# Equivalent Phase Current Harmonic Elimination in Quadruple Three-Phase Drives Based on Carrier Phase Shift Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}T

_{4}and T

_{6}in Figure 1) will turn on; when the fundamental waveform is larger than the carrier waveform, the switch on the top of the converter leg (T

_{1}T

_{3}and T

_{5}in Figure 1) will turn on. Compared with the space vector modulation, the CPWM has lower dc link voltage utilization [20]. This drawback can be avoided by the injection of the zero-sequence harmonics [21]. The implementation of CPWM is straightforward and it can be extended to the control of the multiphase multilevel converters without greatly increasing the complexity of the control algorithm. The phase-shifted CPWM is the commonly used CPWM for the control of multilevel converters, as it has the same switching frequency and conducting periods, which means even power distribution on the power switches of the converter [22,23]. Recent research works have verified that the pulse width modulation (PWM) technique results in high-frequency torque ripple in multiphase drives [24,25]. For instance, [25] shows that the high-frequency torque harmonics are mitigated by choosing appropriate carrier angles in dual three-phase drive systems. The high-frequency PWM-related current harmonics are known as the source of the high-frequency flux linkage harmonics, torque ripple, vibration and noise [26,27]. Therefore, it is of importance to reduce the equivalent current harmonics of the multiphase drive systems by considering the effect the CPWM technique.

## 2. Double Fourier Integral Analysis Method of Pulse Width Modulation

## 3. Modelling of Equivalent Current Harmonics in Multi Three-Phase Drives

^{th}harmonic component. According to Equations (13) and (14), the equivalent phase current ${i}_{total}\left(t\right)$ can be represented as:

## 4. Experimental Results

## 5. Conclusions

- (1)
- The phase-shifted CPWM can be applied into arbitrary multi three-phase drives.
- (2)
- The implementation of the proposed method is simple by changing the initial phase angles of carrier signals in the software.
- (3)
- Compared with previous research works targeted at torque ripple reduction, this work aims to reduce the total equivalent phase current harmonics, which makes the analytical models much easier. Additionally, the elimination of total equivalent phase current harmonics will result in significant machine performance improvement in terms of torque, vibration and noise.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${V}_{\mathrm{dc}}$ | Converter dc-link voltage |

$M$ | Modulation index. |

${\omega}_{\mathrm{o}}$, ${\omega}_{\mathrm{c}}$ | Frequencies of the modulating and the carrier signals respectively. |

${\theta}_{o}$, ${\theta}_{c}$ | Initial phase angles of the modulating and the carrier signals respectively. |

$x$, y | Time-varying angle of the carrier and the modulating signals respectively |

${J}_{n}$ | Bessel function |

${f}_{c}$ | Switching frequency |

$Z\left(h\right)$ | The h^{th} harmonic impedance |

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**Figure 2.**(

**a**) The x-y plane for the sine-triangle modulation (

**b**) The x-y plane for the corresponding pulse width modulation (PWM) output voltage [28].

**Figure 3.**Multi three-phase drive FFT spectra with and without the proposed phase-shifted carrier-based pulse-width modulation (CPWM) under different $M$. (

**a**) $M=0.9$, (

**b**)$M=0.5$, (

**c**) $M=0.1$.

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

Direct current (DC) link voltage (${V}_{dc}$) | 40 V |

Switching frequency (${f}_{c}$) | 2 kHz |

Machine pole pair number | 4 |

Load torque | 3 Nm |

Machine mechanical speed | 200 rpm |

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**MDPI and ACS Style**

Wang, X.; Yan, H.; Buticchi, G.; Gu, C.; Zhang, H.
Equivalent Phase Current Harmonic Elimination in Quadruple Three-Phase Drives Based on Carrier Phase Shift Method. *Energies* **2020**, *13*, 2709.
https://doi.org/10.3390/en13112709

**AMA Style**

Wang X, Yan H, Buticchi G, Gu C, Zhang H.
Equivalent Phase Current Harmonic Elimination in Quadruple Three-Phase Drives Based on Carrier Phase Shift Method. *Energies*. 2020; 13(11):2709.
https://doi.org/10.3390/en13112709

**Chicago/Turabian Style**

Wang, Xuchen, Hao Yan, Giampaolo Buticchi, Chunyang Gu, and He Zhang.
2020. "Equivalent Phase Current Harmonic Elimination in Quadruple Three-Phase Drives Based on Carrier Phase Shift Method" *Energies* 13, no. 11: 2709.
https://doi.org/10.3390/en13112709