#
Determination of the Operating Temperature of the Gas-Insulated Transmission Line^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{6}(sulfur hexafluoride) under pressures ranging from 0.29 to 0.51 MPa (at 20 °C). In the next generation of GILs, SF

_{6}has been replaced with a mixture of nitrogen and SF

_{6}. The operation pressure is dependent on the mixture temperature and is specific in particular installations. Due to environmental protection requirements, the mixture of N

_{2}and SF

_{6}is preferred in applications where large gas quantities are used and where dielectric performance is desired [9,10,11,12,13,14,15,16,17,18,19,20].

## 2. Magneto-Thermal Modeling

_{e}are the power losses in the phase conductor and in the enclosure, respectively, Q

_{C}and Q

_{eC}are the convection heat transfer of the phase conductor and the enclosure, respectively, and Q

_{R}and Q

_{eR}are the radiation heat transfer of the phase conductor and the enclosure, respectively.

_{e}are the temperatures of the phase conductor and the enclosure, respectively, T

_{o}is the ambient temperature, λ is the thermal conductivity of the phase conductor, α is the convective heat transfer coefficient of the phase conductor, ${\sigma}_{o}=5.67\xb7{10}^{-8}\left[\frac{\mathrm{W}}{{\mathrm{m}}^{2}{\mathrm{K}}^{4}}\right]$ is the Stefan–Boltzmann constant and ε

_{n}is emissivity, which can be calculated from the following equation [12]:

_{e}is an emissivity of the enclosure.

_{e}is the convective heat transfer coefficient of the enclosure.

_{e}

_{13}has a following form

_{r}and convection α

_{c}heat transfer coefficient. If radiation heat flow occurs between two surfaces F1 and F2, then the radiation heat transfer coefficient can be calculated by [33]:

_{F,F}

_{1}is a configuration coefficient of surfaces F1 and F2. The configuration coefficient depends on the shape and the mutual location of the surfaces. In the case of the tubular high-current busduct, surface F1 is placed concentric to surface F2 (Figure 2).

_{F}

_{1,F2}can be calculated using the following equation [33]:

- F1 is the area of the outer phase conductor surface,
- F2 is the area of the inner enclosure surface,
- ε
_{1}is the emissivity of the surface F1 and - ε
_{2}is the emissivity of the surface F2.

_{c}can be determined using the similarity theory and non-dimensional parameters, including the Grashof (Gr), Prandtl (Pr), Rayleigh (Ra) and Nusselt (Nu) numbers [28,33]. The Nusselt number, Nu, for the two concentric cylinders can be defined by the following equation [33]:

_{P}is the specific heat, $\Delta T$ is the temperature difference and C and n are dimensionless constants dependent on the system (Table 1) [33]. Index m in Equation (35) indicates that the gas properties, such as ν, η, c

_{P,}should be evaluated at the average temperature ${T}_{m}=0.5\xb7({T}_{S}+{T}_{O})$, where T

_{S}is the temperature of the surface and T

_{O}is the temperature of fluid sufficiently far from the surface. The Nusselt number can be also expressed by the following equation:

_{c}to be calculated.

_{P}, dynamic viscosity η, kinematic viscosity ν), on quality of the surface (emissivity ε) and on the difference in temperatures between the enclosure/phase conductor and the environment. On the other hand, the above mentioned physical properties depend on the temperature of the air as shown in Table 2.

## 3. Numerical Example

_{1}= 12 mm, R

_{2}= 15 mm, R

_{3}= 23 mm, R

_{4}= 25 mm and d = 60 mm. Both the phase conductors and the screen were assumed to be aluminum, which has an electric conductivity of γ = 33 MS·m

^{−1}. The frequency was 50 Hz. Currents in the phase conductors were ${\underset{\xaf}{I}}_{1}=300$A, ${\underset{\xaf}{I}}_{2}=300\mathrm{exp}[-\mathrm{j}\frac{2}{3}\pi ]$A, ${\underset{\xaf}{I}}_{3}=300\mathrm{exp}[\mathrm{j}\frac{2}{3}\pi ]$A. The ambient temperature was T

_{o}= 24 °C. The length of the busduct system was assumed to be l = 3900 mm. The results of the calculations are shown in Table 3.

^{−1}, ${\mu}_{0}=4\pi {10}^{-7}\frac{H}{m}$ and $\lambda =200\frac{W}{mK}$. The radiation was taken into account by setting the boundary condition, known as diffuse surface, on the edges of the areas and by introducing the emissivity coefficient on these surfaces (ε = 0.6). In turn, a natural convection was taken into account by applying the heat transfer in fluid condition to the areas of gas presence and setting the velocity field option at 0.01 m/s along the y axis. Physics-controlled mesh was used. Elements size was set as finer.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Alter, J.; Ammann, M.; Boeck, W.; Degen, W.; Diessner, A.; Koch, H.; Renaud, F.; Poehler, S. N
_{2}/SF_{6}Gas-Insulated Line of a New GIL Generation in Service; CIGRE Session No. 39; CIGRE: Paris, France, 2002; pp. 21–204. [Google Scholar] - Anderson, D.M.; Wollenberg, B.F. Solving for three phase conductively isolated busbar voltages using phase component analysis. IEEE Trans. Power Syst.
**1995**, 10, 98–108. [Google Scholar] [CrossRef] - Bednarek, K.; Jajczyk, J. Effectiveness of optimization methods in heavy-current equipment designing. Przegląd Elektrotechniczny
**2009**, 85, 29–32. [Google Scholar] - Benato, R.; di Mario, C.; Koch, H. High-capability applications of long gas-insulated lines in structures. IEEE Trans. Power Deliv.
**2007**, 22, 619–626. [Google Scholar] [CrossRef] - Benato, R.; Dughiero, F. Solution of coupled electromagnetic and thermal problems in gas insulated transmission lines. IEEE Trans. Magn.
**2003**, 3, 1741–1744. [Google Scholar] [CrossRef] - Benato, R.; Dughiero, F.; Forzan, M.; Paolucci, A. Proximity effect and magnetic field calculation in GIL and in isolated phase bus ducts. IEEE Trans. Magn.
**2002**, 2, 781–784. [Google Scholar] [CrossRef] - CIGRE. Gas Insulated Transmission Lines (GIL); TB 218; CIGRE: Paris, France, 2003. [Google Scholar]
- CIGRE. Application of Long High Capacity Gas Insulated Lines (GIL); TB 351; CIGRE: Paris, France, 2008. [Google Scholar]
- Dokopoulos, P.; Tampakis, D. Analysis of field and losses in a three phase gas cable with thick walls, part I field analysis. IEEE Trans. Power Appar. Syst.
**1984**, PAS-103, 2728–2734. [Google Scholar] [CrossRef] - Dokopoulos, P.; Tampakis, D. Analysis of field and losses in a three phase gas cable with thick walls, part II calculation of losses and results. IEEE Trans. Power Appar. Syst.
**1985**, PAS-104, 9–15. [Google Scholar] - Filippopoulos, G.; Tsanakas, D. Analytical calculation of the magnetic field produced by electric power lines. IEEE Trans. Power Deliv.
**2005**, 20, 1474–1482. [Google Scholar] [CrossRef] - Ho, S.L.; Li, Y.; Lo, E.W.C.; Xu, J.Y.; Lin, X. Analyses of the three-dimensional eddy current field and thermal problems in an isolated phase bus. IEEE Trans. Magn.
**2003**, 39, 1515–1518. [Google Scholar] [CrossRef][Green Version] - Ho, S.L.; Li, Y.; Lin, X.; Lo, E.W.C.; Cheng, K.W.E.; Wong, K.F. Calculations of eddy current, fluid and thermal fields in an air insulated bus duct system. IEEE Trans. Magn.
**2007**, 43, 1433–1436. [Google Scholar] [CrossRef][Green Version] - Hongtao, L.; Naiqiu, S.; Hui, P.; Zipin, L. Electromagnetic-thermal scale model of gas-insulated bus bars. TELKOMNIKA Indones. J. Electr. Eng.
**2014**, 12, 4988–4995. [Google Scholar] - Hwang, C.C.; Chang, J.J.; Jiang, Y.H. Analysis of electromagnetic and thermal fields for a bus duct system. Electr. Power Syst. Res.
**1998**, 45, 39–45. [Google Scholar] [CrossRef] - Jajczyk, J.; Kasprzyk, L. The use of coupled temperature and electromagnetic fields in optimization problems. In Proceedings of the 6th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment (THE’08), Rhodes, Greece, 20–22 August 2008; pp. 226–231. [Google Scholar]
- Kim, H.K.; Oh, Y.H.; Lee, S.H. Calculation of the temperature rise in the gas insulated busbar by coupled magneto-thermal-fluid analysis. J. Electr. Eng. Technol.
**2009**, 4, 510–514. [Google Scholar] [CrossRef][Green Version] - Koch, H. Gas-Insulated Transmission Lines (GIL); John Wiley & Sons: Hoboken, NJ, USA, 2012. [Google Scholar]
- Koch, H.; Schoeffner, G. Gas-insulated transmission line (GIL) an overview. Electra
**2003**, 211, 8–17. [Google Scholar] - Koch, H. Experience with 2nd generation gas-insulated transmission lines GIL. In Proceedings of the JICABLE 03, Versailles, France, 22–26 June 2003; pp. 83–88. [Google Scholar]
- Labridis, D.; Hatziathanassiou, V. Finite element computation of field, forces and inductances in underground SF
_{6}insulated cables using a coupled magneto-thermal formulation. IEEE Trans. Magn.**1994**, 4, 1407–1415. [Google Scholar] [CrossRef] - Labridis, D.; Dokopoulos, P. Finite element computation of field, losses and forces in a three-phase gas cable with non-symmetrical conductor arrangement. IEEE Trans. Power Deliv.
**1988**, 4, 1326–1333. [Google Scholar] [CrossRef] - Murusawa, I.; Ichihara, M.; Kawai, T.; Miyazaki, A.; Takinami, N. Development of long-distance 275 kV gas insulated transmission line (GIL). In Proceedings of the 11th International Conference on Gas Discharge and Their Applications, Tokio, Japan, 11–15 September 1995. [Google Scholar]
- Piątek, Z. Impedances of Tubular High Current Busducts; Polish Academy of Sciences: Warsaw, Poland, 2008. [Google Scholar]
- Piątek, Z. Self and mutual impedances of a finite length gas insulated transmission line (GIL). Electr. Power Syst. Res.
**2007**, 77, 191–203. [Google Scholar] [CrossRef] - Sabot, A.; Volcker, O.; Koch, H. Discussion of “Insulation coordination for gas-insulated transmission lines (GIL)” and closure. IEEE Trans. Power Deliv.
**2001**, 16, 822–824. [Google Scholar] [CrossRef] - Sarajcev, P. Numerical analysis of the magnetic field of high-current busduct and GIL systems. Energies
**2011**, 4, 2196–2211. [Google Scholar] [CrossRef][Green Version] - Sun, G.; Jin, X.; Xie, Z. Analytical calculation of coupled magnetothermal problem in gas insulated transmission lines. TELKOMNIKA Indones. J. Electr. Eng.
**2013**, 11, 645–652. [Google Scholar] [CrossRef][Green Version] - Szczegielniak, T.; Kusiak, D.; Jabłoński, P.; Piątek, Z. Power losses in a three-phase single-pole gas-insulated transmission line (GIL). Int. Rev. Electr. Eng.
**2013**, 8, 1624–1630. [Google Scholar] - Völcker, O.; Koch, H. Insulation co-ordination for gas-insulated transmission lines (GIL). IEEE Trans. Power Deliv.
**2001**, 16, 122–130. [Google Scholar] [CrossRef] - Wu, X.; Shu, N.; Li, H.; Li, L. Thermal analysis in gas insulated transmission lines using an improved finite-element model. TELKOMNIKA
**2013**, 11, 458–467. [Google Scholar] [CrossRef] - Mc Lachlan, N.W. Bessel Functions for Engineers, 2nd ed.; PWN: Warsaw, Poland, 1964. (In Polish) [Google Scholar]
- Hering, M. Termokinetics for Electricians; WNT: Warsaw, Poland, 1980. (In Polish) [Google Scholar]
- Hilsenrath, J. Tables of Thermal Properties of Gases; NBS Circular: Washington, DC, USA, 1955. [Google Scholar]

**Figure 3.**The laboratory stand for temperature measurements in the three-phase busbar system: 1—supply, 2—busduct, 3—temperature recorder, 4—computer, 5—Rogowski coil and 6—oscilloscope.

**Figure 4.**Time variation of the phase conductor temperature: measurements (L1, L2, L3: phase conductors; T

_{o}: ambient temperature).

**Figure 5.**Time variation of the enclosure temperature – measurement (E1, E2, E3: enclosure temperatures; T

_{o}: ambient temperature).

**Figure 8.**Temperature distribution along the segment AB shown in Figure 7—COMSOL.

**Figure 9.**Temperature distribution along the segment CD shown in Figure 7—COMSOL.

Range of Applicability | C | n |
---|---|---|

${10}^{-10}<{\mathrm{Ra}}_{m}\le {10}^{-2}$ | 0.675 | 0.058 |

${10}^{-2}<{\mathrm{Ra}}_{m}\le {10}^{2}$ | 1.020 | 0.148 |

${10}^{2}<{\mathrm{Ra}}_{m}\le {10}^{4}$ | 0.850 | 0.188 |

${10}^{4}<{\mathrm{Ra}}_{m}\le {10}^{7}$ | 0.480 | 0.250 |

${10}^{7}<{\mathrm{Ra}}_{m}\le {10}^{12}$ | 0.125 | 0.333 |

**Table 2.**Thermal properties of air at 1 atm [34].

T | c_{P} | λ | η·10^{−6} | ν·10^{−6} |
---|---|---|---|---|

°C | $\frac{\mathrm{J}}{\mathrm{k}\mathrm{g}\mathrm{K}}$ | $\frac{\mathrm{W}}{\mathrm{m}\mathrm{K}}$ | $\mathrm{P}\mathrm{a}\xb7\mathrm{s}$ | $\frac{{\mathrm{m}}^{2}}{\mathrm{s}}$ |

0 | 1005 | 0.0244 | 17.16 | 13.28 |

10 | 1005 | 0.0251 | 17.65 | 14.16 |

20 | 1005 | 0.0259 | 18.14 | 15.06 |

30 | 1005 | 0.0267 | 18.63 | 16.00 |

40 | 1005 | 0.0276 | 19.12 | 16.96 |

50 | 1005 | 0.0283 | 19.61 | 17.95 |

60 | 1005 | 0.0290 | 20.10 | 18.97 |

70 | 1009 | 0.0297 | 20.59 | 20.02 |

80 | 1009 | 0.0305 | 21.09 | 21.09 |

90 | 1009 | 0.0313 | 21.48 | 22.10 |

100 | 1009 | 0.0321 | 21.87 | 23.13 |

120 | 1009 | 0.0334 | 22.85 | 25.45 |

140 | 1013 | 0.0349 | 23.73 | 27.80 |

160 | 1017 | 0.0364 | 24.52 | 30.09 |

180 | 1021 | 0.0378 | 25.30 | 32.49 |

200 | 1026 | 0.0393 | 25.99 | 34.85 |

**Table 3.**Temperature of particular elements in the considered three-phase high-current busduct [°C].

Method | L1 | L2 | L3 | E1 | E2 | E3 |
---|---|---|---|---|---|---|

Analytical computations | 47.7 | 47.7 | 47.7 | 32.8 | 33.2 | 32.8 |

COMSOL computations | 45.4 | 46.1 | 45.4 | 33.4 | 34.2 | 33.4 |

Measurements | 44 | 45.8 | 43.8 | 31.5 | 35.5 | 31.5 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Szczegielniak, T.; Kusiak, D.; Jabłoński, P.
Determination of the Operating Temperature of the Gas-Insulated Transmission Line. *Appl. Sci.* **2020**, *10*, 8877.
https://doi.org/10.3390/app10248877

**AMA Style**

Szczegielniak T, Kusiak D, Jabłoński P.
Determination of the Operating Temperature of the Gas-Insulated Transmission Line. *Applied Sciences*. 2020; 10(24):8877.
https://doi.org/10.3390/app10248877

**Chicago/Turabian Style**

Szczegielniak, Tomasz, Dariusz Kusiak, and Paweł Jabłoński.
2020. "Determination of the Operating Temperature of the Gas-Insulated Transmission Line" *Applied Sciences* 10, no. 24: 8877.
https://doi.org/10.3390/app10248877