Structural Stability and Weak Points Mechanism of a High and Vertical Enclosed Isolated Phase Bus

Recently, with the rapid rise of new energy generation, pumped storage power stations also have experienced rapid development. Due to the considerable vertical height of these power stations, high and vertical enclosed isolated phase buses (EIPB) are more and more widely used. This type of high and vertical EIPB structure differs from the horizontal EIPB structure, as it is more significantly influenced by the gravitational load during actual operation. Thus, it is crucial to investigate the stability of the novel high and vertical EIPB structure under its own gravity load. In this study, the strength of the I-beam and cross-arm of the EIPB under the influence of the gravitational load was studied through analytical calculations and finite element static analysis. The results indicate that the strength of the I-beam and cross-arm is within the threshold of the corresponding material’s load-bearing capacity, demonstrating the stability of the EIPB structure. This work holds significant value for the structural design and further optimization of high and vertical EIPB.


Introduction
The enclosed isolated phase bus (EIPB) is an important part of the power transmission equipment in the power plant and substation [1][2][3].It has the advantages of effectively reducing the heat of the surrounding steel structure, weakening the interphase electric power of the bus, reducing the ground fault, and avoiding the interphase short circuit.Its performance is related to the safe operation of the power plant and substation and the entire power system.Therefore, it is necessary to make some researches on the analysis of the stability of the bus structure.
EIPBs are typically installed in three different forms: horizontal, inclined, and vertical [4][5][6], with horizontal installation being more common.However, due to geological or artificial conditions, enclosed busbars are increasingly installed in combination with three types of installation [7][8].With the increasing scale of hydropower stations with large vertical spans, such as hydropower stations, the EIPB arranged vertically are getting higher and higher.For example, a high vertical high current enclosed bus with a height difference of more than 100 meters is equipped in Shuibuya Hydropower Station.However, in the case of this kind of relatively high EIPB, the effect of its own gravity during installation and operation is much more significant compared to horizontal EIPBs.The gravitational forces acting on the supported I-beams, cross-arms, and other components of the EIPB induce stress.Therefore, it is essential to conduct stability analysis of the overall structure of the EIPB, including the I-beams and cross-arms.
Meanwhile, performing a weak point analysis at locations prone to bending under stress will facilitate structural optimization of the EIPB.
To address the above issues, the normal stress and bending shear stress of I-beam and cross-arm are calculated and verified, and the rationality and deficiency of theoretical calculation are pointed out in this paper.On this basis, the finite element model of this structure is established, and the static analysis of the whole structure is carried out.Compared with the theoretical calculation, the weakness of this structure is pointed out, and the stability of the cross arm, cylinder and I-beam is verified.This work is supported by Technology Project Funding from State Grid Xinyuan Group Co. Ltd. (SGXY-2022-129).

Structure of EIPB
The workshop floor where the vertical EIPB is situated has a height of 3 meters.The corner platforms of each staircase align with the structural position of each assembly section, ensuring that the I-steel installation platform and the stair platform are at the same height.The following section (3 meters) is taken for modeling and analysis.It is mainly composed of conductor, shell, cylinder, cross-arm through the core (Hereinafter referred to "cross-arm"), clamped insulator and fixed groove.Three-dimensional model of vertical EIPB is shown in figure 1.The diameter and thickness of the shell is 0.97 meters and 0.01 meters.The diameter, thickness and the length of the conductor is 0.512 meters, 0.016 meters and 3 meters.The diameter of the cross-arm is 0.07 meters and the length is 1.73 meters.The diameter and thickness of the cylinder is 0.41 m and 0.02 m.The total length of I-shaped steel is 3.953 m.The edge of I-shaped steel supports the whole structure.The length of I-shaped steel is 2 meters across the whole.The material of conductor, shell and cylinder is aluminum.The material of fixed slot and I-shaped steel is steel.The main material of each insulator is epoxy resin.The properties of these materials are shown in table 1. process can be simplified.The closer the basic assumptions are to reality, the more accurate the results will be.The stability of I-shaped steel, cross-arm and clamped insulator are focused on.

Stress and Strain Calculation of I-shaped Steel.
The middle part of the I-shaped steel lacks support relative to its ends.Therefore, the stability of the middle part is mainly tested.From the crosssection of I-shaped steel, it is mainly composed of flanges at the upper and lower parts and webs in the middle.These structures can be regarded as rectangles, so the distribution of bending shear stress at these parts is similar to that of rectangular sections.
The whole I-shaped steel is regarded as a beam subjected to support forces at both ends, and its equivalent force diagram is shown in figure 2, which is mainly affected by the three-phase component's and its own weight.Figure 2 shows the section diagram of I-shaped steel (in cm).The widths of web and flange differ greatly, because the shear stress is inversely proportional to the width, the shear stress on web should be greater than that on flange, and the bending shear stress is mainly distributed on web.The maximum shear stress on the web will be measured on the neutral axis.

Stress of cross-arm and clamped insulator.
The cross-arm is an important component of the research object in this paper.It bears most of the weight of the conductor and the shell, and is the part that needs strength verification most.It is supported by clamped insulators at both ends, and in the middle contacts and supports the conductor and housing of the bus.However, the cylinder also supports the busbar shell to a certain extent, which leads to the complexity of the actual support.In this paper, only the support of the cross-arm to the busbar conductor is considered in the calculation, and its section is a circle with a radius of 35mm.The simplified model is shown in figure 3.

Establishment of Finite Element Model
The grid size of bus conductor, shell and I-shaped steel is 0. 05m*0.05m, and the shape of the grid is square.The remaining parts of the grid are triangles with a size of 0.02m.The constant load considered for all structures is the gravitational load, while other loads such as water flow excitation are not currently taken into account.A total of 64 grids at both ends of I-shaped steel were subjected to fixed constraints.Friction contact is adopted between the cylinder and the fixed groove and between the horizontal insulator and conductor, as shown in figure 4.

Results and Discussion
The stability of the cross-arm through the core, the clamped insulator and the I-shaped steel is analyzed below, and the results are compared with the calculation results in Chapter 1 to analyze the calculation results.

Stability Analysis of Penetrated Cross-arm.
The distribution of cross-arm is high in the middle and decreasing to both ends.Amongst the displacement of phase B cross-arm at the same position is always near 0.1 mm more than that of phase A. It is due to the lack of support for phase B of I-shaped steel, which bends downward under pressure.For phase B, the curve above is divided into three sections at the connection between conductor and cross-arm, as well as shell and cross-arm.The fitting results of the three sections from the middle to the edge are as follows: It can be seen that the deformation of the cross-arm between the clamped insulator and the shell is the most obvious.The deformation of other parts is relatively minor.The stress cloud diagram of the three-phase cross-arm is depicted in figure 5.It reveals that the highest concentration of stress occurs at the two connections where the cross-arm meets the conductor.In addition, the stress at the connection between the cross-arm and the clamped insulator is larger than its surroundings.At the same time, the maximum point of shear stress is found in the connecting part of phase-C cross-arm and the clamped insulator, which reaches 0.57MPa.Hence, during the strength evaluation of the cross-arm, it is recommended to prioritize phase A or phase C. The three clamped insulators support the cross-arm at an angle of 120 degrees, among which the vertical insulator plays the main supporting role.Considering that the strength of the base part of the insulator is significantly higher than that of the main part composed of epoxy resin and they share similar size and structure, the focus of strength verification primarily lies on the epoxy resin component.Figure 6 and 7 show the equivalent stress and deformation cloud diagrams of the bottom of the vertically clamped insulator in phase B respectively.It can be seen that the stress at the bottom edge is more concentrated, because the support surface is circular and the stress is not uniform.In addition, in comparison to phases A and C, phase B experiences higher stress due to the inclination of the vertical insulator caused by settlement.The maximum pressure is 2.29MPa, while the yield strength of epoxy resin is 100MPa.

Stability Analysis of I-shaped Steel.
Figure 8 shows the equivalent stress cloud of the bottom of I-shaped steel.The equivalent stress at the edges of the supporting components on both sides tends to be higher since these points serve as support for the vertical EIPB from the floor.Compared with other positions, there are components such as clamped insulators and fixed slots under the three-phase crossarm, which is equivalent to increasing the thickness of I-shaped steel.Figure 8 shows displacement cloud of the bottom of I-shaped steel.Similarly, due to the lack of support, the displacement deformation of the middle part is the largest, with a vertical downward direction and a value of 0.277mm.The maximum stress and displacement deformation of I-shaped steel are within the allowable range.

Figure 2 .
Figure 2. Equivalent force diagram of I-shaped steel.

Figure 4 .
Figure 4. Finite element model and fixed constraint.
2.2.Analysis of Stability of Key ComponentsVertical EIPB is a statically indeterminate structure, and the theoretical analysis of its stability is often based on some basic assumptions.When the influence of secondary factors are ignored, the calculation