ac/dc module - kesco current carrying objects inductor, ... • ac/dc module supports magnetic...

AC/DC Module

Electromagnetics in COMSOL Multiphysics is extended by add-on Modules

1) Start Here

2) Add Modules based upon your needs

4) Interface with your CAD data and MATLAB

3) Additional Modules extendthe physics you can address

Types of Electromagnetics Modeling

RF Module

Static Low Frequency Transient High Frequency

0

tE tsinE tE tsinE

Electric and magnetic fields do not vary in time.

Fields vary sinusoidally in time, but there is negligible radiation.

Fields vary arbitrarily in time, radiation may or may not be significant. Objects can be moving.

Fields vary sinusoidallyin time, energy transfer is via radiation.

Wave Optics ModuleAC/DC Module

Static Field Modeling

• DC Electric Currents solves for current flow in conductors• Electrostatics solves for electric fields in perfect insulators• Magnetostatics solves for the magnetic fields around magnets, and the fields

around current carrying objects

Inductor, DC current flow and Magnetostatics

Parallel Plate Capacitor, Electrostatics

Permanent Magnet, Magnetostatics

Mutual Inductance, Magnetic Fields Analysis

Low Frequency Modeling

• AC Electric Currents considers both conduction and displacement currents in conductive and insulating media

• The Magnetic Fields can be solved for in the frequency domain to find the conduction, displacement, and induction currents

• The Magnetic and Electric fields can be solved for, if skin effects in coils require a high accuracy model

Inductive Heating, Magnetic Fields

Inductor, Magnetic and Electric Fields

Transient Modeling

• Transient Electric Currents solves for displacement and conduction currents in insulators and conductors

• Transient Magnetic Fields is suitable for modeling current pulses and nonlinear material response to field strength

• Rotating Machinery considers rotary velocity and acceleration

E-Core Transformer, Transient Magnetic FieldsGenerator, Rotating Machinery

Whenever there are Electromagnetic Losses, there is a Rise in Temperature

Joule Heating Induction Heating

Specialized user interfaces and solvers address the two-way coupled frequency-domain electromagnetic and time-domain thermal problems

Electric Circuits

The Electric Circuits formulation can model a lumped system of circuit elements and couple this to the finite element model

Formulations per Module

COMSOL Multiphysics1 AC/DC Module RF Module

Static Electric CurrentsStatic Joule HeatingElectrostaticsMagnetic Fields2

Electric Currents in SolidsElectric Currents in ShellsJoule HeatingElectrostaticsMagnetic FieldsInduction HeatingMagnetic and Electric FieldsMagnetic Field FormulationRotating MachineryElectric Circuits

Electromagnetic Waves- Frequency Domain- Time Explicit- Transient

Microwave HeatingTransmission Line EquationsElectrical Circuits

1) Core package contains a reduced set of boundary conditions for these formulations 2) 2D and 2D-axisymmetric geometries and static and low frequency formulations only

Wave Optics Module

Electromagnetic Waves- Frequency Domain- Time Explicit- Transient- Beam Envelopes

Laser Heating

Material Models

• All material properties can be:– Constant or nonlinearly dependent upon the fields– Isotropic, Diagonal, or Fully Anisotropic– Defined via Rule-of-Mixtures models– Bi-directionally coupled to any other physics, e.g. Temperature, Strain– Fully User-Definable

• AC/DC Module supports magnetic nonlinearities, B-H curves and electric nonlinearities (superconductors), E-J curves

rr

r

DEDPED

ED

0

0

0

rr

r

BHBMHB

HB

0

00

0

EJ

Data Extraction

• Resistance, Capacitance, Inductance, & Mutual Inductance• Impedance, Admittance, and S-parameters (optional Touchstone file export)• Force calculation due to electric and magnetic fields

Magnetic Forces

2221

1211

ZZZZ

Lumped Parameters

Additional Modules for ElectromagneticsPlasma Module1 MEMS Module2 Particle Tracing Module3

Tunable Cavity Filter

Microwave Plasma

Multipactor

Solves DC Discharge, Capacitively Coupled Plasmas, Inductively Coupled Plasmas, and Microwave Plasmas.

Couples structural mechanics and electrostatics for the modeling of electroactuation, as well as piezoelectric devices.

Computes paths of charged particles through electric and magnetic fields as well as fluid fields.

1) Depending upon the type of plasma being modeled, the AC/DC or the RF Module may also be needed2) Contains the same 3D electrostatic, electric currents in solids, and electric circuits capabilities as the AC/DC Module3) Does not require any other Modules

Additional Modules for Electromagnetics (cont’d)Semiconductor Module1 Wave Optics Module1

MOSFET Mach-Zehnder Modulator

Solves for the electric potential and electron and hole concentrations in semiconductor materials.

1) Does not require any other Modules

Computes electric and magnetic fields for optical systems where the wavelength is comparable to or much smaller than the studied device or system.

The Optimization Module

• Gradient-Free optimization allows for optimization of geometric parameters, and allows for remeshing of the geometry.

- Nelder-Mead, Coordinate Search, and Monte Carlo algorithms.- Optimize one or more geometric dimensions for a CAD model created directly in COMSOL

Multiphysics or via the LiveLink™ products

• Gradient-Based optimization requires more user interaction to set up a differentiable objective function and a moving mesh, but can handle many more design variables, and can solve much faster.

- Adjoint method is used to compute exact sensitivities

Bowtie Antenna Optimization

Resistors

Capacitors

Inductors and Coils

Magnets

Motors and Actuators

Electromagnetic Heating

Example Models, AC/DC Module

Resistor and Capacitor Modeling

• DC Resistive device analysis assumes that all materials are conductors, and solves the equation:

• Electrostatic analysis assumes all materials are insulators, thus:

• AC resistive and AC capacitive devices are both solved in the frequency domain using the same governing equation:

• Transient analysis also uses the same governing equation:

0 V

00 Vr

00 Vj r

00

Vt

V r

Electrostatic, Transient, and Frequency Domain modeling of a Parallel Plate Capacitor

• A parallel plate capacitor is modeled under electrostatic, frequency domain, and transient conditions

• Fringing fields and domain size effects on capacitance are studied

• Frequency domain modeling resolves the losses in dielectric materials

• Transient modeling of the charging behavior agrees with analytic solution

http://www.comsol.com/showroom/gallery/12695/

Advanced boundary conditions

• Electric Currents examples:– Contact Impedance– Distributed Impedance– Electric Shielding– Floating Potential– Periodic Condition– etc.

• Corresponding conditions exist in Electrostatics:– Distributed Capacitance– Thin Low Permittivity Gap– Dielectric Shielding– Floating Potential– Periodic Condition

• Thin high impedance layer between domains• Only interior boundaries• No current tangential to the surface• Handles resistive and capacitive effects

Domain 1

Thin high impedance layerContact impedance d

Domain 2

Contact Impedance

Distributed impedance

• Thin high impedance layer on surface• Only exterior boundaries• No current tangential to the surface• Handles resistive and capacitive effects

Resistor

Thin high impedance layerDistributed impedance

Vref

ds

Electric shielding

• Thin conducting layer• Current path along the surface

Domain 1

Thin conductive layerElectric shielding ds

Domain 2

Floating potential

• Thin metallic sheet – voltage sensing• Unknown isopotential surface• COMSOL solves an extra equation to find this unknown voltage, such that

Inductor and Coil Modeling

BHABJH

1

Static Magnetic Fields are computed by solving:

Where A is the Magnetic Vector Potential, and J is the current density, which can be solved simultaneously, or in a separate analysis

BHAB

JHA

1

2

j

AC Magnetic Fields are computed by solving:

The additional terms represent the induced and the displacement currents

BHAB

JHA

1

t

The displacement currents are not included in the governing equations

Transient Magnetic Fields are computed by solving:

Inductance of a Power Inductor

• At the operating frequency (1kHz) of this power inductor, the skin depth in the coil is comparable to the thickness of the current-carrying wires

• The Magnetic and Electric fields interface is used to capture the skin effect in the wires

• The admittance and inductance is computed


E-core Single Phase Transformer

E‐core

Primary winding

Secondary winding


• Full non-linear time domain analysis at 50 Hz is solved for the induced voltages• Non-linear magnetic material (with saturation effect) is used for the magnetic core• Windings are treated as coil bundles, without modeling each turn of wire

Inductor in Amplifier Circuit

• A nonlinear 2D axisymmetric finite element model is combined with a lumped circuit model

• A 1000 turn coil is wrapped around a core with nonlinear magnetic response, the multi-turn coil domain is used

• A DC bias is applied, and the AC response at this bias is computed• The voltage and current in the device is predicted over time

http://www.comsol.com/showroom/gallery/990/http://www.comsol.com/showroom/gallery/2128/

If there is no current flow in the model, solve:

Where Vm is the Magnetic Scalar Potential

Magnets, Motors & Actuators

mV

HH 0

When modeling rotating objects, solve for the transient magnetic fields and induced currents in the conductive and current carrying domains, but only the magnetic fields only in the surrounding air

mV

HH 0

BHAB

JBvHA

1

t

Magnetic Prospecting of Iron Ore Deposits

• Underground iron ore deposits result in magnetic anomalies• Here, disturbances in the background magnetic field of the Earth, due to the

presence of a ore deposit are computed• The Reduced Field formulation solves for small perturbations to a background field


Assumed ore deposit

Simulating the Moving Parts of a Generator

• The Rotating Machinery, Magnetic interface solves for rotating 2D and 3D domains composed of magnetic materials

• The finite element mesh is allowed to slide at the interface• Nonlinear magnetic materials are included in the model• Induced voltages as a function of rotational speed are computed


Electromagnetic Heating

Displacement Current LossesDipolar molecules rotate in time varying electric field

e-Conduction Current LossesElectrons moving through a conductor lose energy

Induction Current LossesTime varying magnetic fields induce currents in a conductor

J(t)H(t)

All of the above losses can be included in the generalized heat transfer equation

LossesneticElectromagp QTk

tTC

+E(t)

Example: Inductive Heating of a Billet

• Inductive heating is common in the steel industry.

• This model concerns the re-heating of a billet traveling through a coil.

• Frequency Domain (AC) modeling of the magnetic fields is combined with stationary heat transfer.

AC coil

velocity of billet = 0.1m/sBillet

heat loss throughconvection and radiation

Results for 50 Hz

Central cross-section of heat source

Results for 500 Hz Using Symmetry

Central cross-section of heat source

ac/dc module - kesco current carrying objects inductor, ... • ac/dc module supports magnetic...

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