# Analysis and Design of a Compound-Structure Permanent-Magnet Motor for Hybrid Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. System Configuration and Working Mode

#### 2.1. System Configuration

#### 2.2. Working Mode

#### 2.2.1. Pure Electric Mode

_{ICE}= 0, P

_{b1}≠ 0, and P

_{d}≠ 0.

#### 2.2.2. Hybrid Mode

#### 2.2.3. Braking Mode

#### 2.2.4. Over-Speed Mode

## 3. State Equation in Three-Phase Stationary Coordinate System

_{A}, U

_{B}, U

_{C}, U

_{U}, U

_{V}, U

_{W}is the voltage of three-phase stator winding and inner rotor winding; i

_{A}, i

_{B}, i

_{C}, i

_{U}, i

_{V}, i

_{W}is the current of three-phase stator winding and inner rotor winding, and R

_{A}, R

_{B}, R

_{C}, R

_{U}, R

_{V}, R

_{W}is the resistance of them; L

_{XX}is the self-inductance of each phase winding; M

_{XY}is the mutual inductance between different phase windings; and E

_{A}, E

_{B}, E

_{C}, E

_{U}, E

_{V}, E

_{W}is the back EMF produced by the outside and the inside permanent magnet cutting the stator and inner rotor windings.

_{A}, Ψ

_{B}, Ψ

_{C}, Ψ

_{U}, Ψ

_{V}, Ψ

_{W}is the flux linkage of three-phase stator winding and inner rotor winding, which is related to the outer rotor’s position (θ

_{1}), inner rotor’s position (θ

_{2}), current, and the flux linkage of permanent magnet, as shown in Equation (2).

_{m1}is the flux linkage produced by the outside permanent magnet and Ψ

_{m2}is the flux linkage produced by the inside permanent magnet. The relationship between L

_{XX}and M

_{XY}can be written as

_{σ1}and L

_{σ2}is the leakage inductance of outer rotor and inner rotor, respectively; L

_{σ}is the difference between L

_{σ1}and L

_{σ2}; L

_{V}is the average inductance; and L(θ

_{1}), L(θ

_{2}), L(θ

_{2}− θ

_{1}) is the position inductance that is influenced by the position of outer rotor and inner rotor.

_{m}), and the derivative of L

_{m}(L

_{m}’) are shown in Equation (5).

_{1}, ω

_{2}is the electric angular velocity of the outer rotor and inner rotor, and i

_{X}’ is the derivative of i

_{X}.

_{or}) and inner rotor (T

_{ir}) can be obtained in Equation (6) based on the virtual displacement method. Here, P

_{n}is the pole-pair number of CSPM motor, T

_{1}and T

_{3}is the electromagnetic torque produced by stator on the outer rotor and inner rotor, respectively. The electromagnetic torque generated by the outer rotor on the outer rotor or produced by the outer rotor on the inner rotor is identical, which is expressed by T

_{2}.

_{s}, it will generate a magnetic field with the speeds n

_{1}, (1 − s

_{1}) n

_{1,}and (1 − 2s

_{1}) n

_{1}; s

_{1}is the transfer rate in SM, while in DRM, the frequency of inner rotor current is f

_{ir}, which also produces three magnetic fields in the inner air-gap, i.e., n

_{2}, (1 − s

_{2}) n

_{2,}and (1 − 2s

_{2}) n

_{2}; s

_{2}is the transfer rate in DRM. The magnetic field with different speed interactions with each other will result in the torque ripple. These aspects are analyzed in the next part to add the output torque and decrease the torque ripple of CSPM motor.

## 4. Analysis and Optimization of CSPM Motor Based on FEM

- (1)
- The variation range of air-gap length is between 0.35 mm and 0.75 mm, and the variable step is 0.05 mm;
- (2)
- The variation range of core length is 85 mm to 120 mm, and the variation step is 5 mm;
- (3)
- The current frequency of two sets winding changes from 112 Hz to 161 Hz, and the variable step is 5 Hz. The current of stator winding and inner rotor winding is between 150 A and 180 A, and the change step is 10 A.
- (4)
- The variation of the polar arc coefficient for permanent magnet is 0.5–0.9, and the step length is 0.05. The current change rule of stator winding and inner rotor winding is as (3);
- (5)
- The thickness of permanent magnet varies in the range of 3.5–5.5 mm, and the step length is 0.25 mm. The current also changes as (3);
- (6)
- The skewing-slot angle changes from 1 degree to 15 degrees, and the variable step is 1 degree.
- (7)
- The percentage of torque ripple (T
_{ripple}) is defined as follows:

_{max}is the maximum of output torque in CSPM motor, and T

_{avg}is the average of output torque.

#### 4.1. Air-Gap Length

#### 4.2. Core Length

#### 4.3. Different Winding Current Frequency

#### 4.4. Matching between Permanent Magnet Size and Winding Currents

#### 4.5. Skewed Slots

## 5. Performance Comparison before and after Optimization

#### 5.1. Field Distribution

#### 5.2. Induced Voltage before and after Optimization

#### 5.3. Output Torque before and after Optimization

## 6. Conclusions

- (1)
- By increasing the air-gap length properly, the torque ripple will be reduced, and there is little impact on the output torque value;
- (2)
- The longer core should be chosen to add the average torque of the CSPM motor. However, this method also increases the torque ripple;
- (3)
- The average torque increases with the increase of current frequency under the same current; it also increases with the current under the same current frequency. However, the torque will decrease when the current increases to a certain degree. The torque ripple decreases with the increase of current frequency;
- (4)
- Choosing a larger pole arc coefficient and thickness of permanent magnet will add the average torque. The pole arc coefficient has a great influence on the torque ripple, and the increasing speed of torque ripple gradually increases with the thickness when the current unchanged.
- (5)
- The increase of skewing angle decreases the torque ripple of the CSPM motor observably, and the output torque decreases a little.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Diagram of hybrid electric vehicles (HEVs) based on compound-structure permanent-magnet motor (CSPM motor).

**Figure 2.**Power flow process of HEVs based on CSPM motor in different working mode: (

**a**) pure electric mode; (

**b**) CVT mode; (

**c**) auxiliary power mode; (

**d**) driving and parking generation mode; (

**e**) driving and parking generation mode; (

**f**) electric braking mode; (

**g**–

**h**) regenerative braking mode; (

**i**) over-speed mode.

**Figure 4.**Average torque and torque ripple curve of stator machine (SM) and double-rotor machine (DRM) with different air-gap length: (

**a**) Average torque; (

**b**) Torque ripple.

**Figure 5.**Average torque and torque ripple curves of SM and DRM with different core lengths: (

**a**) SM; (

**b**) DRM.

**Figure 6.**Variation of average torque curve in SM and DRM with winding current frequency: (

**a**) SM; (

**b**) DRM.

**Figure 8.**Variation of average torque in SM and DRM with permanent magnet pole arc coefficient: (

**a**) SM; (

**b**) DRM.

**Figure 9.**Variation of torque ripple in SM and DRM with permanent magnet pole arc coefficient: (

**a**) SM; (

**b**) DRM.

**Figure 10.**Relationship of average torque between SM, DRM, and permanent magnet thickness: (

**a**) SM; (

**b**) DRM.

**Figure 11.**Relationship of torque ripple between SM, DRM, and permanent magnet thickness: (

**a**) SM; (

**b**) DRM.

**Figure 12.**Average torque and torque ripple curve of DRM and SM with different skewing angles: (

**a**) Average torque; (

**b**) Torque ripple.

**Figure 15.**Induced voltage of stator windings and inner rotor windings: (

**a**) Stator windings; (

**b**) Inner rotor windings.

Design Parameters | DRM | SM | ||
---|---|---|---|---|

Rated power (kW) | 15 | 30 | ||

Rated speed (rpm) | 5000 | 2200 | ||

Number of phase | 3 | 3 | ||

Number of slot | 24 | 48 | ||

Air-gap length (mm) | before | 0.4 | before | 0.4 |

after | 0.5 | after | 0.65 | |

Iron core length (mm) | before | 105 | before | 105 |

after | 90 | after | 90 | |

Rated current (A) | before | 200 | before | 200 |

after | 160 | after | 160 | |

Current frequency (Hz) | before | 120 | before | 120 |

after | 140 | after | 140 | |

Pole arc coefficient of permanent magnet | before | 0.7 | before | 0.7 |

after | 0.75 | after | 0.8 | |

Thickness of permanent magnet | before | 5.5 | before | 5.5 |

after | 4 | after | 4 | |

Skewing-slot (degree) | before | 0 | before | 0 |

after | 7 | after | 15 | |

Inner diameter of inner rotor (mm) | 60 | |||

Outer diameter of inner rotor (mm) | 99 | |||

Inner diameter of outer rotor (mm) | 100 | |||

Outer diameter of outer rotor (mm) | before | 115 | ||

after | 122 | |||

Inner diameter of stator (mm) | before | 126.8 | ||

after | 131.3 | |||

Outer diameter of stator (mm) | before | 185 | ||

after | 181 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xu, Q.; Sun, J.; Tian, D.; Wang, W.; Huang, J.; Cui, S. Analysis and Design of a Compound-Structure Permanent-Magnet Motor for Hybrid Electric Vehicles. *Energies* **2018**, *11*, 2156.
https://doi.org/10.3390/en11082156

**AMA Style**

Xu Q, Sun J, Tian D, Wang W, Huang J, Cui S. Analysis and Design of a Compound-Structure Permanent-Magnet Motor for Hybrid Electric Vehicles. *Energies*. 2018; 11(8):2156.
https://doi.org/10.3390/en11082156

**Chicago/Turabian Style**

Xu, Qiwei, Jing Sun, Dewen Tian, Wenjuan Wang, Jianshu Huang, and Shumei Cui. 2018. "Analysis and Design of a Compound-Structure Permanent-Magnet Motor for Hybrid Electric Vehicles" *Energies* 11, no. 8: 2156.
https://doi.org/10.3390/en11082156