# Applicability Analysis of Indices-Based Fault Detection Technique of Six-Phase Induction Motor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Six-Phase Induction Motor Model

_{1}b

_{1}c

_{1}and a

_{2}b

_{2}c

_{2}) and it could be built in one of three configurations, namely, symmetrical, asymmetrical and dual configuration. In a symmetrical motor, the spatial displacement (g) between the two three-phase windings equals 60°, whereas in an asymmetrical motor this spatial displacement is 30° and the spatial displacement in a dual three-phase motor is 0°.

_{1}to S

_{12}are the power switches of the inverter and each switch has its own antiparallel diode. Additionally, V

_{a1}, V

_{b1}, V

_{c1}, V

_{a2}, V

_{b2}, and V

_{c2}are the phase voltages of the six-phase induction motor, whereas V

_{dc}is the DC link voltage. The vector space decomposition (VSD) technique is applied here for the case of six-phase induction motor in order to perform a co-ordinate transformation from the physical a

_{1}b

_{1}c

_{1}-a

_{2}b

_{2}c

_{2}reference frame to an arbitrary reference frame. The machine will have six sequence components in the new reference frame, namely α-β, x-y, and 0+-0−. Since the air-gap flux is assumed sinusoidally distributed, the α-β components are completely decoupled from the x-y components, also there is no stator-rotor coupling in the x-y subspace [25]. Additionally, since the two neutrals of the six-phase motor are isolated, the 0+-0− current components are zero and will not be present in the further analysis. In order to develop a model for the six-phase induction motor, the following usual assumptions are made; the air-gap is uniform and the flux is sinusoidally distributed around the air-gap, and magnetic saturation and core losses are neglected.

_{1}b

_{1}c

_{1}-a

_{2}b

_{2}c

_{2}reference frame into an arbitrary reference frame is [26],

## 3. Indices-Based Fault Detection Technique

_{1}, then the phase current of that phase will be zero (i

_{α}

_{1}= 0). Hence, by applying this condition to the first row of the inverse of the Clarke’s transformation matrix (1), the result that ${i}_{\alpha}=-{i}_{x}\text{}$will be found. This result could be used to define the following ratio,

_{1}, and it equals to zero in the healthy condition as i

_{x}is zero in this condition. By following the same approach to the other phases, the following indices can be found.

#### 3.1. Hysteresis Band Filtering

#### 3.2. Moving Average Integration

#### 3.3. Comparison to A Threshold Value

## 4. Application of the Indices-Based Fault Detection Technique to Various Faults

#### 4.1. Open-Switch Fault

_{1}which could be an OPF, OUSF or OLSF. Second, in the case of an OSF, the fault localization feature of this technique does not exist. That is, there is nothing that could determine whether the OSF is in the upper switch or in the lower switch.

_{1}, and the average value of phase a

_{1}current ${I}_{ph-avg}$ will be checked. If ${I}_{ph-avg}$ is positive (above zero), this means that there is an OLSF, and if ${I}_{ph-avg}$ is negative (below zero), this means that there is an OUSF. In addition, if ${I}_{ph-avg}$ is zero, this means that there is an OPF, see Equation (10). However, if there are both OUSF and OLSF, this modified fault detection technique could not differentiate this case from the case of an OPF, as, in these two cases, the phase current of the faulted phase is zero in both positive and negative half cycles.

#### 4.2. Bad Connection Fault

#### 4.3. Broken Rotor Bar Fault

## 5. Experimental and Simulation Results

#### 5.1. Open-Phase Fault (OPF)

_{1}fault. In order to indicate the changes in the fault indices, an open phase fault in a

_{1}phase is introduced and cleared again as shown in Figure 6b. The a

_{1}fault index rises as a consequence of the unbalance of the phase currents, whereas the remaining indices are close to zero.

_{1}current (${I}_{ph-avg}$) should remain zero, in other words, ${I}_{ph-avg}$ has a zero value in the healthy case and in the case of an open-phase fault.

#### 5.2. Open-Switch Fault (OSF)

_{1}is opened at t = 3.75 s through disconnecting the gate signal of that switch. Figure 8a shows OUSF phase current. Thus, ideally, the a

_{1}fault index evolves to one during the positive half cycle and returns back to zero during the negative half cycle. However, practically, it does not have enough time to reach zero because of the high supply frequency, as shown in Figure 8b. Moreover, Figure 8c presents a zoomed-in view of the fault index$\text{}{R}_{a1\text{}}$, and it is demonstrated that the detection time is about 9 msec.

_{1}should be checked to be negative, as shown in Figure 8d, and that means that there is an OUSF.

#### 5.3. Bad Connection Fault

_{1}phase connection. The severity of the bad connection fault is determined by the value of the added resistance (i.e., increasing the resistance value increases the bad connection fault severity and vice versa). In this test, the resistance has increased in two steps to visualize the change of the fault index. At the beginning, there was no bad connection fault; however, at t = 4 s, a 35 Ohms resistance (the first step) is added to simulate a bad connection fault with a moderate severity. Then, at t = 6.5 s, the resistance was increased to be 60 Ohms (the second step) to demonstrate a high severity bad connection fault. At this resistance value, the phase current was zero and the fault index reached to approximately one, so this is the worst bad connection fault case, as these results are similar to that of the open-circuit fault. Finally, the resistance was removed at t = 17.5 s and the current returned to its normal value.

_{1}phase current to approximately zero due to the added resistances, whereas Figure 9b,c show the evolution of the fault index of phase a

_{1}as a consequence of increasing the bad connection fault severity.

#### 5.4. Broken-Rotor Bar (BRB) Fault

^{−3}. The stator phase currents and rotor loop currents are shown in Figure 10 and Figure 11, a zoomed view of one of the rotor loop currents is presented also in Figure 11 for better visualization. Additionally, the mechanical performance of the motor is shown in Figure 12, where the motor started at no load, then at t = 0.6 s, a 4 N.m load torque was applied.

_{1}current in both the healthy case and the one BRB fault case is provided in Figure 14. It can be shown that the amplitudes at about 42 and 58 Hz are increased in the BRB fault case; these side-band frequencies are consistent with $\left(1\pm 2s\right){f}_{s}$ equation, where $s=0.07$ in this case and$\text{}{f}_{s}=50\text{}Hz$.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**(

**a**) OPF or OSF with both upper and lower faulted switches phase current; (

**b**) OUSF phase current; and (

**c**) OLSF phase current.

**Figure 6.**OPF test: (

**a**) Phase current (a1); (

**b**) Fault indices; (

**c**) Detection time (zoom in of the fault indices).

Parameter | Value | |
---|---|---|

Electrical | Stator Resistance (R_{s}) | 4.18 Ω |

Rotor Resistance (R_{r}) | 3.42 Ω | |

Stator Leakage Inductance (Ll_{s}) | 14.67 mH | |

Rotor Leakage Inductance (Ll_{r}) | 14.67 mH | |

Mutual Inductance (M) | 741 mH | |

Rotor-Bar Resistance (R_{b}) | 78 μΩ | |

End-Ring Resistance (R_{e}) | 6.8952 μΩ | |

Rotor-Bar Self-Inductance (Ll_{b}) | 6.7 nH | |

End-Ring Self-Inductance (Ll_{e}) | 0.5923 nH | |

Rated RMS Phase Voltage | 110 V | |

Rated RMS Phase Current | 2.8 A | |

Pole Pairs (p) | 2 | |

Rated Frequency | 50 Hz | |

Mechanical | Moment of Inertia (J) | 0.00157 Kg·m^{2} |

Friction Coefficient (B) | 0.006 Nm/rad/s | |

Rated Speed | 1400 rpm | |

Geometrical | No. of Rotor-Bars/Pole Pairs (m) | 13 |

Number of Phases (n) | 6 | |

Number of Coil Turns (N) | 50 | |

Rotor Radius (r) | 50 mm | |

Core Length (L) | 120 mm | |

Air-Gap Length (g) | 0.4 mm |

Fault Condition | α-Current (rms) | β-Current (rms) | x-Current (rms) | y-Current (rms) |
---|---|---|---|---|

Healthy (no BRB fault) | 1 pu | 1 pu | 0 pu | 0 pu |

One BRB (Bar no. 1) | 1.025 pu | 1.025 pu | 0.012 pu | 0.012 pu |

Two adjacent BRBs (Bars 1 and 2) | 1.065 pu | 1.065 pu | 0.012 pu | 0.012 pu |

Three adjacent BRBs (Bars 1, 2 and 3) | 1.29 pu | 1.29 pu | 0.015 pu | 0.015 pu |

Two non-adjacent BRBs (Bars 1 and 5) | 1.35 pu | 1.35 pu | 0.015 pu | 0.015 pu |

Three non-adjacent BRBs (Bars 1, 4 and 7) | 1.45 pu | 1.45 pu | 0.018 pu | 0.018 pu |

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**MDPI and ACS Style**

Farag, K.; Shawier, A.; Abdel-Khalik, A.S.; Ahmed, M.M.; Ahmed, S.
Applicability Analysis of Indices-Based Fault Detection Technique of Six-Phase Induction Motor. *Energies* **2021**, *14*, 5905.
https://doi.org/10.3390/en14185905

**AMA Style**

Farag K, Shawier A, Abdel-Khalik AS, Ahmed MM, Ahmed S.
Applicability Analysis of Indices-Based Fault Detection Technique of Six-Phase Induction Motor. *Energies*. 2021; 14(18):5905.
https://doi.org/10.3390/en14185905

**Chicago/Turabian Style**

Farag, Khaled, Abdullah Shawier, Ayman S. Abdel-Khalik, Mohamed M. Ahmed, and Shehab Ahmed.
2021. "Applicability Analysis of Indices-Based Fault Detection Technique of Six-Phase Induction Motor" *Energies* 14, no. 18: 5905.
https://doi.org/10.3390/en14185905