# Determination of the Operating Temperature of the Gas-Insulated Transmission Line +
## 4 Conclusions  
This paper presented an analytical approach to the solution of the temperature in the three-phase high-current busduct. The proposed method allowed us to calculate temperature rise in a set of tubular busducts.  
The analytical method was validated using the commercial COMSOL software and laboratory measurements. The mathematical model took into account the skin effect and proximity effects, as well as the electromagnetic coupling between phase conductors and enclosures. The results from the measurements indicated that the analytical method can be used to predict the temperature of any such tubular busduct system with good accuracy. The model predictions were found to be in very good agreement with the measurements.  
Temperature distributions in high-current busducts are usually calculated using numerical methods. Numerical methods allow for the analysis of busduct temperature in various geometric systems, whereas analytical methods are dedicated to specific geometries of busducts. However, the use of numerical methods in the design and optimization processes made it very difficult to generalize the results and to derive simple dependencies supporting the design of specific types of busducts. In turn, the use of analytical methods to analyze specific systems required the use of many simplifying assumptions. Despite the use of some simplifying assumptions, the proposed analytical approach allowed the discovery of the general relationships between various parameters and temperatures. Each extension of an assumption (e.g., taking into account nonlinearities) significantly increased the difficulty of the analytical solution. Moreover, in thermal calculations, based on solving the Fourier-Kirchhoff equation, a significant difficulty is the calculation of convective and radiative heat transfer coefficients. The phenomenon of convection occurring in high-current busducts is related to the movement of a fluid, and, therefore, its description is not sufficient for the law of conservation of energy itself. However, it is also necessary to take into account the law of conservation of mass, momentum and, for gases, the equation of state. As a result, attempts to analytically calculate the value of the convective heat transfer coefficient for real systems led to extremely complex mathematical models. Therefore, in the problem of natural convection, the heat transfer coefficient is usually determined by semi-empirical methods resulting from the theory of similarity. However, regardless of the method used to determine the heat transfer coefficient, its significance in thermal calculations seems the highest. In further research, the proposed analytical method will be tested for more complicated GILs, e.g., three-pole busducts in an enclosure.  
Conceptualization, T.S.; methodology and validation, T.S., P.J. and D.K.; writing--original draft preparation, T.S.; writing--review and editing, D.K. and P.J.; measurements, T.S. and D.K.; supervision, P.J. All authors have read and agreed to the published version of the manuscript.  
Figure 9: Temperature distribution along the segment CD shown in Figure 7—COMSOL.  
Funding: This research received no external funding. The APC was funded by Czestochowa University of Technology. This paper is an extended version of a paper presented in the Conference of Application of Electromagnetism in Modern Engineering and Medicine, Jastarnia, 13-16 September.