# Comparison of AC Losses in the Winding of Electrical Machines with Fixed Strands Positions, Fixed Conductor Shapes and Random Winding

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## Abstract

**:**

## 1. Introduction

## 2. Machine Specification and Methodology

#### 2.1. Finite-Element (FE) Modelling

#### 2.2. Experimental Motorette

_{rms}was used for all analysis in this paper. The AC resistances of the auxiliary components (connecting wires, supply cables) were measured using a precision impedance analyser (E4990A from KEYSIGHT technologies, Santa Rosa, CA, USA). Figure 7 shows the measured AC resistance of the connecting wire against the frequency, measured up to 2 kHz. Since the resistance of the auxiliary components does not change significantly with an increase in frequency, they are considered as DC values, and the losses in these components are considered as DC losses. Furthermore, as with the preceding research presented in [18], no AC losses are assumed to occur at the end-windings, and the DC losses within are calculated analytically.

## 3. Comparison of FEA and Experimental Results

^{2}R loss of the auxiliary components (lead wires, crimp contacts, connecting cables), end-winding DC loss component and the core loss as computed from FEA. The column ‘Total Exp. Loss’ represents the total experimentally measured loss of the motorette setup (with the auxiliary components connected). The column ‘% difference’ represents the percentage difference between the ‘Total Simulated Loss’ and the ‘Total Experimental Loss’. The simulated and experimental total losses match well, with the maximum difference being 9.7% at the measured frequency of 1000 Hz. Finally, the column ‘Total/DC loss (experimental)’ represents the ratio of total experimentally measured loss minus the 2D-FEA computed core loss at high frequency to the total experimentally measured DC loss of the setup.

## 4. Comparison of Fixed Strands Positions and Fixed Conductor Shapes

## 5. Relationship between AC Losses and Copper Filling Factor

## 6. Segregation of Losses

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

R&D | Research and Development |

DoE | Department of Energy |

FEA | Finite Element Analysis |

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**Figure 1.**(

**Left**) Finite element model of the machine motorette with strand-level winding. (

**Right**) Representation of conductor layout and positions in the half side of a slot of the motorette.

**Figure 3.**Slot former used for the experimental motorette: (

**Left**) 3D printed slot former; (

**Right**) 3D render of the slot former.

**Figure 5.**Schematic diagram of the experimental setup showing the AC source, the power analyser and the motorette inserted.

**Figure 6.**Actual experimental setup showing the power analyser, the motorette and the data logger for reading temperature inside the slot.

**Figure 9.**Formers and motorette with fixed conductors’ shape (CASE B); (

**Left**) 3D rendering of the slot former, (

**Centre**) wound motorette with the slot former, (

**Right**) winding in the slot former.

**Figure 10.**Experimental motorettes with varying CFF: (

**Top Left**) 20% CFF; (

**Top Right**) 30% CFF; (

**Bottom Left**) 40% CFF; and (

**Bottom Right**) motorette with 33 ‘strands-in-hand’.

**Figure 12.**The configuration of strands and bundles in the slot as: (

**Left**) horizontal (ARR1); (

**Centre**) vertical bundled (ARR2); (

**Right**) horizontal bundled (ARR3).

**Figure 13.**Circuital representation of the strands and bundle connections in the models with a single supply source.

**Figure 14.**Circuital representation of the strands and bundle connections in the models with multiple supply sources, each connected to an individual strand.

**Figure 15.**Comparison of current density (J) in the strands for the 24 parallel strands models (ARR2) at time instant (0.00194s): (

**Left**) with circulating current; (

**Right**) without circulating current.

Parameter | Specification |
---|---|

Machine type | 3-ph. IPMSM |

Rated Power | 37 kW |

Rated/Peak Speed | 2800/23,000 rpm |

Winding type | 2 layers concentrated |

Strand type | Round Magnet wire |

Strands-in-hand | 33 |

Strand Diameter | 0.704 mm |

Strand nominal diamter | 0.63 mm |

Slot filling factor | 0.42 |

Parameter | Specification |
---|---|

Winding type | Concentrated |

Layers | 2 |

Turns per slot | 20 |

Strands-in-hand | 9 |

Strand type | Round Magnet Wire |

Strand diameter | 0.834 mm |

Strand nominal diameter | 0.8 mm |

Freq. (Hz) | Active Length Loss (W) | Total Sim. Loss (W) | Total Exp. Loss (W) | % Difference | Total/DC Loss (Experimental) |
---|---|---|---|---|---|

DC | 9.74 | 29.06 | 30.2 | 3.92 | 1 |

50 | 9.75 | 29.14 | 29.71 | 1.96 | 1.06 |

100 | 9.79 | 29.26 | 31.35 | 7.14 | 1.22 |

200 | 9.92 | 29.61 | 30.27 | 2.23 | 1.08 |

500 | 10.85 | 31.45 | 32.44 | 3.15 | 1.19 |

666.67 | 11.71 | 32.91 | 34.61 | 5.17 | 1.24 |

1000 | 14.13 | 36.89 | 40.47 | 9.70 | 1.51 |

1500 | 19.42 | 45.08 | 48.99 | 8.67 | 1.65 |

Freq. (Hz) | Measured Total Loss in CASE A (W) | Measured Total Loss in CASE B (W) | Losses in Winding CASE A (W) | Losses in Winding CASE B (W) | Total/DC Loss (Winding) CASE A | Total/DC Loss (Winding) CASE B | % Difference |
---|---|---|---|---|---|---|---|

20 | 30.20 | 25.09 | 30.17 | 25.07 | 1.00 | 1.00 | 0.00 |

50 | 29.71 | 25.08 | 29.64 | 25.01 | 0.98 | 1.00 | 1.58 |

100 | 31.35 | 25.37 | 31.19 | 25.21 | 1.03 | 1.01 | −2.70 |

500 | 32.43 | 26.21 | 31.15 | 24.93 | 1.03 | 0.99 | −3.66 |

666.67 | 34.60 | 28.26 | 32.69 | 26.35 | 1.08 | 1.05 | −2.97 |

1500 | 48.98 | 38.60 | 42.64 | 32.26 | 1.41 | 1.29 | −8.93 |

Parameter | Motorette with CFF 20% | Motorette with CFF 30% | Motorette with CFF 40% | Motorette with CFF 44.5% |
---|---|---|---|---|

Turns per half slot | 10 | 10 | 10 | 10 |

Strands-in-hand | 9 | 14 | 18 | 33 |

Strand diameter (mm) | 0.8 | 0.8 | 0.8 | 0.63 |

Total strands per slot | 180 | 280 | 360 | 660 |

Strand Copper diameter (mm) | 0.8 | 0.8 | 0.8 | 0.63 |

Nominal Current Density (A/mm^{2}) | 6.63 | 4.26 | 3.31 | 2.91 |

Freq. (Hz) | Measured Total Loss 20% CFF (W) | Measured Total Loss 30% CFF (W) | Measured Total Loss 40% CFF (W) | Losses in Winding 20% CFF (W) | Losses in Winding 30% CFF (W) | Losses in Winding 40% CFF (W) | Total/DC Loss (Winding) 20% CFF | Total/DC Loss (Winding) 30% CFF | Total/DC Loss (Winding) 40% CFF |
---|---|---|---|---|---|---|---|---|---|

20 | 24.28 | 19.95 | 15.64 | 24.26 | 19.93 | 15.62 | 1.00 | 1.00 | 1.00 |

50 | 24.32 | 20.50 | 15.95 | 24.25 | 20.43 | 15.88 | 1.00 | 1.03 | 1.02 |

100 | 24.32 | 20.56 | 16.63 | 24.17 | 20.41 | 16.48 | 1.00 | 1.02 | 1.05 |

500 | 26.31 | 22.44 | 19.42 | 25.03 | 21.16 | 18.14 | 1.03 | 1.06 | 1.16 |

666.67 | 27.65 | 23.96 | 20.79 | 25.74 | 22.04 | 18.87 | 1.06 | 1.11 | 1.21 |

1500 | 39.31 | 36.87 | 35.05 | 32.97 | 30.53 | 28.71 | 1.36 | 1.53 | 1.84 |

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**MDPI and ACS Style**

Bardalai, A.; Gerada, D.; Zou, T.; Degano, M.; Zhang, C.; Gerada, C.
Comparison of AC Losses in the Winding of Electrical Machines with Fixed Strands Positions, Fixed Conductor Shapes and Random Winding. *Energies* **2022**, *15*, 5701.
https://doi.org/10.3390/en15155701

**AMA Style**

Bardalai A, Gerada D, Zou T, Degano M, Zhang C, Gerada C.
Comparison of AC Losses in the Winding of Electrical Machines with Fixed Strands Positions, Fixed Conductor Shapes and Random Winding. *Energies*. 2022; 15(15):5701.
https://doi.org/10.3390/en15155701

**Chicago/Turabian Style**

Bardalai, Anuvav, David Gerada, Tianjie Zou, Michele Degano, Chengming Zhang, and Chris Gerada.
2022. "Comparison of AC Losses in the Winding of Electrical Machines with Fixed Strands Positions, Fixed Conductor Shapes and Random Winding" *Energies* 15, no. 15: 5701.
https://doi.org/10.3390/en15155701