Creating Bushing Core Geometries

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MAT-VET-F-21005

Examensarbete 15 hp Juni 2021

Creating Bushing Core Geometries

Hanna Damsgaard Falck Johanna Ring

Erik Svensson

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Teknisk- naturvetenskaplig fakultet UTH-enheten

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Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

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Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Creating Bushing Core Geometries

Hanna Damsgaard Falck, Johanna Ring, Erik Svensson

Bushings are a necessary component of the transformers in the power grid. A bushing is used to control the electric field's strength and shape. It is also an insulator for high-voltage conductors. The

bushing enables a conductor to be safely brought through a grounded barrier. In this report, several methods for creating a 2D axi-

symmetrical bushing core geometry in COMSOL Multiphysics were developed. The geometry includes the conductor, hollow area inside the conductor, the RIP, the mold and aluminum foils. First, the base-

geometry was constructed, which includes all geometry parts except the foils. Afterward, two different approaches were used to construct the foils. The first approach was to automatically build a requested number of foils. The second approach was to create the foils based on data from excel-sheets. The developed method should be able to create both full foils and partial foils. A total of four foil methods were

developed. The first method used COMSOL's Model Builder to create a requested number of foils uniformly distributed within the base-

geometry. The second method used COMSOL's Application Builder to create a requested number of foils based on mathematical expressions.

The third method reads data from an excel sheet to create the foils in COMSOL. Method four is an improved version of method three that can create partial foils as well as the base-geometry. Foil methods II,

III, and IV, created every foil as a separate geometrical object. As a result, an associated method that deletes the foils were also developed for each of these methods. A conclusion that the fourth method was the most realistic method of creating a bushing core could be draw due to, among other factors, it is the only method that can build partial foils.

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Populärvetenskaplig sammanfattning

Spänningen i dagens elnät varierar mellan 230 volt och 400 000 volt. För att kunna omvandla spänningen från en nivå till en annan samt överföra den elektriska energin används transformatorer. När en ledare med hög spänning passerar genom en jordad barriär böjs det elektriska fältet och ström kan passera från ledaren till jord. För att motverka detta används en bussning. Bussningen är en ihålig isolator som isolerar ledaren och förändrar det elektriska fältet så att strömmen kan passera säkert. Bussningen är därför en nödvändig del av elnätets transformatorer.

Ett betydande hjälpmedel under utvecklingen av nya bussningar är simuleringar.

Med hjälp av simuleringar kan bussningars egenskaper utforskas och olika de- signer jämföras. Komplexa bussningsgeometrier kan däremot vara tidskrävande att skapa i simuleringsprogram. Detta projekt har utförts med syftet att utveckla nya metoder som skapar geometrier i det ofta använda simuleringsprogrammet COMSOL Multiphysics. Det är en speciell typ och del av bussningar som denna rapport fokuserar på: kärnan av en RIP bussning. Kärnan består av vad som i rapporten kallas basgeometrin, vilket är hela bussningen förutom folierna som är belägna inuti basgeometrin. Folierna är en viktig del av bussningen, det är folierna som böjer det elektriska fältet. Ett tillvägagångssätt för hur basgeometrin ska skapas har utvecklats tillsammans med fyra metoder som skapar foliegeometrin. De två första foliemetoderna skapar ett önskat antal folier. De andra två skapar folier utifrån data i ett Microsoft Excel kalkylblad. Varje foliemetod har för- och nackdelar som diskuteras i rapporten och utifrån det kunde slutsatsen att den mest realistiska metoden var metod fyra.

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1 Introduction

1.1 Background

Transformers are key elements in all power networks as they transfer electrical energy from one circuit to another. The longevity and availability of the transformers impact the grid’s reliability and profitability greatly. Therefore it is important to create transformers that are efficient to get an efficient power grid.

[1]

Efficiently transporting electricity over long distances with minimum losses will ease the challenge of producing enough energy with renewable sources.

High-voltage direct current (HVDC) technology is one highly efficient method of transmitting large amounts of electricity over long distances. HVDC technology will therefore play an important part when shaping the future’s power grid. A part of the HVDC technology is the HVDC converter transformers. One part of the HVDC converter transformer is the bushing. [2]

A bushings purpose is to insulate conductors with high-voltage current flowing through an earthed conducting barrier safely. The bushing helps to control the electric field’s strength and shape. It also reduces the electrical stresses in the insulating material. There have been different types of bushing designs over the years. The first bushings at the start of the 20th century were dry insulated with bakelite paper and aluminum foil. One edge was attached to the condenser core and had an insulator made of porcelain. Later in the 1960s oil-impregnated and resin-impregnated paper bushings became dominant.

It is possible to perform filling simulations of RIP bushings by using Darcy‘s law and Richards equation. Darcy’s law describes the instantaneous flux, depending on the flow rate divided by the cross-sectional area of the fluid flow. The flow of epoxy through the paper is a case of an incompressible fluid flowing through a non-deformable, porous and unsaturated media [3]. With these conditions, Richards equation can be derived from Darcy´s law [3]. Richards equation is a variant of Darcy´s law but applicable to flow through non-deformable, porous and unsaturated media. Richards equation can be used to simulate the optimal filling speed of epoxy during RIP bushing core manufacturing. To simulate the bushing core the first step is to create a geometry in the relevant simulation software. Because the complexity of bushing geometries varies this step can be time consuming.

1.2 Problem Description

The purpose of this project is to create different methods of building bushing

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The bushing core consists of aluminum foils that are wrapped in paper. By filling the mold with epoxy a Resin Impregnated Paper (RIP) bushing core is created. In this project, several methods that build the bushing core geometry in COMSOL Multiphysics are created. Using these methods different bushing core geometries could easily be built. This will streamline the simulation process of different bushings and by doing so improves the development of new RIP bushings. In figure 1 below an example of a RIP bushing core is shown.

Figure 1: A RIP bushing core in 2D [4].

It is natural to separate the bushing core geometry into two parts: The foils and the base-geometry. The base-geometry includes every part of the core except the foils. The reason being that the base-geometry is not as time consuming to create as the foils. The first attempt to create the foils would instinctively be to insert every foil individually. This would be done by inserting a line in COMSOL and then determine its properties either by directly changing its values or by using mathematical expressions.

There are however a couple of difficulties with creating every foil individually, for example, if a geometry has hundreds of foils this approach is not time efficient. It is also time consuming to increase or decrease the number or placement of the foils. As a result, creating effective foil building methods will have a large impact on streamlining the simulation process.

2 Theory

2.1 Bushing

A bushing is a device that insulates an electric conductor. Its primary purpose is shielding a high voltage electrical conductor [5]. The bushing enables a conductor to be brought through a grounded barrier without risk [4]. Because

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are designed to withstand different types of stress: Mechanical stress, thermal stress and electrical stress [4].

2.1.1 RIP Bushing Core

There are different categories of bushings. This project is focused on the core of a resin impregnated paper (RIP) bushing. A RIP bushing core is manufactured by first winding paper and aluminum foil on a winding tube. The result is a hollow cylinder that serves as a conductor and layers of paper and aluminum foils wrapped around it. The manufacturing of a RIP bushing core can be seen in figure 2.

Figure 2: Manufacturing of a RIP bushing core [4].

Afterward, the core undergoes a vacuum assisted resin infusion process in which the paper is infused with resin [4], or as in this project, epoxy. Figure 3 illustrates a two dimensional axisymmetric figure of a RIP bushing core. The grey area is the hollow part within the core. The red area represents the conductor. The beige area represents the paper that is infused with resin. The thicker black line around the paper illustrates the mold. The black lines within the paper represent the aluminum foils. During manufacturing epoxy glue can get through the paper but not the aluminum foil, meaning the foils direct the flow of epoxy during the infusion process.

Figure 3: 2D axisymmetric figure of a RIP bushing core with both full and partial foils. Figure dimensions is scaled for clarity and not realism.

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can be divided into full foils, that span the whole length of the bushing core, and partial foils that span only a part of the bushing. Figure 4 illustrates how the foils can change the electric field. U is the conductor voltage. It’s common practice to use partial foils because effective use of partial foils can reduce both cost and time during manufacturing.

Figure 4: How the foils affect the electric field distribution [4].

2.2 COMSOL

COMSOL Multiphysics is a multi purpose simulation program. It enables the user to build geometric objects and run simulations on the objects. The areas in which COMSOL can simulate range from electrostatics, fluid flow, heat flow and more. Before a simulation is run a geometric object representing the relevant object is built. COMSOL has two different means to create a geometry, the Model Builder and the Application Builder.

2.2.1 Model Builder

In the Model Builder, the user can create any form of geometry by combining simple geometric objects in the desired way. For example, four rectangles can be combined to create a picture frame. The Model Builder is an easy to understand and intuitive graphical tool. It is however time consuming for larger or more complex geometries.

2.2.2 Application Builder

In the Application Builder, the user can create an application in COMSOL. This application can then be used both within and outside of the main COMSOL program. Furthermore, methods can be written in Java code. For example, a for-loop can be written that creates 100 rectangles next to each other. The Application Builder is a more complex building tool than the Model Builder.

However, this complexity also means the Application Builder is more versatile and therefore the preferred way to create larger or more intricate geometric objects.

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2.2.3 Livelink

Although COMSOL is a versatile program for simulations it lacks features in other areas. This problem can be solved by Livelink. Livelink is a feature in COMSOL in which the COMSOL program can be connected to another program. Some examples are: Microsoft Excel, Solidworks and Matlab. By using e.g. Livelink for MATLAB more computationally demanding tasks can be performed while also utilizing the simulation capabilities of COMSOL. In this paper, Livelink for Excel is used to read data from Excel sheets.

3 Method

3.1 Instruments

• COMSOL Multiphysics

• Microsoft Excel

• Livelink for Excel

3.2 Create Base Geometry

To create the geometry the first step was to build a parameterized base geometry in COMSOL. The base geometry includes the conductor, hollow area inside the conductor, the RIP and lastly the mold. All these parts were parameterized so the scale of the whole bushing could easily be changed. The internal parts of the bushing could also be scaled in relation to each other.

3.2.1 The Conductor

The first geometric object to be built was the center of the bushing, consisting of both the conductor and the hollow part inside the conductor. Both were parameterized with the variables radius, r1, and height, which can be found in table 1. The parameter radius is the radius from the center of the bushing to the outer part of the conductor. The parameter height is the height of the bushing. The parameter r1 is the inner radius of the conductor, this variable can either depend on the outer radius, radius or it can be a chosen value less than the value of the outer radius. A picture of the conductor can be found in figure 5 below.

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Figure 5: The scaled conductor.

Parameter Description

radius The outer radius of conductor.

r1 The inner radius of the conductor.

height Height of the core of the bushing.

Table 1: The parameter’s needed to create conductor.

3.2.2 The RIP and Mold

The geometry for the RIP and the mold was added by creating two polygons.

One polygon for the RIP and one for the mold. The polygon representing the mold included the new parameter mold, which specified the mold thickness. The corners of both polygons were rounded, which can be seen in figure 6 below.

Figure 6: Rounded corners

The polygons had different parameters depending on how the foils were created.

For some cases, the size of the RIP was determined in the parameters and the foils were fitted inside the RIP with a certain distance, called foil_m, from the edge of the RIP to the foil edges. The parameters for this can be found in table 2 below. The heights, and radius often depends on each other with the independent parameter radius, height, mold, and foil_m.

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Parameter Description

r2 Intermediate radius of the RIP.

r3 Outer radius of the RIP.

h1 Lower height of the RIP.

h2 Intermediate height of the RIP.

h3 Intermediate height of the RIP.

h4 Upper height of the RIP.

radius The outer radius of conductor.

foil_m The distance between the foils and the RIP.

mold Mold thickness.

Table 2: The parameter’s needed to create the polygons.

For the other cases, the foils were created from known data and the RIP geometry was created afterward around the foils. The parameters used for this can be found in table 3 below.

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Parameter Expression Description

data _r2 Intermediate radius of

the contour of the foils.

data_r3 Outer radius of the contour of the foils.

data_h1 Lower height of the contour of the foils.

data_h2 Intermediate height of

data_h3 Intermediate height of

data_h4 Upper height of the contour of the foils.

foil_m The distance between the foils and the RIP.

r2 data_r2 + foil_m Intermediate radius of the RIP.

r3 data_r3 + foil_m Outer radius of the RIP.

h1 data_h1 - foil_m Lower height of the RIP.

h2 data_h2 - foil _m Intermediate height of the RIP.

h3 data_h3 + foil_m Intermediate height of the RIP.

h4 data_h4 + foil_m Upper height of the RIP.

Table 3: The parameter’s needed to calculate values from data for the polygons.

In all instances, the distance between the foil edges and the edge of the RIP is equal to the distance foil_m, and the mold has the thickness of the parameter mold. The entire base geometry, including the conductor, the RIP and the mold can be found in figure 7, where figure 7a is the geometry in a realistic scale and figure 7b is scaled for clarity.

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(a) Not scaled geometry. (b) Geometry scaled.

Figure 7: The base geometry

3.2.3 Implementing the Base Geometry

The base geometry was built in two ways, either by building the geometry directly in the Model Builder in a section called "Geometry" or by creating a code in the Application Builder.

Building the base geometry in the "Geometry" section in the Model Builder is done by inserting two rectangles representing the inner and outer conductor, and two polygons representing the RIP and the mold. The corners of the RIP and mold can be rounded by using a function called "fillet". The parameters were loaded from an excel-file into the "Parameter" section of the Model Builder, and used in the "Geometry" section. To build the geometry the function "Build all"

in the Model Builder could be used.

Building the base geometry by writing a code in the Application Builder, was done by reading an excel-file with the values of the points needed to build the base geometry and then building the geometry using code that creates rectangles representing the conductor, and polygons representing the RIP and mold. The corners of the RIP and mold can be created using code for the function "fillet".

To build the geometry the code needed to be run in the "Developer" section in COMSOL.

3.3 Approaches of Creating Foils

The RIP consists of aluminum foils and paper. The foils have a different length depending on their position on the r-axis and they will be placed with equal distance from each other. To solve this issue of having to insert every foil individually, methods that created the desired number of foil were made. This was done using two different approaches.

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3.3.1 Approach 1: Uniform Foil Placement

The first approach was to create a requested number of foils that all had the same distance from the edge of the RIP and the same distance from each other.

A new parameter was added, n_foils, which describes the number of foils. When changing the n_foils parameter the number of foils in the geometry would change. Two strategies were investigated to accomplish this . The first strategy was to create the number of desired foils then use a shape to cut them to fit into the RIP part with the same distance from the edge everywhere. The second strategy was to use programming to cut the foils depending on their radial position, and the ratio between the height of the bushing and the width of the different parts of the bushings. This way the edges of the foil was parallel to the hypotenuse of the upper and under triangular that appeared in the base geometry.

The independent parameter, foil_m was used to determine the minimum distance between the RIP edge and the foil. To place the foils with equal distance from each other a distance between the foils were calculated. This distance was calculated using the number of foils implemented and the minimum distance from the edges. The foils have the same distance from the edge which resulted in them having different lengths depending on their placement.

3.3.2 Approach 2: Using Data from Excel sheets

The second approach was to use data containing the position of the foils on the r-axis and their start and endpoint on the z-axis, from an excel sheet to create the foils in the RIP. The strategy was to use programming to read the excel sheet and use the data-points to build the foils. All the values were given and by programming in the Application Builder, the foil data was used to create the foils. The independent parameter, foil_m, was used to determine the distance between the edge of the foils and the RIP.

3.4 How to Run the Code in the Model Builder

When building geometries using programming, Java code is written in the Application Builder as a "Method" and can be run there. It can also be run in the Model Builder. To run the code in the Model Builder the following steps needs to be taken:

• Click on the "Developer" tab at the upper bar in the Model Builder.

• Click on the button "Run Methods" and choose the relevant method.

• Dependent on the specific method, geometric objects is created or deleted.

The new geometry appears in the graphics window.

When running code from an excel-sheet it is important that the excel-file is located in the same folder as the COMSOL file.

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4 Result

Four methods of building the bushing core geometry were made. The first three methods had only full length foils while the fourth method had both full length and partial foils. The first two methods used a linear correlation to determine the position and length of the foils while the other two used data from an excel sheet to determine those values.

4.1 Foil Method I

The first method to create the foils was built using the "Union" and "Intersection"

tools in the COMSOL Model Builder. To begin a single foil was created with the radial distance foil_m to the conductor. The height of this foil was the same as for the whole bushing. By using the "Array" geometry method in the Model Builder this foil was copied n_foils several times where the last foil had the radial distance foil_m from the bushings outer edge. Each foil was a copy of the first and every foil had the same distance from each other. Then by taking the union of all these foils a single foil geometry in COMSOL was created. This is illustrated in figure 8.

(a) One single foil.

(b) The desired number of foils in Foil Method I.

Figure 8: Creating the foils

Two new polygons were then created. Both were identical in shape to the polygon that represents the original RIP, but with different measurements. The first polygon began with an uplifted z-axis start position of foil_m to the original polygon. The first polygon also had a shortened height that caused it to have a distance of foil_m from the original polygons’ upper edge. The second polygon began with a distance foil_m from the conductor and its outer points were radially reduced to have foil_m distance from the original polygon. The two

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(a) Height reduced polygon. (b) Radially shrunk polygon.

Figure 9: Shaping figures. Because of the different axis scales the radially shrunk polygon appears proportionally smaller than it actually is, while the height reduced polygon appears to be on top of the original polygon.

By taking the intersection of these three geometries a final geometry was created.

This final geometry consisted of n_foils number of foils with radially equidistant placement from each other. All foils had foil_m distance from the edges of the RIP bushing. The final geometry can be seen in figure 10. The values for the parameters can be found in table 4 in Appendix A.1.

(a) Not scaled geometry (b) Scaled geometry Figure 10: Result from Foil Method I

4.2 Foil Method II

The second method used the Application Builder. With the Application Builder, a while-loop could be implemented and used for a selected number of foils. The base of the bushing, conductor, RIP and the mold was designed using the Model Builder. Some of the foils were also created in the Model Builder, these foils did not need to be shortened and they could be performed easily using the array method in COMSOL. For the shortened foils the while-loop is used, for each new foil a new radius, point of top and point of the bottom is calculated and

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used when the foil is designed. The loop continues until all foils are designed and the geometry can be built. In figure 11 the first foils are visible.

Figure 11: Foils from Model builder in Foil Method II

For the calculations of the radius, an initial value is set as the width of the foil _madded with the foil _distance for as many foils that are built in the Model Builder. For each new radius one foil _distance was added. For the point of top value and point of bottom value the calculations are more complex. The top value will decrease for each new foil in the z-direction, a constant will be subtracted from the previous position. As for the bottom value, this value will increase in the z-direction, a constant was added to the previous position. The expressions for the calculations can be seen in code in Appendix B.1.1 section.

For deleting the foils in the geometry a method in Application Builder was used, it can be seen in Appendix B.1.2. The final result can be seen in figure 12.

The values that have been used for the parameters can be found in table 5 in Appendix A.2.

Figure 12: Result from Foil Method II

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4.3 Foil Method III

The goal of the third method was to create foils based on data from an excel sheet.

To do this the Application Builder was used. In the Application Builder, the excel sheet was read using the inbuilt method ”readExcelF ile”, which reads the chosen sheet and cells of the selected excel-file and which gives a two dimensional string array as output. The two dimensional string array was converted into a two dimensional number matrix with the "same" rows and colons as the excel file using two for-loops, one for-loop to create the rows and one for-loop to create the colons. The values were scaled from mm to m since the excel-file has the values in mm but COMSOL reads the values as m.

To build the foils a third for-loop where used. This loop had a length equal to the number of foils and the foils were created using the inputs, r, which is the position of the foil along the r-axis, start, which is the start-point of the foil along the z-axis, and, end, which is the end-point of the foil along the z-axis.

The base geometry was built using the "Geometry" section in Model Builder and created using the "Build all"-function. The values of the base geometry are regulated in the "Parameter" section. The foils were built by running the method from the Application Builder in the "Developer" section in the Model Builder.

The code for building the foils together with the code that deletes them can be seen in Appendix B.2.1. Table 6 in Appendix A.3 shows the values that were used for the parameters. The result is visible in figure 13.

Figure 13: Result from Foil Method III

4.4 Foil Method IV

The fourth method was similar to the third method, but instead of having only full length foils some foils were only partial. This meant that instead of having only three variables to read, as in method 3, this method has five variables.

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z-axis, and the lower foil’s start- and endpoint on the z-axis. The diameters divided by two determine the position on the r-axis for the foils.

The first step in this method was the same as in the third method, to read the excel-file by using the inbuilt command ”readExcelF ile”. The excel-file was read as a two dimensional string, and using two for-loops the string was converted to a two dimensional double. The values were scaled from mm to m since the excel-file has the values in mm but COMSOL reads the values as m.

A third for-loop was used to create the foils. Inside the loop an if-statement was used to separate whether the foils were full or partial. If the start point for the upper foil and the endpoint of the lower foil has the same value the foil is a full foil and a foil with the start point from the lower part and the endpoint from the upper part is created. If the start point of the upper foil and the endpoint of the lower foil is not the same the foil is partial, and one lower and one upper foil is created. The code can be seen in Appendix B.3.1 and the result in figure 14. The values that have been used as parameters can be found in table 7 in Appendix A.4.

Figure 14: Result from Foil Method IV

4.4.1 Code for Base Geometry

For method four a code in the Application Builder was created to build the base geometry. The code to create and delete the base geometry can be found in Appendix B.3.3.

To achieve this the values for the needed position for building the rectangles and polygons were read in the Application Builder using the command

”readExcelF ile”. To use this command the computer needed to have Excel Livelink installed. These values often depends on the parameters and can be found in table 8 and 9 in Appendix A.4. In table 8 the parameters required to

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were converted to a 2D double. Using one for-loop for the rectangles and one for-loop for the polygons the base geometry was created. The rounded corners were created add the command for the fillet function in the for-loop that creates the polygons.

5 Discussion

There are advantages and disadvantages with all the methods depending on the situation. The results of the different methods also diverse in how realistic they are. Some of the methods are a good representation of real bushing cores while others are not.

5.1 Foil Method I

For the first method, where a shape was used to adjust the length of the foil, it is easy to create a uniformly distributed foil geometry with equal distance from the edge of the RIP. It is easy to change the numbers of foils, the distance from the foils and the edge of the RIP, and the size of the bushing by changing the independent parameters in COMSOL. It is also easy to change the way the foils are cut by only changing the shaping figure. Another advantage with this method is that the entire geometry is created using the "Build all"-function in the Model Builder, while for the other methods, which use both the Model Builder and the Application Builder, the entire geometry will not be built using only that function. A disadvantage is that it can only create a uniformly distributed foil geometry, and thereby no changes to an individual foil can be made. The method can also not create partial foils. The real foil structure has both partial and full foils which makes this method unrealistic.

5.2 Foil Method II

The second method creates, as the first method, a uniform geometry but it creates the base geometry and the foils that are not shortened in the Model Builder and the shortened foils using a method created in the Application Builder.

The advantage of this is that it is easy to change the code in the Application Builder. The method has however a few disadvantages. Above all, the independent variables need to be changed both in the "Parameter" section of the Model Builder and the "Input" section in the Application Builder, which is not practical. No efficient or simple way to connect these variables has yet been found. Another disadvantage is that to build the geometry the base geometry and the first foils need to be built using the "Build all"-function and then to

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in the "Developer" section of the Model Builder. To solve this the base geometry and the first few foils could be built using code in the Application Builder, this was however not done since the structure of the method was not as realistic as desired, where it, like Foil Method I, cannot create partial foils. Foil Method II is essentially producing the same results as Foil Method I in a more complicated way.

Although Foil Method II has its disadvantages and at first sight not seems to be useful, the idea of using code with loops to create the foils has potential.

The method could be used as a foundation when creating methods where the foils are not uniform or when building partial foils. Building the geometry using code also has the potential of becoming more flexible and easier to change than building all the geometry in the relatively "stiff" "Geometry" section in COMSOL’s Model Builder.

5.3 Foil Method III

For the third method a different approach was used, the foils are not uniform but created from data points from an excel-file. This makes it easy to change one foil, by just changing its values in the excel-file.

Even if the base is still built in the "Geometry" section the issue from method two does not remain. In contrary to Foil Method II, where some expressions and variables need to be changed in two places, this method has no parameters or variables that are used in both the "Geometry" section of Model Builder and Application Builder. It is however important to be aware that the base geometry is created in the "Geometry" and "Parameter" sections of the Model Builder while the foils are created in the Application Builder and the excel-file, which means that both the "Build all"- function needs to be used as well as running the method for building foils in the "Developer" section of the Model Builder.

To improve this method a code that builds the base geometry could be added, which would mean that the entire geometry could be built in the "Developer"

section.

This method cannot create any partial foils. However, if a RIP bushings man- ufacturer already knows the foil placement in a bushing this method is more practical than the first two.

5.4 Foil Method IV

The fourth method is an improved version of the third method: it both reads data from an excel-file and supports the creation of partial foils. This method creates both partial and full foils and it is easy to change a foil in the excel-file.

For this method, two different ways of implementing the base geometry were used.

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to be aware that when building the geometry it requires the use of both the

"Build all"-function and running the method in the "Developer" section.

If the base geometry is implemented through code from the Application Builder the entire geometry can be built using the "Developer" section. It also means all parameters are in an excel-file and no parameters are in the "Parameter"

section in COMSOL and the "Geometry" section in COMSOL would not be used. This makes it easy to build the geometry and easy to change a value, by only changing the values in excel.

Method four is the most realistic method to create bushing geometry since it can create both partial and full foils.

6 Conclusions

As a conclusion Foil Method IV is the most sufficient for this project due many factors that are discussed in the discussion part, even thought all methods have their advantages. For bushing core geometries it may be important to be able to change individual foils were the core can contain both partial and full foils.

For these requirements Foil Method IV was most satisfactory, but all the past methods played a major role and by using the advantages from these a finalized method was produced. There are still room for improvement and to create a geometry that can be useful for future simulations there are things to refine, but that’s something for future work.

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References

[1] Power Transformers. url: https://www.hitachiabb-powergrids.com/

offering / product - and - system / transformers / power - transformers. (Available: 7 April 2021).

[2] HVDC converter transformers. url: https://www.hitachiabb-powergrids.

com/offering/product-and-system/transformers/power-transformers/

hvdc-converter-transformers. (Available: 7 April 2021).

[3] Florian Klunker et al. “Modelling the Resin Infusion Process, Part I: Flow Modelling and Numerical Investigation for Constant Geometries”. In: Journal of Plastic Technology (2011).

[4] Christos Athanasopoulos. Självständigt arbete i teknisk fysik: meeting 2021- 03-25 [presentation]. Hitatchi ABB Power Grids, 2021.

[5] Bushings. url: https://www.hitachiabb-powergrids.com/offering/

product-and-system/transformer/bushings. (Available: 3 May 2021).

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A Tables

A.1 Values Foil Method I

Parameter Expression Value Description

radius 0.2 The outer radius of conductor.

height 2 Height of the core of the bushing.

mold 0.003 Mold thickness.

r1 radius The inner radius of the conductor.

r2 radius*1.2 Intermediate radius of the RIP.

r3 radius*2 Outer radius of the RIP.

foil_m 0.02 The distance between

the foils and the RIP.

n_foils 100 The number of foils.

h1 height*0.05 Lower height of the RIP.

h2 height*0.1 Intermediate height of the RIP.

h3 height*(0.1 + 1/3) Intermediate height of the RIP.

h4 height*5/6 Upper height of the RIP .

Table 4: All parameters for Foil Method I.

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A.2 Values Foil Method II

radius 0.2 The outer radius

of conductor.

height 6 Height of the core

of the bushing.

r1 radius*9/10 The inner radius

of the conductor.

r2 radius/4 Intermediate ra-

dius of the RIP.

r3 r2 + radius*3/4 Outer radius of the RIP.

h1 height*0.05 Lower height of the RIP.

h2 h1 + height*0.05 Intermediate

height of the RIP.

h3 h2 + height/3 Intermediate

height of the RIP.

h4 height*5/6 Upper height of the RIP.

n_foils 100 Total number of foils.

n1_foils floor((r1 -

2*foil_m)/foil_distance) Number of foils of full length.

n2_foils n_foils - n1_foils Number of foils that

shall be shortened.

n3_foils floor((r1 -

foil_m)/foil_distance)-n1_foils Displacement value.

foil_m 0.02 Distance between

edge of the RIP part and the foils.

foil_start_r radius + foil_m First foil on r-axis.

foil_distance (r2 - 2*foil_m)/n_foils Distance between foils.

ratio_upper ((h4 - h3)/(r2-r1)) Ratio between the sides in the upper triangle.

ratio_under ((h2 - h1)/(r2-r1)) Ratio between the sides

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A.3 Values Foil Method III

r1 radius*0.8 The inner radius of the conductor.

r2 0.15 Intermediate radius of the RIP.

r3 0.28 Outer radius of the RIP.

h1 0.03 Lower height of the RIP.

h2 0.75 Intermediate height of the RIP.

h3 2.2 Intermediate height of the RIP.

h4 5 Upper height of the RIP.

Table 6: All parameters for Foil Method III.

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A.4 Values Foil Method IV

foil_m 0.02 The distance between

the foils and the RIP.

r1 0.08 The inner radius of conductor.

data_r2 0.129 Intermediate radius of

data_r3 0.224 Outer radius of the

contour of the foils.

data_h1 0.1803 Lower height of the

data _h2 1.695 Intermediate height of

data_h3 4.875 Intermediate height of

data_h4 8.1912 Upper height of the

r2 data_r2 + foil _m Intermediate radius of the RIP.

r3 data_r3 + foil _m Outer radius of the RIP.

h1 data_h1 - foil _m Lower height of the RIP.

h2 data_h2 - foil _m Intermediate height of the RIP h3 data_h3 + foil _m Intermediate height of the RIP.

h4 data_h4 + foil _m Upper height of the RIP

Table 7: All parameters for Foil Method IV.

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Rectangle Corner position on r-axis

Corner position on z-axis

Width Length

Hollow area next to conductor

0 0 r1 height

Conductor 0 0 radius height

Table 8: The datapoint for creating the rectangles (conductor).

Polygon Start position

on z-axis

Second position

on z-axis

Third position

on z-axis

End position

on z-axis

Inner position

on r-axis

Middle position

on r-axis

Outer position

on r-axis

RIP h1 h2 h3 h4 radius r2 r3

Mold h1-mold h2-mold h3+mold h4+mold radius r2+mold r3+mold Table 9: The datapoint for creating the polygons (RIP and mold).

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B Code

B.1 Method II

B.1.1 Foil Method II creating foils

12 // Edges o f the RIP on the z−a x i s :

3 double h1 = h e i g h t ∗ 0 . 0 5 ; // Lower h e i g h t RIP .

4 double h2 = h1+h e i g h t ∗ 0 . 0 5 ; // I n t e r m e d i a t e h e i g h t RIP nr 1 . 5 double h3 = h2+h e i g h t / 3 ; // I n t e r m e d i a t e h e i g h t RIP nr 2 . 6 double h4 = 5∗ h e i g h t / 6 ; // Upper h e i g h t RIP .

78

9 // Edges o f the RIP on the r−a x i s :

10 double r2 = 0.25∗ r a d i u s ; // I n t e r m e d i a t e r a d i u s RIP . 11 double r3 = r1 +0.75∗ r a d i u s ; // Outer r a d i u s RIP .

1213 // The r a t i o between the s i d e s o f the upper and under t r i a n g u l a r : 14 double ratio_upper = ( ( h4−h3 ) /( r3−r2 ) ) ; // Ratio between the s i d e s

in the upper t r i a n g l e .

15 double ratio_under = ( ( h2−h1 ) /( r3−r2 ) ) ; // Ratio between the s i d e s i n the under t r i a n g l e .

1617 // The d i s t a n c e between the f o i l s :

18 double f o i l _ d i s t a n c e = ( r3 −2∗foil_m ) / n _ f o i l s ;

1920 // C a l c u l a t i n g the amount o f f o i l s who are to be shorted : 21 double n1 = ( ( r2 −2∗foil_m ) / f o i l _ d i s t a n c e ) ;

22 double n 1 _ f o i l s = Math . f l o o r ( n1 ) ; // The number o f f o i l s o f f u l l − l e n g t h .

23 double n3 = ( ( ( r2−foil_m ) / f o i l _ d i s t a n c e )−n 1 _ f o i l s ) ;

24 double n 3 _ f o i l s = Math . f l o o r ( n3 ) ; // The number o f f o i l s that are i n the area o f " f u l l −l e n g t h " but who s t i l l needs to be shorted . 25 double n 2 _ f o i l s = n _ f o i l s −n 1 _ f o i l s ; // The number o f f o i l s that are

shorted .

2627 double r_start = r a d i u s+foil_m+n 1 _ f o i l s ∗ f o i l _ d i s t a n c e ; // The r−

c o o r d i n a t e f o r the f i r s t f o i l . 28 i n t count = 1 ; // The counting v a r i a b l e .

2930 // Using a while−loop to c r e a t e a l l the f o i l s that are not f u l l l e n g t h :

31 while ( count <= n 2 _ f o i l s ) {

3233 // The p o s i t i o n s o f the c u r r e n t f o i l s on the r and z a x i s :

34 double end_z = h3−foil_m+ratio_upper ∗( r3 −(foil_m+(count+n 1 _ f o i l s+

n 3 _ f o i l s ) ∗ f o i l _ d i s t a n c e ) ) ; // The endpoint o f the c u r r e n t f o i l on the z−a x i s .

35 double start_z = h2+foil_m −(ratio_under ∗( r3−foil_m −(count+

n 1 _ f o i l s+n 3 _ f o i l s ) ∗ f o i l _ d i s t a n c e ) ) ; // The s t a r t p o i n t o f the c u r r e n t f o i l on the z−a x i s .

36 double r = r_start +(count −1)∗ f o i l _ d i s t a n c e ; // The c u r r e n t f o i l s

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39 model . component ("comp1") . geom ("geom1") . c r e a t e ("b1"+count , "

BezierPolygon ") ;

40 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b1"+count ) . s e t ("

type ", "open") ;

41 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b1"+count ) . s e t ("p

", new double[ ] [ ] { { r , r } , { start_z , end_z }}) ;

42 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b1"+count ) . s e t ("

degree ", 1) ;

43 model . component ("comp1") . geom ("geom1") . run ("b1"+count ) ; 4445 count++; // The counting .

46 }

Listing 1: Foil Method II creating foils

B.1.2 Foil Method II deleting foils

1 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b11") ; 2 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b12") ; 3 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b13") ; 4 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b14") ; 5 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b15") ; 6 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b16") ; 7 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b17") ; 8 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b18") ; 9 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b19") ; 10 model . component ("comp1") . geom ("geom1") . f e a t u r e ( ) . remove ("b110") ;

Listing 2: Foil Method II deleting 10 foils

B.2 Method III

B.2.1 Foil Method III creating foils

1 //Method that c r e a t e s the f o i l s based on e x c e l s h e e t data . 23 // Reading data

4 S t r i n g [ ] [ ] e x c e l F i l = r e a d E x c e l F i l e ("method3_data . x l s x ", "ANALYSIS"

, "C16") ; 56

7 // tu rni n g s t r i n g matrix i n t o matrix with numbers 8 i n t rows = e x c e l F i l . l e n g t h ;

9 i n t columns = e x c e l F i l [ 0 ] . l e n g t h ;

10 double[ ] [ ] excelData = new double[ rows ] [ columns ] ;

1112 f o r (i n t i = 0 ; i < rows ; i ++) { // l o o p i n g over every row

13 f o r (i n t j = 0 ; j < columns ; j++) { // l o o p i n g over every column 1415 double value = Double . parseDouble ( e x c e l F i l [ i ] [ j ] ) ;

16 excelData [ i ] [ j ] = value ∗ 0 . 0 0 1 ; // R e s c a l i n g 1718 }

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2122 // Creating f o i l s based on data from e x c e l s h e e t 23 f o r (i n t i = 0 ; i < rows ; i ++) {

24 model . component ("comp1") . geom ("geom1") . c r e a t e ("b"+i , "

BezierPolygon ") ;

25 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b"+i ) . s e t (" type ",

" c l o s e d ") ;

26 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b"+i ) . s e t ("p", new double[ ] [ ] { { excelData [ i ] [ 1 ] , excelData [ i ] [ 1 ] } , { excelData [ i

] [ 2 ] , excelData [ i ] [ 3 ] } } ) ;

27 model . component ("comp1") . geom ("geom1") . f e a t u r e ("b"+i ) . s e t (" degree

", 1) ;

28 model . component ("comp1") . geom ("geom1") . run ("b"+i ) ; 29 }

Listing 3: Foil Method III CreateFoils method

B.2.2 Foil Method III deleting foils

1 //Method that d e l e t e s the f o i l s c r e a t e d by the method " C r e a t e F o i l s

" . 23

4 // Reading data

5 S t r i n g [ ] [ ] e x c e l F i l = r e a d E x c e l F i l e ("method3_data . x l s x ", "ANALYSIS"

, "C16") ;

67 // removing every f o i l

8 f o r (i n t i = 0 ; i < e x c e l F i l . l e n g t h ; i ++) { // l o o p i n g over every 9 model . component ("comp1"row ) . geom ("geom1") . f e a t u r e ( ) . remove ("b"+i ) ; 10 }

Listing 4: Foil Method III DeleteFoils method

B.3 Method IV

B.3.1 Foil Method IV creating foils

1 //Method that c r e a t e s the f o i l s based on e x c e l s h e e t data . 23 // Reading data

4 S t r i n g [ ] [ ] e x c e l F i l = r e a d E x c e l F i l e (" Foil_dimensions . x l s x ", "

ANALYSIS", "D16") ; //Need to change input depending on the

e x c e l f i l e / s h e e t / c e l l s to be read . 56

7 // Preparing parameters and matrix f o r l a t e r use i n code .

8 i n t rows = e x c e l F i l . l e n g t h ; //Number o f rows in e x c e l sheet , e q u a l s number o f f o i l s

9 i n t columns = e x c e l F i l [ 0 ] . l e n g t h ; //Number o f rows i n e x c e l s h e e t .

Creating Bushing Core Geometries

Examensarbete 15 hp Juni 2021

Creating Bushing Core Geometries

Hanna Damsgaard Falck Johanna Ring

Erik Svensson

Abstract

Creating Bushing Core Geometries

Populärvetenskaplig sammanfattning

Contents

1 Introduction

2 Theory

3 Method

4 Result

5 Discussion

6 Conclusions

References

A Tables

B Code