# Iron Loss Analysis of a Concentrated Winding Type Interior Permanent Magnet Synchronous Motor with Single and Dual Layer Magnet Shape

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) was identical. The main operation points were 6540, 4905, 3270, and 1635 rpm with a 24 A phase current, and the expected torque was approximately 7.0. Figure 2 presents the structure of the concentrated windings of the IPMSMs with three types of rotor structures. Figure 3a illustrates a comparison of the induced voltages of the three different rotor shapes with identical concentrated winding stators without an input current at 1000 rpm. Figure 3b shows a fast Fourier transform (FFT) comparison of the frequency domain. The differential of the back electro-motive forces of the three magnet rotor shapes was lower than 0.25%. This is similar to the FFT results.

## 2. Iron Loss Calculation

#### 2.1. First Iron Method

_{hys}, dynamic eddy current losses P

_{eddy}, and excess losses P

_{exs}, with their corresponding coefficients a

_{hys}, b

_{eddy}and c

_{exs}, respectively. Moreover, f is the frequency, and $\stackrel{\vee}{B}$ is the maximum flux density.

#### 2.2. Second Iron Loss Method

#### 2.3. Third Iron Loss Method

- (1)
- The skin effect increases with frequency.
- (2)
- The decrease in permeability owing to saturation increases the skin depth and increases the eddy current loss.
- (3)
- The flux saturation induces harmonic eddy currents.
- (4)
- A greater rotation magnetic flux results in a higher saturation and smaller harmonics for the magnetic field and eddy current.

## 3. Comparison of Study Result

#### 3.1. Comparison of Iron Losses

#### 3.2. Comparison of Hysteresis Losses

#### 3.3. Comparison of Eddy Current Losses

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Single layer V-shape magnet rotor. (

**b**) Dual layer delta-shape magnet rotor. (

**c**) Single layer flat-shape magnet rotor.

**Figure 3.**(

**a**) Comparison of induced voltage of three different types of rotor shape at 1000 rpm without load. (

**b**) Comparison of induced voltage of fast Fourier transform (FFT).

**Figure 4.**(

**a**) Measured iron loss data at 50 kHz and 100 kHz from silicon steel 50PN470. (

**b**) The estimated hysteresis loss factor from two frequencies of iron loss data.

**Figure 5.**(

**a**) Prototype sample picture of the automotive A/C refrigerant compressor IPMSM. (

**b**) The distribution of magnetic flux density in the 2-D plane. (

**c**) The magnetic flux density of point A in the time frame. (

**d**) FFT analysis of the magnetic flux density in point A.

**Figure 6.**(

**a**) End teeth flux density with 12 and 24 A peak phase current input conditions in the time frame. V shape inner permanent magnet rotor surface flux density. (

**b**) Comparison of B-H Loops of end teeth and rotor surface.

**Figure 7.**(

**a**) Estimated iron loss data from the external value of proportional to the input frequency square. (

**b**) Magnetic flux density according to the magnetic field strength.

**Figure 8.**Comparison of (

**a**) iron losses and (

**b**) hysteresis losses of three different calculation methods at 6540 rpm, 24 A phase current.

**Figure 9.**(

**a**) Three different hysteresis loss calculation with 4 steps different operation points. (

**b**) Two different eddy current loss calculation with 4 steps different operation points.

**Figure 10.**Comparison of three (

**a**) rotor and (

**b**) stator structure iron losses using three different calculation methods at 6540 rpm and 24 A phase current.

**Table 1.**Comparison of iron losses of three different calculation methods at 6540 rpm, 24 A phase current.

Iron Loss | 1st Method | 2nd Method | 3rd Method |
---|---|---|---|

Single-V | 138.93 | 132.68 | 134.38 |

Dual-D | 135.35 | 128.74 | 128.67 |

Single-F | 142.86 | 135.89 | 141.69 |

**Table 2.**Comparison of hysteresis losses of three different calculation methods at 6540 rpm, 24 A phase current.

Hysteresis Loss | 1st Method (Frequency Sep.) | 2nd Method (Loop Count.) | 3rd Method (Loop Size Consider) |
---|---|---|---|

Single-V | 28.62 | 22.37 | 24.81 |

Dual-D | 28.05 | 21.45 | 22.56 |

Single-F | 28.99 | 22.02 | 23.61 |

**Table 3.**Efficiency comparison of three different rotor structure at 6540 rpm, 24 A phase current based on three different type of iron loss.

Efficiency | 1st Method | 2nd Method | 3rd Method |
---|---|---|---|

Single-V | 93.52% | 93.64% | 93.52% |

Dual-D | 93.44% | 93.57% | 93.47% |

Single-F | 93.44% | 93.57% | 93.37% |

**Table 4.**Comparison of three rotor structure iron losses in rotor using three different calculation method at 6540 rpm and 24 A phase current.

Response Value | 1st Iron Loss | 2nd Iron Loss | 3rd Iron Loss | ||||||
---|---|---|---|---|---|---|---|---|---|

Single-V | Dual-D | Single-F | Single-V | Dual-D | Single-F | Single-V | Dual-D | Single-F | |

Eddy current loss | 11.76 | 11.38 | 12.02 | 11.76 | 11.38 | 12.02 | 8.93 | 10.02 | 11.22 |

Hysteresis loss | 1.92 | 1.89 | 1.80 | 1.75 | 1.58 | 1.67 | 3.10 | 2.65 | 2.57 |

**Table 5.**Comparison of three rotor structure iron losses in stator using three different calculation method at 6540 rpm and 24 A phase current.

Response Value | 1st Iron Loss | 2nd Iron Loss | 3rd Iron Loss | ||||||
---|---|---|---|---|---|---|---|---|---|

Single-V | Dual-D | Single-F | Single-V | Dual-D | Single-F | Single-V | Dual-D | Single-F | |

Eddy current loss | 98.55 | 95.91 | 101.85 | 98.55 | 95.91 | 101.85 | 100.64 | 96.09 | 106.86 |

Hysteresis loss | 26.71 | 26.16 | 27.19 | 20.63 | 19.87 | 20.35 | 21.71 | 19.91 | 21.04 |

Iron Loss | 1st Method | 2nd Iron Loss | 3rd Iron Loss | |
---|---|---|---|---|

Hysteresis Loss | Method | Frequency Sep. | Loop Count. | Loop Size Consider |

Data | Iron loss data (FFT) | Iron loss data, DC bias | Loop measurement | |

Eddy-current Loss | Method | Frequency Sep. | Homogenization | |

Data | Iron loss data (FFT) | Electrical resistivity |

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**MDPI and ACS Style**

Baek, C.-H.; Shin, H.-S.; Choi, J.-Y.
Iron Loss Analysis of a Concentrated Winding Type Interior Permanent Magnet Synchronous Motor with Single and Dual Layer Magnet Shape. *Machines* **2021**, *9*, 74.
https://doi.org/10.3390/machines9040074

**AMA Style**

Baek C-H, Shin H-S, Choi J-Y.
Iron Loss Analysis of a Concentrated Winding Type Interior Permanent Magnet Synchronous Motor with Single and Dual Layer Magnet Shape. *Machines*. 2021; 9(4):74.
https://doi.org/10.3390/machines9040074

**Chicago/Turabian Style**

Baek, Chan-Ho, Hyo-Seob Shin, and Jang-Young Choi.
2021. "Iron Loss Analysis of a Concentrated Winding Type Interior Permanent Magnet Synchronous Motor with Single and Dual Layer Magnet Shape" *Machines* 9, no. 4: 74.
https://doi.org/10.3390/machines9040074