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Design of Spoke-Type Permanent Magnet Synchronous Generator for Low Capacity Wind Turbine Considering Magnetization and Cogging Torques^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Spoke Type Rotor Magnetization Analysis

#### 2.1. Principle of Magnetization

_{0}is the vacuum permeability; M is the internal magnetization density; and H is the external magnetic field strength. The characteristics of M are determined according to the PM type, and H is the external magnetic field strength, which is determined by the number of turns of the magnetizer and the magnitude of the magnetizing current. The hysteresis curve of the PM is shown in Figure 1 [24]. The non-magnetized PM has a nonlinear initial magnetization curve and an initial point with H = 0 and B = 0.

_{c}passes through a permanent magnetic flux. Ferrite magnets are generally used in the spoke-type setup, and a comparison of the B-H characteristics of ferrite and other PMs is shown in Figure 2 [24].

#### 2.2. PM Magnetization Method

_{m}is the reluctance; l is the length; μ is the permeability; S is the area; N is the number of turns; i is the current; and ϕ is the magnetic flux. Additionally, the saturation of the rotor core and of the magnetizing yoke are high, owing to the application of a large current during magnetization. The magnetic flux passes through the magnetically saturated region and inner side. Due to magnetic saturation, the magnetic permeability of the core in Equation (2) is equal to that of air. Because of this increase in magnetic reluctance, the magnitude of the flux passing through the inner side decreases according to Equation (3) and prevents the smooth magnetization of the inner side, as shown in Figure 5a. Additionally, the distance between the back yoke of the rotor and the PM influences the magnetization performance. Although it has an insignificant effect on the performance of the load operation, as shown in Figure 5a,b, the leakage of the magnetic flux to the back yoke with high magnetic permeability is closer to the PM.

_{mcore}is the reluctance of the magnetizing yoke core, R

_{myoke}is the reluctance of the magnetizing back yoke, R

_{l}is the reluctance of the coil, R

_{gap}is the reluctance of the air gap, R

_{r1}

_{,r2,r3}are the rotor cores, and ϕ

_{l}is the leakage flux on the inner bridge side.

_{r1}, R

_{r2}, and R

_{r3}; thus, the magnitude of the magnetizing flux decreases. Moreover, magnetizing the lower part of the rotor is challenging because the leakage flux ϕ

_{l}is generated by the back yoke of the rotor.

## 3. Spoke-Type PMSG Design Considering Magnetization

## 4. Spoke-Type PMSG Design to Reduce Cogging Torque

## 5. Performance Test and Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Factors that decrease magnetization performance. (

**a**) Reduced flux inside the rotor and leakage flux to back yoke, (

**b**) Position locking of projection in the rotor.

**Figure 12.**Comparison of the conventional and proposed models (

**a**) air−gap magnetic flux density, (

**b**) line voltage THD.

**Figure 15.**Thermal characteristics during generator operation (

**a**) thermal network method, (

**b**) temperature saturation graph for each generator part.

**Figure 17.**Comparison of maximum equivalent stress values during load operation (

**a**) conventional model, (

**b**) proposed model.

Parameter | Value | Unit |
---|---|---|

Power | 500 | W |

Cogging Torque | 410 | mNm |

Voltage | 50 | V_{rms} |

Current | 6 | A_{rms} |

Speed | 350 | rpm |

Efficiency | 90 | % |

Voltage reduction rate | 15 | % |

THD | 5 | % |

**Table 2.**Comparison of no−load performance of the conventional spoke−type model and the proposed model.

Parameter | Conventional Model | Proposed Model | Unit |
---|---|---|---|

Cogging Torque | 456.7 | 91.4 | mNm |

Line Voltage | 56 | 56.9 | V_{rms} |

THD | 2.57 | 1.12 | % |

Parameter | 12 Slot | 24 Slot | 36 Slot | Unit |
---|---|---|---|---|

Cogging Torque | 502.9 | 91.4 | 77.6 | mNm |

Line Voltage THD | 7.26 | 1.12 | 1.46 | % |

Voltage reduction rate | 4.51 | 5.37 | 4.95 | % |

Efficiency | 92.7 | 92.2 | 92.2 | % |

Parameter | Conventional Model | Proposed Model | Unit |
---|---|---|---|

Line Voltage | 53.8 | 53.7 | V_{rms} |

Torque | 14.3 | 14.1 | Nm |

Torque ripple | 1.7 | 1.2 | Nm |

Current | 5.6 | 5.6 | A_{rms} |

Core loss | 11 | 9.7 | W |

Copper loss | 32.5 | 34.8 | W |

Output Power | 526.8 | 523.1 | W |

Efficiency | 92.4 | 92.2 | % |

Voltage reduction rate | 3.8 | 5.4 | % |

Cogging Torque | 465.7 | 91.4 | mNm |

THD | 2.57 | 1.1 | % |

Parameter | FEA | Test | Unit |
---|---|---|---|

Voltage (No Load) | 31.0 | 29.1 | V_{rms} |

Line Voltage (No Load) | 56.9 | 53.6 | V_{rms} |

Line Voltage (Load) | 53.7 | 52.5 | V_{rms} |

Torque | 14.1 | 14.3 | Nm |

Current | 5.6 | 5.9 | A_{rms} |

Output Power | 523.1 | 535.5 | W |

Efficiency | 92.2 | 91.6 | % |

Voltage reduction rate | 5.4 | 6.9 | % |

THD | 1.1 | 0.49 | % |

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## Share and Cite

**MDPI and ACS Style**

Kim, D.-H.; Pyo, H.-J.; Kim, W.-H.; Lee, J.; Lee, K.-D.
Design of Spoke-Type Permanent Magnet Synchronous Generator for Low Capacity Wind Turbine Considering Magnetization and Cogging Torques. *Machines* **2023**, *11*, 301.
https://doi.org/10.3390/machines11020301

**AMA Style**

Kim D-H, Pyo H-J, Kim W-H, Lee J, Lee K-D.
Design of Spoke-Type Permanent Magnet Synchronous Generator for Low Capacity Wind Turbine Considering Magnetization and Cogging Torques. *Machines*. 2023; 11(2):301.
https://doi.org/10.3390/machines11020301

**Chicago/Turabian Style**

Kim, Dong-Ho, Hyun-Jo Pyo, Won-Ho Kim, Ju Lee, and Ki-Doek Lee.
2023. "Design of Spoke-Type Permanent Magnet Synchronous Generator for Low Capacity Wind Turbine Considering Magnetization and Cogging Torques" *Machines* 11, no. 2: 301.
https://doi.org/10.3390/machines11020301