# Stray Flux Multi-Sensor for Stator Fault Detection in Synchronous Machines

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Magnetic Field Measurement

#### 2.1. Principle of the Methodology

#### 2.2. Sensor and Acquisition Characterization

^{2}area. It was easy to install, the measurement was simple, and it did not require any associated electronics, except for amplifying the induced electromotive force signal if necessary (Figure 3).

## 3. Diagnostic Method

- If r
_{i}is close to 0, there is no linear relationship between $me{s}_{1,i}\left(k\right)$ and $me{s}_{2,i}\left(k\right)$ when k varies. Therefore, the amplitudes of the harmonics vary in a different way, which indicates the presence of an inter-turn short-circuit fault in the stator. - If r
_{i}is close to −1, $me{s}_{1,i}\left(k\right)$ and $me{s}_{2,i}\left(k\right)$ vary strictly in opposite direction and linearly in case of load variation. In this case, there is also a stator fault in the machine. - On the contrary, when r
_{i}is close to 1, $me{s}_{1,i}\left(k\right)$ and $me{s}_{2,i}\left(k\right)$ vary together linearly according to load variations. This means that the external magnetic field around the machine keeps a good symmetry. The machine may be in good condition, but this could be confirmed for other positions because the position of the sensors from the faulty turn has also an influence on the Pearson coefficient [20].

_{r,i}as information regarding the presence of a fault provided by each Pearson coefficient r

_{i}obtained at position i. The evolution of the mass function according to the value of the coefficient r

_{i}is given as an example in Figure 6. Considering $N$ number of possible positions of the sensors, $N$ mass functions tied to N information about the presence of a fault on the machine can be obtained. Then, this information can be combined using the following relationships:

_{r}

_{,1}and m

_{r}

_{,2}issued from r

_{1}and r

_{2}, respectively; this equation can be written as follows:

_{1}, r

_{2},…, r

_{N}” are calculated for each position. In the third step, the fusion of the Pearson coefficients is performed, and finally, a decision is obtained by converting the mass function into a probability.

## 4. Experimental Results

#### 4.1. Presentation of the Test Bench

#### 4.2. Measurement Analysis

- −
- Without short circuit;
- −
- Short circuits between 1–2, 2–3, and 1–4, for the three phases;

- −
- Isc = 3A for short circuits on coil ‘1–2’, one turn short circuit;
- −
- Isc = 9A for short circuits on coil ‘2–3’, three turns in short circuit;
- −
- Isc = 15A for short circuits on coil ‘1–4’, five turns in short circuit.

- (1)
- Example of calculation of belief functions, fusion, and probability of fault

- (2)
- Results obtained for global tests

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Signals delivered by two coil sensors S1 and S2 placed at 180° around a 10 kW synchronous machine: (

**a**) electromagnetic force measured for healthy machine: (

**b**) electromagnetic force measured for the faulty machine.

**Figure 6.**Evolution of the mass function as a function of the value of the correlation coefficient r

_{i}.

**Figure 7.**Representation of the proposer procedure method for transforming the fem signal measured by the sensors S1 and S2 in probability information about presence of a short-circuit fault in the machine.

**Figure 8.**Experimental test bench with 10 kW synchronous machine and DC machine used as drive motor.

P1 | P2 | P3 | ||||
---|---|---|---|---|---|---|

loads | S1 (μV) | S4(μV) | S2(μV) | S5 (μV) | S3 (μV) | S6 (μV) |

no load | 5.06 | 1.52 | 5.04 | 3.08 | 4.14 | 2.93 |

load 1 | 7.06 | 3.18 | 6.89 | 5.10 | 5.80 | 4.77 |

load 2 | 8.39 | 3.56 | 8.11 | 5.95 | 6.85 | 4.84 |

load 3 | 9.17 | 3.61 | 8.97 | 6.48 | 7.35 | 5.08 |

load 4 | 9.69 | 4.14 | 9.44 | 7.18 | 7.96 | 5.30 |

P1 | P2 | P3 | ||||
---|---|---|---|---|---|---|

loads | S1 (μV) | S4 (μV) | S2 (μV) | S5 (μV) | S3 (μV) | S6 (μV) |

no load | 9.52 | 13.80 | 4.77 | 5.87 | 6.75 | 4.18 |

load 1 | 9.32 | 16.09 | 5.55 | 6.00 | 6.11 | 5.08 |

load 2 | 11.45 | 15.75 | 6.84 | 8.50 | 7.98 | 5.49 |

load 3 | 12.88 | 16.04 | 7.63 | 9.65 | 9.31 | 5.16 |

load 4 | 12.97 | 16.11 | 7.17 | 9.45 | 9.38 | 4.54 |

**Table 3.**Correlation coefficients obtained from three positions in the faulty machine (healthy only for one case).

P1 | P2 | P3 | |
---|---|---|---|

No fault | 0.964 | 0.993 | 0.937 |

A–3A | 0.542 | 0.973 | 0.129 |

B–3A | 0.802 | 0.846 | 0.513 |

C–3A | −0.692 | 0.960 | 0.821 |

A–6A | 0.984 | 0.992 | −0.032 |

A–15A | 0.989 | 0.952 | 0.960 |

B–15A | 0.986 | 0.948 | −0.649 |

C–15A | 0.996 | 0.972 | 0.015 |

A–18A | 0.886 | 0.997 | 0.988 |

**Table 4.**Mass functions ${m}_{{r}_{i}}$ obtained from the correlation coefficient presented in Table 3.

In Case of the Faulty Machine B–3A | ||
---|---|---|

Position P1 (${r}_{1}=0.802$) | Position P2 (${r}_{2}=0.846$) | Position P3 (${r}_{3}=0.513$) |

${m}_{{r}_{1}}\left(\left\{y\right\}\right)=0.95$ | ${m}_{{r}_{2}}\left(\left\{y\right\}\right)=0.95$ | ${m}_{{r}_{3}}\left(\left\{y\right\}\right)=0.95$ |

${m}_{{r}_{1}}\left(\left\{n\right\}\right)=0$ | ${m}_{{r}_{2}}\left(\left\{n\right\}\right)=0$ | ${m}_{{r}_{3}}\left(\left\{n\right\}\right)=0$ |

${m}_{{r}_{1}}\left(\mathsf{\Omega}\right)=0.05$ | ${m}_{{r}_{2}}\left(\mathsf{\Omega}\right)=0.05$ | ${m}_{{r}_{3}}\left(\mathsf{\Omega}\right)=0.05$ |

${m}_{{r}_{1}}\left(\varnothing \right)=0$ | ${m}_{{r}_{2}}\left(\varnothing \right)=0$ | ${m}_{{r}_{3}}\left(\varnothing \right)=0$ |

**Table 5.**Numerical application example of a combination of the mass functions ${m}_{{r}_{i}}$ (faulty machine B–3A).

Step 1 | |||

${\mathit{m}}_{{\mathit{r}}_{\mathbf{2}}}({\mathit{r}}_{\mathbf{2}}\mathbf{=}\mathbf{0.846}$) | |||

${\mathit{m}}_{{\mathit{r}}_{\mathbf{12}}}\left(\mathit{A}\right)$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{2}}}\left(\left\{\mathit{y}\right\}\right)\mathbf{=}\mathbf{0.95}$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{2}}}\left(\mathbf{\Omega}\right)\mathbf{=}\mathbf{0.05}$ | |

${\mathit{m}}_{{\mathit{r}}_{\mathbf{1}}}$ $({\mathit{r}}_{\mathbf{1}}\mathbf{=}\mathbf{0.802})$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{1}}}\left(\left\{\mathit{y}\right\}\right)\mathbf{=}\mathbf{0.95}$ | $y\cap y=y$ 0.95 × 0.95 = 0.9025 | $y\cap \mathsf{\Omega}=y$ 0.95 × 0.05 = 0.0475 |

${\mathit{m}}_{{\mathit{r}}_{\mathbf{1}}}\left(\Omega \right)\mathbf{=}\mathbf{0.05}$ | $\mathsf{\Omega}\cap y=y$ 0.05 × 0.95 = 0.0475 | $\mathsf{\Omega}\cap \mathsf{\Omega}=\mathsf{\Omega}$ 0.05 × 0.05 = 0.0025 | |

${m}_{{r}_{12}}\left(\left\{y\right\}\right)=0.9975$ , ${m}_{{r}_{12}}\left(\mathsf{\Omega}\right)=0.0025$ | |||

Step 2 | |||

${\mathit{m}}_{{\mathit{r}}_{\mathbf{3}}}({\mathit{r}}_{\mathbf{3}}\mathbf{=}\mathbf{0.513})$ | |||

${\mathit{m}}_{\mathit{r}}\left(\mathit{A}\right)$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{3}}}\left(\left\{\mathit{y}\right\}\right)\mathbf{=}\mathbf{0.95}$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{3}}}\left(\Omega \right)\mathbf{=}\mathbf{0.05}$ | |

${\mathit{m}}_{{\mathit{r}}_{\mathbf{12}}}$ | ${\mathit{m}}_{{\mathit{r}}_{\mathbf{12}}}\left(\left\{\mathit{y}\right\}\right)\mathbf{=}\mathbf{0.9975}$ | $y\cap y=y$ 0.9975 × 0.95 = 0.9476 | $y\cap \mathsf{\Omega}=y$ 0.9975 × 0.05 = 0.0499 |

${\mathit{m}}_{{\mathit{r}}_{\mathbf{12}}}\left(\Omega \right)\mathbf{=}\mathbf{0.0025}$ | $\mathsf{\Omega}\cap y=y$ 0.0025 × 0.95 = 0.0024 | $\mathsf{\Omega}\cap \mathsf{\Omega}=\mathsf{\Omega}$ 0.0025 × 0.05 = 0.0001 | |

${m}_{r}\left(\left\{y\right\}\right)=0.9999$ , ${m}_{r}\left(\mathsf{\Omega}\right)=0.0001$ |

P1 | P2 | P3 | Fusion of the Three Positions |
---|---|---|---|

55.56% (4) | 22.22% (7) | 77.78% (2) | 88.89% (1) |

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**MDPI and ACS Style**

Irhoumah, M.; Pusca, R.; Lefèvre, E.; Mercier, D.; Romary, R.
Stray Flux Multi-Sensor for Stator Fault Detection in Synchronous Machines. *Electronics* **2021**, *10*, 2313.
https://doi.org/10.3390/electronics10182313

**AMA Style**

Irhoumah M, Pusca R, Lefèvre E, Mercier D, Romary R.
Stray Flux Multi-Sensor for Stator Fault Detection in Synchronous Machines. *Electronics*. 2021; 10(18):2313.
https://doi.org/10.3390/electronics10182313

**Chicago/Turabian Style**

Irhoumah, Miftah, Remus Pusca, Eric Lefèvre, David Mercier, and Raphael Romary.
2021. "Stray Flux Multi-Sensor for Stator Fault Detection in Synchronous Machines" *Electronics* 10, no. 18: 2313.
https://doi.org/10.3390/electronics10182313