Transformer and Inductor

Modeling

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Magnus Olsson

COMSOL

• Overview of COMSOL Multiphysics

• Inductor modeling

• Transformer modeling

• Q&A

Agenda

The Multiphysics Approach

Multiphysics in Transformers and Inductors

Inductive coupling

Magnetic saturation

Skin effect

Resistive and Inductive heating

Fluid flow and

convective cooling

Magnetostriction

Capacitive coupling

Noise and vibration

Thermal expansion

External loads and circuits

Devices and Industries

• Transformers

• Inductors

• Litz wire

• Motors/Actuators

• Generators

• Sensors

• Loudspeakers

• Transducers

• ... many more

• Aerospace

• Audio

• Automotive

• Electrical Power

• generation

• Distribution

• Electronics

• Steel and Metal

• ... many more

Types of Devices Industries

Poll Question 1

Essentials for Inductor Modeling

• Inputs

– Device geometry

– Material properties

– Material orientation

– Coupling with other physics?

– Appropriate set of boundary conditions

– Determine analysis type

• Outputs

– Frequency Domain

• Inductive coupling

• Inductive loss / skin effect

– Stationary response

• Static saturation

– Time Domain

• Dynamic saturation

Time to solution increases

2D or 3D?

• High numeric

precision

• Easy drawing

• Quick results

• Resolve skin effect

• Resolve details -

many individual

turns

• Full geometry

• Use 3D CAD

• ”3D effects”

• 3D Visualization

• Homogenized

coils / materials

• Demanding

• Difficult to resolve

• Complementary

2D 3D

Modeling features

• Domain level features

• Boundary level features

Example: Inductive Heating

• 3 turn primary coil

– water cooled

• Secondary

– solid copper cylinder

• Embedded in FR4

Model parameters

Model set up

Results

Coil resistance

Modeling option:

Convective boundary heat flux

Poll Question 2

Coil features and skin effect

r0

2

(Iron) mm 34.01012.1

4000

(Aluminum) mm 1210774.3

1

(Copper) mm 9105.998

1

7

7

7

r

r

r

• Multiturn Coil Domain (no skin effect)

• Sigle Turn Coil Domain (solid)

• Coil Group Domain (solid, many turns)

Boundary layer meshing helps resolving the skin depth

by progressive growth from boundaries

Use triangular and/or mapped meshing elsewhere.

Meshing tips

Transformer with skin effect

Frequency Sweep

Results for 1Hz

Results for 50Hz

Circuits

Simple example

Add circuit elements

with settings

Single Phase E-core Transformer

E-core transformer

E-core

Primary winding

Secondary winding

• Full non-linear time domain analysis at a constant

frequency of 50 Hz is modeled.

• Non-linear magnetic material (with saturation effect) is

used for magnetic core.

• The primary and secondary windings are modeled as

homogenized current carrying domains. Individual wires

are not resolved.

• Skin effect in windings and core is not included.

Model Features

• The model assumes that the primary and secondary windings are made

of thin wire and multiple number of turns.

• If the wire diameter is less than the skin depth and there are “many”

turns, then the coil can be assumed to be a homogeneous current

carrying domain.

Assumption – Coil with thin wire

Coil with thin

wires and

many turns

≈

Equivalent

homogenous

current-carrying

domain

Results (Case 1)

• Number of turns in the coils Np = Ns

• Only induction but no step up/down of voltages

Results (Case 1)

• Ip and Is are different by roughly 4 orders of magnitude

which is also the difference between Rp and Rs

• Is/Ip ≠ Rs/Rp because Is depends only on Vis but Ip

depends on both Vip and Vp

Magnetic flux density distribution (slice plots)

Magnetic flux density distribution

Arrow plot showing

magnetic flux

concentration through

transformer core

Case 2 – Step down transformer

• Global Definitions > Parameters - Rp = Rs (to visualize step down

simulation)

- Np/Ns = 1000

• Model 1 > Definitions > Variables 2 - Vp (peak) = 25000 volt

Results (Case 2)

Vip/Vis = Np/Ns = 1000

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Relevant functionality

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