# Investigation and Experimental Validation of Sideband Harmonic Vibration of IPMSM with and without Skewed Slots for EVs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Simulation

## 3. Experimental Verification and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ning, Z.; Zhu, K. Research on Prevention and Control Technologies of Harbor Pollution. In Proceedings of the 2009 International Conference on Energy and Environment Technology, Guilin, China, 16–18 October 2009; pp. 713–716. [Google Scholar] [CrossRef]
- Remus, N.; Toulabi, M.S.; Mukundan, S.; Dhulipati, H.; Li, W.; Novak, C.; Kar, N.C. Electromagnetic Noise and Vibration in PMSM and Their Sources: An Overview. In Proceedings of the 2020 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), London, ON, Canada, 30 August–2 September 2020; pp. 1–4. [Google Scholar] [CrossRef]
- Zhang, H. Measuring and evaluating the environmental noise in the campus of Southwest Forestry University. In Proceedings of the 2011 International Conference on Electrical and Control Engineering, Yichang, China, 16–18 September 2011; pp. 2325–2328. [Google Scholar] [CrossRef]
- Fang, S.; Liu, H.; Wang, H.; Yang, H.; Lin, H. High Power Density PMSM With Lightweight Structure and High-Performance Soft Magnetic Alloy Core. IEEE Trans. Appl. Supercond.
**2019**, 29, 1–5. [Google Scholar] [CrossRef] - Li, L.; Zhang, J.; Zhang, C.; Yu, J. Research on Electromagnetic and Thermal Issue of High-Efficiency and High-Power-Density Outer-Rotor Motor. IEEE Trans. Appl. Supercond.
**2016**, 26, 1–5. [Google Scholar] [CrossRef] - Yang, R.; Zhang, C.; Wang, M.; Li, L. Effect of structure parameters on the losses and efficiency of Surface-Mounted PMSM. In Proceedings of the 2017 IEEE Workshop on Electrical Machines Design, Control and Diagnosis (WEMDCD), Nottingham, UK, 20–21 April 2017; pp. 75–79. [Google Scholar] [CrossRef]
- Wang, L.; Bao, X.; Di, C.; Li, J. Effects of Novel Skewed Rotor in Squirrel-Cage Induction Motor on Electromagnetic Force. IEEE Trans. Magn.
**2015**, 51, 1–4. [Google Scholar] [CrossRef] - Skalka, M.; Ondrusek, C.; Kurfurst, J.; Cipin, R. Harmonic reduction in induction machine using slot wedges optimization. In Proceedings of the International Symposium on Power Electronics Power Electronics Electrical Drives, Automation and Motion, Sorrento, Italy, 20–22 June 2012; pp. 1252–1255. [Google Scholar] [CrossRef]
- Jung, J.-W.; Kim, D.-J.; Hong, J.-P.; Lee, G.-H.; Jeon, S.-M. Experimental Verification and Effects of Step Skewed Rotor Type IPMSM on Vibration and Noise. IEEE Trans. Magn.
**2011**, 47, 3661–3664. [Google Scholar] [CrossRef] - Blum, J.; Merwerth, J.; Herzog, H.-G. Investigation of the segment order in step-skewing synchronous machines on noise and vibration. In Proceedings of the 2014 4th International Electric Drives Production Conference (EDPC), Nuremberg, Germany, 30 September–1 October 2014; pp. 1–6. [Google Scholar] [CrossRef]
- Li, W.; Xu, Z.; Zhang, Y. Induction motor control system based on FOC algorithm. In Proceedings of the 2019 IEEE 8th Joint International Information Technology and Artificial Intelligence Conference (ITAIC), Chongqing, China, 24–26 May 2019; pp. 1544–1548. [Google Scholar] [CrossRef]
- Zhang, C.; Wang, X.; Wang, D.; Sun, Q.; Ma, G. Comparative Analysis of Electromagnetic Force Inverter Fed PMSM Drive Using Field Oriented Control (FOC) and Direct Torque Control (DTC). In Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 1–4. [Google Scholar] [CrossRef]
- Du, P.; Li, L.; Liu, J.; Yang, R. A Novel Simplified 3-Level SVPWM Modulation Method Based on the Conventional 2-L SVPWM Modulation Method. In Proceedings of the 2018 21st International Conference on Electrical Machines and Systems (ICEMS), Jeju, Korea, 7–10 October 2018; pp. 1799–1803. [Google Scholar] [CrossRef]
- Leedy, A.; Nelms, R. Harmonic Analysis of a Space Vector PWM Inverter Using the Method of Multiple Pulses. In Proceedings of the 2006 IEEE International Symposium on Industrial Electronics, Montreal, QC, Canada, 9–13 July 2006; pp. 1182–1187. [Google Scholar] [CrossRef]
- Deng, H.; Helle, L.; Bo, Y.; Larsen, K.B. A General Solution for Theoretical Harmonic Components of Carrier Based PWM Schemes. In Proceedings of the 2009 Twenty-Fourth Annual IEEE Applied Power Electronics Conference and Exposition, Washington, DC, USA, 15–19 February 2009; pp. 1698–1703. [Google Scholar] [CrossRef]
- Liang, W.; Luk, P.; Fei, W.-Z. Analytical Investigation of Sideband Electromagnetic Vibration in Integral-Slot PMSM Drive with SVPWM Technique. IEEE Trans. Power Electron.
**2017**, 32, 4785–4795. [Google Scholar] [CrossRef] [Green Version] - Liang, W.; Wang, J.; Luk, P.; Fang, W.; Fei, W. Analytical Modeling of Current Harmonic Components in PMSM Drive with Voltage-Source Inverter by SVPWM Technique. IEEE Trans. Energy Convers.
**2014**, 29, 673–680. [Google Scholar] [CrossRef] [Green Version] - Liang, W.; Wang, J.; Fang, W. Analytical Modeling of Sideband Current Harmonic Components in Induction Machine Drive with Voltage Source Inverter by an SVM Technique. IEEE Trans. Power Electron.
**2013**, 28, 5372–5379. [Google Scholar] [CrossRef]

**Figure 4.**Sideband current of the current of two motors: (

**a**) when speed is 1000 rpm; (

**b**) when speed is 3000 rpm.

**Figure 5.**Two-dimensional Fourier decomposition results of the excitation force of the straight slot motors at 1000 rpm.

**Figure 6.**Two-dimensional Fourier decomposition results of the excitation force of the skewed slot motors at 1000 rpm.

**Figure 7.**Two-dimensional Fourier decomposition results of the excitation force of the straight slot motors at 3000 rpm.

**Figure 8.**Two-dimensional Fourier decomposition results of the excitation force of the skewed slot motors at 3000 rpm.

**Figure 9.**Time spectrogram of the excitation force of two motors: (

**a**) when the speed is 1000 rpm; (

**b**) when the speed is 3000 rpm.

**Figure 13.**Current harmonics at different speeds: (

**a**) the low-frequency band and (

**b**) harmonics near the switching frequency.

Parameters | Value |
---|---|

Number of stator slots, z | 48 |

Number of pole pairs, p | 4 |

Stator outer diameter, ${D}_{so}$ | 180 mm |

Rotor outer diameter, ${D}_{ro}$ | 122.2 mm |

Axial length, ${L}_{ax}$ | 96 mm |

Rated power, P | 10 kW |

Rated rotating speed, ${n}_{N}$ | 3000 rpm |

Rated torque, ${T}_{N}$ | 32 N·m |

Harmonic Order | Skewed Slots | Straight Slots |
---|---|---|

5 | 0.72 A | 0.42 A |

7 | 0.30 A | 0.65 A |

11 | 0.10 A | 5.81 A |

13 | 0.28 A | 5.53 A |

Harmonic Order | Skewed Slots | Straight Slots |
---|---|---|

5 | 0.68 A | 0.91 A |

7 | 0.42 A | 0.41 A |

11 | 0.36 A | 1.61 A |

13 | 0.31 A | 0.42 A |

(Space Order, Time Order) | Skewed Slots/Pa | Straight Slots/Pa | Weaken Proportion |
---|---|---|---|

(0, 47) | 1690.197 | 1799.291 | 6.45% |

(0, 53) | 2318.406 | 2506.543 | 8.11% |

(8, 49) | 1094.235 | 1236.586 | 13.01% |

(8, 55) | 844.8169 | 923.367 | 9.30% |

Exciting Force Harmonic Frequency/Hz | Skewed Slots/Pa | Straight Slots/Pa | Weaken Proportion |
---|---|---|---|

9000 | 854.172 | 751.0238 | −12.07% |

9400 | 1850.119 | 1911.404 | 3.31% |

9800 | 1442.411 | 1566.67 | 8.61% |

10,200 | 1617.312 | 1798.004 | 11.17% |

10,600 | 2644.036 | 2945.897 | 11.42% |

11,000 | 1403.132 | 1499.958 | 6.90% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Feng, Z.; Wang, D.; Peng, C.; Feng, W.; Wang, B.; Li, J.; Wang, X.
Investigation and Experimental Validation of Sideband Harmonic Vibration of IPMSM with and without Skewed Slots for EVs. *World Electr. Veh. J.* **2021**, *12*, 223.
https://doi.org/10.3390/wevj12040223

**AMA Style**

Feng Z, Wang D, Peng C, Feng W, Wang B, Li J, Wang X.
Investigation and Experimental Validation of Sideband Harmonic Vibration of IPMSM with and without Skewed Slots for EVs. *World Electric Vehicle Journal*. 2021; 12(4):223.
https://doi.org/10.3390/wevj12040223

**Chicago/Turabian Style**

Feng, Zhenkang, Daohan Wang, Chen Peng, Wentao Feng, Bingdong Wang, Junchen Li, and Xiuhe Wang.
2021. "Investigation and Experimental Validation of Sideband Harmonic Vibration of IPMSM with and without Skewed Slots for EVs" *World Electric Vehicle Journal* 12, no. 4: 223.
https://doi.org/10.3390/wevj12040223