# Detection and Diagnosis of Stator and Rotor Electrical Faults for Three-Phase Induction Motor via Wavelet Energy Approach

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## Abstract

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## 1. Introduction

#### Literature Review and Motivation

- Development of a real-time fault detection algorithm for induction motors using wavelet packet transform;
- Use of Entropy Power Energy (EE) of high frequency subbands of the current signal to determine the condition of the induction motor and, moreover, to classify the type of the fault;
- Calculation of threshold values to differentiate different faults from EE energy signal;
- The real-time implementation and test of the algorithm on real equipment;
- Generalizing the algorithm by testing the algorithm on several induction motors of the same power rating with different parameters.

## 2. Wavelet Packet Transform and Wavelet Energy

## 3. Modeling of a 3-Phase Induction Motor with Electrical Faults

#### 3.1. Modelling the Healthy Condition

#### 3.2. Modeling the Faulty Condition

#### 3.2.1. Fault in the Stator of the Motor

- The localization parameter ($\mathsf{\theta}\mathrm{cc}$): This represents the angle between the new winding, which is generated by the fault, and the first phase winding (a). The value of this angle can be 0°, 120°, or 240° according to the three phases, called a, b, and c.
- The detection parameter (${\mathsf{\eta}}_{\mathrm{cc}}$) represents the percentage of inter-turn short circuit winding, where this ratio is obtained by dividing the number of inter-turn short circuit winding by the total number of the stator winding in one phase. The short circuit current under d-q axis frame can be represented as shown in the following equations [31]:

#### 3.2.2. Fault in Rotor Part

## 4. Simulink Model of the Proposed Technique and Real Time Data Collection

## 5. Proposed Fault Detection and Diagnosis Algorithm

#### Proposed Fault Detection Threshold

## 6. Proposed Fault Diagnosis Method—Threshold Values

## 7. Simulation Results for Detection, Diagnosis and Activating the Trip Signal

## 8. Experimental Results

- Induction motor: 1 hp, rated current 2 A, 3-phase 380 V;
- PC specifications: Core i5, RAM 4GB, hard SSD256GB, windows 7, and the proposed algorithm is implemented in MATLABE 2019B platform and when generating experimental results, no other programs are running on the PC;
- LABJACK UD-U3 is used to capture current samples from the power current lines of the induction motor.

## 9. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 16.**Entropy Energy (EE) value for different operation condition of an induction motor using da2 WPT subband coefficients.

**Figure 17.**Entropy power energy curve for (

**a**) WPT dd2− and (

**b**) ad2 subband’s coefficients, where the regions representing different types of faults have been annotated on the curves.

**Figure 18.**Stator current and trip signals for no-load to full load condition within the diagnosis window.

**Figure 19.**Stator current and trip signals for 10% inter-turn fault in phase-b (application of the proposed method when it uses its non-overlapping window frame algorithm).

**Figure 20.**Stator current and trip signals for 25% inter-turn fault in phase-b and 10% inter-turn fault in phase-a (application of the proposed method when it uses its non-overlapping window frame algorithm).

**Figure 21.**Stator current and trip signals for 10% inter-turn fault in phase-c (application of the proposed method when it uses its moving window frame algorithm).

**Figure 22.**Stator current and trip signals of a broken one bar fault (application of the proposed method when it uses its moving window frame algorithm).

**Figure 23.**The implemented system (

**a**) Block diagram, and (

**b**) practical implementation of the protection system.

**Figure 26.**Entropy power energy value of WPT subband da2’s coefficients for different motor fault conditions, using captured experimental data.

**Figure 27.**Stator currents’ signals and trip signal waveforms for healthy starting condition of an inductive motor.

**Figure 28.**Stator current signals and the trip signal waveforms for 50% stator fault in phase (c) on a no-load condition.

**Figure 29.**Stator current signals and trip signal waveforms for phase (c) to ground fault with load condition.

Wavelet Packet Transform (Used in the Proposed Method) | Stockwell Transform | Hilbert Transform |
---|---|---|

The wavelet packet transform generates a time and frequency representation of the signal at different scales. In this paper, the entropy power Energy of detailed WPT subbands of the induction motor is used to detect and classify the induction motor’s faults. Accurate fault detection in less than a second. | It splits the input signal into a number of sections. Each resulting section is first smoothed using a Gaussian filter. It then determines the frequency components of each section using Fourier transform. It provides a good time-frequency representation of the signal, but there is always a trade-off between its time and frequency accuracy. Moreover, its performance is limited to the size of the window. Authors reported good performance in terms of accuracy in the detection of the faults in a certain section of the motor, e.g., rotors. | It provides a representation of the signal in the same domain (frequency domain). Therefore, it does not provide information about the time of the fault occurrence. However, the focus of the presented research in this paper is on the speed and accuracy of fault detection and classification. |

Authors | Used Techniques | Key Features |
---|---|---|

V.Climente-Alarcon et al. [15] | It uses Wigner–Ville distribution techniques to study rotor asymmetry and mixed eccentricities. | It splits the stator current into several time-frequency components. |

Syed Kamruddin Ahamed et al. [16] | It uses DWT, Root Mean Square (RMS), and Power Density Entropy (PDE) index. | It analyses the window current signal in the steady-state operation of the motor. It determines the PDE of the high frequency wavelet of the motor current to detect faults in the stator winding of the induction motor. |

R. Hammo [17] | It uses the Support Vector Machine (SVM), which is a learning-based method. | Results show that the application of SVM is alleviating some of the limitations of the Artificial Neural Network (ANN) based methods. Moreover, the SVM based method is more effective than ANN based method in detecting faults in terms of accuracy, where SVM uses the Radial Bases Function kernel. |

J. Lu, P. Wang et al. [18] | It uses the MUltiple SIgnal Classification (MUSIC) technique and least-squares magnitude estimation to detect the frequency and amplitude of the faults. | Because the research of step travel produces lower efficiency, they proposed a method to improve MUSIC method using Niche Bare-bones Practical Swarm Optimization (NBPSO), which was used to detect broken bars in an induction motor. |

A. Mejia-Barron et al. [19] | It uses both Shannon Entropy (SE) index and artificial intelligence fuzzy logic. | To diagnose faults in the stator of an induction motor, it applies brick-will band-pass filters at multiple levels on induction motor’s current signal and then calculates SE. |

M. Nemec et al. [21] | It uses the frequency components of inductor motor’s current signal to diagnose faults in the rotor of the motor. | The existence of certain frequency components in the current signal of the induction motor indicates the fault in the motor. This method was applied to two different models of induction motor in MATLAB platform. |

Proposed method | It uses wavelet packet transform and Shannon Entropy (SE) criteria | It uses performs 2 level WPT on induction motor current signal decomposes it into its wavelet subbands. It then determines EE of the fine WPT of the current as a feature to determine the status of the motor. If it was found faulty, it uses some empirically pre-determined thresholds to classify the fault. |

**Table 3.**Entropy Energy values for different operating conditions of the induction motor at its four WPT second level subbands.

Entropy | aa2 | ad2 | da2 | dd2 |
---|---|---|---|---|

Fault | ||||

Healthy no load | −5.08 × 10^{5} | 7.41 × 10^{−5} | 4.30 × 10^{−4} | 8.37 × 10^{−5} |

Healthy full load | −2.65 × 10^{6} | 2.78 × 10^{−4} | 1.30 × 10^{−3} | 2.85 × 10^{−4} |

No load to full load healthy | −1.52 × 10^{7} | 0.0014 | 7.06 × 10^{−4} | 9.30 × 10^{−4} |

10% fault phase-b | −2.13 × 10^{6} | −0.5372 | 0.1605 | −3.4479 |

15% fault phase-b | −2.39 × 10^{6} | −6.6746 | 0.2593 | −20.04 |

25% fault phase-c | −3.28 × 10^{6} | −1.36 × 10^{2} | 0.5235 | −3.14 × 10^{2} |

25% fault phase-b | −3.29 × 10^{6} | −48.5216 | 0.4773 | −121.5733 |

50% fault phase-b | −7.83 × 10^{6} | −446.9326 | 0.2243 | −1.02 × 10^{3} |

50% phase-b and 10% phase-a | −8.08 × 10^{6} | −448.9294 | 0.2169 | −1.02 × 10^{3} |

25% phase-b and 10% phase-a | −3.43 × 10^{6} | −48.5382 | 0.4742 | −121.5034 |

Loss phase-a | −1.48 × 10^{8} | −3.13 × 10^{3} | −7.15 | −6.64 × 10^{3} |

Phase-c to ground | −3.16 × 10^{7} | −3.04 × 10^{3} | −8.88 | −6.65 × 10^{3} |

Three-phase fault | −1.88 × 10^{7} | −17.2076 | 0.1901 | 0.5652 |

Line-a to line-b fault | −3.91 × 10^{7} | 0.5976 | −2.6355 | −78.3431 |

Line-a to line-b to ground fault | −1.55 × 10^{8} | −3.55 × 10^{4} | −1.63 × 10^{3} | −2.97 × 10^{4} |

rotor broken 1-bar fault | −2.07 × 10^{6} | 0.0025 | 0.0704 | 6.44 × 10^{−4} |

rotor broken 2-bars fault | −1.97 × 10^{6} | 3.08 × 10^{−4} | 0.068 | 2.69 × 10^{−4} |

**Table 4.**Entropy power energy threshold values for diagnoses of different types of faults in an induction motor.

Type of Fault | Entropy Power Threshold Value for WPT Subband | |
---|---|---|

ad2 | dd2 | |

Broken one bar | 0.0011 | 3.43 × 10^{−5} |

Broken two bars | 0.0019 | 7.11 × 10^{−5} |

Line-a to line-b fault | 0.7054 | 0.0764 |

Loss phase-a | 18.3 | 0.9424 |

10% inter turn fault phase-b | 21.9939 | 27.0078 |

25% ph. (b) and 10% ph. (a) inter turn fault | 31.7595 | 125.079 |

25% inter turn fault phase-b | 32.74 | 125.168 |

50% inter turn fault phase-b | 446.3932 | 1.02 × 10^{−3} |

25% ph. (b) and 10% ph. (a) inter turn fault | 446.611 | 1.02 × 10^{−3} |

**Table 5.**Entropy power energy values of all four second level WPT subbands’ coefficients for different practical conditions of the induction motor.

Motor Condition | WPT Subbands’ Entropy Power Energy | |||
---|---|---|---|---|

aa2 | ad2 | da2 | dd2 | |

No-load healthy | −189.674 | 0.1468 | 0.0831 | 0.0995 |

Loaded healthy | 781.5769 | 0.1725 | 0.0963 | 0.1224 |

No-load 25% fault (b) | −1.13 × 10^{3} | 2.0998 | 0.4176 | 0.9368 |

No-load 50% fault (c) | −2.56 × 10^{3} | 6.2222 | 3.1577 | 3.0059 |

No-load with loss ph. (b) | −437.3249 | 0.5828 | 0.1027 | 0.1329 |

Load condition with 10%fault (a) | −856.3741 | 0.6139 | 0.2703 | 0.4808 |

Load condition with 25%fault (b) | −2.08 × 10^{3} | 4.9796 | 1.2152 | 2.0776 |

Load condition with 50% fault (c) | −3.14 × 10^{3} | 11.3992 | 4.1454 | 5.4373 |

Load condition with loss ph. (b) | −1.02 × 10^{3} | 0.7889 | 0.1922 | 0.2736 |

Phase to ground fault | −1.27 × 10^{3} | 2.2173 | 0.6971 | 1.259 |

**Table 6.**Computed Entropy power energy threshold values for the classification of the faults using experimental data.

Type of Fault | WPT Subbands’ Entropy Power Energy | |
---|---|---|

ad2 | dd2 | |

10% no load fault-a | 0.5016 | 0.2338 |

40% no load fault-b | 1.3107 | 1.1831 |

50% no load fault-c | 1.5828 | 1.3086 |

Loss phase fault | 1.6341 | 0.8724 |

Phase to ground | 1.7612 | 1.4303 |

50% loaded-c | 1.3877 | 0.9955 |

**Table 7.**Entropy power energy values of all four second level WPT subbands’ coefficients for different practical conditions of the induction motor.

Motor Condition | WPT Subbands’ Entropy Power Energy | |||
---|---|---|---|---|

aa2 | ad2 | da2 | dd2 | |

No-load healthy | −3.8914 × 10^{5} | 1.7736 × 10^{−4} | 0.0191 | 1.2729 × 10^{−4} |

Loaded healthy | −7.9257 × 10^{5} | 3.1433 × 10^{−4} | 0.0334 | 2.2519 × 10^{−4} |

No-load 25% fault(b) | −2.9841 × 10^{7} | −2.2918 × 10^{4} | −1.5434 × 10^{3} | −256.4051 |

No-load 50% fault(c) | −1.1857 × 10^{8} | −1.5737 × 10^{5} | −1.0024 × 10^{4} | −2.4242 × 10^{3} |

No-load with loss phase(b) | −437.3249 | 0.5828 × 10^{7} | 0.1027 | 0.1329 × 10^{4} |

Load condition with 10% fault (a) | −6.1115 × 10^{6} | −1.6653 × 10^{4} | −1.0147 × 10^{3} | −191.9537 |

Load condition with 25% fault (b) | −3.0647 × 10^{7} | −1.1116 × 10^{4} | −735.9312 | −107.2747 |

Load condition with 50% fault(c) | −1.1952 × 10^{8} | −1.7314 × 10^{5} | −1.1123 × 10^{4} | −2.6732 × 10^{3} |

Load condition with loss phase (b) | −1.02 × 10^{3} | 0.7889 × 10^{7} | 0.1922 | 0.2736 × 10^{4} |

Phase to ground fault | −1.27 × 10^{3} | 2.2173 × 10^{7} | 0.6971 | 1.259 × 10^{5} |

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**MDPI and ACS Style**

Hussein, A.M.; Obed, A.A.; Zubo, R.H.A.; Al-Yasir, Y.I.A.; Saleh, A.L.; Fadhel, H.; Sheikh-Akbari, A.; Mokryani, G.; Abd-Alhameed, R.A. Detection and Diagnosis of Stator and Rotor Electrical Faults for Three-Phase Induction Motor via Wavelet Energy Approach. *Electronics* **2022**, *11*, 1253.
https://doi.org/10.3390/electronics11081253

**AMA Style**

Hussein AM, Obed AA, Zubo RHA, Al-Yasir YIA, Saleh AL, Fadhel H, Sheikh-Akbari A, Mokryani G, Abd-Alhameed RA. Detection and Diagnosis of Stator and Rotor Electrical Faults for Three-Phase Induction Motor via Wavelet Energy Approach. *Electronics*. 2022; 11(8):1253.
https://doi.org/10.3390/electronics11081253

**Chicago/Turabian Style**

Hussein, Ameer M., Adel A. Obed, Rana H. A. Zubo, Yasir I. A. Al-Yasir, Ameer L. Saleh, Hussein Fadhel, Akbar Sheikh-Akbari, Geev Mokryani, and Raed A. Abd-Alhameed. 2022. "Detection and Diagnosis of Stator and Rotor Electrical Faults for Three-Phase Induction Motor via Wavelet Energy Approach" *Electronics* 11, no. 8: 1253.
https://doi.org/10.3390/electronics11081253