Subject: standard packages for 1076.1
From: Peter Wilson (prw99r@ecs.soton.ac.uk)
Date: Thu Sep 27 2001 - 08:48:52 PDT
Hi,
Question for Discussion : Electrical Systems (Magnetic Domain) Through
variable Flux or Flux Rate ?
This is an issue that occasionally pops up (every 10 years or so) in
modeling
magnetic systems. There is certainly a case to made for using flux rate
on the standpoint of direct transfer between electrical & magnetic
domains and hence the direct duality of "power". So to understand the
difference let's explain the basic terms, then I will outline the issues
for discussion as I see it.
Case 1 : FLUX RATE
Across : MMF & Through : dFLUX/dt
Case 2 : FLUX
Across : MMF & Through : FLUX
Dualities :
Electrical => Magnetic
Current & MMF
Magnetic=>Electrical
Derivative of Flux & Voltage
Instantaneous "Power":
Electrical VI
Magnetic MMF*dFLUX/dt
I have several points to make at this stage.
The first point to note is that on the duality boundary in both cases
there is a direct scaling between current and
MMF. In the duality of magnetic->electrical however in the flux rate
case scaling, but in the flux case the derivative is taken. So the
advantage of using flux rate is that there is no derivative required.
BUT, and this is a BIG BUT for magnetic modeling, using the rate of flux
precludes the use of initial flux conditions. This is crucial for
initializing the state of magnetic components and is therefore a
significant drawback in using rate of flux as the through variable. In
my own case, this is a potential showstopper. Ah, the response will go,
initialize H or MMF instead, but with hysteresis in magnetics, there are
an infinite number of states of flux for a single value of H, and so it
is not trivial or even possible, to use this approach practically in a
general purpose way. Applications that may have problems include
permanent magnets (magnetic recoil & hysteresis + initial conditions),
Magnetized materials - i.e. ran for several cycles and some remanence
remains, PM Machines, Power Transformers....etc.
The second point I would make at this stage is to move to the
fundamental units [1] . As far as I can see, the only (main?) reason to
make this change is for convenience in a specific instance/application.
Does this justify not using the fundamental physical quantities
generally? I would argue not. In the case specifically cited, of power,
it is trivial to create the derivative of flux, so what is the big deal
? Does that really necessitate the change of the fundamental physical
system in general ? I think not. This is epecially the case when counter
examples are given (as done previously).
The third point I would make is that there are differences between the
types of models generally used in the two domains that dissipate power.
Taking a resistor component - the power is simply VI or I^2R. Notice
that above I used the term "power" in inverted commas because in
magnetic cores that exhibit hysteresis there is the real power
dissipated and the apparent power dissipation (analagous to VI and Power
in an electrical system - not the same). The real power dissipated in a
core with hysteresis is in the area of the BH loop. To just use the
product of MMF and dFLUX/dt will only be the actual real power at the
end of a cycle. To properly obtain the real power requires the
distinction in the magnetic domain of real and reactive power.
So summarise therefore, I believe that FLUX should be the through
variable and the FLUX RATE and POWER remain as secondary derived
variables.
To provide some background to help those not familiar with the general
area, I
have listed some useful papers/material as follows
[1] : Fundamentals !
[2]-[5] : Duality and Inter-domain Modeling
[6]-[15] : Magnetic Modeling and Power Loss
References:
[1] J.C.MAXWELL, "A Treatise on Electricity and Magnetism", Clarendon
Press
Oxford, 1873, 3rd Edition.
[2] E. C. CHERRY, "The duality between inter-linked electric and
magnetic
circuits", Proceedings of the
Physics Society, Volume 62, 1949 pp101-111
[3] E. R. LAITHWAITE, "Magnetic Equivalent Circuits for electrical
machines",
PROC. IEE, Vol. 114,
November 1967, 1805-1809
[4] C.J. CARPENTER, "Magnetic Equivalent Circuits", PROC. IEE.,Vol
115,No 10,
October 1968,
1503-1511
[5] AD BROWN, JN ROSS, KG NICHOLS AND MD PENNY, "Simulation of
Magneto-Electronic
Systems using Kirchoffian Networks", European Conference on Magnetic
Sensors
and Actuators, Sheffield,
July 1998
[6] W. ROSHEN, Ferrite Core Loss for Power Magnetic Component Design,
IEEE
Transactions on
Magnetics, Vol. 27, No 6, Nov 1991, pp4407-4415
[7] J.G ZHU, S.Y.R. HUI & V.S. RAMSDEN, A Generalized dynamic circuit
model of
magnetic cores for
low- and high-frequency applications-Part I: Theoretical Calculation of
the
equivalent core loss resistance, IEEE
Transactions on Power Electronics, Vol. 11, No 2, 1996, pp246-250
[8] J.G ZHU, S.Y.R. HUI & V.S. RAMSDEN, A Generalized dynamic circuit
model of
magnetic cores for
low- and high-frequency applications-Part 2: Circuit Model Formulation
and
Implementation, IEEE
Transactions on Power Electronics, Vol. 11, No 2, 1996, pp251-259
[9] S MULDER, Power Ferrite Loss Formulas for transformer design, PCIM
Magazine, July 1995, pp22-31
[10] P. R. WILSON, J. NEIL ROSS & ANDREW D. BROWN, "Dynamic
Electric-Magnetic-Thermal
Simulation of Magnetic Components", IEEE Conference on Computers in
Power
Electronics (COMPEL
2000), July 2000
[11] C.P. STEINMETZ, "On the Law of Hysteresis", American Institute of
Electrical Engineers Transactions,
Vol. 9, 1892, pp3-64
[12] P. TENANT, J.J. ROUSSEAU, L. ZEGADI, "Hysteresis modeling taking
into
account the temperature",
European Power Electronics Conference proceedings, 1995, Volume 1,
pp1.001-1.006.
[13] MAXIM A., ANDREU D., BOUCHER J., "A Novel Behavioural method of
SPICE
Macromodeling of
Magnetic Components Including the Temperature and Frequency
Dependencies",
Conference Proceedings -
IEEE Applied Power Electronics Conference and Exposition - APEC, Vol. 1,
1998,
pp 393-399
[14] ODENDAAL W.G., FERREIRA J.A., "A thermal model for high frequency
magnetic components", IEEE
IAS Meeting, New Orleans, La., October 1997, pp1115-1122
[15] MAXIM A., ANDREU D., BOUCHER J., "A New Behavioural Macromodeling
method
of Magnetic
Components Including the Self-Heating Process", PESC '99, pp735-740
Peter
-- -- Peter R. Wilson -- -- mailto: prw99r@ecs.soton.ac.uk -- Homepage: http://www.ecs.soton.ac.uk/~prw99r -- Tel/Fax : +44 (0)23 8059 6665/2901 -- -- Room 53/3053, Dept of Electronics & Computer Science, -- University of Southampton, Highfield, Southampton, -- SO17 1BJ,United Kingdom --
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