# Mitigation of High-Frequency Eddy Current Losses in Hairpin Winding Machines

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## Abstract

**:**

## 1. Introduction

## 2. Winding Simulation at Strand Level

#### 2.1. Types of Eddy Current Losses

#### 2.2. Baseline Machine

#### 2.3. Two-Slot Model at Strand Level

#### 2.4. Mitigation of Eddy Current Losses in Hairpin Windings

- (i)
- Reducing the conductor height (${h}_{c}$). However, this method can result in a reduced fill factor and an increased DC resistance component;
- (ii)
- Reducing the external flux density (${B}_{o}$). This is can be done be leaving a space near the slot opening, so that the upper conductors are less affected by the cross-slot leakage flux. However, using this method will result in a lower coil height, and eventually a lower fill factor;
- (ii)
- Increasing the material resistivity ($\rho $) can also be an effective method to reduce the high-frequency eddy current losses. However, this requires the use of a different conducting material than pure copper, with higher resistivity.

#### 2.5. Aluminum as an Alternative to Copper at High Frequency

## 3. Experimental Verification

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Magnetic material characterization for the Si-Fe lamination used in the E-shaped motorette: (

**a**) test setup using an Epstein frame; (

**b**) measurement sample of the BH loop at 400 Hz.

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**Figure 1.**Different types of eddy current losses at the strand level and bundle level: (

**a1**,

**a2**) skin effect losses; (

**b1**,

**b2**) proximity effect losses; (

**c1**,

**c2**) eddy current losses due to the external field; (

**d1**,

**d2**) circulating currents losses in series- and parallel-connected conductors.

**Figure 2.**Baseline machine: 110 kW SynRM and winding configuration with FEM analysis at rated power (2019 Nissan Leaf—model EM57).

**Figure 3.**Figure

**3.**Modeling of a two-slot motorette at the strand level and estimation of the cross-slot leakage flux at high frequencies.

**Figure 4.**Comparison between current density distributions using copper and aluminum materials at 2 kHz.

**Figure 5.**Comparison between flat copper and flat aluminum coils: (

**a**) power loss in each turn at 2 kHz; (

**b**) total power at different frequency levels.

**Figure 7.**Assembly of the test samples with the 2-slot motorette: (

**a**) flat copper coil; (

**b**) flat aluminum coil.

**Figure 9.**Cooling jacket used to control the sample temperature: (

**a**) cooling jacket components; (

**b**) assembly with a flat copper coil; (

**c**) assembly with a flat aluminum coil.

**Figure 10.**Thermal behavior of the test samples under steady-state currents: (

**a**) DC excitation without cooling—uniform temperature; (

**b**) AC excitation without cooling—nonuniform temperature; (

**c**) AC excitation with forced cooling—nonuniform temperature.

Coil 1 | Coil 2 | |
---|---|---|

Type | Flat copper | Flat aluminum |

Mass density | 8.96 gm/cm^{3} | 2.7 g/cm^{3} |

Coil Weight | 183.6 gm | 55.2 gm |

Fill factor | 72.6% | 72.6% |

Resistance Temper. Coeff. | 0.00393 /K | 0.00410 /K |

Total losses@ 2 kHz | 12.1 p.u. | 9.77 p.u. |

Loss ratio (AC to DC) @ 2 kHz | 14 | 4.79 |

Preferable frequency range | Up to 1 kHz | Above 1 kHz |

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**MDPI and ACS Style**

Selema, A.; Ibrahim, M.N.; Sergeant, P.
Mitigation of High-Frequency Eddy Current Losses in Hairpin Winding Machines. *Machines* **2022**, *10*, 328.
https://doi.org/10.3390/machines10050328

**AMA Style**

Selema A, Ibrahim MN, Sergeant P.
Mitigation of High-Frequency Eddy Current Losses in Hairpin Winding Machines. *Machines*. 2022; 10(5):328.
https://doi.org/10.3390/machines10050328

**Chicago/Turabian Style**

Selema, Ahmed, Mohamed N. Ibrahim, and Peter Sergeant.
2022. "Mitigation of High-Frequency Eddy Current Losses in Hairpin Winding Machines" *Machines* 10, no. 5: 328.
https://doi.org/10.3390/machines10050328