# Multiple Synchronous Rotating Frame Transformation-Based 12th Current Harmonic Suppression Method for an IPMSM

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## Abstract

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## 1. Introduction

## 2. Current Harmonic Analysis of IPMSM Vector Control System Considering Back-EMF Nonsinusoidal and Dead-Time Effects

#### 2.1. IPMSM Harmonic Mathematical Model in Vector Control System

_{dh_M}and v

_{qh_M}are the sum of all order stator voltage harmonics of the IPMSM in the d-q axis coordinate system; R is the motor stator resistance value; i

_{dh}and i

_{qh}are the sum of all order stator current harmonics of the IPMSM in the d-q axis coordinate system; λ

_{dh}and λ

_{qh}are the sum of all order permanent magnet flux linkage harmonics of the IPMSM in d-q axis coordinate system, ω

_{e}is the electrical angular velocity of the motor; Δv

_{dh1}and Δv

_{qh1}are the voltage harmonics caused by the permanent magnet flux linkage harmonics; Δv

_{dh2}and Δv

_{qh2}are the voltage harmonics caused by the inverter’s dead-time effect.

#### 2.2. Analysis of Permanent Magnet Flux Harmonics and Current Harmonics

_{sn}and θ

_{n}are the amplitude and initial phase angle of the permanent magnet flux linkage harmonics of each order, respectively.

_{dh12}and λ

_{qh12}are the 12th permanent magnet flux linkage harmonics in the d-q axis coordinate system, respectively.

_{dh12}, χ

_{qh12}, α

_{d12}, and α

_{q12}are the amplitude and initial phase angle of the 12th permanent magnet flux linkage harmonics, respectively.

_{dh112}, I

_{qh112}, μ

_{d12}, and μ

_{q12}are the amplitude and initial phase angle of the 12th voltage harmonics caused by the permanent magnet flux linkage harmonics, respectively.

#### 2.3. Analysis of the Inverter’s Dead-Time Effect and Current Harmonics

_{dead}is the voltage loss caused by the inverter dead-time effect; γ is the angle between the current vector and the q-axis; k = 1, 2, 3….

_{dh212}and Δv

_{qh212}are the 12th voltage harmonics caused by the inverter dead-time effect in the d-q axis coordinate system, respectively.

_{dh212}, V

_{qh212}, ϕ

_{d12}, and ϕ

_{q12}are the amplitudes and initial phase angles of the 12th voltage harmonics caused by the inverter dead-time effect, respectively.

_{dh212,}I

_{qh212}, σ

_{d12}, and σ

_{q12}are the amplitudes and initial phase angles of the 12th current harmonics caused by the inverter dead-time effect, respectively.

## 3. The Proposed Current Harmonic Suppression Strategy

_{a}, i

_{b}, and i

_{c}are the three-phase currents; I

_{sn}and η

_{n}are the amplitude and initial phase angle of each harmonic order in the phase current, respectively.

_{dh12}and i

_{qh12}are the 12th current harmonics in the d-q axis coordinate system, respectively.

_{dh12}, I

_{qh12}, β

_{d12}, and β

_{q12}are the 12th current harmonic amplitudes and initial phase angles in the d-q axis coordinate system, respectively.

## 4. Simulation Results

#### 4.1. Simulation Results for the Proposed Harmonic Extraction Method

#### 4.2. Simulation Results for the Proposed Current Harmonic Suppression Strategy

## 5. Experimental Results

#### 5.1. Experimental Results for the Proposed Harmonic Extraction Method

#### 5.2. Experimental Results for the Proposed Current Harmonic Suppresion Strategy

## 6. Conclusions

- The influencing factors of the current harmonics in the IPMSM vector control system were theoretically analyzed, and the influence mechanism of the inverter dead-time effect and permanent magnet flux linkage harmonics on current harmonics was expounded;
- Based on the MSRFT, a simple current harmonic extraction method was proposed. The proposed method can accurately extract the 12th current harmonic components in the d-q axis current without increasing the difficulty of the algorithm;
- Based on the extracted harmonic current components, a harmonic voltage generation strategy was established, and a current harmonic suppression strategy was formed with the proposed current harmonic extraction method;
- The feasibility and effectiveness of the proposed method were verified via MATLAB/Simulink simulations and experiments, respectively. The simulation and experimental results showed that the proposed current harmonic extract method can accurately extract the current harmonic components, and the proposed current harmonic suppression strategy can effectively suppress the 11th and 13th harmonics in the IPMSM stator three-phase current.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of the inverter’s dead time: (

**a**) structural diagram of the A-phase bridge arm; (

**b**) switch tube signal waveform and output voltage waveform.

**Figure 7.**Simulation results for extracting the 12th current harmonic components using the traditional method: (

**a**) the motor speed is 100 rpm; (

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

**Figure 8.**Simulation results for extracting the 12th current harmonic components using the proposed method: (

**a**) the motor speed is 100 rpm; (

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

**Figure 9.**Simulation results for the d-q axis current and 12th current harmonic component: (

**a**) the motor speed is 100 rpm and the proposed strategy is not applied; (

**b**) the motor speed is 100 rpm and the proposed strategy is applied; (

**c**) the motor speed is 3000 rpm and the proposed strategy is not applied; (

**d**) the motor speed is 3000 rpm and the proposed strategy is applied.

**Figure 10.**Simulation results for three-phase current waveform and the A-phase current FFT analysis results when the motor speed is 500 rpm and the load torque is 72 Nm: (

**a**) before applying the proposed strategy; (

**b**) after applying the proposed strategy.

**Figure 12.**Experimental results for extracting the 12th current harmonic components using the traditional method: (

**a**) the motor speed is 100 rpm; (

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

**Figure 13.**Experimental results for extracting the 12th current harmonic components using the proposed method: (

**a**) the motor speed is 100 rpm; (

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

**Figure 14.**Experimental results for the d-q axis current and 12th current harmonic component: (

**a**) the motor speed is 100 rpm and the proposed strategy is not applied; (

**b**) the motor speed is 100 rpm and the proposed strategy is applied; (

**c**) the motor speed is 3000 rpm and the proposed strategy is not applied; (

**d**) the motor speed is 3000 rpm and the proposed strategy is applied.

**Figure 15.**Experimental results for three-phase current waveform and the A-phase current FFT analysis results when the motor speed is 500 rpm and the load torque is 72 Nm: (

**a**) before applying the proposed strategy; (

**b**) after applying the proposed strategy.

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

Pole pairs | n_{p} | 4 |

Permanent magnet flux linkage | λ_{f} | 0.038749 Wb |

Stator resistance | R_{s} | 0.003 Ω |

d-axis inductance | L_{d} | 0.1099 mH |

q-axis inductance | L_{q} | 0.3453 mH |

Rated speed | n | 3000 rpm |

Rated torque | T_{N} | 72 Nm |

Rated voltage | U_{N} | 320 V |

Rated current | I_{N} | 180 A |

Control frequency | f_{s} | 10 kHz |

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## Share and Cite

**MDPI and ACS Style**

Xu, Y.; Miao, Q.; Zeng, P.; Lin, Z.; Li, Y.; Li, X.
Multiple Synchronous Rotating Frame Transformation-Based 12th Current Harmonic Suppression Method for an IPMSM. *World Electr. Veh. J.* **2022**, *13*, 194.
https://doi.org/10.3390/wevj13100194

**AMA Style**

Xu Y, Miao Q, Zeng P, Lin Z, Li Y, Li X.
Multiple Synchronous Rotating Frame Transformation-Based 12th Current Harmonic Suppression Method for an IPMSM. *World Electric Vehicle Journal*. 2022; 13(10):194.
https://doi.org/10.3390/wevj13100194

**Chicago/Turabian Style**

Xu, Yamei, Qiang Miao, Pin Zeng, Zhichen Lin, Yiyang Li, and Xinmin Li.
2022. "Multiple Synchronous Rotating Frame Transformation-Based 12th Current Harmonic Suppression Method for an IPMSM" *World Electric Vehicle Journal* 13, no. 10: 194.
https://doi.org/10.3390/wevj13100194