# Analysis of a Three-Phase Induction Motor with a Double–Triple-Layer Stator Winding Configuration Operating with Broken Rotor Bar Faults

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Materials and Methodology

#### 3.1. Specifications and Ratings

#### 3.2. Double–Triple-Layer Stator Winding Configuration

_{ss}= −17, +19, −35, +37, −53, +55, −71, +73… and v

_{sb}= −5, +7, −11, +13, −17, +19, −23, +25, −29, +31…. The 43 rotor cage bars are placed in slots. The stator MMF harmonics have orders like v

_{rs}= −21, +23, −43, +45, −65, +67….

#### 3.3. Approach

## 4. Results and Discussions

#### 4.1. Effect of Broken Rotor Bars on Flux Density

#### 4.2. Effect of Broken Rotor Bars on the Current Signature of the Loaded SCIM

#### 4.3. Machines’ Parameters

#### 4.4. Analysis of Measured Stator Currents

#### 4.5. Analysis of Key Performance Parameters

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Winding arrangement in stator slots. Only one of the four poles in the stator is shown: (

**a**) CDL winding configuration, (

**b**) DTL winding configuration.

**Figure 2.**DTL winding configuration of the three-phase squirrel cage induction motor: (

**a**) phase A, (

**b**) phase B, (

**c**) phase C.

**Figure 4.**Squirrel cage rotor: (

**a**) healthy rotor, (

**b**) rotor with three broken rotor bars, (

**c**) rotor with six broken rotor bars.

**Figure 6.**Flux density distribution on the full load of the IM with the CDL: (

**a**) healthy, (

**b**) 3BRB, (

**c**) 6BRB.

**Figure 7.**Flux density distribution on the full load of the IM with the DTL: (

**a**) healthy, (

**b**) 3BRB, (

**c**) 6BRB.

**Figure 8.**Airgap flux density characteristic of the healthy machines under no-load operation: (

**a**) airgap flux density profile, (

**b**) FFT of the airgap flux density profile.

**Figure 9.**Airgap flux density characteristic of the faulty machines with 3BRB under no-load operation: (

**a**) airgap flux density profile, (

**b**) FFT of the airgap flux density profile.

**Figure 10.**Airgap flux density characteristic of the faulty machines with 6BRB under no-load operation: (

**a**) airgap flux density profile, (

**b**) FFT of the airgap flux density profile.

**Figure 11.**Airgap flux density characteristic of the SCIM with a CDL winding operating with load torque of 30 Nm: (

**a**) airgap flux density profile, (

**b**) FFT of the airgap flux density profile.

**Figure 12.**Airgap flux density characteristic of the SCIM with a DTL winding operating with load torque of 30 Nm: (

**a**) airgap flux density profile, (

**b**) FFT of the airgap flux density profile.

**Figure 13.**FEA loaded current characteristics of the SCIMs with a CDL winding configuration: (

**a**) current waveforms for healthy operation, (

**b**) current waveforms for faulty operation with 3BRB, (

**c**) current waveforms for faulty operation with 6BRB, (

**d**) FFT current spectrum of phase A recorded at 150 ms and 200 ms.

**Figure 14.**FEA loaded current characteristics of the SCIMs with a DTL winding configuration: (

**a**) current waveforms for healthy operation, (

**b**) current waveforms for faulty operation with 3BRB, (

**c**) current waveforms for faulty operation with 6BRB, (

**d**) FFT current spectrum of phase A recorded at 150 ms and 200 ms.

**Figure 18.**Harmonic components of phase A current profiles for the CDL: (

**a**) operation with a load torque of 0 Nm, (

**b**) operation with a load torque of 30 Nm.

**Figure 19.**Harmonic components of phase A current profiles for the DTL: (

**a**) operation with a load torque of 0 Nm, (

**b**) operation with a load torque of 30 Nm.

**Figure 20.**The DFT zoom current spectrum of phase A under the steady state of the SCIM with a CDL winding configuration: (

**a**) operation with a load torque of 0 Nm, (

**b**) operation with a load torque of 30 Nm.

**Figure 21.**The zoomed DFT current spectrum of phase A under the steady state of the SCIM with a DTL winding configuration: (

**a**) operation with a load torque of 0 Nm, (

**b**) operation with a load torque of 30 Nm.

**Figure 22.**Shaft torque of loaded SCIMs: (

**a**) healthy operation, (

**b**) 3BRB faulty operation, (

**c**) 6BRB faulty operation.

Description | Values | Unit |
---|---|---|

Rated current | 12.6 | A |

Rated power | 5.5 | kW |

Nominal voltage | 380 | V |

Nominal frequency | 50 | Hz |

Rated speed | 1478 | rpm |

Number of poles | 4 | - |

Number of stator slots | 36 | - |

Number of rotor bars | 43 | - |

Number of turns per phase | 54 | - |

External diameter | 210 | mm |

Airgap length | 0.35 | mm |

Core length | 160 | mm |

Harmonic Order | |||||||
---|---|---|---|---|---|---|---|

Winding | 1st | 5th | 7th | 11th | 13th | 17th | 19th |

CDL | 0.94 | 0.13 | −0.06 | −0.10 | −0.13 | −0.94 | −0.94 |

DTL | 0.91 | −0.07 | −0.08 | −0.08 | −0.07 | −0.91 | 0.91 |

Healthy | 3BRB | 6BRB | ||||
---|---|---|---|---|---|---|

Parameters | EXP | FEA | EXP | FEA | EXP | FEA |

${\mathrm{X}}_{\mathrm{m}}\left(\mathsf{\Omega}\right)$ | 56.32 | 60.35 | 48.16 | 52.07 | 35.48 | 43.78 |

${\mathrm{R}}_{\mathrm{c}}\left(\mathsf{\Omega}\right)$ | 220.59 | - | 213.54 | - | 188.06 | - |

${\mathrm{X}}_{\mathrm{l}}^{\mathrm{s}}\left(\mathsf{\Omega}\right)$ | 3.03 | 3.27 | 2.97 | 3.19 | 2.79 | 3.08 |

${\mathrm{R}}_{\mathrm{r}}^{\mathrm{s}}\left(\mathsf{\Omega}\right)$ | 1.12 | 0.97 | 1.03 | 0.87 | 0.94 | 0.81 |

Healthy | 3BRB | 6BRB | ||||
---|---|---|---|---|---|---|

Parameters | EXP | FEA | EXP | FEA | EXP | FEA |

${\mathrm{X}}_{\mathrm{m}}\left(\mathsf{\Omega}\right)$ | 46.31 | 57.60 | 41.81 | 50.12 | 34.97 | 41.17 |

${\mathrm{R}}_{\mathrm{c}}\left(\mathsf{\Omega}\right)$ | 207.28 | - | 191.54 | - | 189.53 | - |

${\mathrm{X}}_{\mathrm{l}}^{\mathrm{s}}\left(\mathsf{\Omega}\right)$ | 2.84 | 3.17 | 2.77 | 3.12 | 2.72 | 2.98 |

${\mathrm{R}}_{\mathrm{r}}^{\mathrm{s}}\left(\mathsf{\Omega}\right)$ | 1.24 | 0.88 | 0.97 | 0.81 | 0.90 | 0.75 |

Healthy | 3BRB | 6BRB | ||||
---|---|---|---|---|---|---|

Parameters | EXP | FEA | EXP | FEA | EXP | FEA |

${\mathrm{T}}_{\mathrm{av}}\left(\mathrm{Nm}\right)$ | 32.9 | 34.3 | 30.3 | 32.1 | 28.3 | 29.7 |

${\mathrm{T}}_{\mathrm{ripple}}\left(\%\right)$ | 10.5 | 14.6 | 26.4 | 31.4 | 31.5 | 37.9 |

${\mathrm{I}}_{\mathrm{steady}}\left(\mathrm{A}\right)$ | 9.60 | 8.64 | 10.40 | 10.14 | 11.11 | 11.43 |

${\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}\left(\mathrm{A}\right)$ | 84.8 | - | 78.8 | - | 76.4 | - |

${\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}/{\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{y}}$ | 8.83 | - | 7.57 | - | 6.87 | - |

$\mathrm{Eff}\left(\%\right)$ | 86.2 | 87.5 | 84.7 | 86.2 | 81.9 | 82.6 |

${\mathrm{P}}_{\mathrm{T}\mathrm{C}\mathrm{u}}\left(\mathrm{W}\right)$ | 508.2 | 437.2 | 566.8 | 496.5 | 607.8 | 523.1 |

${\mathrm{P}}_{\mathrm{T}\mathrm{i}}\left(\mathrm{W}\right)$ | 230.4 | 275.9 | 265.4 | 281.0 | 263.8 | 280.7 |

${\mathrm{P}}_{\mathrm{a}\mathrm{d}\mathrm{d}}\left(\mathrm{W}\right)$ | 39.1 | - | 36.24 | - | 35.04 | - |

$\mathrm{PF}\left(\mathrm{per}\mathrm{unit}\right)$ | 0.839 | 0.857 | 0.831 | 0.849 | 0.807 | 0.828 |

Healthy | 3BRB | 6BRB | ||||
---|---|---|---|---|---|---|

Parameters | EXP | FEA | EXP | FEA | EXP | FEA |

${\mathrm{T}}_{\mathrm{a}\mathrm{v}}\left(\mathrm{Nm}\right)$ | 33.4 | 35.1 | 32.9 | 33.7 | 31.5 | 32.3 |

${\mathrm{T}}_{\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{e}}\left(\%\right)$ | 8.8 | 12.9 | 14.1 | 19.21 | 18.3 | 23.7 |

${\mathrm{I}}_{\mathrm{steady}}\left(\mathrm{A}\right)$ | 8.44 | 8.88 | 10.41 | 9.42 | 10.75 | 11.32 |

${\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}\left(\mathrm{A}\right)$ | 80.2 | - | 77.5 | - | 72.7 | - |

${\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}/{\mathrm{I}}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{y}}$ | 9.50 | - | 7.43 | - | 6.76 | - |

$\mathrm{Eff}\left(\%\right)$ | 86.9 | 88.1 | 85.1 | 87.2 | 82.3 | 85.7 |

${\mathrm{P}}_{\mathrm{T}\mathrm{c}\mathrm{u}}\left(\mathrm{W}\right)$ | 537.5 | 421.8 | 549.9 | 478.0 | 582.7 | 506.8 |

${\mathrm{P}}_{\mathrm{T}\mathrm{i}}\left(\mathrm{W}\right)$ | 221.0 | 242.4 | 253.5 | 267.9 | 262.6 | 274.2 |

${\mathrm{P}}_{\mathrm{a}\mathrm{d}\mathrm{d}}\left(\mathrm{W}\right)$ | 37.7 | - | 37.01 | - | 36.34 | - |

$\mathrm{P}\mathrm{F}\left(\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\right)$ | 0.849 | 0.89 | 0.833 | 0.842 | 0.802 | 0.820 |

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**MDPI and ACS Style**

Muteba, M.
Analysis of a Three-Phase Induction Motor with a Double–Triple-Layer Stator Winding Configuration Operating with Broken Rotor Bar Faults. *Machines* **2023**, *11*, 1023.
https://doi.org/10.3390/machines11111023

**AMA Style**

Muteba M.
Analysis of a Three-Phase Induction Motor with a Double–Triple-Layer Stator Winding Configuration Operating with Broken Rotor Bar Faults. *Machines*. 2023; 11(11):1023.
https://doi.org/10.3390/machines11111023

**Chicago/Turabian Style**

Muteba, Mbika.
2023. "Analysis of a Three-Phase Induction Motor with a Double–Triple-Layer Stator Winding Configuration Operating with Broken Rotor Bar Faults" *Machines* 11, no. 11: 1023.
https://doi.org/10.3390/machines11111023