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# Re: [femm] Calculating skin effect using FEMM?

- To: femm@egroups.com
- Subject: Re: [femm] Calculating skin effect using FEMM?
- From: dcm3c@aol.com
- Date: Sat, 6 Jan 2001 21:47:17 EST

    In an attachment to message dated 1/5/01 7:37:10 AM EST,
    dgorenc@koncar-institut.hr writes:

    > I am using "Finite Element Method Magnetics" programs for
    > calculation of eddy current losses in enclosure of three-phase
    > segregated and nonsegregated busbars. Thanks to you, until now
    > I have successfully calculated losses in enclosure for several
    > configuration of busbars.

    > In FEMM Users Manual you said that for bulk coils ( in my case
    > they carry currents Jsrc) conductivity of zero should be defined.
    > In that case I could calculate only a eddy current losses in
    > enclosure, and losses in conductors are zero.

    What I mean by "bulk coils" are coils with many turns that are
    approximated as one block of constant current density. It
    isn't appropriate for the current to redistribute itself in an
    eddy current problem in a wound coil the way that it would in
    a solid bus bar, so you have to assign the conductivity to be
    zero so that the current distribution in the block is
    unchanged by eddy currents.

    > Since the equation that FEMM actually solves for planar (2D)
    > problems is:
    >
    > \nabla^2 A - j \omega \mu \sigma A = - \mu Jsrc (1)
    >
    > and this is the same as:
    >
    > \nabla^2 A - j \omega \mu \sigma A = - \mu \sigma U (2)
    >
    > where ((U=Jsrc, and U is the voltage applied to a conductor in
    > which skin effect is to be calculated. (Equation (2) was taken
    > from "Teoretska elektrotehnika" by Z. Haznadar)
    > If I define a nonzero conductivity for conductors (bulk coils)
    > and define such voltage which will give the real value of
    > current through the conductors, I could actually calculate
    > resistive losses or skin effect factor in conductors as
    > kskin=Pac/Pdc, where Pac are resistive losses for alternating
    > current, and Pdc losses for direct current.
    >

    > To get the real current through the conductors (real amplitude
    > and phase, for example: for three phase current i1=I cos(t),
    > i2=Icos((t+120(), i3=Icos((t-120() or as phasor i1=I+j0,
    > i2=-0.5I+j0.866I, i3=-0.5I-j0.866I, where I is amplitude of
    > sinusoidal time varying current) I must do several iterations.
    > When I achieve real values of currents through the conductors
    > then I can calculate losses in conductors and losses in
    > enclosure. I made several calculations with and without taking
    > in consideration skin effect in conductors. In both cases the
    > eddy current losses in enclosure was the same. I also made
    > several calculations of skin effect in conductors (without
    > enclosure). For two parallel Al conductors 100x10 mm on
    > distance 30 mm through which alternating (in first
    > calculation) and direct (in second calculation) current of
    > 200A flows, I obtained kskin=1.22. For the same conductors in
    > some books I found kskin=1.19 and in others kskin=1.23. The
    > difference probably happened because electrical conductivity
    > of Al used in my calculation was little different than those
    > used in other Literature.
    >
    > Is it possible to calculate losses in conductors for
    > alternating current in this way using FEMM?

    Your development is correct. In the 2.1a version of the
    program, this was the only way to approach eddy current
    problems in which a fixed current is desired in a conductive
    region. I kept running into eddy current problems where
    I needed to place constraints on the total current flowing
    in a set of conductive regions in an eddy current problem, so
    I fixed in this in the 3.0 Beta version. Unfortunately, I
    haven't gotten around to documenting it in the manual yet.

    Anyhow, the "Circuit" property in the 3.0 version is just
    what you need. The name "circuit" is sort of a misnomer;
    this property really just allows one to apply constraints on
    the total current carried by a block or group of blocks. What
    the circuit properties actually do is apply an additional
    voltage to each block defined with a particular circuit
    property. Additional equations are then solved during the
    solution process so that the voltages are chosen to satisfy the
    current constraints--doing automatically what you have been
    doing manually. The circuit properties are located in the
    "Properties" part of the main menu. They are defined in a way
    that is conceptually similar to point, boundary, and material
    properties.

    For your problem, you would want to make four separate
    "circuits": One for each of your three phases, and a fourth
    "circuit" for the aluminum enclosure. For the A, B, and C
    phases, you'd enter the total current as you have described
    above:

    Phase A = I+j0;
    Phase B = -0.5I+j0.866I
    Phase C = -0.5I-j0.866I

    The purpose of the circuit for the enclosure is to ensure that
    eddy currents induced in the enclosure are conserved within the
    enclosure. You'd just assign the total current for the
    enclosure to be:

    Aluminum Enclosure = 0 + j0

    Then, these circuit properties have to be applied to the
    appropriate areas of the solution. The circuit properties are
    applied to block labels in just the same way that material
    properties are applied to a block label. (i.e. select desired
    label with right mouse click; hit <space> to "open" the
    label's properties; choose desired circuit from the "In
    Circuit" drop list)

    I have attached an example of your geometry that does just
    this, assuming that the current carried by each phase is 1000
    Amps RMS. I also assumed that the left-most pair of bars
    carries the Phase A current, the center pair the Phase B
    current, and the right-most the Phase C current.

    The multiple bars per phase illustrates an interesting feature
    of the "circuit" properties--if you label multiple blocks with
    the same circuit, it assumes that all blocks are driven in
    series, and that the _total_ current in _all_ blocks that are
    defined with a particular circuit property adds up to meet the
    constraint. If you examine the two bars composing each phase,
    you will find that each bar carries a slightly different
    current, but the total current adds up to be the desired phase
    current.

    Another interesting postprocessing feature is that you can
    examine what voltage was required to enforce the current
    constraint. Just pick View | Circuit Props off of the main
    menu in femmview. A dialog will then pop up, displaying the
    current, voltage, and impedance for each circuit.

    > In all of my calculations I used Dirichlet boundary condition.

    That's fine, as long as the A=0 boundary is drawn "far enough"
    away from the region of interest so as not to disturb things.
    A lot of the time, I will use the "Asymptotic Boundary
    Condition" described in the "Open Boundary Problems" section
    of the appendix in the femm manual. This generally lets you
    get away with drawing the boundary fairly close to the parts
    that you are interested in without much loss of accuracy. I
    have used this technique for the outer boundary in the
    attached example.

    Dave Meeker
    --
    http://members.aol.com/dcm3c

    --part1_15.e1c78bc.278932b5_alt_boundary
    Content-Type: text/html; charset="US-ASCII"
    Content-Transfer-Encoding: 7bit

    <HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In an attachment to message dated 1/5/01 7:37:10 AM EST, <BR>dgorenc@koncar-institut.hr writes:
    <BR>
    <BR>&gt; I am using "Finite Element Method Magnetics" programs for
    <BR>&gt; calculation of eddy current losses in enclosure of three-phase
    <BR>&gt; segregated and nonsegregated busbars. Thanks to you, until now
    <BR>&gt; I have successfully calculated losses in enclosure for several
    <BR>&gt; configuration of busbars.
    <BR>
    <BR>&gt; In FEMM Users Manual you said that for bulk coils ( in my case
    <BR>&gt; they carry currents Jsrc) conductivity of zero should be defined.
    <BR>&gt; In that case I could calculate only a eddy current losses in
    <BR>&gt; enclosure, and losses in conductors are zero.
    <BR>
    <BR>What I mean by "bulk coils" are coils with many turns that are
    <BR>approximated as one block of constant current density. &nbsp;It
    <BR>isn't appropriate for the current to redistribute itself in an
    <BR>eddy current problem in a wound coil the way that it would in
    <BR>a solid bus bar, so you have to assign the conductivity to be
    <BR>zero so that the current distribution in the block is
    <BR>unchanged by eddy currents.
    <BR>
    <BR>&gt; Since the equation that FEMM actually solves for planar (2D)
    <BR>&gt; problems is:
    <BR>&gt;
    <BR>&gt; \nabla^2 A - j \omega \mu \sigma A = - \mu Jsrc &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)
    <BR>&gt;
    <BR>&gt; and this is the same as:
    <BR>&gt;
    <BR>&gt; \nabla^2 A - j \omega \mu \sigma A = - \mu \sigma U &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)
    <BR>&gt;
    <BR>&gt; where ((U=Jsrc, and U is the voltage applied to a conductor in
    <BR>&gt; which skin effect is to be calculated. (Equation (2) was taken
    <BR>&gt; from "Teoretska elektrotehnika" by Z. Haznadar)
    <BR>&gt; If I define a nonzero conductivity for conductors (bulk coils)
    <BR>&gt; and define such voltage which will give the real value of
    <BR>&gt; current through the conductors, I could actually calculate
    <BR>&gt; resistive losses or skin effect factor in conductors as
    <BR>&gt; kskin=Pac/Pdc, where Pac are resistive losses for alternating
    <BR>&gt; current, and Pdc losses for direct current.
    <BR>&gt;
    <BR>
    <BR>&gt; To get the real current through the conductors (real amplitude
    <BR>&gt; and phase, for example: for three phase current i1=I cos(t),
    <BR>&gt; i2=Icos((t+120(), i3=Icos((t-120() or as phasor i1=I+j0,
    <BR>&gt; i2=-0.5I+j0.866I, i3=-0.5I-j0.866I, where I is amplitude of
    <BR>&gt; sinusoidal time varying current) I must do several iterations.
    <BR>&gt; When I achieve real values of currents through the conductors
    <BR>&gt; then I can calculate losses in conductors and losses in
    <BR>&gt; enclosure. I made several calculations with and without taking
    <BR>&gt; in consideration skin effect in conductors. In both cases the
    <BR>&gt; eddy current losses in enclosure was the same. &nbsp;I also made
    <BR>&gt; several calculations of skin effect in conductors (without
    <BR>&gt; enclosure). For two parallel Al conductors 100x10 mm on
    <BR>&gt; distance 30 mm through which alternating (in first
    <BR>&gt; calculation) and direct (in second calculation) current of
    <BR>&gt; 200A flows, I obtained kskin=1.22. For the same conductors in
    <BR>&gt; some books I found kskin=1.19 and in others kskin=1.23. &nbsp;The
    <BR>&gt; difference probably happened because electrical conductivity
    <BR>&gt; of Al used in my calculation was little different than those
    <BR>&gt; used in other Literature.
    <BR>&gt;
    <BR>&gt; Is it possible to calculate losses in conductors for
    <BR>&gt; alternating current in this way using FEMM?
    <BR>
    <BR>Your development is correct. &nbsp;In the 2.1a version of the
    <BR>program, this was the only way to approach eddy current
    <BR>problems in which a fixed current is desired in a conductive
    <BR>region. I kept running into eddy current problems where
    <BR>I needed to place constraints on the total current flowing
    <BR>in a set of conductive regions in an eddy current problem, so
    <BR>I fixed in this in the 3.0 Beta version. &nbsp;Unfortunately, I
    <BR>haven't gotten around to documenting it in the manual yet.
    <BR>
    <BR>Anyhow, the "Circuit" property in the 3.0 version is just
    <BR>what you need. &nbsp;The name "circuit" is sort of a misnomer;
    <BR>this property really just allows one to apply constraints on
    <BR>the total current carried by a block or group of blocks. &nbsp;What
    <BR>the circuit properties actually do is apply an additional
    <BR>voltage to each block defined with a particular circuit
    <BR>property. &nbsp;Additional equations are then solved during the
    <BR>solution process so that the voltages are chosen to satisfy the
    <BR>current constraints--doing automatically what you have been
    <BR>doing manually. &nbsp;The circuit properties are located in the
    <BR>"Properties" part of the main menu. &nbsp;They are defined in a way
    <BR>that is conceptually similar to point, boundary, and material
    <BR>properties.
    <BR>
    <BR>For your problem, you would want to make four separate
    <BR>"circuits": One for each of your three phases, and a fourth
    <BR>"circuit" for the aluminum enclosure. &nbsp;For the A, B, and C
    <BR>phases, you'd enter the total current as you have described
    <BR>above:
    <BR>
    <BR>Phase A = I+j0;
    <BR>Phase B = -0.5I+j0.866I
    <BR>Phase C = -0.5I-j0.866I
    <BR>
    <BR>The purpose of the circuit for the enclosure is to ensure that
    <BR>eddy currents induced in the enclosure are conserved within the
    <BR>enclosure. &nbsp;You'd just assign the total current for the
    <BR>enclosure to be:
    <BR>
    <BR>Aluminum Enclosure = 0 + j0
    <BR>
    <BR>Then, these circuit properties have to be applied to the
    <BR>appropriate areas of the solution. &nbsp;The circuit properties are
    <BR>applied to block labels in just the same way that material
    <BR>properties are applied to a block label. &nbsp;(i.e. select desired
    <BR>label with right mouse click; hit &lt;space&gt; to "open" the
    <BR>label's properties; choose desired circuit from the "In
    <BR>Circuit" drop list)
    <BR>
    <BR>I have attached an example of your geometry that does just
    <BR>this, assuming that the current carried by each phase is 1000
    <BR>Amps RMS. &nbsp;I also assumed that the left-most pair of bars
    <BR>carries the Phase A current, the center pair the Phase B
    <BR>current, and the right-most the Phase C current. &nbsp;
    <BR>
    <BR>The multiple bars per phase illustrates an interesting feature
    <BR>of the "circuit" properties--if you label multiple blocks with
    <BR>the same circuit, it assumes that all blocks are driven in
    <BR>series, and that the _total_ current in _all_ blocks that are
    <BR>defined with a particular circuit property adds up to meet the
    <BR>constraint. &nbsp;If you examine the two bars composing each phase,
    <BR>you will find that each bar carries a slightly different
    <BR>current, but the total current adds up to be the desired phase
    <BR>current.
    <BR>
    <BR>Another interesting postprocessing feature is that you can
    <BR>examine what voltage was required to enforce the current
    <BR>constraint. &nbsp;Just pick View | Circuit Props off of the main
    <BR>menu in femmview. &nbsp;A dialog will then pop up, displaying the
    <BR>current, voltage, and impedance for each circuit.
    <BR>
    <BR>&gt; In all of my calculations I used Dirichlet boundary condition.
    <BR>
    <BR>That's fine, as long as the A=0 boundary is drawn "far enough"
    <BR>away from the region of interest so as not to disturb things.
    <BR>A lot of the time, I will use the "Asymptotic Boundary
    <BR>Condition" described in the "Open Boundary Problems" section
    <BR>of the appendix in the femm manual. &nbsp;This generally lets you
    <BR>get away with drawing the boundary fairly close to the parts
    <BR>that you are interested in without much loss of accuracy. &nbsp;I
    <BR>have used this technique for the outer boundary in the
    <BR>attached example.
    <BR>
    <BR>Dave Meeker
    <BR>--
    <BR>http://members.aol.com/dcm3c
    <BR></FONT></HTML>

    --part1_15.e1c78bc.278932b5_alt_boundary--

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