# Stator Faults Detection in Asymmetrical Six-Phase Induction Motor Drives with Single and Dual Isolated Neutral Point, Adopting a Model Predictive Controller

^{*}

## Abstract

**:**

## 1. Introduction

^{n}(n being the number of phases) [8]; reduction of current harmonic distortion [9]; the rotor quantities are not measured and act as a disturbance in the predictive model [10]; the drive performance can be highly affected by not using exact system parameters [11]; parameter identification [12], fault detection and post-fault operation. The MPC takes into account a restricted number of switching states given by the power converters, where the mathematical model is used to predict the future behavior of the controlled variables [13]. The best switching state is then selected as the one to use in the subsequent sampling time, since it has the minimum error in the established cost function [7].

## 2. Asymmetrical Six-Phase Induction Motor Drives with Single and Dual Isolated Neutral Points

## 3. Model Predictive Control

## 4. The Proposed ITSC Detection Method

- ➢
**Phase 1:**The proposed indication is retrieved in real-time using fundamental measurements of stator voltages and currents, as seen in Figure 7. Then, for each voltage signal, the amplitudes and phase angles of the fundamental harmonic are estimated and tracked using the STLSP method. The positive and zero sequences will then be computed using the Fortescue transform to build the ZVF. The suggested indications are calculated as a ratio of magnitudes after getting the symmetrical components of the three-phase system [31,34].

- ➢
**Phase 2:**Let ${V}_{{a}_{1}{b}_{1}{c}_{1}{a}_{2}{b}_{2}{c}_{2}}$ be a set of balanced line-to-neutral stator voltages. For a healthy ASPIM,${V}_{{a}_{1}{b}_{1}{c}_{1}{a}_{2}{b}_{2}{c}_{2}}$ can be expressed as [39,40]:$$\{\begin{array}{l}{v}_{{a}_{1}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t\right)\\ {v}_{{b}_{1}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t-\raisebox{1ex}{$2\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)\hspace{0.17em}\\ {v}_{{c}_{1}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t-\raisebox{1ex}{$4\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)\end{array}\hspace{1em}\hspace{1em}\{\begin{array}{l}{v}_{{a}_{2}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t-\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)\\ {v}_{{b}_{2}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t-\raisebox{1ex}{$5\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.\right)\hspace{0.17em}\\ {v}_{{c}_{2}}\left(t\right)={V}_{m}\mathrm{sin}\left({\omega}_{s}t+\raisebox{1ex}{$3\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\end{array}$$

_{1}B

_{1}C

_{1}) and second three-phase set (A

_{2}B

_{2}C

_{2}) [41]:

- ➢

## 5. Experimental Validation

#### 5.1. Robustness of ZVF to Load and Speed Variations

#### 5.2. Robustness of ZVF to Different Stator topologies (Single and Dual Isolated Neutral Points)

_{A1B1C1}and ZVF

_{A2B2C2}). This curve offers a solid physical interpretation of the ITSC defect, as is evident. In reality, the ZVF evolution displays steady values with tiny amplitudes when the motor is operating in the healthy mode (verified due to the motor inherent asymmetries). The indication goes up to significantly higher values after a minor ITSC defect is added, which is in excellent accordance with the prior mathematical evidence. In fact, Figure 14 shows that ZVF

_{A1B1C1}increases noticeably and quickly (less than 0.2 s), from 0.005 p.u. to 0.027 p.u., or a 440% increase. In addition, Figure 14 shows that ZVF

_{A2B2C2}almost did not change. The qualitative (Figure 13) and quantitative (Table 2) results unequivocally show that when an ITSC fault occurs, the suggested fault indicator changes in a predictable and significant way. This is highly helpful for identifying low severity stator defects, which could go unnoticed by the majority of cutting-edge techniques.

#### 5.3. Robustness of ZVF to Various ITSCF Severities

## 6. Conclusions

- ✓
- Online implementation.
- ✓
- Reliability with load torque/speed variations.
- ✓
- Detection of transients available.
- ✓
- Fault localization.
- ✓
- Validated via experiment.
- ✓
- Not affected by similar faults and conditions (e.g., USV condition).
- ✓
- Applicable to both open- and closed-loop systems.
- ✓
- High resolution with a very small number of samples (N = 50).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Asymmetrical six-phase stator windings with (

**a**) single and (

**b**) dual isolated neutral points.

**Figure 4.**MPC scheme for an ASPIM: (

**a**) single isolated neutral configuration; (

**b**) dual isolated neutral configuration.

**Figure 5.**Demonstration of the ITSC fault related to 1NP on the six-phase inverter-fed and ASPIM stator windings.

**Figure 6.**Demonstration of the ITSC fault related to 2NP on the six-phase inverter-fed and ASPIM stator windings.

**Figure 7.**Illustration of the suggested technique’s online process [41].

**Figure 8.**Experimental setup. (

**a**) Voltage source inverters; (

**b**) DAQ system; (

**c**) Implementation of the fault detection algorithm in LabVIEW; (

**d**) ASPIM.

**Figure 10.**ASPIM under torque variation from 1.5 to 10.6 Nm in the healthy condition: ((

**a**) plots) ASPIM at 1.5 Nm with transient fault condition at 2 s, ((

**b**) plots) ASPIM in a speed transition from 1500 to 1200 rpm under the healthy condition, and ((

**c**) plots) ASPIM in a speed transition from 1500 to 1200 rpm under a faulty condition ((

**d**) plots). From top to bottom: (I) ${a}_{1},{b}_{1},{c}_{1},{a}_{2},{b}_{2},{c}_{2}$ phase currents, (II) motor speed.

**Figure 11.**ZVF indicator and estimated impedances, assessed for healthy state and in the presence of load transient conditions. (

**a**) ZVF; (

**b**) Z

_{A1}; (

**c**) Z

_{B1}; (

**d**) Z

_{C1}.

**Figure 12.**ZVF indicator and estimated impedances with different values of rotation speed. (

**a**) ZVF; (

**b**) Z

_{A1}; (

**c**) Z

_{B1}; (

**d**) Z

_{C1}.

**Figure 13.**ZVF indicator and estimated impedances, assessed for healthy state and in the presence of 21 shorted turns in phase a

_{1}. (

**a**) ZVF (V

_{A1,B1,C1}and V

_{A2,B2,C2}); (

**b**) Z

_{A1}; (

**c**) Z

_{B1}; (

**d**) Z

_{C1}.

**Figure 14.**ZVF indicator and estimated impedances, assessed for the healthy state and in the presence of 21 shorted turns, phase a1, for the two topologies (1NP and 2NP). (

**a**) ZVF; (

**b**) Z

_{A1}; (

**c**) Z

_{B1}; (

**d**) Z

_{C1}.

Parameters | Values |
---|---|

Power ($\mathrm{k}\mathrm{W}$) | 7.5 |

DC-link Voltage ($\mathrm{V}$) | 350 |

I_{peak} ($\mathrm{A}$) | 8.35 |

${n}_{m}\left(\mathrm{r}/\mathrm{m}\mathrm{i}\mathrm{n}\right)$ | 1500 |

${R}_{s}(\Omega )$ | 1.03 |

${R}_{r}(\Omega )$ | 0.8208 |

${L}_{m}\left(\mathrm{m}\mathrm{H}\right)$ | 0.199 |

${L}_{ls}\left(\mathrm{m}\mathrm{H}\right)$ | 0.0059 |

${L}_{lr}\left(\mathrm{m}\mathrm{H}\right)$ | 0.0059 |

Itsc Indicators | Healthy State | 21 Turns | Variation (%) |
---|---|---|---|

ZVF_{A1B1C1} | 0.005 | 0.027 | 440% |

ZVF_{A2B2C2} | 0.005 | 0.005 | 0% |

Faulty | Topology | Values | Variation (%) |
---|---|---|---|

21 TURNS | 1 NP | 0.017 | 240% |

2 NP | 0.027 | 440% |

Healthy State | Faulty State | Values | Variation (%) |
---|---|---|---|

0.00509 | 06 turns | 0.008 | 60% |

18 turns | 0.021 | 320% | |

24 turns | 0.034 | 580% |

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**MDPI and ACS Style**

Laadjal, K.; Serra, J.; Cardoso, A.J.M.
Stator Faults Detection in Asymmetrical Six-Phase Induction Motor Drives with Single and Dual Isolated Neutral Point, Adopting a Model Predictive Controller. *Machines* **2023**, *11*, 132.
https://doi.org/10.3390/machines11020132

**AMA Style**

Laadjal K, Serra J, Cardoso AJM.
Stator Faults Detection in Asymmetrical Six-Phase Induction Motor Drives with Single and Dual Isolated Neutral Point, Adopting a Model Predictive Controller. *Machines*. 2023; 11(2):132.
https://doi.org/10.3390/machines11020132

**Chicago/Turabian Style**

Laadjal, Khaled, João Serra, and Antonio J. Marques Cardoso.
2023. "Stator Faults Detection in Asymmetrical Six-Phase Induction Motor Drives with Single and Dual Isolated Neutral Point, Adopting a Model Predictive Controller" *Machines* 11, no. 2: 132.
https://doi.org/10.3390/machines11020132