# Predictive-Fixed Switching Current Control Strategy Applied to Six-Phase Induction Machine

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## Abstract

**:**

## 1. Introduction

## 2. Six-Phase IM Drive Model

## 3. Drive Control

#### 3.1. Speed Control

#### 3.2. Classic MPC

#### Cost Function

#### 3.3. Proposed Current Controller (Pfsccs)

## 4. Simulation and Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FOC | Field Oriented Control |

IM | Induction Machine |

MPC | Model Predictive Control |

PFSCCS | Predictive-Fixed Switching Current Control Strategy |

MSE | Mean Squared Error |

PI | Proportional-Integral |

PWM | Pulse-Width Modulation |

SVM | Space Vector Modulation |

THD | Total Harmonic Distortion |

VSI | Voltage Source Inverter |

VSD | Vector Space Decomposition |

## References

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**Figure 2.**Mapping of the space vectors in the ($\alpha $-$\beta $)-(x-y) frame for a two-level six-phase VSI.

**Figure 4.**Considered sectors for the six-phase VSI in the ($\alpha $-$\beta $) frame: (

**a**) Available vectors; (

**b**) A selected specific sector shown as zoom.

**Figure 5.**Simulation performance in steady-state condition of stator currents in ($\alpha $-$\beta $) and (x-y) sub-spaces for a sampling frequency of 8 kHz at different speeds (${\omega}_{m}$): (

**a**) 500 rpm; (

**b**) 1000 rpm; (

**c**) 1500 rpm.

**Figure 7.**Experimental results in the ($\alpha $-$\beta $)-(x-y) frame for stator currents at 8 kHz of sampling frequency and 500 rpm rotor speed considering: (

**a**) ${\lambda}_{xy}$ = 0.05; (

**b**) ${\lambda}_{xy}$ = 0.1.

**Figure 8.**Experimental performance for PFSCCS at 8 kHz of sampling frequency and 500 rpm: (

**a**) Spectrum of the measured stator current; (

**b**) Switching pattern in the VSI.

**Figure 9.**Experimental transient test in q-axis of stator currents from a speed change of 500 rpm to $-500$ rpm at 8 kHz of sampling frequency considering: (

**a**) ${\lambda}_{xy}$ = 0.05; (

**b**) ${\lambda}_{xy}$ = 0.1.

**Figure 10.**Experimental transient test in q-axis of stator currents from a speed change of 1500 rpm to 200 rpm at 16 kHz and 8 kHz of sampling frequency, respectively: (

**a**) Classic MPC; (

**b**) PFSCCS.

${R}_{r}$ | 6.9 $\mathsf{\Omega}$ | ${L}_{s}$ | 654.4 mH |

${L}_{lr}$ | 12.8 mH | ${L}_{r}$ | 626.8 mH |

${L}_{ls}$ | 5.3 mH | ${P}_{w}$ | 2 kW |

${R}_{s}$ | 6.7 $\mathsf{\Omega}$ | ${J}_{i}$ | 0.07 kg.m${}^{2}$ |

${L}_{m}$ | 614 mH | ${B}_{i}$ | 0.0004 kg.m${}^{2}$/s |

P | 1 | ${\omega}_{r-nom}$ | 3000 rpm |

**Table 2.**Simulation performance test of stator currents ($\alpha $-$\beta $), (x-y), MSE (A), THD (%) at different rotor speeds (rpm).

${\mathit{f}}_{\mathit{s}}$ =$\phantom{\rule{3.33333pt}{0ex}}8$ kHz | ||||||
---|---|---|---|---|---|---|

${\omega}_{m}^{*}$ | MSE${}_{\alpha}$ | MSE${}_{\beta}$ | MSE${}_{x}$ | MSE${}_{y}$ | THD${}_{\alpha}$ | THD${}_{\beta}$ |

500 | 0.065 | 0.064 | 0.174 | 0.172 | 5.73 | 5.46 |

1000 | 0.076 | 0.075 | 0.211 | 0.203 | 5.43 | 5.34 |

1500 | 0.110 | 0.110 | 0.219 | 0.216 | 6.46 | 6.38 |

**Table 3.**Experimental performance test of stator currents ($\alpha $-$\beta $), (x-y), MSE (A), THD (%) between classic MPC and the PFSCCS at different rotor speeds (rpm).

${\mathit{f}}_{\mathit{s}}$ = 8 kHz for Classic MPC | ||||||

${\omega}_{m}^{*}$ | MSE${}_{\alpha}$ | MSE${}_{\beta}$ | MSE${}_{x}$ | MSE${}_{y}$ | THD${}_{\alpha}$ | THD${}_{\beta}$ |

500 | 0.140 | 0.130 | 0.821 | 0.822 | 8.30 | 8.40 |

1000 | 0.147 | 0.138 | 0.953 | 0.934 | 7.40 | 7.30 |

${\mathit{f}}_{\mathit{s}}$ = 16 kHz for Classic MPC | ||||||

${\omega}_{m}^{*}$ | MSE${}_{\alpha}$ | MSE${}_{\beta}$ | MSE${}_{x}$ | MSE${}_{y}$ | THD${}_{\alpha}$ | THD${}_{\beta}$ |

500 | 0.073 | 0.072 | 0.491 | 0.483 | 8.40 | 8.30 |

1000 | 0.084 | 0.082 | 0.538 | 0.534 | 7.50 | 7.40 |

${\mathit{f}}_{\mathit{s}}$ = 8 kHz for PFSCCS | ||||||

${\omega}_{m}^{*}$ | MSE${}_{\alpha}$ | MSE${}_{\beta}$ | MSE${}_{x}$ | MSE${}_{y}$ | THD${}_{\alpha}$ | THD${}_{\beta}$ |

500 | 0.042 | 0.045 | 0.135 | 0.130 | 4.89 | 5.08 |

1000 | 0.069 | 0.068 | 0.197 | 0.204 | 4.69 | 4.78 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gonzalez, O.; Ayala, M.; Doval-Gandoy, J.; Rodas, J.; Gregor, R.; Rivera, M.
Predictive-Fixed Switching Current Control Strategy Applied to Six-Phase Induction Machine. *Energies* **2019**, *12*, 2294.
https://doi.org/10.3390/en12122294

**AMA Style**

Gonzalez O, Ayala M, Doval-Gandoy J, Rodas J, Gregor R, Rivera M.
Predictive-Fixed Switching Current Control Strategy Applied to Six-Phase Induction Machine. *Energies*. 2019; 12(12):2294.
https://doi.org/10.3390/en12122294

**Chicago/Turabian Style**

Gonzalez, Osvaldo, Magno Ayala, Jesus Doval-Gandoy, Jorge Rodas, Raul Gregor, and Marco Rivera.
2019. "Predictive-Fixed Switching Current Control Strategy Applied to Six-Phase Induction Machine" *Energies* 12, no. 12: 2294.
https://doi.org/10.3390/en12122294