# A Novel Sub-Harmonic Synchronous Machine Using Three-Layer Winding Topology

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Topology and Principle of Operation

#### 2.1. Proposed Sub-Harmonic Synchronous Machine Topology

#### 2.2. Principle of Operation

_{e}is the electrical angular frequency, and t is the time.

## 3. Design and Analysis of the Proposed Machine

_{1}is the Slot fill factor of ABC winding, S

_{2}is the Slot fill factor of XYZ winding, and S

_{3}is the slot fill factor when the slots are occupied by both ABC and XYZ windings, looking at Figure 6, the average slot fill factor, S

_{avg}, is,

_{m}, where ω

_{m}is the frequency in mechanical space domain. Whereas in the case of winding XYZ with its 2-pole configuration, it delivers the sub-harmonic MMF component with the frequency of (ω

_{m})/4. Thus, the two components rotate at a different speed. In the rotor, on the other hand, the harmonic winding is placed on the rotor such that it aligns magnetically with the stator XYZ winding. Moreover, the field winding having an 8-pole arrangement aligns magnetically with winding ABC. With all that, the proposed SHSM achieves its brushless operation by inducing voltages in harmonic winding, due to the sub-harmonic MMF. These voltages then get rectified and DC current is fed to the field winding of the rotor, which magnetically locks it with the stator fundamental MMF.

## 4. 2-D Finite Element Analysis

## 5. Conclusions

- Significantly greater torque generation.
- Utilizes maximum allowable stator slot space.
- Single inverter brushless usage
- No requirement of imposing complex unbalanced-cooling system.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**2-layer ABC and XYZ winding configuration in over 360-mechanical degrees presented in [15].

**Figure 9.**Induced voltage and current at the rotor harmonic winding: (

**a**) Induced voltage; (

**b**) Induced current.

**Figure 10.**Rectified voltage and current at the rotor field winding: (

**a**) Rectified voltage; (

**b**) Rectified current.

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

Rated power | W | 1281 |

Operating speed | rpm | 900 |

Stator outer diameter | mm | 177 |

Stator inner diameter | mm | 95 |

Air-gap length | mm | 0.5 |

Shaft diameter | mm | 25 |

Stack length | mm | 80 |

Number of poles of stator ABC winding | - | 8 |

Number of poles of stator XYZ winding | - | 2 |

Number of poles of rotor harmonic winding | - | 2 |

Number of poles of rotor field winding | - | 8 |

Number of stator slots | - | 48 |

Conductors per stator slot in ABC winding | - | 30 |

Conductors per stator slot in XYZ winding | - | 10 |

Conductors per pole of harmonic winding | - | 50 |

Conductors per pole of field winding | - | 24 |

Indicator | Unit | WRSM [14] | BL-WRSM [15] | Novel SHSM |
---|---|---|---|---|

Stator current | A_{rms} | 4.50 | 4.50 | 4.50 |

Filed current | A_{avg} | 9.5 | 9.8 | 20.18 |

Harmonic current | A_{rms} | 0 | 5.1 | 14.05 |

Terminal voltage | V_{rms} | 68.10 | 72.0 | 113.89 |

Average torque | N_{m} | 7.30 | 7.83 | 12.53 |

Torque ripple | % | 16.67 | 18.0 | 32 |

Number of layers of stator winding | 2 | 2 | 3 | |

Number of poles for rotor harmonic winding | - | 4 | 2 | |

Number of ABC conductors/slot of stator winding | 40 | 40 | 30 | |

Number of XYZ conductors/slot of stator winding | - | 20 | 10 |

Indicator | Unit | Number of Conductors per Slot in XYZ Winding While Having 30 Conductors per Slot in ABC Winding | ||||
---|---|---|---|---|---|---|

10 | 8 | 6 | 4 | 2 | ||

Stator current | A_{rms} | 4.50 | 4.50 | 4.50 | 4.50 | 4.50 |

Field current | A_{avg} | 20.18 | 15.74 | 10.81 | 6.09 | 1.78 |

Harmonic current | A_{rms} | 14.05 | 11.28 | 8.27 | 5.07 | 1.81 |

Terminal voltage | V_{rms} | 113.89 | 102.46 | 87.64 | 68.48 | 50.86 |

Induced field voltage | V_{rms} | 6.11 | 5.67 | 5.01 | 4.02 | 2.73 |

Rotor voltage | V_{avg} | 1.57 | 1.38 | 1.09 | 0.69 | 0.22 |

Average torque | N_{m} | 12.53 | 11.15 | 9.10 | 6.04 | 2.02 |

Torque ripple | % | 32 | 31 | 31 | 33 | 38 |

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**MDPI and ACS Style**

Rafin, S.M.S.H.; Ali, Q.; Lipo, T.A.
A Novel Sub-Harmonic Synchronous Machine Using Three-Layer Winding Topology. *World Electr. Veh. J.* **2022**, *13*, 16.
https://doi.org/10.3390/wevj13010016

**AMA Style**

Rafin SMSH, Ali Q, Lipo TA.
A Novel Sub-Harmonic Synchronous Machine Using Three-Layer Winding Topology. *World Electric Vehicle Journal*. 2022; 13(1):16.
https://doi.org/10.3390/wevj13010016

**Chicago/Turabian Style**

Rafin, S M Sajjad Hossain, Qasim Ali, and Thomas A. Lipo.
2022. "A Novel Sub-Harmonic Synchronous Machine Using Three-Layer Winding Topology" *World Electric Vehicle Journal* 13, no. 1: 16.
https://doi.org/10.3390/wevj13010016