# Hybrid Carrier Frequency Modulation Based on Rotor Position to Reduce Sideband Vibro-Acoustics in PMSM Used by Electric Vehicles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hybrid Carrier Frequency Modulation

#### 2.1. Principle and Implementation of the HCFM

_{0}and T

_{7}. Moreover, the time durations are also related to the rotor position [19]. Hence, the hybrid carrier frequency modulation is based on the rotor position to combine the corresponding periodic and random signal-based dithering methods that are presented in Figure 4.

#### 2.2. Explanation of the Sideband Harmonics Reduction

_{e}is the rotating electric angle; i

_{d}and i

_{q}are the d-q axes current components; ψ

_{f}is the PM flux; and L

_{d}and L

_{q}are the d-q axes synchronous inductance components.

_{4}and U

_{6}separately, d-q-axes voltages can be expressed, respectively, as

_{4}and T

_{6}can be expressed by using the phase voltage amplitude (U

_{m}) and the vector clamping angle (θ).

_{q}

_{1}and ∆i

_{q}

_{2}, can be presented as

_{q}is determined by T

_{0}, L

_{q}, and U

_{q}. In this study, T

_{0}can thus be optimized by the rotor position to reduce the sideband harmonics. The optimized configuration is shown in Figure 4 and expressed as

_{c}is the carrier frequency and ∆f is the dithering index defining the harmonics spread range that sets 1000 Hz in this study. In addition, f

_{t}

_{1}is the frequency of the sinusoidal wave, f

_{t}

_{2}is the frequency of the sawtooth wave meeting as [–1, 1], and R

_{i}is the random modulation index. According to the above analysis, the novel HCFM based on rotor position not only reduces harmonic currents but also achieves a wider spectrum extension.

#### 2.3. Power Spectral Density Explanation of HCFM

_{H}can be satisfied with the following Formula (12).

_{c}is the carrier frequency, f

_{m}is the frequency of the sawtooth signal, C

_{n}is the magnitude of the sideband current harmonics, n = 1, 2, 3 …. J(∙) is the Bessel function, and k = 1, 2, 3 …. β is the modulation factor related to the frequency and amplitude of the sawtooth signal.

_{e}.

## 3. Experimental Test Setup

## 4. Results and Discussion

#### 4.1. Sideband Current Harmonics

_{c}± 2f

_{0}and f

_{c}± 4f

_{0}, where f

_{0}is the fundamental frequency of the electrical supply, can be calculated by the rotation frequency f

_{r}(i.e., f

_{r}= n/60 and f

_{0}= p·f

_{r}) Considering that f

_{0}is 83.34 Hz under 1000 r/min, the main sidebands can be obtained with four main orders where the peak magnitude is −27.56 dB/Hz.

#### 4.2. Sideband Vibro-Acoustic Responses

_{c}± f

_{0}, f

_{c}± 3f

_{0}, and f

_{c}± 5f

_{0}.

## 5. Conclusions

^{2}vibration reduction and 10 dBA acoustic noise reduction. The reduction efforts in the HCFM are more significant than those in the RPWM. The results can provide a reference for multi-strategy control to achieve low vibro-acoustics and EMI reduction in EV and HEV application in addition to other PWM-fed motor applications. Further work including efficiency evaluation, torque ripple, and controller loss can be studied based on the proposed investigation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Momen, F.; Rahman, K.; Son, Y. Electrical propulsion system design of Chevrolet Bolt battery electric vehicle. In Proceedings of the 2016 IEEE Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, USA, 18–22 September 2017; IEEE: Piscataway, NJ, USA, 2017. [Google Scholar]
- Yang, Z.; Shang, F.; Brown, I.P.; Krishnamurthy, M. Comparative Study of Interior Permanent Magnet, Induction, and Switched Reluctance Motor Drives for EV and HEV Applications. IEEE Trans. Transp. Electrif.
**2015**, 1, 245–254. [Google Scholar] [CrossRef] - A Hannan, M.; Azidin, F.; Mohamed, A. Hybrid electric vehicles and their challenges: A review. Renew. Sustain. Energy Rev.
**2014**, 29, 135–150. [Google Scholar] [CrossRef] - Fang, Y.; Zhang, T. Sound Quality of the Acoustic Noise Radiated by PWM-Fed Electric Powertrain. IEEE Trans. Ind. Electron.
**2017**, 65, 4534–4541. [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.
**2016**, 32, 4785–4795. [Google Scholar] [CrossRef] [Green Version] - Liang, W.; Fei, W.; Luk, P.C.-K. An Improved Sideband Current Harmonic Model of Interior PMSM Drive by Considering Magnetic Saturation and Cross-Coupling Effects. IEEE Trans. Ind. Electron.
**2016**, 63, 4097–4104. [Google Scholar] [CrossRef] [Green Version] - Qiu, Z.; Chen, Y.; Liu, X.; Kang, Y.; Liu, H. Analysis of the sideband current harmonics and vibro-acoustics in the PMSM with SVPWM. IET Power Electron.
**2020**, 13, 1033–1040. [Google Scholar] [CrossRef] - Wu, L.J.; Zhu, Z.Q.; Staton, D.A.; Popescu, M.; Hawkins, D. Comparison of Analytical Models of Cogging Torque in Surface-Mounted PM Machines. In Proceedings of the XIX International Conference on Electrical Machines, Rome, Italy, 6–8 September 2010; IEEE: Piscataway, NJ, USA, 2010; pp. 1–6. [Google Scholar]
- Fei, W.; Zhu, Z.Q. Comparison of Cogging Torque Reduction in Permanent Magnet Brushless Machines by Conventional and Herringbone Skewing Techniques. IEEE Trans. Energy Convers.
**2013**, 28, 664–674. [Google Scholar] [CrossRef] - Grasso, E.; Palmieri, M.; Corti, F.; Nienhaus, M.; Cupertino, F.; Grasso, F. Detection of stator turns short-circuit during sensorless operation by means of the Direct Flux Control technique. In Proceedings of the 2020 AEIT International Annual Conference (AEIT), Catania, Italy, 23–25 September 2020; pp. 1–6. [Google Scholar]
- Huang, Y.; Xu, Y.; Zhang, W.; Zou, J. Hybrid periodic carrier frequency modulation technique based on modified SVPWM to reduce the PWM noise. IET Power Electron.
**2019**, 12, 515–520. [Google Scholar] [CrossRef] - Qiu, Z.; Kang, Y.; Chen, Y.; Liu, X.; Gu, F. Investigation into Periodic Signal-based Dithering Modulations for Suppression Sideband Vibro-acoustics in PMSM Used by Electric Vehicles. IEEE Trans. Energy Convers.
**2021**, 1. [Google Scholar] [CrossRef] - Pindoriya, R.M.; Rajpurohit, B.S.; Kumar, R. A Novel Application of Harmonics Spread Spectrum Technique for Acoustic Noise and Vibration Reduction of PMSM Drive. IEEE Access
**2020**, 8, 103273–103284. [Google Scholar] [CrossRef] - Huang, Y.; Xu, Y.; Li, Y.; Yang, G.; Zou, J. PWM Frequency Voltage Noise Cancelation in Three-Phase VSI Using the Novel SVPWM Strategy. IEEE Trans. Power Electron.
**2017**, 33, 8596–8606. [Google Scholar] [CrossRef] - Xu, Y.; Yao, Y.; Yuan, Q.; Zou, J.; Shang, J. Reduction of the acoustic noise in PMSM drives by the periodic frequency mod-ulation. In Proceedings of the 2011 International Conference on Electrical Machines and Systems, Beijing, China, 20–23 August 2011; pp. 1–5. [Google Scholar]
- Ruiz-Gonzalez, A.; Meco-Gutierrez, M.; Heredia-Larrubia, J.; Perez-Hidalgo, F.; Vargas-Merino, F. Pulse width modulation technique with harmonic injection in the modulating wave and discontinuous frequency modulation for the carrier wave to reduce vibrations in asynchronous machines. IET Power Electron.
**2019**, 12, 2865–2872. [Google Scholar] [CrossRef] - Zhang, W.; Xu, Y.; Ren, J.; Su, J.; Zou, J. Synchronous random switching frequency modulation technique based on the carrier phase shift to reduce the PWM noise. IET Power Electron.
**2020**, 13, 892–897. [Google Scholar] [CrossRef] - Wang, G.; Zheng, B.; Xu, Y. A Novel SVPWM Strategy for High-Frequency Noise Suppression of Dual Three-phase PMSM. In Proceedings of the PCIM Asia 2018, International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Shanghai, China, 26–28 June 2018; pp. 1–4. [Google Scholar]
- Chen, K.; Xie, Y. Multiphase optimal injection PWM with dual carrier frequency to reduce current THD. IET Power Electron.
**2017**, 10, 1061–1076. [Google Scholar] [CrossRef] - Lee, K.; Shen, G.; Yao, W.; Lu, Z. Performance Characterization of Random Pulse Width Modulation Algorithms in Industrial and Commercial Adjustable-Speed Drives. IEEE Trans. Ind. Appl.
**2017**, 53, 1078–1087. [Google Scholar] [CrossRef]

**Figure 4.**The variation laws and corresponding carrier waves of the carrier frequency with the HCFM.

Item | Value | Item | Value |

Number of slots | 12 | Type of controller | VSI |

Number of poles | 10 | Carrier frequency | 8000 Hz |

Rated speed | 2000 r/min | DC link voltage | 540 V |

Rated torque | 8 Nm | Rated power | 1.8 kW |

Schemes | Sideband Current Harmonics | Vibration | Acoustics | |||
---|---|---|---|---|---|---|

Peak Frequency | Amplitude | Peak Frequency | Amplitude | Peak Frequency | Amplitude | |

SVPWM | 8167 Hz | −27.56 dB/Hz | 8250 Hz | 0.154 m/s^{2} | 7750 Hz | 52.7 dBA |

RPWM | 8042 Hz | −39.56 dB/Hz | 7833 Hz | 0.063 m/s^{2} | 7833 Hz | 47.2 dBA |

HCFM | 7889 Hz | −48.78 dB/Hz | 8000 Hz | 0.026 m/s^{2} | 7750 Hz | 41.9 dBA |

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**

Qiu, Z.; Chen, Y.; Lin, X.; Cheng, H.; Kang, Y.; Liu, X.
Hybrid Carrier Frequency Modulation Based on Rotor Position to Reduce Sideband Vibro-Acoustics in PMSM Used by Electric Vehicles. *World Electr. Veh. J.* **2021**, *12*, 100.
https://doi.org/10.3390/wevj12030100

**AMA Style**

Qiu Z, Chen Y, Lin X, Cheng H, Kang Y, Liu X.
Hybrid Carrier Frequency Modulation Based on Rotor Position to Reduce Sideband Vibro-Acoustics in PMSM Used by Electric Vehicles. *World Electric Vehicle Journal*. 2021; 12(3):100.
https://doi.org/10.3390/wevj12030100

**Chicago/Turabian Style**

Qiu, Zizhen, Yong Chen, Xiaozhe Lin, Haiquan Cheng, Yang Kang, and Xu Liu.
2021. "Hybrid Carrier Frequency Modulation Based on Rotor Position to Reduce Sideband Vibro-Acoustics in PMSM Used by Electric Vehicles" *World Electric Vehicle Journal* 12, no. 3: 100.
https://doi.org/10.3390/wevj12030100