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Electrical Heating in a Busbar
Introduction
This example analyzes a busbar designed to conduct a direct current from a transformer to an electrical device; see Figure 1. The current conducted in the busbar produces heat due to the resistive losses, a phenomenon referred to as Joule heating. The Joule heating effect is described by conservation laws for electric current and energy. Once solved for, the two conservation laws give the temperature and electric field, respectively.
Figure 1: Photo of a busbar installation, and the geometry of the busbar used in this example.
The goal of your simulation is to precisely calculate how much the busbar heats up, and to study the influence of two design parameters, the width and length of the device, on the phenomenon. By conducting a parametric sweep over a range of these parameters you can determine which combinations of the width and length parameters result in a temperature increase that is less than 30° above the ambient temperature.
Model Definition
The busbar is made of copper while for the bolts, instead of the usual steel, we choose titanium assuming a highly corrosive environment. This choice of materials is important since titanium has a lower electrical conductivity than copper and is subjected to a higher current density.
All surfaces, except the bolt contact surfaces, are cooled by natural convection in the air surrounding the busbar. We can assume that the bolt cross-section boundaries do not contribute to cooling or heating of the device. The electric potential at the upper-right vertical bolt surface is 20 mV, and that the potential at the two horizontal surfaces of the lower bolts is 0 V.
Figure 2: Material and boundary settings in the model.
Results and Discussion
The plot shown in Figure 3 displays the temperature in the busbar, which is substantially higher than the ambient temperature 293 K. The temperature difference in the device is less than 10 K, due to the high thermal conductivity of copper and titanium. The temperature variations are largest on the top bolt, which conducts double the amount of current compared to the two lower ones.
Figure 3: Temperature distribution in the busbar.
The color range of the plot in Figure 4 better illustrates the low temperature variation in the copper part of the device. The temperature distribution is symmetric with a vertical mirror plane running between the two lower titanium bolts and running across the middle of the upper bolt. In this case, the model does not require much computing power and you can model the whole geometry. For more complex models, you should consider using symmetries in order to reduce the size of the model.
Figure 4: Temperature distribution in the copper part of the busbar.
Increasing the size of the busbar by increasing the width and length dimensions, while keeping the applied potential constant, leads to a lower temperature in the device. While the increased cross-sectional area leads to more heat produced by resistive losses, there is an even larger increase in the cooling effect as the total surface area increases, resulting in the lowering of the temperature.
By plotting the average temperature increase above the ambient temperature against the width and length parameters, and formatting the plot according to Figure 5, we can easily determine which width and length combinations lead to an acceptable value of the temperature increase.
Figure 5: Average temperature increase above ambient temperature in the busbar plotted against the width and length parameters and formatted to show the parameter combinations that lead to a temperature increase of more than 30°.
Notes About the COMSOL Implementation
The busbar geometry you are using in this example comes from an AutoCAD drawing. The LiveLink interface transfers the geometry from AutoCAD to COMSOL Multiphysics. Using the interface you are also able to update the dimensions of the busbar in the AutoCAD file. In order for this to work you need to have both programs running during modeling, and you need to make sure that the busbar drawing file is the active file in AutoCAD.
Application Library path: LiveLink_for_AutoCAD/Tutorials,_LiveLink_Interface/busbar_llac
Modeling Instructions
 
1
In AutoCAD open the file busbar_surface.dwg located in the model’s Application Library folder.
2
Switch to the COMSOL Desktop.
COMSOL Desktop
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Heat Transfer>Electromagnetic Heating>Joule Heating.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
Make sure that the CAD Import Module kernel is used.
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Advanced section.
3
From the Geometry representation list, choose CAD kernel.
LiveLink for AutoCAD 1 (cad1)
1
In the Home toolbar, click  LiveLink and choose LiveLink for AutoCAD.
2
In the Settings window for LiveLink for AutoCAD, locate the Synchronize section.
3
Click Synchronize.
After a few moments the geometry of the busbar assembly appears in the Graphics window.
4
Click to expand the Parameters in CAD Package section. The table contains the two parameters, width and d5, which are part of the AutoCAD model. In AutoCAD, the Parameter Selection button on the COMSOL Multiphysics tab allows you to select and view parameters for synchronization. These parameters are retrieved, and appear in the CAD name column of the table. The corresponding entries in the COMSOL name column, LL_width and LL_d5, are global parameters in the COMSOL model. These are automatically generated during synchronization, and are assigned the values of the linked AutoCAD dimensions. The parameter values are displayed in the COMSOL value column.
Global parameters in a model allow you to parameterize settings and can be controlled by the parametric solver to perform parametric sweeps. Thus, by linking AutoCAD parameters to COMSOL global parameters, the parametric solver can automatically update and synchronize the geometry for each new value in a sweep.
5
Click to expand the Object Selections section. The selections displayed here are automatically generated based on the assigned materials in the AutoCAD file.
Knit to Solid 1 (knit1)
1
In the Geometry toolbar, click  Defeaturing and Repair and choose Knit to Solid.
2
Click in the Graphics window and then press Ctrl+A to select all objects.
3
In the Settings window for Knit to Solid, click  Build Selected.
Copper
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Copper in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Add.
5
In the Add dialog box, select Copper.surface in the Input selections list.
6
Click OK.
7
In the Settings window for Adjacent Selection, locate the Output Entities section.
8
From the Geometric entity level list, choose Adjacent domains.
Titanium
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Titanium in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Add.
5
In the Add dialog box, select Titanium.surface in the Input selections list.
6
Click OK.
7
In the Settings window for Adjacent Selection, locate the Output Entities section.
8
From the Geometric entity level list, choose Adjacent domains.
Form Union (fin)
In the Model Builder window, right-click Form Union (fin) and choose Build Selected.
Grounded boundaries
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Grounded boundaries in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 8 and 15 only. These are the bolt faces labeled with Ground in Figure 2.
Electric potential boundary
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Electric potential boundary in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundary 31 only. This is the bolt face labeled with Electric potential in Figure 2.
Heat flux boundaries
1
In the Geometry toolbar, click  Selections and choose Difference Selection.
2
In the Settings window for Difference Selection, type Heat flux boundaries in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Click  Add.
5
In the Add dialog box, in the Selections to add list, choose Copper.surface and Titanium.surface.
6
Click OK.
7
In the Settings window for Difference Selection, locate the Input Entities section.
8
Click  Add.
9
In the Add dialog box, in the Selections to subtract list, choose Grounded boundaries and Electric potential boundary.
10
Click OK.
Global Definitions
Parameters 1
The table already contains the automatically generated global parameters that are linked to the AutoCAD parameters. It is possible to edit the values of these parameters here, and then synchronize, to modify the geometry. But here we will use the parametric solver to modify the parameters.
Continue with loading additional parameters for setting up the physics.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file busbar_parameters.txt.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the Search text field, type copper.
4
Click Search.
5
In the tree, select Built-in>Copper.
6
Click Add to Component in the window toolbar.
Materials
Copper (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Copper.
Add Material
1
Go to the Add Material window.
2
In the Search text field, type titanium.
3
Click Search.
4
In the tree, select Built-in>Titanium beta-21S.
5
Click Add to Component in the window toolbar.
Materials
Titanium beta-21S (mat2)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Titanium.
Electric Currents (ec)
Ground 1
1
In the Model Builder window, under Component 1 (comp1) right-click Electric Currents (ec) and choose Ground.
2
In the Settings window for Ground, locate the Boundary Selection section.
3
From the Selection list, choose Grounded boundaries.
Electric Potential 1
1
In the Physics toolbar, click  Boundaries and choose Electric Potential.
2
In the Settings window for Electric Potential, locate the Boundary Selection section.
3
From the Selection list, choose Electric potential boundary.
4
Locate the Electric Potential section. In the V0 text field, type Vtot.
Heat Transfer in Solids (ht)
In the Model Builder window, under Component 1 (comp1) click Heat Transfer in Solids (ht).
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Heat flux boundaries.
4
Locate the Heat Flux section. Click the Convective heat flux button.
5
In the h text field, type htca.
Study 1
Parametric Sweep
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add.
4
From the list in the Parameter name column, choose LL_width.
5
Click  Range.
6
In the Range dialog box, type 40[mm] in the Start text field.
7
In the Step text field, type 10[mm].
8
In the Stop text field, type 70[mm].
9
Click Replace.
10
In the Parameter unit column, enter mm.
11
In the Settings window for Parametric Sweep, locate the Study Settings section.
12
Click  Add.
13
Click to select row number 2 in the table.
14
From the list in the Parameter name column, choose LL_d5.
15
Click  Range.
16
In the Range dialog box, type 60[mm] in the Start text field.
17
In the Step text field, type 10[mm].
18
In the Stop text field, type 90[mm].
19
Click Replace.
20
In the Parameter unit column, enter mm.
As the last step before computing the solution, configure the sweep to include all combinations of the two parameters.
21
In the Settings window for Parametric Sweep, locate the Study Settings section.
22
From the Sweep type list, choose All combinations.
23
In the Study toolbar, click  Compute.
Results
Temperature (ht)
1
In the Model Builder window, click Temperature (ht).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
From the Color list, choose Gray.
Surface
1
In the Model Builder window, expand the Temperature (ht) node, then click Surface.
2
In the Settings window for Surface, locate the Expression section.
3
From the Unit list, choose degC.
4
Locate the Coloring and Style section. From the Color table list, choose HeatCameraLight.
5
In the Temperature (ht) toolbar, click  Plot.
6
Rotate the plot in the Graphics window to get a view similar to the plot displayed in Figure 3.
7
Click to expand the Range section. Select the Manual color range check box.
8
In the Maximum text field, type 42.6.
9
In the Temperature (ht) toolbar, click  Plot.
10
Click the  Go to Default View button in the Graphics toolbar.
You should now see a plot similar to the one in Figure 4.
Definitions
Add a domain probe to calculate the average temperature increase from ambient temperature in the device.
Domain Probe 1 (dom1)
1
In the Definitions toolbar, click  Probes and choose Domain Probe.
2
In the Settings window for Domain Probe, locate the Expression section.
3
In the Expression text field, type T-20[degC].
4
Click  Update Results.
Table
1
Go to the Table window.
2
Click Table Surface in the window toolbar.
A plot similar to the one displayed below appears.
Results
In the last few steps you can add annotations and format the plot to make it easier to read which parameter combinations result in an accepted temperature increase.
Table Surface 2
1
In the Model Builder window, under Results>2D Plot Group 5 right-click Table Surface 1 and choose Duplicate.
2
In the Settings window for Table Surface, click to expand the Title section.
3
From the Title type list, choose None.
4
Click to expand the Range section. Select the Manual data range check box.
5
In the Maximum text field, type 30.
6
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
7
From the Color list, choose Green.
Table Surface 1
1
In the Model Builder window, click Table Surface 1.
2
In the Settings window for Table Surface, locate the Range section.
3
Select the Manual data range check box.
4
In the Minimum text field, type 30.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
2D Plot Group 5
1
In the Model Builder window, click 2D Plot Group 5.
2
In the Settings window for 2D Plot Group, locate the Plot Settings section.
3
Select the x-axis label check box.
4
In the associated text field, type Busbar width (width) (mm).
5
Select the y-axis label check box.
6
In the associated text field, type Busbar length (d5) (mm).
Annotation 1
1
Right-click 2D Plot Group 5 and choose Annotation.
2
In the Settings window for Annotation, locate the Data section.
3
From the Dataset list, choose Domain Probe 1.
4
Locate the Annotation section. In the Text text field, type $\Delta T\ >\ 30 \degree$.
5
Locate the Position section. In the x text field, type 49[mm].
6
In the y text field, type 73[mm].
7
Locate the Coloring and Style section. Select the LaTeX markup check box.
8
Clear the Show point check box.
Annotation 2
1
Right-click 2D Plot Group 5 and choose Annotation.
2
In the Settings window for Annotation, locate the Data section.
3
From the Dataset list, choose Domain Probe 1.
4
Locate the Annotation section. In the Text text field, type $\Delta T\ <\ 30 \degree$.
5
Locate the Position section. In the x text field, type 61[mm].
6
In the y text field, type 83[mm].
7
Locate the Coloring and Style section. Select the LaTeX markup check box.
8
Clear the Show point check box.
9
In the 2D Plot Group 5 toolbar, click  Plot.
The plot in the Graphics window should now look similar to the one in Figure 5.