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_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 represented 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. The teeth of the rotor are permanent magnets from 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 arrived 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:

•

must be used on the sides of the sector symmetry. 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.

•

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, .

•

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 the Linear or Circular category. 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 the 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 subfeature, under the node.

The Mixed FormulatioN

The application uses the Mixed formulation functionality of the Rotating Machinery, Magnetic interface. It solves the magnetic scalar potential Vm in nonconductive regions and for the magnetic vector potential A. 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:

•

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 loop chaining a current (for example, it cannot be used in the air region surrounding the coil).

Care must be taken when using 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 Rotating Machinery, Magnetic 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. In the case of magnetic simulations, some operations are required to ensure that the problem has a unique solution:

•

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, it is necessary to choose (fix) the gauge by using the feature in all domains where the vector formulation is used. More information about the electromagnetic gauge and gauge fixing can be found in the AC/DC Module User’s Guide.

•

In the scalar potential formulation, only the gradient of the potential (and not the potential itself) appears, unless Dirichlet (fixed value) conditions are applied somewhere in the model. As a consequence, the solution is unique only up to a constant. To ensure a globally unique solution, add a Dirichlet point constraint by means of a point feature.

Results and Discussion

A sector plot of magnetic flux density and the coil voltage 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. The global coil voltage is represented as a volume plot on the coil itself.

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

To properly account for the antisymmetry, select the in the data set. 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 and the global coil voltages 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 multi-turn coil and the symmetry.

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

ACDC_Module/Tutorials/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 .

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 .

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.

Explicit 1

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.

In the toolbar, click .

In the window, expand the node, then click .

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

Click the button in the toolbar.

Select Domains 11–17 only(the domains belonging to the coil).

Explicit 2

In the toolbar, click .

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

Select Domain 4 only(the magnet domain ).

Explicit 3

In the toolbar, click .

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

Select Domains 1–4 only(all the domains in the rotor).

Component 1 (comp1)

Complement 1

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

In the toolbar, click .

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

Locate the section. Under , click .

In the dialog box, select in the list.

Click .

Explicit 4

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, 4, 5, 9, and 13 only.

Explicit 5

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 24, 27, 30, and 31 only.

Explicit 6

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 33, 36, 39, 41, 86, and 88 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 .

Click .

In the tree, select .

Click .

In the tree, select .

Click in the window toolbar.

In the toolbar, click to close the window.

Materials

Soft Iron (Without Losses) (mat2)

In the window, under click .

Select Domains 2 and 10 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 1

In the window, under right-click and choose .

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

Select Domains 1, 3, 5, and 6 only.

Magnetic Flux Conservation 2

In the toolbar, click and choose .

Select Domain 4 only.

In the window for , locate the section.

From the list, choose .

In the text field, type Magnetic Flux Conservation: Magnet.

Locate the section. From the || B r || list, choose . In the associated text field, type 1.4.

Magnetic Flux Conservation 3

In the toolbar, click and choose .

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

Select Domain 2 only.

Locate the section. From the list, choose .

Ampère’s Law 2

In the toolbar, click and choose .

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

Select Domain 10 only.

Locate the section. From the list, choose .

Coil 1

In the toolbar, click and choose .

Select Domain 13 only.

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

This setting requires to solve a preprocessing step.

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

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

In the acoil text field, type d_wire.

Geometry Analysis 1

In the window, click .

In the window for , locate the section.

Find the subsection. In the FL text field, type 16.

Input 1

In the window, expand the node, then click .

Select Boundary 57 only(one of the two boundaries at the symmetry cut).

Geometry Analysis 1

The coil domain is only 1/16 of the total lenght 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 .

Output 1

In the toolbar, click and choose .

Select Boundary 70 only(the other boundary at the symmetry cut).

Gauge Fixing for A-field 1

The default solver for the 3D Rotating Machinery, Magnetic 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 so to be able to support regions with zero conductivity.

In the toolbar, click and choose .

Click the button in the toolbar.

In the dialog box, in the tree, select the check box for the node .

Click .

In the window, click .

In the window for , locate the section.

From the list, choose .

Zero Magnetic Scalar Potential 1

In the toolbar, click and choose .

Select Point 1 only, or any other point belonging to the scalar potential region.

Sector Symmetry 1

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

In the toolbar, in the section, click and choose .

In the window for , locate the section.

Under , click .

In the dialog box, select in the list.

Click .

In the window for , locate the section.

In the nsect text field, type 8.

From the list, choose .

Click to expand the section. Select the check box.

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 .

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.

Rotating Machinery, Magnetic (rmm)

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

Mesh 1

Set up the mesh for the problem; physics controlled mesh will automatically generate a mesh that is conformal on the two side of the symmetry. This is a strong requirement for all faces where the fields are desribed by vector potential A.

In the window, under right-click and choose .

Click the button in the toolbar.

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.

Stationary

In the toolbar, click and choose .

Time Dependent