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# RE: [femm] SRM Inductance plot at constant current

- To: <femm@yahoogroups.com>
- Subject: RE: [femm] SRM Inductance plot at constant current
- From: <por@iet.auc.dk>
- Date: Wed, 7 May 2003 20:40:48 +0200 (CEST)
- Importance: Normal
- In-reply-to: <002101c31499$661ec430$66eb5e18@bradsgateway>
- References: <3EB7C495.8090700@ieee.org> <002101c31499$661ec430$66eb5e18@bradsgateway>

    Hi Brad and other interested users

    For some time ago I made a software package ?SRDaS? dedicated to design a
    simulation of SR-systems. Information about the software can be found at

    http://www.iet.auc.dk/~por/SRDaS/SRDaS.html

    If you send me a personal e-mail (por@iet.auc.dk) I will give you a link
    were you can download the software free.

    You can use external FEM results (from for instance FEMM) in the package
    to time stepping simulations. But be very care-full to use 2D-FEM results
    directly!. It is very common that SRM?s has large end effects in the
    unaligned position, which for classical sized machines are in a range of
    10-25 %.

    The program is dealing static model parameters, which gives reasonable
    results at typical operational speeds for electrical motors. I also have
    good experience with the program and a practical single phase SRM
    operating above 50.000 rpm.

    I think you may deal with a very strange application (or some funny
    limitations) since you are using a four phase machine were the iron-losses
    may become a very serious problem.

    Regards
    Peter Omand Rasmussen

    > I corrected my current value and I am getting the results I expected.
    > The analysis I ran assumes constant current throughout the stroke angle.
    > I am using this analysis as a first iteration design check to get an
    > idea for the magnitude of current I need to produce a certain amount of
    > torque. Here comes the hard part (I think).
    >
    > I am attempting to simulate the best I can, a high speed case. The rotor
    > will be commutated at 75,000 rpm. I do realize the torque profile will
    > take on a different shape at this speed. The current needs a finite time
    > to build in the coil. I was wondering what is the best way to perform a
    > pseudo time stepping integration.
    >
    > The inductance is a function of rotor position and coil current. This
    > becomes an interesting differential equation to solve in my opinion. I
    > was thinking of stepping the rotor in small finite angles in FEEM. Each
    > time adjusting the current in the blocks to better simulate the "real
    > world" case. Would it be sufficient to just re compute the current value
    > at each rotor position with simple current rise time formulas, inserting
    > the appropriate incremental inductance value each time? The conduction
    > angle happens very fast when the rotor is spinning at 75,000. We are
    > talking micro seconds in this case.
    >
    > I realize I may be trying to do something that may not be done easily in
    > FEMM.
    >
    > Many thanks,
    >
    > Brad
    > -----Original Message-----
    > From: David Meeker [mailto:dmeeker@ieee.org]
    > Sent: Tuesday, May 06, 2003 9:20 AM
    > To: femm@yahoogroups.com
    > Subject: Re: [femm] SRM Inductance plot at constant current
    >
    > Brad Frustaglio wrote:
    >
    >> Hi All,
    >>
    >>
    >>
    >> I have been using FEMM for a few years now. Many thanks to Dave,
    >> excellent program.
    >>
    >>
    >>
    >> I have question on evaluating the A-J integral and then calculating
    >> the self inductance from the result.
    >>
    >>
    >>
    >> I am modeling a 4 phase SRM with 8 stator poles and 6 rotor poles. I
    >> am attempting to extract the torque profile and inductance profile
    >> with one phase excited at constant current as the rotor moves through
    >> one stroke. The torque magnitude and shape looks reasonable. However I
    >
    >> am having trouble understanding how to calculate the inductance
    >> correctly. The profile shape looks as expected I am just concerned on
    >> the magnitude of inductance. My method is:
    >>
    >>
    >>
    >> 1. Highlight the blocks with the current flowing ( In my case there
    >> are 2 current blocks per pole (one on each side of the stator
    >> pole) for a total of 4 current blocks per phase.
    >> 2. Evaluate the A-J integral at each respective rotor position 3.
    >> The self inductance as defined is int(A-J)dV /i^2) where i is
    >> the coil current
    >>
    >>
    >>
    >> I think I am running into trouble on the coil current term. What is
    >> the correct coil current to use to evaluate the inductance correctly?
    >>
    >>
    >>
    >> The value of one current block or the sum of all current blocks. Also
    >> this is actually amp-turns. Not the actual current flowing in the wire
    >
    >> itself. Right?
    >>
    >>
    >>
    >> For instance: the current in one block in the model is defined as
    >> 11.15 MA/m^2. The coil area is 2.6903 x 10^-5 m^2. So the magnitude of
    >
    >> current in the coil block is 300 A-T. Is this the current I use for
    >> the evaluation of self inductance using the A-J integral?
    >>
    >>
    >>
    >> Regards,
    >>
    >>
    >>
    >> Brad Frustaglio
    >>
    > The /i/ in the equation actually /is /the actual current flowing in the
    > wire itself. Like in your example, say that your coil is made of 60
    > turns of wire. Since you have 300 Amp*Turns, the current in the wire
    > would be 5 Amps. The 5 Amps is then the value that you'd use as /i/ in
    > the equation. There's also an example that might be relevant to you at
    > http://femm.berlios.de/induct1/induct1.htm
    >
    > One last thought--switched reluctance motors are typically run in a
    > highly saturated condition. The quantity that you are computing with
    > the A.J integral is (flux linkage/current), but it doesn't have the same
    >
    > relationship to stored energy as inductance in a linear problem.
    > Furthermore, this "nonlinear inductance" appears in a subtly different
    > way in any electric circuit equations that you might write. For
    > example,
    > the electric circuit equation that applies to your case is:
    > D(flux linkage)/Dt + R i = v
    > where the Dt is meant to represent the /total/ derivative with respect
    > to time. If inductance, L, is not a function of current, this
    > simplifies to the usual:
    > L di/dt + R i = v
    > However, if L is a function of i, we'd get:
    > (L(i) + i*dL/di)*di/dt + R i = v
    >
    > Dave.
    > --
    > David Meeker
    > email: dmeeker@ieee.org
    > www: http://femm.berlios.de/dmeeker
    >
    >
    >
    >
    >
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- References:
  - Re: [femm] SRM Inductance plot at constant current
    - From: David Meeker <dmeeker@ieee.org>
  - RE: [femm] SRM Inductance plot at constant current
    - From: "Brad Frustaglio" <fuzz@wildrail.net>

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