# A Stator Fault Diagnosis Method Based on the Offline Motor Parameter Measurement for PMSM

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{f}is added to the fault part, and thus the fault model is built to obtain the resistance and inductance under fault. Section 4 compares the resistance and inductance of the health and fault motor, and then the fault indicators are introduced to detect and locate the stator fault. In Section 5, the proposed fault diagnosis methods are validated through test results.

## 2. Line-to-Line Resistance and Inductance Analysis of a Healthy Motor

#### 2.1. Line-to-Line Resistance Analysis

_{A}, R

_{B}and R

_{C}are the stator resistances of phases A, B and C, respectively. For simplicity, it gives the assumption that the motor is symmetrical for a healthy PMSM, i.e., R

_{A}= R

_{B}= R

_{C}= R

_{s}. Hence the line-to-line resistance between any two phases of the motor can be calculated as Equation (1) according to the equivalent circuit.

_{AB}, R

_{CA}, and R

_{BC}are the line-to-line resistances of any two phases of the stator.

#### 2.2. Line-to-Line Inductance Analysis

_{AB}is the flux between A and B, i

_{AB}is the current that flows through phases A and B, i

_{A}and i

_{B}are the current of phases A and B, respectively, and L

_{AA}, L

_{BB}and L

_{CC}are the self-inductances of phases A, B and C, respectively. Here, the AC frequency is high (>400 Hz) to ensure ωL >> R. Hence the stator resistances can be ignored relative to the inductance.

_{A}and ψ

_{B}are the flux of phase A and B respectively, L

_{AB}is the mutual-inductance between phases A and B. Then, the ψ

_{AB}can be derived as

_{d}and L

_{q}are the d-axis and q-axis inductance in the PMSM), and θ is the rotor location angle.

## 3. Line-to-Line Resistance and Inductance Analysis for Stator Fault

#### 3.1. Line-to-Line Resistance Analysis

_{f}is added to the fault part of phase A. Accordingly, the DC equivalent circuit of the motor is shown in Figure 3, where R

_{f}represents an additional resistance between the shorted turns, η represents the fault severity and η = n

_{cc}/N

_{s}(n

_{cc}is the number of the shorted turns and N

_{s}is the total number of stator windings).

_{AB}and R

_{CA}in the stator fault motor are less than those in the healthy motor.

#### 3.2. Line-to-Line Inductance Analysis

_{d}≤ L

_{q}, and then it can be obtained that $({L}_{1}-2\sqrt{3}{L}_{2}/3)>0$. Therefore, when the stator fault occurs, the fault-phase-related inductance decreases compared to the healthy motor.

## 4. Detection and Evaluation for the Stator Fault

_{x}represents the new measured line-to-line resistance, which can be one of R

_{AB}, R

_{BC}and R

_{CA}; R

_{x}

_{0}represents corresponding initial line-to-line resistance.

_{1}, which is independent of the rotor position θ. For a stator fault motor, the sum of the inductances can be derived as:

^{R}, FI

^{∆R}, and FI

^{∆L}—and then the stator fault can be further detected and located through the evaluation of the fault indicators.

## 5. Experiment

#### 5.1. Tested PMSM with the Stator Fault Injection

#### 5.2. Test Results

_{AB}and R

_{CA}decrease with the increasing the number of the shorted turns, whereas R

_{BC}is almost unchanged. Similarly, as shown in Figure 7, when the number of the shortened turns increases, the line-to-line inductances ${L}_{\mathrm{A}\mathrm{B}}^{\mathrm{e}\mathrm{q}}$ and ${L}_{\mathrm{C}\mathrm{A}}^{\mathrm{e}\mathrm{q}}$ decrease, whereas ${L}_{\mathrm{B}\mathrm{C}}^{\mathrm{e}\mathrm{q}}$ is constant. Comparing Figure 6 and Figure 7, it can be seen that the fault inductances drop sharply relatively to the resistances. This phenomenon reflects that the stator fault has a greater influence on the inductance than resistance, which indicates that inductance is an excellent parameter to recognize the stator fault.

^{R}and FI

^{∆R}can be calculated through the measured data. These two fault indicators under different fault severities are performed, as the curves shown in Figure 8 and Figure 9. In Figure 8, the fault indicator FI

^{R}increases with the number of shorted turns from 0.182% to 2.565%. Figure 9 shows that the fault indicators FI

^{∆RAB}and FI

^{∆RBC}increase from 0% to 3.475%, whereas FI

^{∆RCA}is almost unchanged (nearly 0), which indicates that phases B and C are healthy and phase A has a stator fault. Therefore, the fault indicator FI

^{R}can determine whether the motor has a stator fault, and the FI

^{∆RAB}, FI

^{∆RBC}, and FI

^{∆RCA}can identify the fault phase.

^{∆L}can be calculated through Equation (19), and the calculation results are drawn as the curve shown in Figure 10, where FI

^{∆L}increases from 0% to 16.4%, which changes significantly compared to the resistance fault indicator FI

^{∆R}.

_{AB}, R

_{CA}and the inductances ${L}_{\mathrm{A}\mathrm{B}}^{\mathrm{e}\mathrm{q}}$, ${L}_{\mathrm{C}\mathrm{A}}^{\mathrm{e}\mathrm{q}}$ increase with the number of the shorted turns, whereas the R

_{BC}and ${L}_{\mathrm{B}\mathrm{C}}^{\mathrm{e}\mathrm{q}}$ are almost unchanged, which is in agreement with the proposed algorithm in this paper. Correspondingly, the resistance fault indicators FI

^{R}and FI

^{∆R}have different degrees of change, which can be adopted to detect the stator fault and locate the fault phase. Compared with the resistance fault indicator, the inductance fault indicator FI

^{∆L}increases obviously, which is valuable for stator fault diagnosis.

## 6. Conclusions

^{R}, FI

^{∆R}and FI

^{∆L}, are proposed to detect and locate the stator fault. The test results of a 400 W PMSM under different fault severities lead to the following conclusions:

- When a stator fault occurs, the line-to-line resistance and inductance related to the fault phase decrease, whereas the others are unchanged.
- The fault indicator FI
^{R}that represents the imbalance of the resistances increases with the number of shorted turns, which can be used to detect the stator fault. - The fault indicator FI
^{∆R}describes the rate of resistance change. When a stator fault occurs, the FI^{∆R}related to the fault phase increases, whereas the other is nearly 0, which can provide a powerful basis to detect and locate the stator fault. - The fault indicator FI
^{∆L}increases significantly when the motor has a stator fault, which is valuable for stator fault diagnosis.

^{R}, FI

^{∆R}, and FI

^{∆L}to their thresholds. Here, the stator fault has a great influence on the fault indicator FI

^{∆L}, so it can obtain an excellent fault diagnosis result by using the FI

^{∆L}. Compared to the online method, the offline method proposed in this paper has the advantage of easily implementation and high accuracy.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Equivalent circuit when a high frequency AC voltage is applied to phase A and B of a healthy motor.

**Figure 4.**AC equivalent circuit of the stator fault, where the fault occurs in phase A and i

_{f}is the current that flows through the fault part.

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

Rated power/(W) | 400 |

Rated voltage/(V) | 220 |

Rated current/(A) | 2.8 |

Rated speed/(rpm) | 3000 |

Rated torque/(N.m) | 1.27 |

Line-to-line resistance/(Ω) | 3.43 |

Line-to-line inductance/(mH) | 6.6 |

Inertia/(kg/m^{2} × 10^{−4}) | 0.32 |

The Number of Shorted Turns | Line-to-Line Resistance/(Ω) | Line-to-Line Inductance/(mH) | ||||
---|---|---|---|---|---|---|

R_{AB} | R_{BC} | R_{CA} | ${\mathit{L}}_{\mathbf{A}\mathbf{B}}^{\mathbf{e}\mathbf{q}}$ | ${\mathit{L}}_{\mathbf{B}\mathbf{C}}^{\mathbf{e}\mathbf{q}}$ | ${\mathit{L}}_{\mathbf{C}\mathbf{A}}^{\mathbf{e}\mathbf{q}}$ | |

health | 2.8345 | 2.8490 | 2.8480 | 7.4559 | 7.3719 | 7.3049 |

2 turns | 2.8310 | 2.8480 | 2.8440 | 6.5480 | 7.3425 | 6.6970 |

3 turns | 2.8260 | 2.8493 | 2.8400 | 6.0690 | 7.3200 | 6.4120 |

5 turns | 2.8170 | 2.8487 | 2.8260 | 5.7000 | 7.3067 | 6.1410 |

7 turns | 2.8020 | 2.8497 | 2.8120 | 5.5250 | 7.2980 | 6.0580 |

8 turns | 2.8000 | 2.8490 | 2.8100 | 5.4370 | 7.2940 | 6.0026 |

10 turns | 2.7760 | 2.8490 | 2.7890 | 5.3840 | 7.2919 | 5.9718 |

13 turns | 2.7580 | 2.8490 | 2.7645 | 5.3150 | 7.2890 | 5.9254 |

15 turns | 2.7360 | 2.8494 | 2.7490 | 5.2970 | 7.2880 | 5.9174 |

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**MDPI and ACS Style**

Tang, J.; Liang, C.; Wang, Y.; Lu, S.; Zhou, J.
A Stator Fault Diagnosis Method Based on the Offline Motor Parameter Measurement for PMSM. *World Electr. Veh. J.* **2021**, *12*, 248.
https://doi.org/10.3390/wevj12040248

**AMA Style**

Tang J, Liang C, Wang Y, Lu S, Zhou J.
A Stator Fault Diagnosis Method Based on the Offline Motor Parameter Measurement for PMSM. *World Electric Vehicle Journal*. 2021; 12(4):248.
https://doi.org/10.3390/wevj12040248

**Chicago/Turabian Style**

Tang, Jing, Chao Liang, Yuanhang Wang, Shuhan Lu, and Jian Zhou.
2021. "A Stator Fault Diagnosis Method Based on the Offline Motor Parameter Measurement for PMSM" *World Electric Vehicle Journal* 12, no. 4: 248.
https://doi.org/10.3390/wevj12040248