# Search-Coil Based Stator Interturn Fault Detection in Permanent Magnet Machines Running under Dynamic Condition

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Flexible PCB is used to make search coils, and the number of turns can be increased if the full rate of the slot is certain, and increased mutual inductance makes it easier to detect fault signals.
- (2)
- A demodulation algorithm based on the Digital Lock-In Amplifier (DLIA) is proposed, which can be used under non-stationary conditions.
- (3)
- The voltage at the characteristic frequency of the search coil is standardized and its variance is considered as the fault characteristic quantity, which can make robust detection of motor speed.

## 2. Principle of Proposed Method

#### 2.1. Back EMF in Search Coils

**M**

_{ps},

**i**, ψ

_{f}, θ, and

**F**(θ) are the mutual inductance of phase winding and search coils, phase current, amplitude of permanent magnet flux, angular position of rotor, and unit flux linkage of search coils, respectively. The second part of Equation (1) remains unchanged, while the phase current, and mutual inductance of phase winding and search coils change with variations in EMF when ITSC fault occurs.

#### 2.2. Six-Phase Equivalent Circuit Model with ITSC Fault

_{1}, ϕ, and f

_{h}are the amplitude, initial phase angle and frequency of voltage. G. Holmes [33] analyzed the voltage components under PWM supply. In case of a naturally sampled reference and double-edge carrier, the voltage can be expressed as:

_{dc}, M, ω

_{0}, ω

_{c}and J

_{x}are the DC bus voltage, voltage modulation ratio, fundamental wave angular frequency, carrier angular frequency, and Bessel function. Note that a

_{1}in Equation (9) can be calculated by taking m = n = 1 in Equation (10).

_{c}± ω

_{0}) is selected as the characteristic frequency.

_{0}is a variable under the variable operating conditions, which also means that the spectrum in Figure 1 changes as the operating conditions change. Because of this, the conventional spectrum analysis methods are no longer applicable.

**M**

_{psf}and ${\overrightarrow{\mathit{i}}}_{hF}$ are the mutual inductance matrices between the phase windings and search coils and the high frequency component of phase current, respectively.

#### 2.3. Method for Estimating Voltage Amplitude

- (1)
- Multiply the original signal by two quadrature reference signals at the carrier frequency;
- (2)
- Obtain the signal envelope by low-pass filtering;
- (3)
- Obtain the amplitude by the two envelopes of sine and cosine.

## 3. Validation through Simulation

#### 3.1. Search Coil Arrangement Scheme

#### 3.2. Precise Modeling for Analyzing Impact of Fault Location

_{f}is the fault part winding of phase a. So, it is seen that no distinction can be made between the fault locations in the same slot.

#### 3.3. Simulation Results

#### 3.3.1. DLIA

#### 3.3.2. Normalization Process

## 4. Experimental Validation

#### 4.1. Experimental Platform

#### 4.2. Calibration

#### 4.3. Test Results under Failure

#### 4.3.1. Change in Short Circuit Resistance

#### 4.3.2. Change in Short Circuit Turns

#### 4.3.3. Change in Short Circuit Position

#### 4.3.4. Change in Load

#### 4.3.5. Change in Speed

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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

Length of unilateral air gap | 2 mm | Slot width | 4.2 mm |

Stator outer diameter | 290 mm | Thickness of permanent magnet | 9 mm |

Inner diameter of stator | 180 mm | Overlaying coefficient | 0.97 |

Rotor outer diameter | 176 mm | Number of stator slots | 72 |

Inside diameter of rotor | 80 mm | Number of conductors per slot | 72 |

Stator core length | 88 mm | Number of parallel branches | 1 |

Yoke thickness | 22 mm | Pitch | 6 |

Stator core material | 50WW310 | Winding coefficient | 1 |

Rotor core material | 16Mn | Permanent magnet material | SmCo30 |

## Appendix B

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**Figure 6.**Cross section of prototype with inter-turn short fault in phase a. Shorting circuit windings are distinguished by red color. Case1 and Case2 represent two fault locations, respectively, where the fault location is closer to the bottom of the slot in Case2 compared with Case1.

**Figure 7.**Signal waveform of SC1 (

**a**) Original voltage signal. (

**b**) Voltage signal after bandpass filtering, red and blue represent orthogonal sine and cosine signals, respectively.

**Figure 8.**Test results under variable speed operation. (

**a**) Calculated amplitude of voltage of SCs. (

**b**) Rotational speed curve.

**Figure 9.**Simulation results of the health state under variable speed operation. (

**a**) Calculated amplitude of voltage. (

**b**) Normalized voltage value.

**Figure 10.**Simulation results of fault state under variable speed operation. (

**a**) Calculated amplitude of voltage. (

**b**) Normalized voltage value.

**Figure 13.**Amplitude of each search coil in healthy condition. (

**a**) Before calibration. (

**b**) After calibration.

**Figure 14.**Detection result with the fault of 1 ohm and 15 short circuit turns. (

**a**) Measured voltage value. (

**b**) Normalized voltage value at three random moments.

**Figure 15.**Detection results at different short resistance. (

**a**) Variance of voltage. (

**b**) Rotational speed curve.

**Figure 16.**Variance of search coil output values at a different number of short-circuit turns with the short circuit resistance set to 1 ohm.

**Figure 17.**Detection results at different fault positions. (

**a**) Normalized voltage value at different fault position. (

**b**) Variance of normalized voltage at different moments.

**Figure 18.**Voltage variance under different loads with the same short circuit resistance and short circuit turns.

Rated Power (kW) | 0.94 | Rated Speed (r/min) | 300 |

Rated Torque (Nm) | 30 | Stator Resistance (Ω) | 4.3 |

Number of Pole Pairs | 6 | PM Flux Linkage (Wb) | 0.98 |

a | b | c | u | v | w | a_{f} | |
---|---|---|---|---|---|---|---|

SC1 | −0.00728 | −0.00823 | −0.0051 | −0.01157 | 0.00345 | −0.00457 | 0.1552 |

SC2 | 0.00498 | 0.01234 | 0.00044 | 0.00795 | 0.00723 | −0.00985 | 0.01348 |

SC3 | −0.03312 | −0.00842 | −0.00524 | −0.01152 | 0.00342 | −0.00464 | 0.21956 |

SC4 | 0.00828 | 0.0126 | −0.00492 | 0.00735 | 0.00778 | −0.01182 | −0.04365 |

SC5 | 0.00372 | −0.00777 | −0.00524 | −0.01185 | 0.00647 | −0.00461 | 0.00227 |

SC6 | 0.00741 | 0.0125 | −0.00169 | 0.00796 | 0.0078 | −0.01193 | 0.01668 |

SC7 | 0.00442 | −0.00801 | −0.00473 | −0.01118 | 0.00369 | −0.00423 | 0.00389 |

SC8 | 0.00653 | 0.01217 | 0.00085 | 0.0081 | 0.00721 | −0.01075 | 0.01682 |

SC9 | 0.00379 | −0.00812 | −0.00528 | −0.01179 | 0.00403 | −0.00469 | 0.00417 |

SC10 | 0.00718 | 0.01242 | −0.0026 | 0.00787 | 0.00761 | −0.01165 | 0.0177 |

SC11 | 0.00236 | −0.00753 | −0.0052 | −0.01172 | 0.0059 | −0.00458 | 0.00484 |

SC12 | 0.00677 | 0.0126 | −0.0031 | 0.00783 | 0.00752 | −0.01035 | 0.01801 |

SC13 | 0.00404 | −0.00802 | −0.00506 | −0.01158 | 0.00379 | −0.00446 | 0.00539 |

SC14 | 0.00695 | 0.01244 | −9.946 × 10^{−4} | 0.00773 | 0.00738 | −0.0098 | 0.01795 |

SC15 | 0.0034 | −0.00766 | −0.00522 | −0.01182 | 0.00531 | −0.0046 | 0.00548 |

SC16 | 0.00668 | 0.01262 | −0.00249 | 0.00776 | 0.00747 | −0.01057 | 0.01805 |

SC17 | 0.00309 | −0.00751 | −0.00517 | −0.01183 | 0.00559 | −0.00451 | 0.00556 |

SC18 | 0.00722 | 0.01264 | −0.00193 | 0.00788 | 0.00766 | −0.01048 | 0.01796 |

SC19 | 0.0036 | −0.00764 | −0.00489 | −0.01155 | 0.00517 | −0.00428 | 0.00565 |

SC20 | 0.00685 | 0.01218 | −0.00196 | 0.0079 | 0.00755 | −0.01316 | 0.01748 |

SC21 | 0.00408 | −0.008 | −0.00509 | −0.01165 | 0.00347 | −0.00452 | 0.005 |

SC22 | 0.00707 | 0.01255 | −0.00194 | 0.00776 | 0.00749 | −0.01018 | 0.01668 |

SC23 | 0.003 | −0.00796 | −0.00483 | −0.0112 | 0.00346 | −0.00422 | 0.00475 |

SC24 | 0.007 | 0.01243 | −0.00448 | 0.00725 | 0.00765 | −0.01199 | 0.01248 |

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## Share and Cite

**MDPI and ACS Style**

Huang, W.; Chen, J.; Hu, J.; Lv, K.; Liu, H.
Search-Coil Based Stator Interturn Fault Detection in Permanent Magnet Machines Running under Dynamic Condition. *Electronics* **2023**, *12*, 2827.
https://doi.org/10.3390/electronics12132827

**AMA Style**

Huang W, Chen J, Hu J, Lv K, Liu H.
Search-Coil Based Stator Interturn Fault Detection in Permanent Magnet Machines Running under Dynamic Condition. *Electronics*. 2023; 12(13):2827.
https://doi.org/10.3390/electronics12132827

**Chicago/Turabian Style**

Huang, Wen, Junquan Chen, Jinghua Hu, Ke Lv, and Haitao Liu.
2023. "Search-Coil Based Stator Interturn Fault Detection in Permanent Magnet Machines Running under Dynamic Condition" *Electronics* 12, no. 13: 2827.
https://doi.org/10.3390/electronics12132827