# Pre-Arcing Time Prediction in a Making Test for a 420 kV 63 kA High-Speed Earthing Switch

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## Abstract

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## 1. Introduction

_{6}insulation technology using the streamer discharge theory [16,17,18]. In particular, partial discharges and breakdown at protrusions in uniform electric fields in SF

_{6}have been discussed in both experimental and theoretical ways in Reference [16]. The steamer radius and length, which are important parameters for breakdown process, were experimentally investigated in Reference [17]. The formulation of the breakdown voltage was well organized and the condition to build a streamer in SF

_{6}was introduced in Reference [18]. Using the breakdown formulation in Reference [18], this paper suggests a process for predicting the pre-arcing time for the HSES making performance by comparing the results from the theoretical calculations and numerical simulations. Moreover, a development test was conducted to verify the making performance of the HSES by applying a 63 kA short-circuit current in a high-power laboratory.

## 2. Streamer Discharge Theory

_{6}is relatively high when compared to that of other insulating gases, due to its electron affinity. The electron affinity of an atom or a molecule is defined as the amount of energy released when an electron is added to a neutral atom or a molecule in a gaseous state to form a negative ion. In general, halogen atoms release the highest amounts of energy (F = 3.40 eV, Cl = 3.61 eV, Br = 3.36 eV, I = 3.06 eV) to gain an electron, as they become more stable when a filled valence shell is obtained [19]. Therefore, the electron affinity of SF

_{6}, which contains six fluorine atoms, is comparatively higher than that of common gases. Because of its high electron affinity, SF

_{6}has a high insulating performance as it combines with free electrons generated in the electric field. Nevertheless, when a high electric field is applied, the SF

_{6}molecules are ionized and produce many free electrons via a self-propagation process.

_{crit}. After exceeding N

_{crit}, the electron avalanche gradually progresses as a streamer. The authors in Reference [18] introduced the following relationship to calculate N

_{crit}.

_{crit}is the critical distance where α = η. The author in Reference [21] suggested that the critical value N

_{crit}reached the order of 10

^{8}regardless of gas type or the field uniformity, and Reference [18] took N

_{crit}as 10

^{8}. To calculate the effective ionization coefficient α′ = α − η, the linear relation between α′ and (E/P) is given as follows [18]:

_{crit}of SF

_{6}is 3.3 times that of air, which helps to maintain an improved dielectric performance. It is well known that the dielectric strength of air is 30–40% that of SF

_{6}. By substituting Equation (2) into Equation (1), the breakdown electric field E

_{bd}can be calculated from the following equation [18]:

_{crit}become constant so that the integral term can be worked out as ${E}_{bd}^{\mathrm{max}}$ × l where ${E}_{bd}^{\mathrm{max}}$ is the maximum breakdown electric field strength and l is the gap length. In the case of non-uniform electric fields, E(x) and x

_{crit}are not constants; rather, they are functions defined as follows:

_{crit}is relatively small compared to R

_{1}and R

_{2}. By substituting Equations (4) and (5) into Equation (3), the following can be obtained:

## 3. Making Test Conditions

- The high-voltage interval is the time from the commencement of the test to the moment of breakdown (from commencement to t
_{0}). - The pre-arcing interval is the time from the moment of breakdown across the contact gap to the touching of the contacts (from t
_{0}to t_{1}). - The latching interval is the time from the touching of the contacts to the moment when the contacts reach the fully closed (latched) position (from t
_{1}to t_{2}).

_{0}, t

_{1}, and t

_{2}are shown in Figure 2. t

_{0}is the moment that the short-circuit current begins to flow, t

_{1}is the moment of contact touch, and t

_{2}is the moment that the closing operation finishes. For the short-circuit making test, the HSES should be subjected to symmetrical and asymmetrical test procedures in accordance with Table 1 [24]. The symmetry of short-circuit making current is determined by the time of the making moment. If both contacts of the HSES make at the peak value of the rated voltage with a tolerance of −30 electrical degrees to +15 electrical degrees, the short-circuit making current flows symmetrically, leading to the longest pre-arcing time. Meanwhile, the asymmetrical current flows between contacts with no arc when they make at the voltage zero point. Therefore, the two moments of t

_{0}and t

_{1}are the same. Figure 2 presents two examples of making test waveforms that are (a) symmetrical and (b) asymmetrical short-circuit currents for the HSES. As shown in these waveforms, for the symmetrical case, the short-circuit current began near the voltage peak position, and the pre-arc exists until the contact touch point. For the asymmetrical case, the short-circuit current occurred at the voltage zero without generating a pre-arc.

_{r}is a rated voltage of 420 kV, with a peak value of approximately 343 kV [24].

## 4. Closing Operation Timing Measurement

## 5. Simulation and Experimental Results

#### 5.1. Simulation Results

_{6}as 0.55 MPa and the harmonic average radius of the contacts of our HSES model. The graph in Figure 5 shows the results of the comparison between the average breakdown electric field strength (${E}_{bd}^{av}$) and the peak value of electric field distribution (E

_{peak}) in the electrostatic numerical simulation.

#### 5.2. Experimental Result Comparisons

_{exp}) and the predicted pre-arcing times (t

_{sim}) was found. The difference of these results was analyzed as being caused by the dielectric difference between the ideal condition consistent with design drawings and the real experimental condition. For example, in real situations, there are many variables such as metallic particles, eccentricity of moving parts, assembly tolerance, etc. that can deteriorate the dielectric strength between the contacts, especially if the contacts have been damaged by the arc energy from repeated test procedures. If the dielectric strength deteriorated for these reasons, the pre-arcing time could be prolonged.

_{av}) calculation result of each test condition is shown in Figure 10 using the Cassie arc model introduced in Reference [28]. According to the Cassie arc model, which is suitable for arcs with a high current, the following differential equation for the arc conductance is represented.

_{arc}and i

_{arc}are the arc voltage and current; τ and U

_{c}are the constants that determine the arc characteristic. By comparing the test results and simulation results, the researchers in Reference [28] calculated that τ = 0.000012 and U

_{c}= 80. From the arc voltage in Equation (12) and the arc current measured from our test results, the average arc energy can be calculated as follows:

## 6. Conclusions

- The average breakdown electric field strength was calculated based on the streamer discharge theory, considering the gas pressure, harmonic radius of contacts, distance between electrodes, etc.
- The real travel distance data from switches (HSES, DS, and CB) were obtained by measuring the operating characteristics.
- The two-dimensional or three-dimensional electric field distributions of the test objects were analyzed using finite element method analysis tools in accordance with the real travel distance data.
- The results of the calculated average breakdown electric field strength and peak value of the simulated electric field distribution were compared.
- The breakdown factor λ was calculated and the time when this factor became greater than 1 was found.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${N}_{crit}$ | average number of electrons in the avalanche at the moment when the number of electrons exceed that of positive ions |

$\alpha $ | ionization coefficient |

$\eta $ | electron attachment coefficient |

$\alpha \prime $ | effective ionization coefficient |

${x}_{crit}$ | critical distance where α = η |

$E(x)$ | electric field strength at a gap length x |

$P$ | gas pressure |

$K$ | coefficient |

${E}_{bd}$ | breakdown electric field strength |

${E}_{bd}^{\mathrm{max}}$ | maximum breakdown electric field strength |

${E}_{bd}^{av}$ | average breakdown electric field strength |

$R$ | harmonic radius of positive and negative poles |

${R}_{1}$, ${R}_{2}$ | radii of positive and negative poles |

$m$ | coefficient |

$l$ | contact gap length |

$u$ | field utilization factor |

$d$ | wire diameter of spring |

$D$ | average diameter of spring |

${D}_{1}$ | inner diameter of spring |

${D}_{2}$ | outer diameter of spring |

${N}_{a}$ | number of active coils |

$G$ | shear modulus of elasticity |

$L$ | free length of spring |

${P}_{1}$, ${P}_{2}$ | loads for stretching |

$k$ | spring constant |

${\tau}_{1}$, ${\tau}_{2}$ | loads for stretching |

${U}_{r}$ | rated voltage |

$\lambda $ | breakdown factor |

${t}_{\mathrm{exp}}$, ${t}_{sim}$ | experimental and simulation pre-arcing times |

${W}_{av}$ | average arc energy |

$g$, ${u}_{arc}$, ${i}_{arc}$ | arc conductance, voltage and current |

$\tau $, ${U}_{c}$ | arc time constant and voltage constant |

${t}_{arc}$ | arcing time |

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**Figure 2.**Waveforms of the high-speed earthing switch making test results: (

**a**) symmetrical test; (

**b**) asymmetrical test.

**Figure 5.**Comparison of graphs of the analytical average breakdown and the numerical simulation’s peak values of electric field strength with the pre-arcing time prediction result.

**Figure 6.**Results of electrostatic simulation at a 15 mm contact gap: (

**a**) electric potential [kV]; (

**b**) electric field strength [kV/mm].

**Figure 7.**Results of breakdown factor λ and field utilization factor u: (

**a**) three-dimensional distribution of breakdown factor; and (

**b**) graphs of breakdown factor and field utilization factor.

**Figure 10.**Comparison between the experiment (t

_{exp}) and simulation (t

_{sim}) results of pre-arcing time with average arc energy (W

_{av}) calculated from the measured short-circuit current.

Procedures | Conditions | Outputs |
---|---|---|

Symmetrical | Making at the peak of the voltage wave with a tolerance of −30 electrical degrees to +15 electrical degrees | Symmetrical short-circuit current with the longest per-arcing time |

Asymmetrical | Making at the zero of the voltage wave | Asymmetrical short-circuit current without pre-arcing |

Symbol | Meaning of Symbol | Value | |

d | 10 mm | Wire diameter | |

D | Average diameter | 47.5 mm | |

D_{2} | Outer diameter | 57.5 mm | |

N_{a} | Number of active coils | 17 turns | |

G | Shear modulus of elasticity | 8000 N/mm^{2} | |

L | Free length | 275 mm | |

P_{1} | Load for stretching 25 mm | 203.22 N | |

P_{2} | Load for stretching 65 mm | 422.87 N | |

k | Spring constant | 5.49 N/mm | |

τ_{1} | Shear stress by P_{1} | 24.59 N/mm^{2} | |

τ_{2} | Shear stress by P_{2} | 51.15 N/mm^{2} |

Test No. | Breakdown Voltage [kV] | Making Current [kA_{rms}] | Pre-Arcing Time [ms] | Make Time [ms] |
---|---|---|---|---|

16-0530-020 (#20) | 105.6 | 21.08 | 2.9 | 80.1 |

16-0530-021 (#21) | 172.5 | 20.94 | 4.9 | 77.8 |

16-0530-025 (#25) | 221.9 | 22.90 | 7.4 | 74.3 |

16-0530-048 (#48) | 271.7 | 31.81 | 7.2 | 69.4 |

16-0530-050 (#50) | 300.3 | 60.74 | 10.8 | 70.3 |

16-0530-051 (#51) | 332.0 | 64.65 | 11.8 | 69.6 |

Classification | Good | Fair | Poor |
---|---|---|---|

Width ratio of contact chip | ≥99% | 98–99% | ≤98% |

1st inspection (after Test #25) | 44.4% | 55.6% | 0% |

2nd inspection (after Test #51) | 16.7% | 36.1% | 47.2% |

No. | Initial | 1st Inspection | 2nd Inspection |
---|---|---|---|

1 | 6.90 μΩ | 26.60 μΩ | 29.50 μΩ |

2 | 6.80 μΩ | 26.30 μΩ | 28.20 μΩ |

3 | 6.80 μΩ | 26.10 μΩ | 27.60 μΩ |

Average | 6.83 μΩ | 26.33 μΩ | 28.43 μΩ |

Ratio of average | 1 | 3.85 | 4.16 |

Elongation Length | Inspection No. | Initial Value | Spring 1 | Spring 2 | Spring 3 | Spring 4 |
---|---|---|---|---|---|---|

40 mm (N) | 1st | 70.41 | 68.84 | 72.96 | 76.10 | 70.41 |

2nd | 70.41 | 70.41 | 76.88 | 77.47 | 72.96 | |

55 mm (N) | 1st | 117.48 | 115.33 | 119.44 | 122.98 | 116.90 |

2nd | 117.48 | 115.33 | 123.37 | 123.76 | 118.86 | |

Spring Constant (N/mm) | 1st | 3.138 | 3.100 | 3.100 | 3.128 | 3.100 |

2nd | 3.138 | 2.991 | 3.100 | 3.089 | 3.060 |

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**MDPI and ACS Style**

Kang, M.-C.; Kim, K.-H.; Yoon, Y.T.
Pre-Arcing Time Prediction in a Making Test for a 420 kV 63 kA High-Speed Earthing Switch. *Energies* **2017**, *10*, 1584.
https://doi.org/10.3390/en10101584

**AMA Style**

Kang M-C, Kim K-H, Yoon YT.
Pre-Arcing Time Prediction in a Making Test for a 420 kV 63 kA High-Speed Earthing Switch. *Energies*. 2017; 10(10):1584.
https://doi.org/10.3390/en10101584

**Chicago/Turabian Style**

Kang, Min-Cheol, Kyong-Hoe Kim, and Yong Tae Yoon.
2017. "Pre-Arcing Time Prediction in a Making Test for a 420 kV 63 kA High-Speed Earthing Switch" *Energies* 10, no. 10: 1584.
https://doi.org/10.3390/en10101584