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# Re: [femm] hysteresis losses in enclosures

- To: femm@egroups.com
- Subject: Re: [femm] hysteresis losses in enclosures
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Fri, 27 Oct 2000 10:14:11 -0400
- Organization: Foster-Miller, Inc.
- References: <8t6759+ojni@eGroups.com>

    erik_t_viking@my-deja.com wrote:

    > Hello All,
    >
    > First of all, I'm new to this newsgroup and also to FEA and FEMM in
    > particular. Having studied in Germany, I'll do my best to translate
    > what little I know of electromagnetics into English.
    >
    > I'm trying to model hysteresis and eddy current losses we are
    > experiencing in certain parts of enclosures of high-voltage
    > switchgear our company is developing.
    >
    > The enclosures are oval, with half-circles (46 cm diameter) on each
    > end, connected by parallel straight walls of 90 cm length. Thickness
    > is 1 cm. Height varies between 80 and 150 cm for various design
    > options. In this are, equally spaced with 45 cm, the three round
    > aluminium conductors (diameter 10 cm) for phases R,S and T. Current
    > is 4000 Amps (rms) at 50 Hz.
    > The enclosure is filled with insulating gas (mu rel. = 1), the
    > outside is plain air.
    >
    > Trying to reduce cost, the enclosures are made of low-grade steel
    > known as Fe37, which has similar properties as the Steel M-36 from
    > the Materials Library of FEMM. (mu rel. approx. 1600, sigma = 9.5
    > MS/m)
    > Experimental measurements of heat production result in 300-600 W/m2
    > on the high-stressed left and right sides.
    > However, results from FEMM show a maximum |B| of 0.15 T, reducing
    > rapidly towards the outside. According to the hysteris curves I have,
    > this should result in far less than 100 W/m2 hysteresis losses. Eddy
    > current losses are then also neglegible.
    >
    > I'm using the following (planar) geometry:
    > _______
    > / \
    > | O O O |
    > \_______/ \_Fe37, 1 cm thickness
    >
    > R S T
    >
    > R: I=5657 + j0 Amps
    > S: I=-2828 - j4898 Amps
    > T: I=-2828 + j4898 Amps
    >
    > And now my questions, related to FEMM:
    >
    > 1. Why is the electrical conductivity of ALL steels in FEMM set to 0?
    > I'm using 9.5 MS/m as a normal value, about 1/3 of the 34.4 MS/m of
    > Al.

    I didn't have information on the conductivities of all of the materials when
    I made up this library. The point of most of those materials is to get a
    B-H curve for magnetostatic analyses. I've recently obtained some
    manufacturer's data sheets on a lot of these materials, so I'll try to
    update the library as soon as I can. The value that you used may be
    reasonable for "cheap" iron. The conductivity of steel varies from about 2
    MS/m for good silicon steel laminations to about 10 MS/m for rolled steel
    that's not particularly intended for EM applications, with different types
    of steel falling everywhere within this range.

    > 2. Can I model various phase-shifted currents by setting the real and
    > imaginary parts of the current density? I'm using 0.72 MA/m2
    > (resulting in a total peak value of 4000xsrt(2) Amps for the given
    > conductors).

    Yes, that exactly right. However, some sort of subtle things happen when
    you do this. The current density that you assign via the material
    properties dialog is really just a _source_ current density--that is, the
    current that would be there at 0 Hz. At frequency, eddy currents are
    induced that knock down the total current carried in your conductor. To
    actually fix the total current in a conductor in a harmonic problem, you
    need to get ahold of the femm30 beta version (available at
    http://www.egroups.com/files/femm/). You can then specify total currents
    carried by sections of the model via the new "Circuit" properties. This is
    what I've done in the attached examples.

    > 3. What boundary conditions to specify for this kind of problems?

    Well, the skin depth of your problem is really small. Skin depth =
    Sqrt[1/(sigma*mu*Pi*freq)] where sigma is the conductivity in MS/m, mu is
    the absolute permeability, and freq is the frequency in Hz. The result is in
    meters. For the properties you described, the skin depth is about 0.58 mm.
    This means that the field doesn't get through to the outside part of the
    iron, and it is sufficient to specify A=0 on the outside of the iron. This
    is what I've done in the attached "viking1.fem" example. Note that in this
    problem, I have defined a very thin region about 1 mm width the inner
    surface of the iron that is finely meshed in order to capture the skin
    effects in the iron in "enough" detail. The result is a mesh with a _lot_
    of nodes that takes a long time to solve.

    An alternative is to specify a "small skin depth" impedance boundary
    condition on the _inside_ of the iron, making that the edge of your domain.
    This greatly decreases the size of the problem, since you don't have to
    worry about explicitly modeling the skin depth region in the enclosure--this
    is taken care of by the boundary condition. The attached "viking2.fem"
    takes this approach. There are two down sides to this approach--it is more
    difficult to back out the losses in the enclosure. This requires a surface
    integral of |A|^2 that the postprocessor doesn't currently perform, but
    which you can do by exporting the profile of A along the surface. After you
    do this integral, you need to multiply the result by (1/4) * (2*Pi*freq)^2
    * sigma * (skin depth) to get total losses. Also, femm currently doesn't
    allow you to define a hysteresis lag in the boundary material. I'll add
    this in eventually, because it is really a small modification.

    > 4. Along the inner surface of the enclosure, I've specified a mesh of
    > 0.02 cm. Is this fine enough given the skin dept of slightly less
    > than 1 mm? More nodes seems to crash this machine :-(

    Yes, this ought to be good enough. See answer to (2)

    > 5. Does anyone know a steel with a relative permeability of around
    > 1600 with 'worse' hysteresis properties as the M-36 steel?
    >
    > 6. If |H| and |B| are known, then how do I estimate the resulting
    > heat losess for this situation. I only have detailed curves for
    > laminated transformer steels for |B| > 1 T, which of course are
    > softer ferrites.

    You can obtain losses directly from the program with block integrals.
    Switch to the block integral mode by cliking on the green square on the
    femmview toolbar. Then, select the region of interest by clicking somewhere
    inside it with the left mouse button. The area selected with light up in
    green. When you've selected all the areas of interest, click the integral
    sign on the toolbar. Then, choose the "total losses" integral. It will add
    up all of the predicted hysteresis and eddy current losses.

    Note--to get hysteresis losses, you have to specify some nonzero number for
    the phi_h parmameter in the material property dialog. This parameter
    defines a frequency-independent phase lag between B and H in a material,
    which is a relatively crude but easy to handle model of hysteresis effects.
    To get really good results, you ought to do some tests on a toroid made out
    of the material of interests to identify a parameter that makes the losses
    matched the observed. Failing that, Stoll's "Analysis of Eddy Currents"
    says that the hysteresis lag is "usually less than 20 degrees", so for a
    cheap steel not specifically intended for magnetic applications, 20 degrees
    is probably a reasonable value to assume.

    > I would appreciate the comments or experiences of anybody who has
    > ever used FEMM for AC current magnetic fields.
    >
    > Thanks in advance,
    >
    > Erik Evertz
    > VA TECH ELIN HOLEC HIGH VOLTAGE BV
    > R&D Dep.
    > Amersfoort,The Netherlands

    Anyhow, the losses in the attached example of the example problems loss
    numbers in the end sections average out to like 760 W/m^2 for the surface
    impedance model w/out hysteresis, and more like 960 W/m^2 for the
    brute-force one that also includes hysteresis losses. These losses are
    highly dependent on the material parameters that you use. The brute-force
    model also shows that the skin region in the enclosure is highly
    saturated--however, the harmonic analyses are all linear, so you have to
    take the results with a bit of a grain of salt....

    Dave.

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