# Streamer Propagation along the Insulator with the Different Curved Profiles of the Shed

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Arrangement and Measurement System

^{9}Ω under the test condition.

## 3. Experimental Results

#### 3.1. Streamer Propagation Fields

_{st}corresponding to streamer propagation probability of 97.5% [15]. Figure 4 shows that the relation between the pulse amplitude and the streamer “stability” propagation fields is linear. There is inverse proportional relationship between the streamer “stability” propagation fields and the pulse amplitude, as same as the result in the literature [18]. The streamer “stability” propagation fields for the insulator with a shed are larger than that for the smooth insulation surface and the air alone. Specifically, the streamer “stability” propagation fields are inversely proportional to the fillet diameters of the curved profiles of the sheds.

#### 3.2. Light Emission

#### 3.3. Streamer Propagation Velocity

_{st}were defined as the velocities of streamer propagation at the stability fields [22]. The velocities of streamers propagating along the insulators with a shed decreases linearly but slowly with the pulse amplitude in Figure 12. The velocities of the “air” component along the insulators with a shed are higher than that along the smooth insulator in Figure 13. The reason could be found in the literature [15]. It is obvious that the “air” component velocities are proportional to the fillet diameters of the curved profiles of the sheds.

#### 3.4. Evolution of Streamer to Flashover

_{50}corresponding to flashover propagation probability of 50% could be acquired by the method of acquiring the streamer “stability” propagation fields E

_{st}. Table 1 shows that the flashover “stability” propagation fields E

_{50}increase with streamer “stability” propagation fields E

_{50}. The flashover “stability” propagation fields are also inversely proportional to the fillet diameters of the curved profiles of the sheds. Hence, the applied electric field has the same effect on the streamer propagation and the subsequent flashover propagation.

## 4. Discussion

#### 4.1. Tangential Electric Field along Streamer Propagation Path

#### 4.2. Streamer Propagation Energy Loss at the Shed

_{shc}) differed by an error (Q

_{ste}) from the real energy loss (L

_{shc}) as shown in Equation (1).

_{st1}is the stability fields for streamer propagation along insulators with a shed. v

_{1}/v

_{2}is the “air” component velocity before/after the shed at E

_{st1}. Q

_{Ef1}/Q

_{Es1}is the energy obtained from ambient electric field before/after the shed. E

_{f2}is the ambient field corresponding to the same value of v

_{1}when streamer propagates along smooth insulators during the first half part of air gap. E

_{s2}is the ambient field corresponding to the same value of v

_{2}when streamer propagates in air alone during the second half part of air gap. Q

_{Ef2}/Q

_{Es2}is the energy obtained from ambient electric field E

_{f2}/E

_{s2}in its case.

_{shc}) is inversely proportional to the fillet diameters of the curved profile of the shed. From the perspective of the energy loss, the streamer propagation energy loss at the shed is inversely proportional to the fillet diameters of the curved profile of the shed. Therefore, the streamer “stability” propagation fields are inversely proportional to the fillet diameters, and the streamer propagation velocities are proportional to the fillet diameters under the same electric field.

#### 4.3. Influence of the Material Properties

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Streamer discharge photographs (Insulator A). (

**a**) 570 kV/m, (

**b**) 590 kV/m, (

**c**) 630 kV/m, (

**d**) 680 kV/m, (

**e**) 710 kV/m, (

**f**) 740 kV/m.

**Figure 6.**Streamer discharge photographs (Insulator B). (

**a**) 610 kV/m, (

**b**) 630 kV/m, (

**c**) 650 kV/m, (

**d**) 690 kV/m, (

**e**) 710 kV/m, (

**f**) 750 kV/m.

**Figure 7.**Streamer discharge photographs (Insulator C). (

**a**) 630 kV/m, (

**b**) 650 kV/m, (

**c**) 690 kV/m, (

**d**) 720 kV/m, (

**e**) 750 kV/m, (

**f**) 780 kV/m.

**Figure 8.**Streamer propagation photographs measured by ICCD camera (Insulator A). (

**a**) 618 kV/m (

**b**) 643 kV/m, (

**c**) 690 kV/m, (

**d**) 720 kV/m.

**Figure 9.**Streamer propagation photographs measured by ICCD camera (Insulator B). (

**a**) 620 kV/m, (

**b**) 660 kV/m, (

**c**) 700 kV/m, (

**d**) 740 kV/m.

**Figure 10.**Streamer propagation photographs measured by ICCD camera (Insulator C). (

**a**) 640 kV/m (

**b**) 680 kV/m, (

**c**) 720 kV/m (

**d**) 760 kV/m.

**Figure 14.**Photographs of flashover along the insulator with the shed. (

**a**) Insulator A. (

**b**) Insulator B. (

**c**) Insulator C.

**Figure 19.**Vector plots of the electric field distribution along the surface of the polymer. (

**a**) no surface charge, (

**b**) −10 μC/m

^{2}surface charge. The darker part is polymer material, the white part is air.

**Table 1.**The comparison of streamer “stability” propagation fields Est and flashover “stability” propagation fields E50.

Shed Configuration | E_{st}(kV/m) | E_{50}(kV/m) |
---|---|---|

Insulator A | 585 | 824 |

Insulator B | 605 | 842 |

Insulator C | 630 | 863 |

Shed Configuration | Insulator A | Insulator B | Insulator C |
---|---|---|---|

E_{st1}(kV/m) | 585 | 605 | 630 |

v_{1}(10^{5} m/s) | 1.4 | 1.45 | 1.52 |

v_{2}(10^{5} m/s) | 2.48 | 2.68 | 2.84 |

Q_{Ef1}(10^{4} J/C) | 2.93 | 3.03 | 3.15 |

Q_{Es1}(10^{4} J/C) | 2.93 | 3.03 | 3.15 |

E_{f2}(kV/m) | 580 | 595 | 610 |

E_{s2}(kV/m) | 527 | 535 | 550 |

Q_{Ef2}(10^{4} J/C) | 2.9 | 2.975 | 3.05 |

Q_{Es2}(10^{4} J/C) | 2.635 | 2.675 | 2.75 |

L_{shc}(10^{4} J/C) | 0.315 | 0.4 | 0.5 |

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**MDPI and ACS Style**

Meng, X.; Wang, L.; Mei, H.; Cao, B.; Bian, X.
Streamer Propagation along the Insulator with the Different Curved Profiles of the Shed. *Polymers* **2022**, *14*, 897.
https://doi.org/10.3390/polym14050897

**AMA Style**

Meng X, Wang L, Mei H, Cao B, Bian X.
Streamer Propagation along the Insulator with the Different Curved Profiles of the Shed. *Polymers*. 2022; 14(5):897.
https://doi.org/10.3390/polym14050897

**Chicago/Turabian Style**

Meng, Xiaobo, Liming Wang, Hongwei Mei, Bin Cao, and Xingming Bian.
2022. "Streamer Propagation along the Insulator with the Different Curved Profiles of the Shed" *Polymers* 14, no. 5: 897.
https://doi.org/10.3390/polym14050897