# High-Frequency Core Loss Analysis of High-Speed Flux-Switching Permanent Magnet Machines

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Machine Parameters and Core Loss Calculation

#### 2.1. Machine Parameters

_{t}changes significantly whilst the radial one B

_{r}remains unchanged, which is totally reversed for Point 3, where B

_{t}remains unchanged and B

_{r}varies considerably. For Points 2 and 4, both B

_{r}and B

_{t}vary versus rotor positions but with the same and double the frequencies, respectively. However, for Points 5–8 in the stator, a significant DC-biased component can be found in the component of B

_{r}of Points 5 and 6. In Point 7, a phase-shift of nearly 90° exists between B

_{r}and B

_{t}. However, for Point 8, B

_{r}is almost zero within a period of two rotor pitches (72°).

_{s}= 60/(n × P

_{r}), where n is the rotor speed (rpm) and P

_{r}is the number of rotor pole pairs (being the same as the rotor tooth number), and the mechanical angle corresponding to one electrical cycle is 360°/P

_{r}= 36°. For the rotor core, it should be rotated through at least two stator teeth before its radial and tangential flux density coincides with its initial position. So, the period of flux density variation on the rotor core is T

_{r}= 60/(n × P

_{s}/2), where P

_{s}is the number of stator slots, and the mechanical angle corresponding to one electrical cycle is 360°/(P

_{s}/2) = 60°.

#### 2.2. Core Loss Calculation Model

_{r}and B

_{t}. Since at any moment the core flux density can be regarded as the vector sum of B

_{r}and B

_{t}[20], the core loss is the sum of two components due to alternating magnetizations in the radial and tangential directions:

_{h}, k

_{c}, and k

_{e}are the coefficient of hysteresis loss, additional loss, and eddy current loss, respectively; f is the alternating current frequency; and B

_{rm}and B

_{tm}are the maximum values of the radial and tangential components of the flux density, respectively.

_{h}is mainly affected by the local hysteresis loop, whereas the eddy current losses P

_{e}and the additional losses P

_{c}are mainly influenced by the harmonic components [19,21]. After taking into account the local hysteresis loop and the impact of the harmonic components on the core loss, the equation for the calculation of hysteresis loss should be modified to (2), and the equation for the calculation of unit volume eddy current losses and additional losses should be modified to (3).

_{pr}and N

_{pt}are the number of hysteresis loops within one cycle of B

_{r}and B

_{t}, respectively; B

_{rmj}and B

_{tmj}are the hysteresis amplitude of the jth hysteresis loops in the radial and tangential directions, respectively; and B

_{rmk}and B

_{tmk}are the amplitude of the kth harmonic component in the radial and tangential directions, respectively.

_{dc}and α are constants with the average values of k

_{dc}= 0.65 and α = 2.1, respectively, by numerically fitting five silicon steel sheet materials in [23], P

_{hdc}and P

_{h}are the hysteresis loss considering the DC magnetization component or not, respectively, and B

_{dc}is the value of the DC magnetization component.

## 3. Calculation of Core Loss Coefficients

_{1}and a secondary winding N

_{2}wrapped around the core in turn. The number of turns for both the primary and secondary windings is 80.

_{e}can be calculated as [19,24]

_{2}is the instance voltage waveform of the measuring coil, i(t) is the current waveform measured in the excitation coil, and L

_{e}is the effective length of the silicon steel sheets.

_{sc}and P

_{se}are the calculated and measured specific loss, respectively.

_{h}, k

_{e}, and k

_{c}of 20JNEH1200 are 188, 0.079, and 2.01, and for 10JNEX900 they are 143, 0.0154, and 1.3, respectively.

## 4. Soft Iron Material and Driver Harmonics Effects

#### 4.1. Effects of Soft Iron Materials on Core Loss

#### 4.2. Effect of Driving Modes on Core Loss

## 5. Verification

## 6. Conclusions

^{2}, the core loss of a 0.1 mm thickness silicon steel sheet is 73.6%, 70.9%, and 71.8% lower than that of the 0.35 mm, 0.27 mm, 0.25 mm, and 0.2 mm thickness silicon steel sheets, respectively. The variation in rotor loss is similar to that of the stator.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Cross-section of a 12/10 FSPM machine and eight key points. (

**a**) 2D machine cross-section, (

**b**) eight key points.

**Figure 4.**AC measurement system for soft magnetic materials. (

**a**) Test platform and (

**b**) magnetizing characteristics of the silicon steel sheet.

**Figure 6.**The current and harmonic content of different driving methods. (

**a**) BLDC, (

**b**) Ideal-Sin, (

**c**) SVPWM, (

**d**) Current THD.

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

Number of stator slots, P_{s} | 12 |

Number of rotor pole pairs, P_{r} | 10 |

Stator outer diameter, mm | 173 |

Stator inner diameter, mm | 112 |

Axial iron core length, mm | 43 |

Number of turns/slot | 18 |

Winding layers | 2 |

Peak power, kW | 54.7 |

Rated speed, rpm | 10,000 |

Rated torque, Nm | 26.52 |

Rated power, kW | 27.7 |

Rated current, A | 100 |

Current density, A/mm^{2} | 10 |

Rated frequency, Hz | 1666.7 |

Silicon steel sheet material | 20JNEH1200 |

Permanent magnet material | N35UH |

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**MDPI and ACS Style**

Yu, W.; Hua, W.; Zhang, Z.
High-Frequency Core Loss Analysis of High-Speed Flux-Switching Permanent Magnet Machines. *Electronics* **2021**, *10*, 1076.
https://doi.org/10.3390/electronics10091076

**AMA Style**

Yu W, Hua W, Zhang Z.
High-Frequency Core Loss Analysis of High-Speed Flux-Switching Permanent Magnet Machines. *Electronics*. 2021; 10(9):1076.
https://doi.org/10.3390/electronics10091076

**Chicago/Turabian Style**

Yu, Wenfei, Wei Hua, and Zhiheng Zhang.
2021. "High-Frequency Core Loss Analysis of High-Speed Flux-Switching Permanent Magnet Machines" *Electronics* 10, no. 9: 1076.
https://doi.org/10.3390/electronics10091076