COMSOL 6.3 - Modeling of an Electric Generator in 3D

This application illustrates how to model an electric machine, such as a generator, motor, or drive, by exploiting its sector symmetry to reduce the size of the problem. The machine being studied is a simplified electric generator in 3D, based on the geometry used in the Generator in 2D application.

The application uses the interface. It is recommended to have a look at the model Rotating Machinery 3D Tutorial before proceeding with this application.

Model Definition

The complete geometry is shown in Figure 1. Parts of the stator have been removed to show the rotor. The core of the rotor and the stator consists of laminated (σ = 0 S/m), saturable iron, and the teeth of the rotor are permanent magnets using available materials.

The generator rotates with a rotational velocity of 60 rpm, and the model is solved in the time domain from t = 0 s to t = 0.25 s, after which the rotor arrives to a configuration symmetrically equivalent to the starting one.

Figure 1: Geometry of the generator.

The geometry has two types of symmetry: the sector symmetry and a reflection symmetry with respect to the midplane orthogonal to the axis, so it can be reduced to the sector geometry shown in Figure 2. The figure indicates the appropriate conditions to use on the symmetry cut boundaries:

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must be used on the sides of the sector. The type of periodicity chosen is , since the inputs to the model (the remanent flux density in the permanent magnets) change sign in adjacent sectors.

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The pair condition is applied on the identity pair created by the geometry at the contact boundary between rotor and stator. The type of periodicity must match the type specified in the Periodic Boundary Condition features, that is, .

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The reflection symmetry forces the normal component of the magnetic field to be zero at the midplane. This condition is imposed by the default feature.

Figure 2: Boundary conditions used to take into account the model symmetry.

Modeling the Coil

The stator coil has a nonregular shape, that does not fall in either of the or categories. The direction of the coil can be computed in a preprocessing step.

The stator coil is affected by the symmetry cut as well. The modeled length of the coil is 1/16 of its actual length (due to the 8-fold sector symmetry and the mirror symmetry). To ensure that the lumped quantities such as the coil voltage or the current are computed correctly, specify appropriate in the subnode under the node.

The Mixed Formulation

The application uses the mixed formulation functionality of the interface. It solves for the magnetic scalar potential Vm in nonconductive regions and for the magnetic vector potential A in conductive regions. The scalar formulation is solved by features, while the vector formulation is solved by features. Advantages of using the scalar potential formulation in the air gap and nonconductive regions are:

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More accurate magnetic flux conservation by the pair coupling (Sector Symmetry). For this reason, it is important to use the scalar potential in the regions adjacent to a pair.

•

Decreased number of degrees of freedom compared with the vector formulation.

The limitation of the scalar formulation is that it cannot be used in conductive domains or domains carrying currents, nor in regions that contain closed loops of current (for example, it cannot be used in the air region surrounding the coil).

Care must be taken when using a periodic condition in a sector-symmetric model, since the topological condition on the scalar potential regions must be fulfilled in the complete geometry as well.

Direct Solvers and uniqueness of the solution

The interface, by default, uses a direct solver for stationary and transient simulations. Direct solvers are typically better performing than iterative solvers at the cost of increased memory usage.

Direct solvers can only find a solution if it is unique, unlike iterative solvers. The vector potential formulation is subject to gauge freedom, meaning that the solution is unique up to a gauge transformation. To ensure a globally unique solution for the stationary study step, it is necessary to choose (fix) the gauge by using the feature in all domains where the vector formulation is used. For the time-dependent study step, however, the gauge fixing is not required if the conductivity of these domains is not zero in the numerical sense. More information about the electromagnetic gauge and gauge fixing can be found in the AC/DC Module User’s Guide.

Loss Calculation

The resistive and iron losses are computed with the use of a subfeature and a study. For the iron part of the generator, the Bertotti loss model is selected to compute the cycle averaged loss power density. A volume integration is then made to compute the total loss power of the generator. The generated voltage and the losses are compared with the 2D counterpart of this model, that is, Generator in 2D.

Results and Discussion

A sector plot of magnetic flux density is presented in Figure 3. The solution is plotted in the spatial frame, in which the rotor moves.

Figure 3: Sector plot of the magnetic flux density.

To visualize the solution in the complete geometry, reconstruct it using and datasets. These specialized datasets create another solution by rotating and mirroring other datasets according to the specification.

To properly account for the antisymmetry, select the checkbox in the dataset. This functionality changes the sign of the solution when creating adjacent sectors. The resulting plot is shown in Figure 4.

Figure 4: Plot of the magnetic flux density in the complete, reconstructed geometry.

Finally, Figure 5 shows the induced coil voltage as a function of time. The voltage takes into account the number of wires in the multiturn coil and the symmetry. The simulated voltage is in good agreement with the result from the corresponding 2D model, see Figure 3 in the application Generator in 2D.

Figure 5: Voltage induced in the complete coil as a function of time.

ACDC_Module/Devices,_Motors_and_Generators/sector_generator_3d

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Define model parameters: global, constant expressions that can be used anywhere in the application.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
d_wire	3[mm]	0.003 m	Diameter of wire in the winding
N	100	100	Number of turns in the winding
rpm	60[rpm]	1 1/s	Angular velocity of the rotor

Geometry 1

Insert the geometry sequence from a separate file using the functionality. This functionality copies all the subnodes of the geometry node in the chosen file to the current model.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file sector_generator_3d_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

The geometry represents a sector of the complete generator, further halved along the xy-symmetry plane. The geometry is composed of two objects, one for the rotor and one for the stator. They have been constructed from the individual components using two operations. The geometry is finalized by using , which detects the touching boundaries and creates an connecting them.

Disable the analysis of the geometry as the remaining small geometric details can be kept.

In the window, under click .

In the window for , locate the section.

Clear the checkbox.

Definitions

Proceed to the definition of nodes: named collection of geometric entities (such as domains or boundaries) that can be reused when applying equations, boundary conditions, and other features. New selections can also be obtained by applying more advanced operations on other selections, such as taking the complement or the adjacent entities. Using selections simplifies the workflow, especially in models with complex geometries. selections are named selections in which the entities (domains, in this case) are selected explicitly.

Cylindrical System 2 (sys2)

In the toolbar, click

and choose .

The cylindrical coordinate system just created will be used to plot the radial flux density in postprocessing.

Stator Coil

In the toolbar, click

In the window for , type Stator Coil in the text field.

Click the

button in the toolbar.

You can conveniently add domain entities with the view instead of clicking the domains manually:

Locate the section. Click

In the dialog, type 17 19 20 22 23 24 in the text field (the domains belonging to the coil).

Click .

Permanent Magnet

In the toolbar, click

In the window for , type Permanent Magnet in the text field.

Select Domains 9 and 10 only (the magnet domain).

Rotating Domains

In the toolbar, click

In the window for , type Rotating Domains in the text field.

Select Domains 1–10 only (all the domains in the rotor).

Definitions

Create a selection for the stationary domains by taking the complement of the rotor selection.

Stationary Domains

In the toolbar, click

In the window for , type Stationary Domains in the text field.

Locate the section. Under , click

In the dialog, select in the list.

Click .

Periodic Condition: Rotor

In the toolbar, click

In the window for , type Periodic Condition: Rotor in the text field.

Locate the section. From the list, choose .

Select Boundaries 1, 2, 6, 7, 14, 18, 23, and 27 only.

Periodic Condition: Stator, Scalar Potential

In the toolbar, click

In the window for , type Periodic Condition: Stator, Scalar Potential in the text field.

Locate the section. From the list, choose .

Select Boundaries 49, 52, 56, and 59 only.

Periodic Condition: Stator, Vector Potential

In the toolbar, click

In the window for , type Periodic Condition: Stator, Vector Potential in the text field.

Locate the section. From the list, choose .

Select Boundaries 75, 78, 96, 98, 118, and 125 only.

Destination

In the toolbar, click

In the window for , type Destination in the text field.

Locate the section. From the list, choose .

Select Boundaries 41–44 only.

Source

In the toolbar, click

In the window for , type Source in the text field.

Locate the section. From the list, choose .

Select Boundaries 48, 51, 55, and 58 only.

Identity Boundary Pair 1 (ap1)

Finally, ensure that the side of the identity pair is on the moving domain. This gives a better performance during the solution.

Check the and the and make sure that the moving domains are in the destination side. The boundaries are numbered progressively with increasing x-coordinate, so the boundaries on the rotor side have lower numbers. Click the button to swap the boundary assignment and put the boundaries with the lower numbers in the destination side.

Add Material

Proceed with the definition of the materials.

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Right-click and choose .

In the tree, select > .

Right-click and choose .

In the tree, select > > > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Soft Iron (Without Losses) (mat2)

Select Domains 1, 2, 5, 6, 15, and 16 only.

N50 (Sintered NdFeB) (mat3)

In the window, click .

In the window for , locate the section.

From the list, choose .

Rotating Machinery, Magnetic (rmm)

Move on to the setup of the physics interface.

Magnetic Flux Conservation: Air Gap

In the toolbar, click

and choose .

In the window for , type Magnetic Flux Conservation: Air Gap in the text field.

Select Domains 3, 4, 7, 8, and 11–14 only.

Magnetic Flux Conservation: Rotor Iron

In the toolbar, click

and choose .

In the window for , type Magnetic Flux Conservation: Rotor Iron in the text field.

Select Domains 1, 2, 5, and 6 only.

Locate the section. From the list, choose .

Loss Calculation 1

In the toolbar, click

and choose .

Set loss model to .

In the window for , locate the section.

From the list, choose .

Ampère’s Law: Stator Iron

In the toolbar, click

and choose .

In the window for , type Ampère's Law: Stator Iron in the text field.

Select Domains 15 and 16 only.

Locate the section. From the list, choose .

Loss Calculation 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Add a feature to define remanent flux of the permanent magnet. Set no constraint for induced currents to obtain similar results as for the 2D counterpart of this model.

Conducting Magnet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

North 1

In the window, click .

Select Boundaries 45 and 46 only.

South 1

In the window, click .

Select Boundaries 30 and 34 only.

Conducting Magnet 1

In the window, click .

Loss Calculation 1

In the toolbar, click

and choose .

Domain Coil 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

This setting requires solving a preprocessing step.

In the Icoil text field, type 0[A].

Locate the section. In the N text field, type N.

From the list, choose .

In the d text field, type d_wire.

Geometry Analysis 1

The coil domain is only 1/16 of the total length of the coil (due to symmetry). Use the functionality in the subfeature to apply the appropriate corrections to the lumped quantities, such as the induced voltage.

In the window, click .

In the window for , click to expand the section.

In the FL text field, type 16.

Input 1

In the window, expand the node, then click .

Select Boundary 97 only (one of the two boundaries at the symmetry cut).

Geometry Analysis 1

In the window, click .

Output 1

In the toolbar, click

and choose .

Select Boundary 76 only (the other boundary at the symmetry cut).

Gauge Fixing for A-Field 1

The default solver for the 3D interface is the direct solver, which gives better performance in time-dependent studies and with the mixed formulation. A direct solver requires that the solution is unique, so it is necessary to apply the feature. The stationary form of gauge fixing is enforced in order to be able to support regions with zero conductivity.

In the toolbar, click

and choose .

Sector Symmetry 1

The feature sets up the appropriate rotational-periodic coupling at the identity pair.

In the toolbar, click

and choose .

In the window for , locate the section.

Click

In the dialog, select in the list.

Click .

In the window for , locate the section.

In the nsect text field, type 8.

From the list, choose .

Periodic Condition 1

Apply periodic conditions on the periodic boundaries.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Periodic Condition 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Periodic Condition 3

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Component 1 (comp1)

Rotating Domain 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

In the f text field, type rpm.

Set the electric conductivity of air and soft iron to a finite small value (1[S/m]) to improve the numerical stability.

Materials

Air (mat1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	1[S/m]	S/m	Basic

Soft Iron (Without Losses) (mat2)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	1[S/m]	S/m	Basic

Mesh 1

For curl elements that describe the vector potential A, it is important that the mesh is congruent on the two symmetry surfaces, that is, there is a one-to-one mapping between the mesh elements on either side. This eliminates the need for interpolation between mismatching mesh elements which would have a negative impact on accuracy and solver stability. Create a congruent mesh by meshing half of the sector geometry and copying it to the remaining domains. You can also utilize the extrusion along the rotational axis by using a swept mesh, which reduces the size of the problem. Begin by meshing half of the nonextruded domains:

Free Tetrahedral 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domains 4, 14, and 21–23 only.

Click

Swept 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domains 2, 6, 8, 10, 13, 16, and 24 only.

Distribution 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type 10.

From the list, choose .

Click

Copy Domain 1

In the window, right-click and choose > .

Select Domains 2, 4, 6, 8, 10, 13, 14, 16, and 21–24 only.

In the window for , locate the section.

Click to select the

toggle button.

Select Domains 1, 3, 5, 7, 9, 11, 12, 15, and 17–20 only.

Right-click and choose .

Study 1

Complete the definition of the study. After the step added earlier, add a step (to compute the initial values for the transient step) and the main step.

Step 2: Stationary

In the toolbar, click

Step 3: Time Dependent

In the toolbar, click

In the window for , locate the section.

In the text field, type range(0,0.005,0.25).

For a time-dependent study with finite conductivity in all domains, it is not necessary to use the gauge fixing. Next, it is disabled to make the model cheaper to solve.

Locate the section. Select the checkbox.

In the tree, select > > .

Right-click and choose .

Before proceeding with computing the solution, prepare a plot that is to be shown during solving. Start by adding a selection to the main dataset.

Solution 1 (sol1)

In the toolbar, click

Results

In the window, expand the node.

Study 1/Solution 1 (sol1)

In the window, expand the > node, then click .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Domains 1, 2, 5, 6, 9, 10, 15, and 16 only.

Reconstruct the complete geometry using and datasets.

Sector 3D 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 8.

Click to expand the section. Find the subsection. Select the checkbox.

Complete Geometry, Iron

In the toolbar, click

and choose .

In the window for , type Complete Geometry, Iron in the text field.

Locate the section. From the list, choose .

Magnetic Flux Density (Radial Component)

In the toolbar, click

In the window for , type Magnetic Flux Density (Radial Component) in the text field.

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

Visualize the solution in the spatial frame (the fixed "laboratory" frame), in which the rotor is moving.

Locate the section. From the list, choose .

Locate the section. Select the checkbox.

Select the checkbox.

Volume 1

Right-click and choose .

One way to define the radial component of B, is to write it as r·B, where r is a unit vector pointing in the radial direction. You can retrieve it from the cylindrical coordinate system.