# A Detection Method for Slight Inter-Turn Short-Circuit Fault in Dry-Type Air-Core Shunt Reactors

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Equivalent Circuit

^{th}coil is shown in Figure 1. In the figure, ${I}_{i}$, ${R}_{i}$, and ${L}_{i}$ represent the branch current, resistance, and self-inductance of the i

^{th}coil, respectively; I

_{n}

_{+1}, R

_{n}

_{+1}, and L

_{n}

_{+1}represent the induced current, resistance, and self-inductance of the short-circuit loop, respectively; ${R}_{f}$ represents the insulation resistance; M

_{ij}represents the mutual inductance between the i

^{th}and j

^{th}coils; M

_{i}

_{(n+1)}represents the mutual inductance between the i

^{th}coil and the short-circuit loop; I represents the bus current; and U represents the terminal voltage.

#### 2.2. Inter-Turn Short-Circuit Fault When ${R}_{f}=0$

#### 2.2.1. ISCF Occurring in Different Coils within the Same Encapsulate

#### 2.2.2. ISCF Occurring in Different Encapsulates

#### 2.3. Local Inter-Turn Short-Circuit Fault When ${R}_{f}\ne 0$

#### 2.3.1. ISCF Detection Method

_{sc}and I

_{N}, respectively. Then the active power under an ISCF and under normal conditions can be expressed as

_{A}in (10).

_{A}are equal to 1. However, after an ISCF occurs in the reactor, the equivalent resistance increases, causing both parameters to be greater than 1. Therefore, the operational status of the reactor can be determined based on the amplitudes of these parameters.

_{A}at different insulation resistances are shown in Figure 5. As shown in the figure, with the development of the fault, as the insulation resistance decreases, all four parameters increase. The curves of the equivalent resistance change ratio and the active power change ratio overlap. PLF and PLF

_{A}are essentially equal, and both are greater than the other two parameters, indicating higher sensitivity. However, at the early stages of the fault, when the insulation resistance ${R}_{f}>40\mathsf{\Omega}$, the amplitudes of the above parameters tend to stabilize (equivalent resistance ratio ≈ active power ratio ≈ 1.028, PLF ≈ PLF

_{A}≈ 1.055). With an increase in insulation resistance, there is no significant change. Therefore, it can be concluded that if an ISCF occurs at a height closer to the end of the winding, at the early stages of insulation damage (${R}_{f}>40\mathsf{\Omega}$), the amplitudes of the above parameters tend to approach 1, which may lead to misjudgment. Therefore, based on PLF, this paper proposes a higher sensitivity method for ISCF detection in reactors.

_{A}with variable a yields the fault detection factor (FDF). The expression for the FDF is given by (11),

#### 2.3.2. The Impact of Noise Signals on Fault Detection Reliability

## 3. Results

## 4. Conclusions

- (1)
- For different coils within the same encapsulate of dry-type air-core reactors, the equivalent resistance and active power of a global ISCF at the same height show almost no change. As the fault moves outside the encapsulate, both the equivalent resistance and active power increase initially and then decrease. Moving from the middle to the end of the fault height results in a decreasing trend.
- (2)
- The equivalent resistance and active power experience significant increments in the presence of an ISCF, reaching up to 50 and 60 times the rated values, respectively, without accounting for insulation resistance.
- (3)
- At the initial stage of a local ISCF with one turn, the insulation resistance is relatively high, making it challenging to detect the fault. A larger exponent ‘a’ in the FDF has better sensitivity in detecting ISCFs under the aforementioned condition without considering the noise signal.
- (4)
- The FDF applied with an MAF can improve the reliability of the proposed method by reducing the fluctuation amplitude of the FDF to reduce the misjudgment likelihood in ISCF detection while guaranteeing the sensitivity of the detection proposed method when the signal noise in the monitoring system is considered.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**The fault factor curve with the variation in exponent a when the reactor is under normal conditions.

**Figure 8.**The fault factor curve with the variation in exponent a when the reactor is under an inter-turn short-circuit fault condition.

**Figure 9.**The fault factor curve handled by a moving average filter with the variation in exponent a when the reactor is under normal conditions.

**Figure 10.**The fault factor curve handled by a moving average filter with the variation in exponent a when the reactor is under an inter-turn short circuit-fault condition.

**Figure 11.**The fault factor curve handled by a moving average filter with the variation in exponent a when reactor II is under normal conditions.

**Figure 12.**The fault factor curve handled by a moving average filter with the variation in exponent a when reactor II is under an inter-turn short-circuit fault condition.

Parameters | Value | Parameters | Value |
---|---|---|---|

Rated capacity (kVar) | 20,000 | Rated current (A) | 989.7 |

Rated voltage (kV) | 20.21 | Height (mm) | 1990 |

Number of encapsulates | 13 | Outer radius (mm) | 2807.1 |

Number of coils | 44 | Equivalent reactance (Ω) | 20.42 |

Rated frequency (Hz) | 50 | Equivalent resistance (Ω) | 0.051 |

**Table 2.**The ratio of variables for a global inter-turn short-circuit fault at each winding at Height 1.

Encapsulate | Coil | Equivalent Resistance Ratio | Active Power Ratio |
---|---|---|---|

1 | 1 | 15.982 | 16.176 |

2 | 16.117 | 16.317 | |

3 | 16.260 | 16.463 | |

4 | 16.394 | 16.600 | |

5 | 16.535 | 16.744 | |

3 | 1 | 26.506 | 27.299 |

2 | 26.693 | 27.499 | |

3 | 26.878 | 27.695 | |

4 | 27.077 | 27.905 | |

11 | 1 | 53.580 | 60.194 |

2 | 53.485 | 60.078 | |

3 | 53.420 | 59.988 |

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

Rated capacity (kVar) | 20,000 | Rated current (A) | 989.7 |

Rated voltage (kV) | 20.21 | Height (mm) | 2540 |

Number of encapsulates | 14 | Outer radius (mm) | 3024 |

Number of coils | 44 | Equivalent reactance (Ω) | 20.65 |

Rated frequency (Hz) | 50 | Equivalent resistance (Ω) | 0.039 |

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**MDPI and ACS Style**

Wu, J.; Zhen, W.; Chang, Z.; Zhang, M.; Peng, Y.; Liu, Y.; Huang, Q.
A Detection Method for Slight Inter-Turn Short-Circuit Fault in Dry-Type Air-Core Shunt Reactors. *Energies* **2024**, *17*, 1709.
https://doi.org/10.3390/en17071709

**AMA Style**

Wu J, Zhen W, Chang Z, Zhang M, Peng Y, Liu Y, Huang Q.
A Detection Method for Slight Inter-Turn Short-Circuit Fault in Dry-Type Air-Core Shunt Reactors. *Energies*. 2024; 17(7):1709.
https://doi.org/10.3390/en17071709

**Chicago/Turabian Style**

Wu, Jie, Wei Zhen, Zhengwei Chang, Man Zhang, Yumin Peng, Ying Liu, and Qi Huang.
2024. "A Detection Method for Slight Inter-Turn Short-Circuit Fault in Dry-Type Air-Core Shunt Reactors" *Energies* 17, no. 7: 1709.
https://doi.org/10.3390/en17071709