c**) total loss; and (

**d**) efficiency.

**Figure 7.**Efficiency and loss maps of the optimal PM brushless machine. (

**a**) Efficiency; (

**b**) iron loss; (

**c**) copper loss; and (

**d**) total loss.

#### 4.3. Performances Comparison over the Urban Dynamometer Driving Schedule

**Figure 10.**Simulation results of the initial and optimal PM brushless machines. (

**a**) Speed; and (

**b**) state of charge (SOC).

**Table 4.**Comparison of acceleration ability and equivalent fuel economy of EVs applying initial and optimal PM brushless machines.

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

Acceleration time of 0–30 mph (s) | 6.2 | 6.1 |

Acceleration time of 20–55 mph (s) | 12.7 | 10.6 |

Acceleration time of 0–55 mph (s) | 34.1 | 24 |

Maximum acceleration (ft/s2) | 7.2 | 7.9 |

Maximum speed (mph) | 59.9 | 65.2 |

Gasoline equivalent (mpg) | 102.9 | 106.7 |

**Figure 11.**Operation conditions of the optimal PM brushless machine over the urban dynamometer driving schedule (UDDS).

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/en81212410

**AMA Style**

Gu W, Zhu X, Quan L, Du Y.
Design and Optimization of Permanent Magnet Brushless Machines for Electric Vehicle Applications. *Energies*. 2015; 8(12):13996-14008.
https://doi.org/10.3390/en81212410

**Chicago/Turabian Style**

Gu, Weiwei, Xiaoyong Zhu, Li Quan, and Yi Du.
2015. "Design and Optimization of Permanent Magnet Brushless Machines for Electric Vehicle Applications" *Energies* 8, no. 12: 13996-14008.
https://doi.org/10.3390/en81212410