IEC TR 62383:2006

TECHNICAL IEC
REPORT TR 62383
First edition
2006-01
Determination of magnetic loss
under magnetic polarization waveforms
including higher harmonic components –
Measurement, modelling and calculation
methods
Reference number
IEC/TR 62383:2006(E)
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TECHNICAL IEC
REPORT TR 62383
First edition
2006-01
Determination of magnetic loss
under magnetic polarization waveforms
including higher harmonic components –
Measurement, modelling and calculation
methods
© IEC 2006 ⎯ Copyright - all rights reserved
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– 2 – TR 62383 © IEC:2006(E)
CONTENTS
FOREWORD.4
INTRODUCTION.6
1 Scope.7
2 Normative references .7
3 Principles of measurement .7
3.1 General .7
3.2 Yokes, windings and test specimen .8
3.3 Power amplifier .8
3.4 Waveform synthesizer .8
3.5 Digitiser.8
3.6 Control of secondary voltage .9
3.7 Peak reading apparatus .9
3.8 Air flux compensation .9
4 Measuring system .10
5 Measurements.10
5.1 Generation of the magnetic polarization waveform including higher
harmonics .10
5.2 Determination of peak value of magnetic polarization .11
5.3 Determination of the magnetic polarization .11
5.4 Determination of magnetic field strength.12
5.5 Determination of the magnetic loss.12
5.6 Plotting the a.c. hysteresis loop including the higher harmonics .12
6 Example of measurement .12
6.1 Magnetic loss measurement of non-oriented electrical steel sheets .12
6.2 Magnetic loss measurement under stator tooth waveform conditions .13
7 Prediction of magnetic loss including higher harmonic polarization .17
7.1 General .17
7.2 Energy loss separation [14] .17
7.3 Neural network method [17].23
7.4 Modified superposition formula [20] .25
8 Summary.30
Bibliography.31
Figure 1 – Block diagram of the measuring system for the measurement of magnetic
loss of electrical steel sheets under magnetic polarization waveforms which include
higher harmonic components .10
Figure 2a – Magnetic polarization J(t) .13
Figure 2b – Magnetic field strength H(t) .14
Figure 2c – AC hysteresis loops.14
Figure 2 – Dependency on the higher harmonic polarization components of the
magnetic polarization J(t) ; magnetic field strength H(t), and a.c. hysteresis loops of
non-oriented electrical steel at a fundamental magnetizing frequency f = 60 Hz and a
ˆ
maximum magnetic polarization J = 1,5 T, and for higher harmonic frequency of
f =23f .14
h 1
TR 62383 © IEC:2006(E) – 3 –
Figure 3 – Specific total loss depending on the higher harmonic frequency and higher
ˆ
harmonic polarization for the non-oriented electrical steel sheet at J = 1,5 T.15
Figure 4 – B-coil winding positions of stator tooth of a 3,75 kW induction motor to
measure the a.c. hysteresis of the stator tooth depending on the load .16
Figure 5 – AC hysteresis loop of the stator teeth of a 3,75 kW induction motor
measured in single sheet tester .16
Figure 6 – Specific total loss of the stator tooth depending on the load .17
Figure 7 – Examples of experimental dependence of the quantity
W =W −W =W +W on the square root of frequency in grain-oriented Fe-Si
dif cl h exc
laminations (thickness 0,29 mm).19
Figure 8 – Energy loss per cycle W and its analysis in a non-oriented Fe-(3wt %)Si
lamination energy loss with arbitrary flux waveform and minor loops.20
Figure 9 – Examples of composite experimental (solid lines) and reconstructed
ˆ
(dashed lines) d.c. hysteresis loops at peak magnetization J = 1,4 T in non-oriented
Fe-(3 wt %) Si laminations (thickness 0,34 mm) generated by the J(t) waveforms.22
Figure 10 – Experimental dependence of the statistical parameter of the
magnetization process V on the peak magnetization value in the tested non-oriented
o
Fe-Si laminations.22
Figure 11 – Loss evolution with the number of minor loops in a non-oriented Fe-Si
dJ(t)
ˆ
()
lamination, subjected to controlled constant magnetization rate = 4f ⋅ J + 2J ,
m
dt
ˆ
with J = 1,4 T and 2nJ = 1,2 T .23
m
Figure 12 – Artificial neuron (also termed as unit or nodes) .23
Figure 13 – Neural network design topology .24
dJ(t)
Figure 14 – Waveforms of , H(t) and J(t) when higher harmonic polarization
dt
is included .26
Figure 15 – Generation of two symmetrical a.c. minor loop measured in zero
polarization region, and in saturation polarization region, of the fundamental hysteresis
loop; magnetization in the rolling direction and perpendicular to the rolling direction.27
Figure 16 – Specific total loss P of the combined waves, with harmonic frequency
c
23f , depending on the position of a.c. minor loop at maximum magnetic polarization of
1,0 T and of 1,5 T respectively.27
Figure 17 – Specific total loss depending on the higher harmonic frequency.29
ˆ
Figure 18 – Constant k vs. peak value of magnetic polarization J .29
Table 1 – Network design .24
Table 2 – Error of the specific total loss recalled from the trained neural network
compared with the measured values at 1,6 T (point not used during the training).25
Table 3 – Error of the specific total loss recalled from the trained neural network
compared with the measured values at 1,5 T (point used during the training).25

– 4 – TR 62383 © IEC:2006(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
DETERMINATION OF MAGNETIC LOSS
UNDER MAGNETIC POLARIZATION WAVEFORMS
INCLUDING HIGHER HARMONIC COMPONENTS –
MEASUREMENT, MODELLING AND CALCULATION METHODS
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC/TR 62383, which is a technical report, has been prepared by IEC technical committee 68:
Magnetic alloys and steels.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
68/309/DTR 68/315/RVC
Full information on the voting for the approval of this technical report can be found in the
report on voting indicated in the above table.

TR 62383 © IEC:2006(E) – 5 –
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in
the data related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.

– 6 – TR 62383 © IEC:2006(E)
INTRODUCTION
The specific total loss has to be measured for the design of electrical machines and
classification of electrical steel sheets. During the last 20 years, electrical engineers have
)
determined the magnetic induction waveforms of electrical machines [1] to [4] , and
calculated the magnetic power loss under non-sinusoidal waveform of magnetic
polarization [5] to [13]. They designed electrical machines using numeric calculation (FEM,
BEM) and high speed computers, including non-linear and hysteresis properties of magnetic
materials.
Under standard measurement conditions, the specific total loss of electrical steel is to be
measured only under the condition of sinusoidal waveform of the magnetic polarization.
However, the actual magnetic polarization waveforms of the electric machine are almost
always not sinusoidal because of the material behaviour (anisotropy, non-linear B-H
performance in high polarization regions such as the stator tooth of electrical machines),
because of PWM modulated voltage for variable speed motors and because of the layout of
the magnetic circuit and the winding scheme (tooth harmonics).
Specific total loss values obtained by the standard method are not really applicable to an
actual electrical machine design because the specific total loss of ferromagnetic material
cannot be predicted easily due to non-linear and hysteresis effects, but these higher harmonic
polarizations bring about a large increase in magnetic loss.
—————————
)
The figures in square brackets refer to the Bibliography.

TR 62383 © IEC:2006(E) – 7 –
DETERMINATION OF MAGNETIC LOSS
UNDER MAGNETIC POLARIZATION WAVEFORMS
INCLUDING HIGHER HARMONIC COMPONENTS –
MEASUREMENT, MODELLING AND CALCULATION METHODS
1 Scope
Nowadays, by computer aided testing (CAT), a.c. magnetic properties of electrical steel
sheets can be measured under various measuring conditions automatically. For example, the
magnetic loss in the presence of higher harmonic frequency components of magnetic
polarization can be measured using the arbitrary waveform synthesizer, digitiser and
computer.
The present standard methods (IEC 60404-2, IEC 60404-3 and IEC 60404-10) for the
determination of specific total loss are restricted to the sinusoidal waveform of magnetic
polarization, and these standards are still important for the characterization of core materials.
However, actual waveforms of magnetic polarization in the electrical machines and
transformers always include higher harmonic polarizations, and nowadays electrical machines
can be designed using numerical methods including higher harmonics. But for these
conditions, there is still no standard testing method.
This technical report reviews methods for measurement of the magnetic loss of soft magnetic
materials under the condition of magnetic polarization which includes higher harmonic
components.
2 Normative references
The following referenced documents are indispensable for the application of this document.
For dated references, only the edition cited applies. For undated references, the latest edition
of the referenced document (including any amendments) applies.
IEC 60404-2, Magnetic materials í Part 2: Methods of measurement of the magnetic
properties of electrical steel sheet and strip by means of an Epstein frame
IEC 60404-3:1992, Magnetic materials í Part 3: Methods of measurement of the magnetic
properties of magnetic sheet and strip by means of a single sheet tester
IEC 60404-6, Magnetic materials í Part 6: Methods of measurement of the magnetic
properties of magnetically soft metallic and powder materials at frequencies in the range
20 Hz to 200 kHz by the use of ring specimens
IEC 60404-10, Magnetic materials í Part 8: Specifications for individual materials – Section 10:
Specification for magnetic materials (iron and steel) for use in relays
3 Principles of measurement
3.1 General
The described method of measurement with the inclusion of higher harmonics is, in principle,
also applicable using the Epstein frame or a ring core as a magnetic circuit. With the Epstein
frame, one should be aware of the particular path length characteristics which are also not
exactly known in the higher frequency range.

– 8 – TR 62383 © IEC:2006(E)
The proposed test apparatus is based on the magnetic circuit of a double U-yoke SST. It can
be considered to consist of the following parts.
3.2 Yokes, windings and test specimen
Each yoke is formed in the shape of a U and is made up of an insulated sheet of electrical
steel or nickel iron alloy. The construction methods of yokes could follow the instructions of
Annex A of IEC 60404-3. The dimensions of the yokes and specimen are not restricted, but if
the yoke size becomes smaller, the effective magnetic path length l should be equal to the
eff
inside width corresponding to the procedure given in IEC 60404-3. It is preferable that the
initial permeability of the yoke should be reasonably constant with frequency up to the
maximum higher harmonic frequency to be measured. Regarding the windings and the test
specimen, it should again be referred to IEC 60404-3 and, in the case of ring specimens, to
IEC 60404-6.
Capacitance and dielectric effects become an issue for higher frequency components. The
dielectric loss should be minimised by careful management of the winding space and
dielectric constants of the formers and wire insulation.
The temperature of the test specimen should be measured at all times. For higher frequency
measurements, the temperature rise becomes a major factor and steps should be taken to
minimize this.
3.3 Power amplifier
The power amplifier shall have low output impedance, and the frequency bandwidth of the
power amplifier should be higher than the highest harmonic frequency to be measured. The
output voltage of the power amplifier should be high enough to magnetize the specimen over
the full higher harmonic frequency range. For details, reference should be made to
IEC 60404-2, IEC 60404-3 and IEC 60404-6.
3.4 Waveform synthesizer
An arbitrary waveform can be synthesized by computer programming. The frequency of the
generated wave should be synchronized with the digitiser frequency, and the frequency
uncertainty of the waveform synthesizer shall be better than 0,01 %. The waveform
synthesizer output should allow arbitrary waveforms generated by synthesized digital wave
data. The relative uncertainty of the frequency should be less than 0,01 %.
3.5 Digitiser
For the digitisation of the secondary induced voltage U (t) and the voltage U (t) across the
2 s
non-inductive precision resistor R which is connected in series with the primary winding to
s
determine the magnetizing current, a 2-channel digitiser is necessary. The 2 channels must
be sampled simultaneously and then digitised. Following this, the data are recorded in a
memory.
If the length of the period divided by the time interval between the measuring points, i.e. the
sampling frequency ratio f divided by the magnetizing frequency f , is an integer (Nyquist
s m
condition), the power integral can be, without mathematical error, be replaced by the
th
corresponding sum.GThe sum correctly represents the power integral up to the n harmonic
where 2n is the number of samples per fundamental period. Keeping the Nyquist condition is
possible only where the sampling frequency f and the magnetizing frequency f are
s m
synchronized to a common fundamental clock and thus have a fixed integer ratio.

TR 62383 © IEC:2006(E) – 9 –
In that case, the hysteresis loop must be scanned using a sampling frequency f higher than
s
twice the bandwidth of the B- and H-signals,
f = 2nf (1)
s m
where n is the highest harmonic to be measured.
However, the commercial hardware components are not usually synchronized in this way and
the ratio f /f is then not an integer. In that case, the sampling frequency must be
s m
considerably higher (for instance 1 024 samples per period) in order to keep the deviation of
the true period length from the closest multiple of intervals of sampled measurements small.
Keeping the Nyquist condition becomes a deciding advantage in the case of higher
frequencies. The use of a low-pass antialiasing filter must be considered in order to avoid
contributions from low-frequency apparent harmonics which do not exist in the measurement
signal. The antialiasing filter must limit the system bandwidth to s
Regarding the amplitude resolution, with a lower than 12-bit resolution, the digitalization error
can be considerable, particularly for non-oriented material with high silicon content. Thus, at
least a 12-bit amplitude resolution is recommended. Moreover, the two voltage channels
should transfer the signals without a significant phase shift. The phase shift should be so
small that the total uncertainty is not significantly affected.
When magnetic loss is measured under conditions of magnetic polarization which include
higher harmonic components and the higher harmonic amplitude becomes high enough to
produce minor loops, the digital sampling condition for the higher harmonics should also
satisfy the above described sampling conditions.
3.6 Control of secondary voltage
The waveform of the secondary voltage should be controlled to have the required
components. This control can be achieved by feedback techniques using digital or analog
means.
The deviation should be below 1 % for each harmonic component.
3.7 Peak reading apparatus
For the measurement of the peak value of the magnetic polarization, a Miller type analog
integrator and a peak reader should be used with a frequency bandwidth higher than the
highest harmonic frequency f to be measured.
h
The peak reader should be able to repeat peak readings at an appropriate time rate.
The uncertainty of the peak reading apparatus should be better than 0,2 %.
NOTE An average type voltmeter may not be used for measurement of the peak value of the magnetic
polarization because the secondary induced voltage may have more than two zero crossing per period.
3.8 Air flux compensation
Air flux should be compensated. This can be achieved by a mutual inductor. The primary
winding of the mutual inductor is connected in series with the primary winding of the test
apparatus, while the secondary winding of the mutual inductor is connected to the secondary
winding of the test apparatus in series opposition.

– 10 – TR 62383 © IEC:2006(E)
The adjustment of the value of the mutual inductance shall be made so that, when passing an
alternating current through the primary windings in the absence of the specimen in the
apparatus, the voltage measured between the non-common terminals of the secondary
windings shall be no more than 0,1 % of the voltage appearing across the secondary winding
of the test apparatus alone.
4 Measuring system
The measuring system can be constructed using the components which are described in
Clause 2 . The block diagram of the circuit is shown in Figure 1.
Components
N magnetizing winding
N secondary winding
M mutual inductor
R non-inductive precision resistor
s
Figure 1 – Block diagram of the measuring system for the measurement
of magnetic loss of electrical steel sheets under magnetic polarization waveforms
which include higher harmonic components
5 Measurements
5.1 Generation of the magnetic polarization waveform including higher harmonics
The time dependent magnetic polarization including higher harmonics can be described by
N
J(t) = J sin[(2j +1)ω t + φ ]
(2)
¦ (2j +1) 1 (2j +1)
j =0
where
j is a non-negative integer;
N corresponds to the highest harmonic frequency f ;
h
ω is the fundamental angular frequency( ω = 2ʌf );
1 1 1
th
J is the amplitude of the (2j+1) harmonic at the angular frequency ω = (2j + 1)ω ;
(2j+1) h 1
φ is the phase angle.
(2j+1)
TR 62383 © IEC:2006(E) – 11 –
The synthesized reference voltage U(t) is as follows;
N
U(t) = N A (2j + 1)ω J cos[(2j + 1)ω t + φ ] (3)
2¦ 1 (2j+1) 1 (2j+1)
j=0
where
N is the number of turns of secondary winding;
A is the cross sectional area of specimen.
The procedure of setting the desired magnetic polarization follows the following steps.
First the relative amplitudes of fundamental and higher harmonics waves are set, the resulting
peak value of the magnetic polarization is measured and then the gain of the synthesizer is
set so that the required amplitude of magnetic polarization is achieved.
5.2 Determination of peak value of magnetic polarization
ˆ
The peak value of magnetic polarization J should be measured using a Miller type analogue
integrator and a peak reader. The relation between the peak value of magnetic polarization
ˆ
and the output voltage U of the peak reader is:
J
N A
ˆ 2 ˆ
U = J
(4)
J
RC
where RC is the time constant of the Miller integrator.
5.3 Determination of the magnetic polarization
The instantaneous value of the magnetic polarization J(i) at the time t = i/nf of the specimen
can be calculated from the secondary induced voltage U (t) using the following numeric
equation:
i
J(i) = − [U (k) +U (k + 1)]/ 2 −J (5)
2 2 0
¦
N A nf
2 s
k =1
where
i is an integer;
n is the number of sampling points per period;
f is the magnetizing frequency;
J   is the integration constant such that
n
J(i) = 0  (6)
¦
i =1
The peak value of the magnetic polarization J(t) is identical to the maximum value of J(i) .

– 12 – TR 62383 © IEC:2006(E)
5.4 Determination of magnetic field strength
The instantaneous value of the magnetic field strength H(i) at the time t = i/nf can be
calculated from the digitised value of the voltage U (i) across the non-inductive precision
s
resistor R :
s
N
H(i) = U (i)  (7)
s
l R
eff s
where
l is the effective magnetic path length;
eff
N is the number of turns of primary winding.
5.5 Determination of the magnetic loss
The magnetic loss P could be calculated using the data from the 2-channel digitiser, the
c
secondary induced voltage U (t) and the voltage U (t) across the non-inductive precision
2 s
resistor R which is connected in series with the primary winding:
s
n
N
P = − U (i) ⋅U (i) (8)
c ¦ 2 s
nρ N Al R
m 2 eff s
i=1
where
P is the specific total loss, in watt per kilogram;
c
i  is an integer;
n is the number of sampling points per period;
N is the number of turns of primary winding;
N is the number of turns of secondary winding;
A is the cross sectional area of specimen;
ρ is density of the test specimen in kilogram per cubic meter.
m
5.6 Plotting the a.c. hysteresis loop including the higher harmonics
The a.c. hysteresis loop can be plotted using the magnetic polarization from equation (5) and
the magnetic field strength from equation (7).
6 Example of measurement
6.1 Magnetic loss measurement of non-oriented electrical steel sheets
Figure 2 shows the results measured on a specimen of non-oriented electrical steel at the
ˆ
fundamental frequency of 60 Hz and maximum magnetic polarization of J of 1,5 T under
different harmonic amplitude conditions, Figure 2a shows the magnetic polarization curves,
Figure 2b the magnetic field strength curves, and Figure 2c the a.c. hysteresis loops. The
ˆ
higher harmonic frequency is f = 23f and the higher harmonic amplitudesJ amount to
h 1 23
ˆ
2 %, 5 % and 10 % of J .
TR 62383 © IEC:2006(E) – 13 –
Figure 3 shows the total loss depending on the higher harmonic frequency f and higher
h
ˆ ˆ
harmonic polarization J for the non-oriented electrical steel sheet at J = 1,5 T. For the case
h
of a 0,5 mm thickness specimen, the total loss depending on the higher harmonic frequency f
h
ˆ
and higher harmonic polarization J was much higher than that of the material with a
h
thickness of 0,35 mm due to the eddy current effect.
6.2 Magnetic loss measurement under stator tooth waveform conditions
For the determination of the a.c. hysteresis loop of the stator-tooth of an induction motor, the
magnetic polarization of the tooth can be measured using search coil windings, but the
magnetic field strength measurement is not so easy inside the actual motor. One measuring
method for the a.c. hysteresis loop of the stator-tooth could be to obtain the amplified induced
voltage from the B-coil and to connect it directly to the input of the measuring system which is
described in Clause 4, and then to measure the a.c. magnetic properties of a specimen
consisting of the same material as that of the stator-tooth. In doing so, the gain of the
amplifier is adjusted to satisfy equation (9) so that the magnetic polarization of the sample in
the yoke meets the same magnetic polarization condition as the stator tooth to be achieved.
AN
s s
U =( )U  (9)
s m
A N
m m
where A , N and U are the cross sectional areas of the sample, number of B-coil windings,
s s s
and the voltage applied to the single sheet tester, respectively. A , N and U are the cross
m m m
sectional area of the stator tooth, number of B-coil windings, and the voltage induced from the
B-coil of the induction motor, respectively.
For the measurement of the a.c. hysteresis loop of the stator-tooth of an induction motor, we
prepared a 10 cm × 10 cm double U-yoke SST and a 3-phase 3,75 kW induction motor which
has 4 poles, 36 stator teeth, and 44 rotor teeth. Two B-coils, one in the rolling direction and
the other one perpendicular to the rolling direction of the stator core were each wound with
10 turns on only one sheet as shown in Figure 4. In this case, we can not measure magnetic
polarization J but magnetic induction B. When magnetic field strength is not so high, air flux is
small compared to the magnetic flux density of the core, we can measure magnetic
polarization J using the voltage induced from the B-coil as an approximation. An a.c.
dynamometer may be used to load the induction motor.
1.5
Fundamental frequency f = 60 Hz
Higher harmonic frequency f = 23f
h 1
1.0
0.5
0.0
Higher harmonic
-0.5 polarization
component(%)
0%
-1.0
2%
5%
-1.5
10%
-500 0 500 1000 1500 2000 2500 3000 3500
Sampling Number
Figure 2a – Magnetic polarization J(t)
Magnetic Polarization (T)
– 14 – TR 62383 © IEC:2006(E)
Fundamental frequency f = 60 Hz
800 Higher harmonic frequency f = 23f
h 1
-200
Higher harmonic
-400
polarization
component(%)
-600
0%
2%
-800 5%
10%
-1000
-500 0 500 1000 1500 2000 2500 3000 3500
Sampling Number
Figure 2b – Magnetic field strength H(t)
Fundam ental frequency f = 60 Hz
Higher harm onic frequency f = 23f
1.5 h 1
1.0
0.5
0.0
Higher harm onic
polarization
-0.5
component(%)
0%
-1.0
2%
5%
10%
-1.5
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
Magnetic Field Strength (A/m )
Figure 2c – AC hysteresis loops
ˆ
The higher harmonic amplitude was 0 %, 2 %, 5 %, and 10 % of J respectively.
Figure 2 – Dependency on the higher harmonic polarization components of the
magnetic polarization J(t) ; magnetic field strength H(t), and a.c. hysteresis loops of
non-oriented electrical steel at a fundamental magnetizing frequency f = 60 Hz and a
ˆ
maximum magnetic polarization J = 1,5 T, and for higher harmonic frequency of f =23f
h 1
Magnetic Polarization (T)
Magnetic Field Strength (A/m)
)
higher harmonic frequency ( f =nf , f =60 Hz
h 1 1
Higher harmonic frequency ( f =nf , f = 60 Hz )
h 1 1
TR 62383 © IEC:2006(E) – 15 –
Thickness : 0.35 mm
^
Pol. J = 1.5 T
0.10
0.08
0.06
0.04
0.02
(a) For a specimen 0,35 mm thick
Thickness : 0.5 mm
^
Pol. J =1.5 T
0.10
0.08
25 0.06
0.04
0.02
(b) For a specimen 0,5 mm thick
Figure 3 – Specific total loss depending on the higher harmonic frequency and higher
ˆ
harmonic polarization for the non-oriented electrical steel sheet at J = 1,5 T
Higher harm. pol. (J /J )
h 1
Higher harm. pol. (J /J )
h 1
Total loss (W/kg)
Total loss (W/kg)
– 16 – TR 62383 © IEC:2006(E)
Figure 4 – B-coil winding positions of stator tooth of a 3,75 kW induction motor to
measure the a.c. hysteresis of the stator tooth depending on the load
Figure 5 shows the a.c. hysteresis loops for the case of a rotor having no skew, and the B-coil
being wound coaxially with the rolling direction of non-oriented electrical steel. Figure 5a
shows the a.c. hysteresis loop under sinusoidal magnetic polarization. Figure 5b shows the
a.c. hysteresis loop of the stator-tooth under no load, both under the same maximum
ˆ
magnetic polarizationJ however the difference in the specific total loss between the cases of
,
Figure 5a and Figure 5b was more than 10 %. Figure 5c and Figure 5d show a.c. hysteresis
loops of the stator-tooth under 40 % and 80 % of the full load. The specific total loss values
were increased by more than 30 % and 50 %, respectively. Figure 6 shows the specific total
loss depending on the load of the induction motor. The specific total loss also turned out to
depend on the direction of magnetization due to the macroscopic magnetic anisotropy of the
non-oriented electrical steel.






a) sinusoidal polarization waveform (standard method)     b) no load
c) 1,5 kW load                   d) 3 kW load
Figure 5 – AC hysteresis loop of the stator teeth of a 3,75 kW induction motor measured
in single sheet tester
TR 62383 © IEC:2006(E) – 17 –
Motor power (kW)
ٻ
Ŷ : parallel to the rolling direction of non-oriented electrical steel when rotor has no skew
Ɣ : perpendicular to the rolling direction of non-oriented electrical steel when rotor has no skew
Figure 6 – Specific total loss of the stator tooth depending on the load
7 Prediction of magnetic loss including higher harmonic polarization
7.1 General
Magnetization process of magnetic materials always shows non-linear and hysteresis
behaviour which is very difficult to describe physically. Until now, a hysteresis loop can not be
described as a mathematically analytical function. A reasonable model to predict magnetic
loss during the magnetization process should be used. Some typical methods which describe
the prediction of total loss will be introduced in this report.
7.2 Energy loss separation [14]
7.2.1 General
The physically based separation of specific total loss P(f)at a given frequency f is expressed
as the sum of the hysteresis lossP , classical eddy current loss P (f), and excess loss
h cl
P (f) components
exc
P(f) =P(f) +P (f) +P (f) (10)
h cl exc
where P(f) =W f , with W the hysteresis energy loss per cycle. Except in a few special
h h h
cases [15], W is always considered as a frequency independent quantity. Equation (10) can
h
then equivalently be written in terms of the energy loss per cycle W =P/ f
W( f ) =W +W ( f ) +W ( f ) (11)
h cl exc
There are no limitations, in principle, as to the kind of polarization waveform. The fundamental
aim is the prediction of W , W (f) , and W (f) .
h cl exc
Total loss at stator tooth (W/kg)

– 18 – TR 62383 © IEC:2006(E)
7.2.2 Energy losses with arbitrary flux waveform and no minor loops
The instantaneous classical eddy current loss per unit volume P (t)can be defined for a
cl
magnetic lamination of conductivity σ and thickness d as
σd dJ(t)
P (t) = ( ) (12)
cl
12 dt
This relationship is only valid when the flux penetrates the material completely.
The classical energy loss per cycle T = 1/f is then obtained as
T T
σd dJ(t)
W (f ) = P (t)dt = ( ) dt (13)
cl cl
³ ³
0 0
12 dt
and it can be calculated exactly for all waveforms of J(t) .
In the absence of minor loops, the hysteresis loss is independent of the polarization
waveform. The instantaneous excess loss P (t) is given in its most general form, by
exc
equation (14):
§ ·
n V 4σGSV
dJ(t) dJ(t)
o o ¨ o ¸
P (t) = ⋅ 1+ − 1 ⋅ (14)
exc
¨ 2 2 ¸
2 dt dt
n V
o o
© ¹
where
n is the number of simultaneously active magnetic objects in the limit fÆ 0;
o
V is a parameter defining the statistics of the magnetic objects;
o
S is the cross-sectional area of the lamination.
The magnetic object (MO) is defined as an ensemble of neighbouring walls interacting so
strongly that they can be treated as a single object. The dynamic behaviour of a single MO is
characterized by a damping coefficient G, which is to a good approximation independent of
the internal details of the MO. G is a dimensionless parameter and its theoretically calculated
value is G = 0,135 6. It is stressed that V , which lumps the effect on the excess loss of the
o
ˆ
material structure, is a function of J . In a large number of cases, the value of n is
o
sufficiently small to ensure that, in all practical respects,
4σGSV
dJ(t)
o
>> 1 (15)
2 2
dt
n V
o o
and the excess energy loss becomes
T T
dJ(t)
3 / 2
W (f ) = P (t)dt = σGSV ⋅ dt (16)
exc exc o
³ ³
0 0
dt
which is easily specialized to the desired J(t) waveform.
By combination of equation (11), equation (13) and equation (16), energy loss per cycle
becomes as follows:
TR 62383 © IEC:2006(E) – 19 –
T T
σd dJ(t) dJ(t)
2 3 / 2
W(f ) =W +W (f ) +W (f ) =W + ( ) dt + σGSV ⋅ dt (17)
h cl exc h o
³ ³
0 0
12 dt dt
In order to predict the total loss for a given J(t), the following quantities are required:
conductivity σ, cross-sectional area S and the pre-emptive determination of W and V only.
o
h
Let us consider the typical experiment in a grain-oriented Fe-Si lamination reported in
Figure 7, where the behaviour of the quantity
W (f) =W(f) −W (f) =W +W (f) (18)
dif cl h exc
measured under sinusoidal flux, from its best straight fitting line, as provided by equation (18),
1/ 2
as a function of f . It can be seen that W and V are obtained from the intercept value
h o
and the slope of the theoretical line, respectively.
Figure 8 shows the frequency behaviour of the magnetic energy loss experimentally found in
non-oriented Fe-(3 wt %)Si lamination under sinusoidal polarization at peak magnetization
ˆ
J = 1,4 T. The fitting lines have been predicted according to the method outlined in the
previous clause, focused on the loss separation equation (18), the direct calculation of W
cl
1/ 2
and the representation W =W −W =W +W as a function of f . By this
dif cl h exc
representation the previously contemplated case is met, where W exhibits a deviation from
dif
1/ 2
the f dependence at low frequencies. Then the best fit of W can be made in Figure 8
dif
and provide for the parameters W and V .
h1 o
GO Fe-(3wt%)Si
J = 1.6 T
p
a)
W
h
0 5 10 15
1/2 1/2
f (Hz )
Figure 7 – Examples of experimental dependence of the quantity W =W −W =W +W
dif cl h exc
on the square root of frequency in grain-oriented Fe-Si laminations (thickness 0,29 mm)
W +W (mJ/kg)
h exc
– 20 – TR 62383 © IEC:2006(E)
NO Fe-(3wt%)Si
J = 1.4 T
p
Sinusoidal J (t)
W
exc
W
h
W
h1
b)
0 5 10 15 20
1/2 1/2
f (Hz )
1/ 2
The experimental quantity W =W −W =W +W is plotted as a function of f . This
dif cl h exc
results in the dash-dot straight fitting line, by which the two parameters W and V are
h1 o
determined.
Figure 8 – Energy loss per cycle W and its analysis in a non-oriented Fe-(3wt %)Si
lamination energy loss with arbitrary flux waveform and minor loops
For the total loss at a given frequency f in the presence
...