3-Phase Choke with Heat Transfer

Introduction

As the demand for sustainable and clean electrical power continues to rise, the integration of power electronic components, such as inverters and converters, has become increasingly critical within modern power systems. These components, characterized by their non-linear behavior, introduce harmonic distortions into the system. The voltage output from these converters often contains unwanted harmonics, which can significantly impact the power system by reducing transmission capacity, causing electromagnetic interference with other equipment, and compromising overall system performance and longevity. To mitigate these issues and ensure the maintenance of power quality and grid stability in both transmission and distribution networks, filters are employed to regulate and minimize the harmonic fluctuations generated by non-linear power electronic devices. This has heightened the demand for gapped inductors tailored to the unique characteristics of these systems.
In this document, TRAFOLO employs Finite Element Methods (FEM) to model and simulate key parameters, including core material selection, air gap size, winding configuration, support brackets, and overall geometry, to optimize the performance of power filters. These simulations enable engineers to conduct detailed analyses of heat dissipation, loss mechanisms, and temperature distribution, as well as perform comprehensive harmonic analysis. This methodical approach allows for precise fine-tuning of inductors, resulting in maximized performance, minimized losses, improved efficiency, and enhanced overall power quality.

Model description

A 3-phase gapped inductor constructed from laminated electrical steel with foil windings is being modeled. The inductor operates at a frequency of 500 Hz with a current of 100 A and it includes a harmonic component at 10 kHz with an amplitude of 5 A. To securely hold the gapped inductor in place, aluminum brackets are carefully positioned around the core Dielectric spacers, similar to bobbins, are used to improve thermal conduction between the core and the coil. Additionally, a heat sink is positioned at the bottom of the core to aid in thermal management.

Laminated core three-phase gapped inductor with foil windings, supported by thermal management components.

Modeling Instructions

Setup

  1. From the Model Builder, click the Setup tab.
  2. Locate the General section and set the Domain type as Symmetric(z=0 plane).
    This setting is beneficial for models with a plane of symmetry that divides the core and coil into symmetrical segments. This method ensures that the computed values reflect the complete system despite only modeling a symmetrical section. Subsequently, parameters such as voltage, resistance, losses, inductance, and other related values are appropriately scaled to represent the entire geometry accurately.
  3. In the Simulation Type section, set Electromagnetics to Harmonic.
    Harmonic simulation is suitable for signals with a few harmonics and as in the case of magnetostatic or quasi-magnetostatic simulations (0 Hz). It calculates magnetic field, current amplitudes, and losses using the superposition, summing results from individual harmonics.
    This approach is preferable when the base frequency current significantly exceeds harmonic currents. This ensures that the core material’s nonlinear behavior at the base frequency dominates, providing a streamlined yet precise representation of loss mechanisms across the considered frequency range.
  4. Additionally, set Heat transfer to Steady-state.
  5. Set the Phases to 3.
    In the simulation type settings, electromagnetics is set to harmonics, and heat transfer is set to steady-state. Also 3-phase setting is enabled.

    Domain type and Simulation type settings for 3-phase choke analysis.

Materials

  1. From the Model Builder, select the Materials tab.
  2. From the Global Material section, select Aluminium and click the Copy button.
  3. Copy Polyethylene terephthalate (PET), Fiberglass Reinforced Epoxy (FR4), and 35CS550_China Steel from the Global Materials section to the Local Materials section in a similar manner.
  4. In the Default Materials section, select the material type for each component from the dropdown list as per the table below:
    Component Core Coil Other Bobbin Gaps
    Material type 35CS550_China Steel Aluminium Aluminium Polyethylene terephthalate (PET) Fiberglass Reinforced Epoxy (FR4)
    The "Materials" tab for choke design displays global materials on the left and selected local materials on the right. Users can copy, add, and set default materials for core, coil, and bobbin components.

    Interface for material selection for different components of the model.

Core

  1. From the Model Builder, click on the Core tab.
  2. Click the New Group button. The Group1core will be added.
  3. Click the Open in new tab icon. The Group1core will open.
  4. From the Source list, select Template.
  5. From the Scale list, select mm.
  6. From the Gap Type list, select Physical. This will cut the core geometry and create a gap as a separate body with assigned material properties.
  7. Under the Geometry Builder section, select Three Limb from the Type list.
    The 2, 3, 4, and 5 limb core geometries are linked with the brackets (clamp) template in the Other geometry group, streamlining their construction process by sharing core dimensions.
  8. Set the dimensions (mm) as per the table below:
    x1 x2 y1 y2 z r
    60.0 60.0 60.0 200.0 80.0 0.0
  9. Click the Apply button.
  10. Click the New Gap button.
  11. In the gMin and gMax text fields and Limb dropdown list, enter values as per the table below.
    Gap 1 Gap 2 Gap 3 Gap 4 Gap 5
    gMin -100.0 -54.0 -4.0 46.0 96.0
    gMax -96.0 -46.0 4.0 54.0 100.0
    Limb All Limbs All Limbs All Limbs All Limbs All Limbs
    Gap size (mm) 4.0 8.0 8.0 8.0 4.0
  12. Click the Apply button.
    This image shows the configuration settings for creating the core geometry and gap settings, along with a visualization of the 3D model.

    3D model visualization of core geometry and gap settings.

Coil

  1. From the Model Builder, click on the Coil tab.
  2. Click the New Group tab. Group1coil will be added.
  3. Click the Open in new tab icon. The Group1coil tab will open.
  4. From the Source list, select Template.
  5. From the Scale list, select mm.
  6. From the Wire Type list, select Foil.
  7. Set the Turns per solid to 15. This parameter allows approximation of multiple turns with simple geometry, reducing the geometry’s complexity and facilitating faster results by avoiding excessively small meshing in that area.
  8. Under the Geometry Builder section, select Filled from the Type list and set the Linked core as Group1core. Set the dimensions (mm) as per the table below:
    a b c R h
    83.0 60.0 15.0 10.0 180.0
    Configuration settings for creating the coil geometry, along with a visualization of the 3D model.

    Geometry configuration along with 3D visualization for the 3-phase windings.

    The “linked core” feature enables the software to use core geometry data to construct the coil, streamlining the user’s workflow. By linking the coil to Group1core in this model, the software automatically calculates the distances between the centers of the core limbs, onto which the windings for all three phases are to be placed, thereby eliminating the need for manual input of these distances.

  9. Click the Apply button.
  10. Click the Configure Wire button.
  11. From the Rac computation methods, select the Rac/Rdc coefficient method. This method assumes a constant Rac/Rdc ratio for all frequencies for a given coil. It is applicable in this case as we have just one harmonic. TRAFOLO uses this coefficient to adjust the conductor’s conductivity and calculate AC resistance and losses.
  12. In the Fill Factor text field, enter 0.5. This indicates that 50% of the coil geometry is made of conducting material, while the other 50% is dielectric. The fill factor directly affects the effective conductivity of the material, with higher fill factors resulting in greater effective conductivity.
  13. As foil-type wire is used in this model, enter 1.0 in the Proximity Factor text field.
    The presence of gaps within the core leads to the concentration of eddy current near these gaps. Since the eddy current is perpendicular to the magnetic field, the solver will calculate the current distribution along the y-axis in this particular case.
  14. Click the Apply button.
    Due to few harmonics in waveform, Rac/Rdc method is used for the computing AC resistance

    Rac computational methods and Fill factor Calculator for the winding.

Other

  1. Under the Model Builder, click on the Other tab.
  2. Click the New Group tab. Group1othergeometry will be added.
  3. Click the Open in new tab icon. The Group1othergeometry tab will open.
  4. From the Source list, select Template.
  5. From the Scale list, select mm.
  6. Locate the Geometry Builder section.
  7. From the Type list, select Brackets.
  8. From the Linked Core, select Group1core. This links the core to the bracket, enabling the software to use the core and gap dimensions to create the bracket accordingly.
  9. In the z text field, enter 3.0 to set the thickness of the brackets.

    Brackets configuration by linking to core.

    Geometry configuration along with 3D visualization for the brackets.

Bobbin

  1. From the Model Builder, click on the Bobbin tab.
  2. Click the New Group button. The Group1bobbin will be added.
  3. Click the Open in new tab icon. The Group1bobbin tab will open.
  4. From the Source list, select Template.
  5. From the Scale list, select mm.
  6. Locate the Geometry Builder section.
  7. Enter the details as per the below table.
    Type Linked Coil xg zg dr dh
    Default Group1coil 46.0 73.0 0.0 0.0

    The “linked coil” feature enables the software to automatically generate a bobbin that precisely fits between the core and the coil. By linking the bobbin to the Group1coil winding, the software utilizes the existing dimensions of the core and coil to accurately define the bobbin’s geometry. This feature eliminates the need for users to manually input measurements, such as the bobbin’s length or thickness.
    The xg and zg parameters define the lengths of the bobbin walls that need to be cut away to create spacers. Simply put, these parameters represent the distance between the spacer edges.

  8. Click the Apply button.
    Interface to build spacers in bobbin tab.

    Geometry configuration and 3D visualization of Group1bobbin to build spacers.

Assembly

  1. Click the Assembly tab under the Model Builder.
  2. Click the Assemble Geometry button. The assembled geometry will be displayed.
    Symmetrical section of the assembled geometry with component details.

    Symmetric section of the assembled geometry with component details.

EIMag

  1. From the Model Builder, open the EIMag tab.
  2. Locate the Primary Winding section.
  3. Set the Excitation to Irms [A] and the Coil group connection type to Series from the dropdown list.
  4. Under Coil Group, set the Winding to Primary and Connection to Series.
    Connections and excitation for 3 phase winding in EI Mag tab.

    Connection and excitation for 3-phase winding in EI Mag.

Circuits

  1. From the Model Builder, select the Circuits tab.
  2. The software sets up circuits automatically, connecting FEM components and sources in series. Equal indexes for positive/negative nodes indicate that elements are connected. Nodes that are not connected should have different indexes.
  3. Click the Apply button.
    Electrical circuit indices to build the 3-phase inductor.

    Electrical circuit indices to build the 3-phase inductor.

Waveform

  1. From the Model Builder, select the Waveform tab.
  2. Generally, the base frequency exhibits the largest amplitude and is used to calculate effective permeability distribution in the core. This distribution is then applied to the other harmonics with smaller amplitudes, allowing for an accurate assessment of the core’s magnetic behavior across various frequencies. Specify the Base frequency and the corresponding current excitation. In this case, the Frequency is 500.0 [Hz] with a Primary Irms of 100.0 [A].
  3. In the Harmonics section, enter the values for the harmonics. In this case, we have only one harmonic with the frequency, F [Hz] of 10000.0 and Primary Irms [A] of 5.0.
    Waveform Generator section with input fields for frequency and current settings.

    Waveform Generator for Base and Harmonic Frequency and Current Configuration.

Heat

  1. From the Model Builder, click the Heat tab.
  2. In the Settings section, set the Initial Temperature to 80 deg C. The initial temperature is set as a preliminary guess. After obtaining the first result, the user can adjust the temperature to an appropriate value based on the temperature distribution in the geometry. Alternatively, the user can increase the number of iterations, though this will require solving electromagnetic and thermal problems multiple times.
  3. In the Temperature Iteration text field, enter 1.
  4. Locate the Boundary Conditions section.
  5. Click the Geometry.
  6. In the Type list, select Convection.
  7. In the External temperature (deg C) text field, type 20.
  8. In the Heat transfer coefficient (W/m2/K) text field, type 5.0. Generally, the Heat transfer coefficient for natural cooling is around 5.0 W/m2K. It can also be calculated using the Heat transfer coefficient calculator link or empirical equations.

    Thermal settings showing initial steady state temperature and boundary conditions for the choke.

    Initial steady-state temperature setting and configuring boundary conditions in the Heat tab.

  9. To create a heat sink at the bottom of the core, click on the lower face of the core geometry and update its Heat transfer coefficient to 20.0 W/m²/K.
    Heat sink is set up on the lower face of the core by adjusting the boundary conditions.

    Configuring heat sink parameters for the selected core face.

Mesh

  1. From the Model Builder, click the Mesh tab.
  2. In the Settings section, from the Mesh Refinement list, select Coarse.
  3. Click the Evaluate Mesh button.
  4. Click the mesh corresponding to each geometry group and adjust the mesh refinement by specifying the All Max Element Edge Size (mm) value according to the table below:
    Group1coil Group1core Group1bobbin Group1othergeometry Group1gap
    5.0 15.0 180.0 60.0 60.0
  5. Click the Compute Mesh button.
    Meshed geometry along with depicting how element size can be adjusted.

    Generated mesh for the simulation.

Solve

  1. From the Model Builder, click the Solve tab.
  2. Click on the Simulation Setup button followed by the Run Simulation button.
    Solver settings to run the simulation for the choke.

    Solver settings to run the simulation.

Results and Discussion

  1. From the Model Builder, click on the Results tab.
  2. Click on the Summary tab to obtain the average values of losses and electrical parameters across various frequencies, as well as the overall hotspot temperature.
    TRAFOLO calculates the losses for all parts, including the structural elements like brackets.
    It can be inferred from the Results Summary that the losses in brackets contribute nearly half of the total losses. Winding losses are also exceptionally high in this inductor model.

    The Results Summary tab provides the average values of losses and electrical parameters across various frequencies, as well as the overall hotspot temperature.

    The Results Summary tab provides the average values of losses and electrical parameters across various frequencies, as well as the overall hotspot temperature.

  3. Furthermore, the user can switch between the Results tabs to visualize the processed data at the base frequency, its harmonics, and the superposition of frequencies.
    The magnetic flux density distribution indicates that flux tends to concentrate near the edges, particularly around the gaps, where fringing effects occur. As a result, flux lines extend through the air and the aluminum brackets.

    Cross-sectional view of the magnetic flux distribution on the symmetrically cut surface of the core indicating that flux tends to concentrate near the edges, particularly around the gaps, where fringing effects occur.

    Cross-sectional view of the magnetic flux distribution on the symmetrically cut surface of the core.

    The figure below illustrates significant losses in the brackets around the gaps, comparable to winding losses. These losses are caused by eddy currents induced by the fringing effect. To mitigate these losses, engineers may consider repositioning the brackets outside the coils or replacing the aluminum with a dielectric material. Additionally, perforating the brackets near the gap region could further reduce these losses.

    The figure illustrates significant losses in the brackets around the gaps, comparable to winding losses.

    Distribution of losses in brackets near gaps due to the fringing effect.

    Using Finite Element Method (FEM), the software models the current distribution within each foil and the proximity effect between foils. This enables the precise identification of regions with higher current densities and associated losses. In this inductor, significant losses are observed in the coil around the gaps and at the edges due to the fringing effect and proximity effect, as illustrated in the figure below.

    Significant losses are observed in the coil around the gaps and at the edges due to the fringing effect and proximity effect.

    Significant losses in coil near gaps and at edges due to fringing and proximity effects.

    Core losses are accurately calculated through superposition, given the presence of only a few harmonics and the significantly higher current at the base frequency compared to other frequencies. This leads to the nonlinear behavior of losses at the base frequency dominating the overall loss profile.

    Cross-sectional view of the core loss distribution on the surface of the core computed using superposition.

    Cross-sectional view of the core loss distribution on the surface of the core.

    The surface temperature distribution indicates heating in the core limbs and the brackets, with a hotspot of 88.5°C in their central region. Implementing a heat sink at the bottom of the core effectively cools the transformer, thereby maintaining the temperature well below critical levels.

    The surface temperature distribution indicates heating in the core limbs and the brackets. Implementing a heat sink at the bottom of the core effectively cools the transformer.

    Surface temperature distribution across the symmetrical cross-section of the gapped inductor.

  4. Click the Open in ParaView button to open simulation results in post-processing software. It allows manipulation with results, changing color schemes, making slices, and doing any other manipulations with results.
    ParaView has been used for detailed visualization and analysis of the flux density, temperature, and loss distribution, as shown in the accompanying figures.

    Detailed visualization and analysis of the flux density, temperature, and loss distribution, using ParaView.

    Detailed analysis of losses, temperature, and flux density distribution in ParaView.

    The figure shows that the magnetic flux around the edges concentrates due to the presence of air gaps, resulting in a maximum flux density of approximately 0.230 T, which is well below the saturation point. Additionally, the temperature distribution in the core limbs and brackets is depicted, highlighting significant heating primarily in the central regions of the limbs and brackets and cooling in the lower part due to heat sink.

    The figure shows that the magnetic flux around the edges concentrates due to the presence of air gaps. Additionally, the temperature distribution in the core limbs and brackets is depicted.

    Top surface flux density distribution on the core and temperature mapping on the core and bracket surfaces.

 

Was this page helpful?
Yes No