# Condition Monitoring Accuracy in Inverter-Driven Permanent Magnet Synchronous Machines Based on Motor Voltage Signature Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. PMSM Faults and MVSA Approach

#### 2.2. PMSM Drives

#### 2.2.1. Field Oriented Control

_{d}and i

_{q}) of the rotor flux linkage frame are regulated separately using a proportional–integral (PI) controllers in FOC so that the output torque is regulated indirectly. Hence, FOC is also called indirect torque control. Figure 1 depicts the implementation of FOC-driven PMSM, where an encoder is needed to estimate the rotor position (${\theta}_{r}$) required for current vector decoupling. The widely applied modulation technique to control the inverter switching scheme in FOC is the Space Vector Pulse Width Modulation (SVPWM) due to its high utilization of the DC link and low harmonic distortion [33]. The principle behind SVPWM is to synthesize a reference space voltage vector using timely applied active and zero voltage vectors at a fixed switching frequency.

#### 2.2.2. Direct Torque Control

#### 2.3. Supervised Classification

## 3. Finite Element Analysis Simulations

#### 3.1. Healthy Machine Modeling and Control

#### 3.2. Turn-to-Turn Short Circuit Fault Implementation

#### 3.3. High Resistance Contact Fault Implementation

#### 3.4. Static Eccentricity Fault Implementation

#### 3.5. Local Demagnetization Fault Implementation

## 4. Numerical Results

#### 4.1. Analysis in FOC-Driven PMSM

#### 4.2. Analysis in DTC-Driven PMSM

## 5. Diagnosis Approach

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DTC | Direct Torque Control |

FEM | Finite Element Model |

FFT | Fast Fourier Transform |

FOC | Field Oriented Control |

HRC | High Resistance Contact |

k-NN | K-Nearest Neighbor |

LDA | Linear Discriminate Analysis |

MCC | Motor Control Center |

MTPA | Maximum Torque Per Amperes |

MVSA/MCSA | Machine Voltage or Current Signature Analysis |

NdFeB | Neodymium-Iron-Boron Magnet |

NVH | Noise, Vibration, and Harshness |

PMSM | Permanent Magnet Synchronous Machine |

SNR | Signal-to-Noise Ratio |

STFT | Short Time Fourier transform |

SVM | Support Vector Machines |

SVPWM | Space Vector Pulse Width Modulation |

TTSC | Turn-to-Turn Short Circuit |

VFD | Variable Frequency Drives |

ZSVC | Zero-Sequence Voltage Component |

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**Figure 3.**The electromagnetic simulation of studied PMSM machine: (

**a**) FEM of the studied machine and (

**b**) Mesh of the machine model.

**Figure 10.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under TTSC fault in FOC drive.

**Figure 11.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under HRC fault in FOC drive.

**Figure 12.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under eccentricity fault in FOC drive.

**Figure 13.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under demagnetization fault in FOC drive.

**Figure 15.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under TTSC fault in DTC drive.

**Figure 16.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under HRC fault in DTC drive.

**Figure 17.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under eccentricity fault in DTC drive.

**Figure 18.**Variations in the harmonic content of stator voltage spectrum for healthy and faulty machine under demagnetization fault in DTC drive.

**Figure 20.**Confusion matrix of LDA classifier for fault diagnosis for: (

**a**) FOC drives and (

**b**) DTC drives.

Machine Specification | Symbol | Value | Machine Specification | Symbol | Value |
---|---|---|---|---|---|

Pole pairs | ${P}_{n}$ | 5 | d-axis inductance | ${L}_{d}$ | 31.3 mH |

Slots | Q | 12 | q-axis inductance | ${L}_{q}$ | 62.4 mH |

Turns per slot | ${N}_{s}$ | 150 | Mutual inductance | ${M}_{s}$ | ≈0 H |

Air gap length | g | 1 mm | Rated phase current | ${I}_{rms}$ | 18 A |

Residual flux density | ${B}_{r}$ | 1.2 T | Rated line voltage | ${V}_{rms}$ | 480 V |

Magnet flux linkage | ${\lambda}_{PM}$ | 287 mWb | Rated torque | ${T}_{e}$ | 65 N·m |

Phase resistance | ${r}_{s}$ | 1.5 $\mathsf{\Omega}$ | Rated speed | ${n}_{m}$ | 800 rpm |

Case | ${\mathit{N}}_{\mathit{f}}$ | ${\mathit{R}}_{\mathit{f}}$ |
---|---|---|

SC1 | 15 | 0.5 $\mathsf{\Omega}$ |

SC2 | 15 | 0.25 $\mathsf{\Omega}$ |

SC3 | 30 | 0.5 $\mathsf{\Omega}$ |

SC4 | 30 | 0.25 $\mathsf{\Omega}$ |

Case | $\frac{\mathbf{\Delta}{\mathit{r}}_{\mathit{s}}}{{\mathit{r}}_{\mathit{s}}}\%$ |
---|---|

HRC1 | 50% |

HRC2 | 100% |

HRC3 | 150% |

Case | $\frac{\mathit{\u03f5}}{\mathit{g}}\%$ |
---|---|

ECC1 | 10% |

ECC2 | 40% |

ECC3 | 60% |

ECC4 | 80% |

Case | Severity |
---|---|

Demag1 | One Magnet |

Demag2 | Two Adjacent Magnets |

Demag3 | Three Nonadjacent Magnets |

Case | FOC | DTC | ||||
---|---|---|---|---|---|---|

LDA | k-NN | SVM | LDA | k-NN | SVM | |

Healthy | 100% | 100% | 97.5% | 0% | 0% | 50% |

TTSC | 100% | 100% | 100% | 80% | 70% | 75% |

HRC | 70% | 100% | 80% | 40% | 40% | 67.5% |

Eccentricity | 70% | 100% | 97.5% | 30% | 50% | 57.5% |

Demagnetization | 80% | 70% | 87.5% | 70% | 40% | 80% |

Overall | 84% | 94% | 92.5% | 44% | 42% | 66% |

**Table 7.**The accuracy of fault severity estimation using MVSA approach for FOC- and DTC-driven PMSM.

Fault Type | FOC | DTC | ||
---|---|---|---|---|

LDA | SVM | LDA | SVM | |

TTSC | 85% | 97.5% | 42.5% | 64.167% |

SC1 | 100% | 100% | 50% | 63.333% |

SC2 | 100% | 100% | 40% | 66.667% |

SC3 | 80% | 93.333% | 30% | 66.667% |

SC4 | 60% | 96.667% | 50% | 60% |

HRC | 96.667% | 86.667% | 30% | 38.333% |

HRC1 | 100% | 100% | 30% | 35% |

HRC2 | 90% | 80% | 20% | 30% |

HRC3 | 100% | 100% | 40% | 50% |

Eccentricity | 100% | 100% | 30% | 62.5% |

ECC1 | 100% | 100% | 20% | 53.333% |

ECC2 | 100% | 100% | 20% | 53.333% |

ECC3 | 100% | 100% | 40% | 70% |

ECC4 | 100% | 100% | 40% | 73.333% |

Demagnetization | 86.667% | 71.667% | 46.667% | 56.667% |

Demag1 | 100% | 100% | 80% | 75% |

Demag2 | 90% | 50% | 20% | 55% |

Demag3 | 70% | 60% | 40% | 40% |

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## Share and Cite

**MDPI and ACS Style**

Allafi, I.M.; Foster, S.N.
Condition Monitoring Accuracy in Inverter-Driven Permanent Magnet Synchronous Machines Based on Motor Voltage Signature Analysis. *Energies* **2023**, *16*, 1477.
https://doi.org/10.3390/en16031477

**AMA Style**

Allafi IM, Foster SN.
Condition Monitoring Accuracy in Inverter-Driven Permanent Magnet Synchronous Machines Based on Motor Voltage Signature Analysis. *Energies*. 2023; 16(3):1477.
https://doi.org/10.3390/en16031477

**Chicago/Turabian Style**

Allafi, Ibrahim M., and Shanelle N. Foster.
2023. "Condition Monitoring Accuracy in Inverter-Driven Permanent Magnet Synchronous Machines Based on Motor Voltage Signature Analysis" *Energies* 16, no. 3: 1477.
https://doi.org/10.3390/en16031477