# Novel Single Inverter-Controlled Brushless Wound Field Synchronous Machine Topology

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Inverter Topology

_{a}, i*

_{b}, and i*

_{c}used for the employed hysteresis current control scheme are generated through the following equation:

_{x}, and i

_{x}represent the proposed CCVSI output voltage and current, respectively. R and L represent the armature winding resistance and inductance of the machine.

## 3. Machine Topology and Working Principle

_{abc}) generated through the method discussed in Section 2 are given to the machine’s armature winding. A 4-pole, 42-slot (4p42s) machine with a concentrated, double-layered armature winding, which has a winding factor of 0.932, is employed to validate the proposed brushless WFSM topology. The employed machine along with its stator and rotor winding configurations are shown in Figure 4a,b, respectively. As seen from Figure 4b, the rotor of the machine has four main teeth to accommodate the four-pole rotor field winding, whereas each main tooth is further altered to have two sub-teeth to house the rotor harmonic winding. The rotor harmonic winding is based on a twelve-pole winding configuration to harness the harmonic power generated in the air gap flux. The detailed winding specifications are presented in Table 1.

_{abc}) with a different magnitude of dc offset/bias. In case 1 and 2, the armature winding is supplied with currents having a dc offset of 0.6 A and 1.2 A for each phase, respectively. However, a dc offset of 1.8 A and 2.4 A is achieved for the stator armature currents of the employed machine in case 3 and 4, respectively. The input armature currents during all operating conditions, i.e., case 1 to 4, are presented in Figure 5a–d.

_{s}= electrical angle (spatial), and

_{1}is the fundamental and I

_{bias}is the magnitude of the dc offset for the armature winding currents for each phase.

_{abc}) of the armature winding is expressed as:

_{abc}consists of the normal fundamental MMF rotating at synchronous speed and the spatial-location-fixed MMF generated by the dc offset component of the armature currents. These two fields are not coupled due to the difference of frequencies.

_{0}is the rotor excitation winding initial position angle, the spatial position of the excitation winding can be calculated as:

_{h}is the rotor excitation winding number of turns, and P

_{g}is the air gap permeance.

_{h}) in the rotor harmonic winding is rectified by a rotating rectifier to supply dc to the rotor field winding to archive brushless operation for WFSM [19,20].

## 4. Finite Element Analysis

#### No-Load Analysis

_{rms}was generated in the stator winding of the machine and is presented in Figure 12a. To show the harmonics present in the induced back-EMF, a FFT plot of the back-EMF was generated and is shown in Figure 12b. The cogging torque of the machine is 0.04 Nm (peak-to-peak). The generated cogging torque is presented in Figure 13. The no-load analysis results are presented in Table 4.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Proposed inverter topology, (

**b**) reference and controlled output current for phase A, and (

**c**) controlled three-phase output currents of the inverter.

**Figure 5.**Armature winding currents with (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase.

**Figure 6.**Flux linkages of the machine having (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase of armature currents.

**Figure 7.**FFT of flux linkages of the machine having (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase of armature currents.

**Figure 8.**Magnetic field density plots of the machine having (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase of armature currents.

**Figure 9.**Rotor currents of the machine having (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase of armature currents.

**Figure 10.**Output torque of the machine having (

**a**) 0.6 A, (

**b**) 1.2 A, (

**c**) 1.8 A, and (

**d**) 2.4 A dc offset for each phase of armature currents.

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

Number of poles/slots/layers | 4/42/2 |

Coil span | 9 slots |

Pole pitch | 10.5 slots |

Periodicities | 2 |

Winding factor | 0.932 |

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

Rated power | 1 kW |

Machine poles/Stator slots | 4/42 |

Rated speed | 1800 rpm |

Frequency | 60 Hz |

Stator outer/inner diameter | 88.5/50 mm |

Air gap | 0.5 mm |

Rotor diameter | 49.5 mm |

Rotor main/sub-teeth | 4/8 |

Harmonic/Field winding number of turns | 9/150 |

Armature winding number of turns | 20 |

Stack length | 80 mm |

Attribute | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

Average output torque (in Nm) | 3.1980 | 5.2520 | 6.4478 | 7.2367 |

Torque ripple (in %) | 60.97 | 65.689 | 71.342 | 76 |

Maximum torque (in Nm) | 4.36 | 7.25 | 8.85 | 10.15 |

Attribute | Case 4 |
---|---|

Back-EMF (in V_{rms}) | 76.671 |

Cogging torque (in peak-to-peak Nm) | 0.04 |

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**MDPI and ACS Style**

Bukhari, S.S.H.; Memon, A.A.; Madanzadeh, S.; Sirewal, G.J.; Doval-Gandoy, J.; Ro, J.-S.
Novel Single Inverter-Controlled Brushless Wound Field Synchronous Machine Topology. *Mathematics* **2021**, *9*, 1739.
https://doi.org/10.3390/math9151739

**AMA Style**

Bukhari SSH, Memon AA, Madanzadeh S, Sirewal GJ, Doval-Gandoy J, Ro J-S.
Novel Single Inverter-Controlled Brushless Wound Field Synchronous Machine Topology. *Mathematics*. 2021; 9(15):1739.
https://doi.org/10.3390/math9151739

**Chicago/Turabian Style**

Bukhari, Syed Sabir Hussain, Ali Asghar Memon, Sadjad Madanzadeh, Ghulam Jawad Sirewal, Jesús Doval-Gandoy, and Jong-Suk Ro.
2021. "Novel Single Inverter-Controlled Brushless Wound Field Synchronous Machine Topology" *Mathematics* 9, no. 15: 1739.
https://doi.org/10.3390/math9151739