Multi-physical Field Analysis Method for Enclosed Isolated Phase Busbar of Hydropower Station

In this paper, geometrical modelling and finite element multi-physical field analysis method are carried out for the actual layout of the enclosed isolated phase busbar (EIPB) of a hydropower station, for the horizontal and vertical connection parts that can hardly be considered in the analytical calculation process. The finite element model is able to accurately represent the main structure of the EIPB by reasonably simplifying some of the components. Meanwhile, the finite element model incorporates the coupling of magnetic field and transient structural field, allowing for analysis of the magnetic field distribution, stress-strain distribution, modal analysis, and harmonic response of each component of the EIPB. It is capable of analyzing the vibration response of the complex horizontal-vertical structure EIPB under different excitations. This method can overcome the limitations of analytical calculation methods in calculating complex structure EIPBs. It can also provide valuable guidance for the structural optimization design of future EIPBs.


Introduction
Enclosed Isolated Phase Bus (EIPB) is a large current transmission device widely used in the outgoing line circuit and auxiliary branch circuit of 50MW and above generators, playing an important role in the normal operation of the power system [1] [2].EIPB operates under high currents of different values for a long time, with conductive bars and supporting insulators bearing varying electromotive forces.Prolonged vibrations can result in mechanical damage to components, such as localized deformation, loosening, and detachment.In severe cases, this can lead to EIPB damage and unexpected shutdowns.In order to prevent the above accidents, it is necessary to analyze the operating conditions of each section of the EIPB in order to prevent faults and handle them properly after they occur.
Stability analysis method is one of the commonly used methods.Guo [3] established a simplified physical model for the vertical section of the EIPB, taking the Three Gorges underground hydropower station as an example.By utilizing numerical simulations, an analysis of the thermal balance under natural ventilation conditions was performed, and a mixed ventilation heat dissipation mode was proposed.Zhao [4] conducted a static analysis on the insulators and casing of a vertically long-distance enclosed busbar.The study revealed that the insulators in the vertical section are prone to shear fractures.In addition, the high vertical section of the conductor exhibits poor heat dissipation, leading to weak points such as the "chimney effect."Xie [5] analyzed the structural design and installation methods of IOP Publishing doi:10.1088/1742-6596/2731/1/012004 2 the vertical section of the EIPB.Detailed stress analysis and strength calculations were conducted on the connecting bolts, insulators, insulator seats, and connecting plates.Moreover, the rationality of the installation structure was discussed, and the strength of each component was validated.The researches [6][7][8] have conducted stability analysis on the vertical and horizontal sections of EIPB, as well as their insulation support structures, effectively improving the working environment of EIPB.However, due to the complexity of the connection structure, the analysis and calculation cannot accurately determine its vibration characteristics.However, the finite element method can be used to conduct a detailed analysis of the connection situation.
Based on this, this paper establishes a multi-physical field analysis process for analyzing EIPB, and obtains the electromagnetic field distribution characteristics, modal characteristics, harmonic response laws, and strain stress changes at the turning point of EIPB.This work is supported by Technology Project Funding from State Grid Xinyuan Group Co. Ltd. (SGXY-2022-129).

Structure and Layout of EIPB
EIPB is mainly composed of a shell, conductors, insulation support materials, and related accessories, as shown in figure 1. Conductors are generally made of aluminum and copper with high conductivity.Due to the low cost of aluminum, aluminum conductors are commonly used.The outer part of the conductor is supported by insulators and shells, while the busbar, shell, and insulator are fixed connections.The contact between the shell and the clamp is frictional, and the clamp and other supporting devices are fixed connections.It also shows the supporting structure including the hoop.EIPB generally has installation forms such as horizontal, inclined, and vertical.

Finite Element Model
The actual EIPB equipment has horizontal, oblique, and vertical structures.Taking horizontal structure EIPB as an example, a horizontal model of EIPB equipment is established in SolidWorks.The EIPB structure model includes support devices such as busbar conductors, busbar shells, insulators, and clamps, as shown in figure 2. The busbar, shell and insulator are connected in a fixed manner, and

Modal Analysis
By setting the solution for the top 10 modes, focusing only on the top 10 modes, the representative mode shapes are selected from each mode of the first 10 steps, as shown in figure 3. It can be seen that from low to high order modes, the frequency gradually increases.The corresponding vibration modes include various vibration states such as stretching, bending, and swinging.The vibration mode of the lowerorder mode is mainly the rolling of the busbar conductor and shell along the radial direction and the expansion and contraction along the axial direction.The deformation displacement of higher-order modes is more concentrated at the turning point, but the amplitude is smaller.The vibration amplitude of the part far from the hoop is significantly greater than that of the part near the hoop.

Electromagnetic-field Analysis
The vibration of EIPB is a complex electromagnetic structural coupling process, as shown in the simulation results of the magnetic field in the figure 4. It can be seen that the magnetic field intensity and magnetic induction intensity of the wire are the highest, while the magnetic induction intensity at the shell is very low, which means that most of the magnetic field lines are shielded inside the aluminum shell, playing a good magnetic shielding role.

Structural Field Analysis
Under the action of electromotive force, both the EIPB shell and conductor are subjected to varying degrees of stress and strain changes, so it is necessary to analyze the stress and strain of the shell and conductor separately.The results of shell stress and strain are shown in figure 5.The areas with high stress also have high strain, mainly concentrated in the lower part of the shell.As the height increases, the stress and strain also decrease.The stress and strain of the supporting structure are shown in figure 6.From the results, it can be seen that the stress distribution of the support structure is relatively uniform.The horizontal support has a greater deformation at the top due to the distance between the top and the bottom support.The vertical support channel steel has a greater deformation in the middle due to its only being supported at both ends, and the actual sinking load in the middle.

Conclusion
This work focuses on the actual arrangement of EIPB in hydropower stations and analyzes multiphysical field simulation.The results are as follows: 1) The shell has been verified to have a good shielding effect on the magnetic field inside the EIPB shell; 2) The top 10 vibration modes of EIPB at different orders have been calculated, it shows that the vibration amplitude of the part far from the hoop is significantly greater than that of the part near the hoop; 3) Frequency sweep analysis has been conducted on EIPB, and the highest range of EIPB vibration response has been obtained, around 20Hz. 4) Stress and strain analysis has been conducted on key structures in different parts of EIPB, and the identification of weak points has been completed.This work can provide substantial evidence and analysis for the design and operational assessment of the EIPB.

Figure 1 .
Figure 1.Layout of Isolated Phase Bus.
.1088/1742-6596/2731/1/012004 3 friction contact is used between the shell and the hoop.The hoop and other supporting devices are all connected in a fixed manner.The materials include aluminum alloy, structural steel and epoxy resin.

Figure 2 .
Figure 2. Finite element model of isolated phase enclosed busbar.

Figure 5 .
Figure 5. Structural field results of the shell.

Figure 6 .
Figure 6.Structural field results of supporting structures.