# Three-Phase Induction Motors Online Protection against Unbalanced Supply Voltages

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Proposed USV Detection Method

_{a}, V

_{b}, V

_{c}) of an induction motor leads to three symmetrical components: positive (V

_{+}or Direct), negative (V

_{−}or Inverse) and zero (V

_{o}or Homopolar). These symmetrical components can be obtained as expressed in the following matrix form:

**Step 01:**Acquisition of the three-phase currents and voltages $\left({V}_{a},{V}_{b},{V}_{c},{I}_{a},{I}_{b},{I}_{c}\right)$;

**Step 02:**Extraction of the fundamental harmonics (magnitudes and phase angles) related to the three-phase voltages and currents $\left({V}_{a.1fs},{V}_{b.1fs},{V}_{c.1fs},{I}_{a.1fs},{I}_{b.1fs},{I}_{c.1fs}\right)$. This can be performed thanks to the short time least square Prony’s (STLSP) method which is a high-resolution signal processing technique that has the ability to estimate and track accurately all the attributes (frequency, amplitude, phase, and damping factor) of any harmonics from a short data record signal. This allows the consideration of the non-stationary aspect of the problem [24]. To reduce the impact of some influential features, and thus obtaining improved results, a preprocessing of the acquired signals is necessary. In fact, data acquisition parameters, filtering, DC components removal, and dawn sampling are the main involved tasks [24,25].

_{0}= 1). Then, the unknown parameters ak that fit the observed data are selected to minimize the linear prediction total squared error. This can be done by using the least square method.

**Step 03:**Calculation of the symmetrical components related to the supply voltages and stator currents (${V}_{1fs}^{+},{V}_{1fs}^{-},{V}_{1fs}^{0},{I}_{1fs}^{+},{I}_{1fs}^{-},{I}_{1fs}^{0}$).

**Step 04:**Calculation of the symmetrical components related the stator winding impedances:

**Step 05:**Generation of the three-unbalance factors NVF, NCF, and NIF using Equations (1), (3), and (4), respectively.

## 3. Experimental Validation

#### 3.1. Sensitivity to the Occurrence of Low USV

#### 3.2. Sensitivity to the USV’s Severity

#### 3.3. Robustness against Load Variations

#### 3.4. Robustness against Similar Faults

- (1)
- Start the motor in a healthy state, with balanced supply voltages, at no load;
- (2)
- Increase the motor load by 20% (the motor always in healthy state);
- (3)
- Introduce an ITSCF of 18 turns in the phase “a”, under 20% of load, with balanced supply voltages;
- (4)
- Increase the motor load to 40% (the motor remains with ITSCF and balanced supply voltages);
- (5)
- Introduce an USV of 1.8% in the presence of ITSCF.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**IM voltage and current waveforms for a balanced supply condition, under different step load variations.

**Figure 9.**The studied factors for a balanced supply condition, under different step load variations.

General | Power [kW] | 2.2 |

Speed [r/min] | 1435 | |

Frequency [Hz] | 50 | |

Torque [N·m] | 14.6 | |

Voltage [V] | 400, Star Connection | |

Current [A] | 4.56, Star Connection | |

Number of Poles | 4 | |

Cooling | Closed Motor with external ventilation-IC 411 |

n = 100 Samples | Unbalance Supply Voltage Severity (%) | ||
---|---|---|---|

Unbalance Factors | 0% | 1% | Rate of Variation (%) |

NVF | 0.002863 | 0.0101 | +252% |

NCF | 0.006534 | 0.04419 | +576% |

NIF | 0.4343 | 0.2292 | −47.22% |

Monitoring Factors | Factor’s Magnitudes for Balanced Voltages (p.u.) | Rate of Variations for Different Severities of USV | ||
---|---|---|---|---|

USV of 1% | USV of 1.8% | USV of 2.56% | ||

NVF | 0.003632 | +200% | +402% | +608% |

NCF | 0.009469 | +377% | +786% | +1190% |

NIF | 0.3834 | −37.8% | −43.9% | −45% |

Inter-Turn Short-Circuit Fault | |||
---|---|---|---|

Unbalance Factors | Healthy | 9 Turns | Rate of Variation (%) |

NVF | 0.00288 | 0.002929 | +3.5% |

NCF | 0.00654 | 0.02324 | +255% |

NIF | 0.445 | 0.1276 | −71.3% |

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**MDPI and ACS Style**

Laadjal, K.; Sahraoui, M.; Alloui, A.; Cardoso, A.J.M.
Three-Phase Induction Motors Online Protection against Unbalanced Supply Voltages. *Machines* **2021**, *9*, 203.
https://doi.org/10.3390/machines9090203

**AMA Style**

Laadjal K, Sahraoui M, Alloui A, Cardoso AJM.
Three-Phase Induction Motors Online Protection against Unbalanced Supply Voltages. *Machines*. 2021; 9(9):203.
https://doi.org/10.3390/machines9090203

**Chicago/Turabian Style**

Laadjal, Khaled, Mohamed Sahraoui, Abdeldjalil Alloui, and Antonio J. Marques Cardoso.
2021. "Three-Phase Induction Motors Online Protection against Unbalanced Supply Voltages" *Machines* 9, no. 9: 203.
https://doi.org/10.3390/machines9090203