# Proposal of Hybrid Discontinuous PWM Technique for Five-Phase Inverters under Open-Phase Fault Operation

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## Abstract

**:**

## 1. Introduction

## 2. Fault-Tolerant Control

## 3. Proposed Hybrid Discontinuous Modulation

#### 3.1. Principle of the HD-PWM

#### 3.2. HD-PWM Harmonic Distortion Factor

## 4. Simulation-Based Switching Loss Analysis of the Proposed HD-PWM

## 5. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

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

$\omega $ | Angular frequency |

${T}_{sw}$ | Commutation period |

${\overline{V}}_{N0}$ | Neutral-point voltage mean value |

${\psi}_{m}$ | Motor flux |

$\theta $ | Angular position |

${M}_{{a}_{max}}$ | Maximum modulation index |

${V}_{re{f}_{max}}$ | Maximum phase-to-neutral voltage |

${M}_{a}$ | Modulation index |

${t}_{0}$ | Zero-vector application time |

${v}_{{x}_{ref}}$ | Modulation signal |

${v}_{zss}$ | Zero-sequence signal |

${\delta}_{clamp}$ | Clamping time |

${V}_{DC}$ | DC voltage level |

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**Figure 6.**Squared harmonic flux of studied modulation techniques for $\theta \in \left(\right)open="["\; close="]">0,\pi \phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2$.

Sectors 1 and 5 | Sectors 2 and 6 | Sectors 3 and 7 | Sectors 4 and 8 | |
---|---|---|---|---|

${\mathbf{t}}_{\mathbf{1}}$ = ${\mathbf{t}}_{\mathbf{3}}$ | $\left(\right)open="("\; close=")">{v}_{{b}_{ref}}-{v}_{{e}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{b}_{ref}}-{v}_{{c}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{c}_{ref}}-{v}_{{b}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{c}_{ref}}-{v}_{{d}_{ref}}{T}_{sw}$ |

${\mathbf{t}}_{\mathbf{2}}$ | $\left(\right)open="("\; close=")">{v}_{{e}_{ref}}-{v}_{{c}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{c}_{ref}}-{v}_{{e}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{b}_{ref}}-{v}_{{d}_{ref}}{T}_{sw}$ | $\left(\right)open="("\; close=")">{v}_{{d}_{ref}}-{v}_{{b}_{ref}}{T}_{sw}$ |

${\mathbf{t}}_{\mathbf{0}}$ | $0.5\left(\right)open="("\; close=")">{T}_{sw}-{t}_{1}-{t}_{2}-{t}_{3}$ |

1st Harm. | 3rd Harm. | 5th Harm. | 7th Harm. | 9th Harm. | |
---|---|---|---|---|---|

S−PWM | 100 | 1.94 | 0.83 | 0.13 | 0.07 |

HD−PWM | 100 | 1.75 | 0.95 | 0.24 | 0.11 |

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**MDPI and ACS Style**

Fernandez, M.; Robles, E.; Aretxabaleta, I.; Kortabarria, I.; Martín, J.L.
Proposal of Hybrid Discontinuous PWM Technique for Five-Phase Inverters under Open-Phase Fault Operation. *Machines* **2023**, *11*, 404.
https://doi.org/10.3390/machines11030404

**AMA Style**

Fernandez M, Robles E, Aretxabaleta I, Kortabarria I, Martín JL.
Proposal of Hybrid Discontinuous PWM Technique for Five-Phase Inverters under Open-Phase Fault Operation. *Machines*. 2023; 11(3):404.
https://doi.org/10.3390/machines11030404

**Chicago/Turabian Style**

Fernandez, Markel, Endika Robles, Iker Aretxabaleta, Iñigo Kortabarria, and José Luis Martín.
2023. "Proposal of Hybrid Discontinuous PWM Technique for Five-Phase Inverters under Open-Phase Fault Operation" *Machines* 11, no. 3: 404.
https://doi.org/10.3390/machines11030404