1318 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 2, MARCH 2004
A Dynamic Core Loss Model for Soft Ferromagnetic
and Power Ferrite Materials in Transient
Finite Element Analysis
D. Lin, P. Zhou, W. N. Fu, Z. Badics, and Z. J. Cendes
Abstract—A dynamic core loss model is proposed to estimate
core loss in both soft ferromagnetic and power ferrite materials
with arbitrary flux waveforms. The required parameters are the
standard core loss coefficients that are either directly provided by
manufacturers or extracted from the loss curve associated with si-
nusoidal excitation. The model is applied to calculating core loss
in both two-dimensional and three-dimensional transient finite el-
ement analysis, and the results are compared with measured data.
Index Terms—Core loss, finite element analysis, hysteresis,
minor loop, power ferrite, soft ferromagnetic, transient.
I. INTRODUCTION
I
T IS STILL challenging to predict core loss under transient
conditions in the design of magnetic power devices such
as inductors, transformers, and electric machines. While ap-
proaches exist for loss computation in power devices in the fre-
quency domain, an appropriate method for core loss computa-
tion in the time domain remains unclear.
In the frequency domain, loss separation is widely used with
problems involving magnetic laminations. Loss separation
breaks the total core loss into static hysteresis loss
, classical
eddy current loss
, and excess loss [1]
(1)
Given the coefficients
, and the parameter , the total
core loss per unit volume
in the frequency domain can be
calculated in terms of peak magnetic flux density
and fre-
quency
. When this approach is applied to the time domain,
the computation of the eddy current loss and the excess loss is
straightforward. However, the computation of hysteresis loss is
still difficult.
With ferrite materials, a well-known empirical approach pro-
posed by Steinmetz a century ago is normally used
(2)
where
, and are empirical parameters obtained from
experimental measurement under sinusoidal excitation [2]. In
Manuscript received July 1, 2003.
The authors are with Ansoft Corporation, Pittsburgh, PA 15219 USA (e-mail:
dlin@ansoft.com).
Digital Object Identifier 10.1109/TMAG.2004.825025
order to estimate the power loss with nonsinusoidal excitation,
a modified Steinmetz equation (MSE) was developed [3]
(3)
where
is the equivalent frequency of the nonsinusoidal in-
duction waveform, and
is the repeated frequency. With the in-
troduction of an equivalent frequency, MSE provides a good fit
to experimental measurements under triangular magnetization
[3]. However, MSE is only suitable in the frequency domain.
Many time-domain hysteresis models have been proposed for
instantaneous loss calculation. These are mainly based on the
Jiles–Atherton model [4], [5] or the Preisach model [6]. Al-
though these models describe hysteresis phenomena quite well,
their practical use is limited by the high number of empirical pa-
rameters and/or the prohibitive experimental effort required [3].
In this paper, an alternative time domain dynamic hysteresis
model is developed for soft magnetic and power ferrite materials
based on the idea of an equivalent elliptical loop. This model is
able to consider the effects of minor loops and predicts instan-
taneous hysteresis loss with good accuracy. In addition, the re-
quired parameters in the model are the same as those required in
the frequency domain approaches (1) and (2). These parameters
are either directly available from manufacturers or can be easily
extracted from standard loss curves under sinusoidal excitation.
II. F
ORMULATIONS
A typical value of hysteresis loss parameter
in (1) is 2. In
this case, the magnetic field
in a static hysteresis loop can
be decomposed into two components: a reversible component
and an irreversible component . As a result, hysteresis
loss can be computed by
(4)
The reversible component can be directly obtained from the
normal
curve without considering a hysteresis loop. In
fact,
is related to the reactive power in the material and
is associated with the hysteresis loss. Consequently, the in-
stantaneous hysteresis loss is
(5)
0018-9464/04$20.00 © 2004 IEEE