COMSOL 6.3 - Generator in 2D

This example shows how the circular motion of a rotor with permanent magnets generates an induced EMF in a stator winding. The generated voltage is calculated as a function of time during the rotation. The model also shows the influence on the voltage from material parameters, rotation velocity, and number of turns in the winding.

The center of the rotor consists of annealed medium carbon steel, which is a material with a high relative permeability. The center is surrounded with several blocks of a permanent magnet made of sintered NdFeB, creating a strong magnetic field. The stator is made of the same permeable material as the center of the rotor, confining the field in closed loops through the winding. The winding is wound around the stator poles. Figure 1 shows the generator with part of the stator sliced in order to show the winding and the rotor.

Figure 1: Drawing of a generator showing how the rotor, stator, and stator winding are constructed. The coils are connected in series in order to give the highest possible voltage.

Modeling in COMSOL Multiphysics

The COMSOL Multiphysics model of the generator is a time-dependent 2D problem on a cross section through the generator. This is a true time-dependent model where the motion of the magnetic sources in the rotor is accounted for in the boundary condition between the stator and rotor geometries. Thus, there is no Lorentz term in the equation, resulting in the PDE

where the magnetic vector potential only has a z component.

Rotation is modeled using a ready-made physics interface for rotating machinery. The center part of the geometry, containing the rotor and part of the air-gap, rotates relative to the coordinate system of the stator. The rotor and the stator are built as two separate geometry objects, so it is possible to use an assembly (see Finalizing the Geometry in the COMSOL Multiphysics Reference Manual for details). This has several advantages: the coupling between the rotor and the stator is done automatically, the parts are meshed independently, and it allows for a discontinuity in the vector potential at the interface between the two geometry objects (called slits). The rotor problem is solved in a rotating coordinate system where the rotor is fixed (the rotor frame), whereas the stator problem is solved in a coordinate system that is fixed with respect to the stator (the stator frame). An identity pair connecting the rotating rotor frame with the fixed stator frame is created between the rotor and the stator. The identity pair enforces continuity for the vector potential in the global fixed coordinate system (the stator frame).

The stator and center of the rotor are made of annealed medium-carbon steel (soft iron), which is implemented in COMSOL Multiphysics as an interpolation function of the B-H curve of the material; see Figure 2.

Figure 2: The norm of the magnetic flux, |B|, versus the norm of the magnetic field, |H|, for the rotor and stator materials.

The generated voltage is computed automatically with the use of the Coil feature. In this simplified example all coils are connected in series, making out a single stator winding. The series connection of coils is realized in COMSOL Multiphysics by adding coil domains to a Coil group. In this way, the output voltage is the sum of voltages generated by each coil even though they are not geometrically connected in the 2D model.

The resistive and iron losses are computed with the use of a Loss Calculation subfeature and a Time to Frequency Losses study. In this 2D model, the magnets are modeled by using the Coil feature, which allows for the calculation of induced currents and resistive losses. The settings impose a zero net perpendicular current in each of the magnets by activating the Coil group checkbox. For the iron part of the generator, the Bertotti loss model is selected to compute the cycle averaged loss power density. A surface integration is then made to compute the total loss power of the generator. The generated voltage and the losses are compared with the 3D counterpart of this model, that is, Modeling of an Electric Generator in 3D.

Results and Discussion

The generated voltage in the rotor winding is close to a sinusoidal signal. At a rotation speed of 60 rpm the voltage has an amplitude of 700 V in total; see Figure 3.

Figure 3: The generated voltage over one quarter of a revolution. This simulation used a 100-turn winding.

The norm of the magnetic flux density, |B|, and the B field lines are shown below in Figure 4 at the time 0.20 s.

Figure 4: The norm and the field lines of the magnetic flux density after 0.2 s of rotation. Note the darker regions, which indicate the position of the permanent magnets in the rotor.

The cycle averaged losses power density is shown below in Figure 5.

Figure 5: The volumetric loss density of the generator.

ACDC_Module/Devices,_Motors_and_Generators/generator_2d

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

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
L	0.4[m]	0.4 m	Length of generator
rpm	60[1/min]	1 1/s	Rotational speed of rotor
d_wire	3[mm]	0.003 m	Diameter of wire in the winding
N	100	100	Number of turns in the winding

Next, build the generator using rotor and stator parts from the geometry part library. Initialize the parts, and tick the selections that are predefined to make it convenient to assign material properties and magnetization direction.

Part Libraries

In the toolbar, click

and choose .

In the window, select > > > > in the tree.

Click

Part Libraries

In the toolbar, click

and choose .

In the window, under click .

In the window, select > > > > in the tree.

Click

Geometry 1

In the toolbar, click

Click the

button in the toolbar.

In the window, under click .

Internal Rotor – Surface Mounted Magnets 1 (pi1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
number_of_poles	8	8	Number of magnetic poles in rotor
number_of_modeled_poles	8	8	Number of magnetic poles included in the geometry
shaft_diam	10[cm]	0.1 m	Diameter of the shaft
rotor_diam	30[cm]+2*6.5[cm]	0.43 m	Diameter of the rotor
cont_diam	0.45[m]	0.45 m	Diameter of the stator-rotor continuity interface
magnet_h	6.5[cm]	0.065 m	Height of the magnets
magnet_w	10[cm]	0.1 m	Width of the magnets (set to 0 to use all available space)
magnet_fillet_size	0.6[cm]	0.006 m	Radius of magnet fillet

Click to expand the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Shaft	√	√	None
Rotor iron	√	√	None
Odd magnets	√	√	None
Even magnets	√	√	None
Rotor magnets	√	√	None
Rotor solid domains	√	√	None
Rotor air	√	√	None
All	√	√	None

External Stator – Slotted 1 (pi2)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
number_of_slots	8	8	Number of slots in stator
number_of_modeled_slots	8	8	Number of slots included in the geometry
backiron_th	6[cm]	0.06 m	Thickness of back-iron
stator_diam	80[cm]	0.8 m	Diameter of the stator
external_air_size	0[cm]	0 m	Size of air external to stator
cont_diam	45[cm]	0.45 m	Diameter of the stator-rotor continuity interface
shoe_h	1.75[cm]	0.0175 m	Height of the shoe
shoe_w	11.5[cm]	0.115 m	Width of the shoe
tooth_h	10.5[cm]	0.105 m	Height of the tooth
tooth_w	9[cm]	0.09 m	Width of the tooth
shoe_fillet_size	0.4[cm]	0.004 m	Radius of the shoe fillet
slot_outer_fillet_size	0.4[cm]	0.004 m	Radius of the outer slot fillet
slot_inner_fillet_size	0.4[cm]	0.004 m	Radius of the inner slot fillet
slot_winding_type	2	2	Slot winding type: 1-No partition, 2-Radial partition, 3-Azimuthal partition, 4-Radial and azimuthal partition.

Locate the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Stator iron	√	√	None
Stator slots	√	√	None
Stator air	√	√	None
All	√	√	None

Definitions

Iron

In the toolbar, click

In the window for , locate the section.

Under , click

In the dialog, in the list, choose , , and .

Click .

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

Iron and Magnets

In the toolbar, click

In the window for , locate the section.

Under , click

In the dialog, in the list, choose and .

Click .

In the window for , type Iron and Magnets in the text field.

Create an assembly from the two geometry objects, connected by a pair boundary.

Geometry 1

Form Union (fin)

In the window, under > click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

In the window, click .

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the tree, select > .

Click the button in the window toolbar.

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)

In the window for , locate the section.

From the list, choose .

N50 (Sintered NdFeB) (mat3)

In the window, click .

In the window for , locate the section.

From the list, choose .

Rotating Machinery, Magnetic (rmm)

In the window, under click .

In the window for , locate the section.

In the d text field, type L.

Next, use a Rotating Domain feature to specify the rotor’s rotational velocity.

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.

To define the remanent flux direction of all magnets, use the Conducting Magnet feature.

Rotating Machinery, Magnetic (rmm)

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 .

From the list, choose .

North 1

In the window, click .

Select Boundary 212 only.

South 1

In the window, click .

Select Boundary 218 only.

Conducting Magnet 1

In the window, click .

Loss Calculation 1

In the toolbar, click

and choose .

Iron

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the text field, type Iron.

Add the subfeature to compute iron losses.

Loss Calculation 1

In the toolbar, click

and choose .

Set loss model to .

In the window for , locate the section.

From the list, 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 .

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.

Locate the section. Select the checkbox.

Reversed Current Direction 1

In the toolbar, click

and choose .

Select Domains 1, 4, 8, 10, 11, 13, 16, and 18 only.

Study 1

Step 2: Time Dependent

In the toolbar, click

In the window for , locate the section.

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

Before solving refine the mesh on boundaries associated with the condition for more accurate results.

Definitions

Identity Boundary Pair 1 (ap1)

In the window, under > click .

In the window for , locate the section.

Click

In the dialog, type source in the text field.

Click .

In the window for , locate the section.

Click

In the dialog, type destination in the text field.

Click .

Airgap Boundaries

In the toolbar, click

In the window for , type Airgap Boundaries in the text field.

Locate the section. From the list, choose .

Locate the section. Under , click

In the dialog, in the list, choose and .

Click .

Mesh 1

Free Triangular 1

In the toolbar, click

Size

In the window, click .

In the window for , locate the section.

From the list, choose .

Click the button.

Locate the section. In the text field, type 0.015.

Size 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Click

Study 1

In the toolbar, click

Postprocessing the Results

Now, plot the solution in the spatial frame (the stator’s fixed frame) at the time t = 0.2 s.

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Figure 4 shows the rotor position at t = 0.2 s, as well as the magnetic flux density norm and magnetic flux density lines. Next, plot the induced EMF in a quarter of the cycle.

Induced Coil Voltage

In the toolbar, click