Measurement and Modeling of Iron
Losses in Electrical Machines
Andreas Krings, Shafigh Nategh, Alexander Stening, Henrik Grop, Oskar Wallmark,
Juliette Soulard
Laboratory of Electrical Energy Conversion (E2C), Royal Institute of Technology (KTH)
Teknikringen 33
SE-100 44 Stockholm, Sweden
Email: {andreas.krings, shafigh.nategh, alexander.stening, henrik.grop, oskar.wallmark,
This paper gives an overview of nowadays used simulation models and measurement methods in order to determine iron losses in electrical machinery. The paper provides machine
designers and system engineers with an overview of suitable iron loss models applicable for
the machine design process and simulations. Furthermore, possible methods for iron loss
measurements in electrical machines are presented from ongoing research projects. Besides standard electrical power measurements, iron losses are determined by thermal and
magnetic property measurements, taking into account different IEC and IEEE standards.
The goal is to emphasize the different possibilities of iron loss measurement methods and
possible application areas for electrical machinery.
1 Introduction
Iron losses in electrical machines have been a concern for decades. They are one of the
key points when it comes to efficiency optimization and the development of future high
power density machines. But even if electrical machines and iron losses have been studied
for more than 100 years, there is still a discrepancy between simulated and measured
iron losses in electrical machines. So called "loss correction factors", "machine factors" or
"build factors" are used to match the simulations to the corresponding measurement results.
These factors are often as large as 2 or even higher, which means that errors between the
simulation and measurement results of more than 100% are not uncommon.
The first part of this paper gives a short overview about iron loss models used in the machine design and manufacturing process nowadays. The largest problem for these models
is the material parameter identification of the iron sheets. They can change significantly
during the manufacturing process of the machine [1,2]. Especially the cutting and punching
Figure 1: Model approaches to determine iron losses in electrical machines.
processes influence the material properties and create inhomogeneous stresses inside the
sheets. The effect is depending on the alloy composite, whereas the grain size in the sheets
seems to be the main influencing factor, especially for operating ranges between 0.4 T to
1.5 T [3, 4]. Similar deteriorations due to the cutting and punching effect are obtained by the
stacking and welding process during the machine core assembly. Especially the welding
process deteriorates the material properties of the assembled core which, in turn, generates
higher iron losses [5].
The second part focuses on methods to measure and investigate iron losses in different
kinds of electrical machines. The iron losses in an induction machine are determined by a
loss separation approach based on the total losses measured at no-load. Another iron loss
determination approach is to investigate the iron losses by local thermal measurements in
conjunction with previously determined thermal models. This approach is validated with a
permanent magnet assisted synchronous reluctance machine (PMaSRM). Afterwards, iron
loss measurement methods are presented, where the losses are determined by magnetic
material investigations and electrical power measurements. These measurements are done
on the stator core of small high speed slot-less permanent magnet machines. The same
method is used for ring core test specimen made of construction steel to investigate iron
losses in passive structure parts of large synchronous generators. Finally, for the same
machine a core flux test method is presented to detect iron loss hot spots in the stator yoke
by thermal measurements.
2 Iron Loss Models - Overview
A plethora of different iron loss simulation models are used nowadays, from simple empirical
Steinmetz equation models to the Preisach and/or Jiles-Atherton and even more complex
multidimensional vector based models [6]. Figure 1 gives an overview of several methods
which are used for determining iron losses in electrical machines. It should be noted that
this overview is not intended to be exhaustive.
2.1 Steinmetz based models
The first group of models is based on the Steinmetz Equation (SE) [7]
pFe = CSE f α B̂ β
where B̂ is the peak value of the flux density in the device under test. The three coefficients
CSE , α and β are determined by fitting the loss model to curves from measurement data.
Eq. (1) assumes a purely sinusoidal flux density.
A modification of the Steinmetz equation is the Generalized Steinmetz Equation (GSE) [8].
It is based on the idea that the instantaneous iron loss is a single-valued function of the flux
density B and the rate of change of the flux density dB/dt. A formula is derived which uses
this single-valued function and connects it to the Steinmetz coefficients, according to (2).
dB α
dt |B(t)|
An advantage is that the GSE has a DC-bias sensitivity. A disadvantage of the GSE is the
accuracy limitation if the third or another relatively low-ordered harmonic of the flux density
becomes significant, i.e. if multiple peaks are occurring in the flux density waveform.
To overcome this problem, the GSE was upgraded to the improved Generalized Steinmetz
Equation (iGSE) [9]. The iGSE splits the waveform in one major and one or more minor
loops and thus takes sub loops of the full hysteresis loop into account. This is achieved by
a recursive algorithm which calculates the iron losses for each loop separately by
dB α
dt |∆B|
where ∆B is the peak-to-peak flux density of the current major or minor loop of the waveform.
It should be pointed out that all modifications of the Steinmetz equation have the well known
problem that the Steinmetz coefficients vary with frequency. Thus, for waveforms with a high
harmonic content, it can be difficult to find applicable coefficients which give good results
over the full frequency range of the applied waveform.
2.2 Iron loss separation models
Another approach is to separate the iron losses based on the Steinmetz Equation (1) into
static hysteresis losses and dynamic eddy current losses [10]:
pFe = physt + pec = Chyst f B̂ 2 + Cec f 2 B̂ 2
with Chyst and Cec the hysteresis loss coefficient and the eddy current loss coefficient, respectively. It is assumed that the hysteresis losses are proportional to the hysteresis loop
area of the material at low frequencies (f → 0 Hz). The eddy current part of the losses pec
can be derived from Maxwell’s equations:
pec =
12 ρ γ
where B(t) is the flux density as a function of time, d is the thickness of the electric sheet,
ρ its specific resistivity and γ the material density.
Equation (4) has been proven correct for several Nickel-Iron (NiFe) alloys but lacks accuracy
for SiFe alloys [11]. For this reason, an empirical correction factor ηexc , called the excess
loss factor or anomalous loss factor, was introduced [12]. It extends (4) to
pFe = physt + ηa pec = Chyst f B̂ 2 + ηexc Cec f 2 B̂ 2
with ηexc = pec_measured /pec_calculated > 1. For thin grain oriented SiFe alloys, ηexc reaches
values between 2 and 3 [11].
In another approach, the excess losses, as a function of the flux density and frequency, are
taken into account by adding an additional loss term pexc in (4). Thus, the iron loss formula
pFe is separated into three factors, the static hysteresis losses physt , dynamic eddy current
losses pec and the excess losses pexc :
pFe = physt + pec + pexc = Chyst f B̂ 2 + Cec f 2 B̂ 2 + Cexc f 1.5 B̂ 1.5
where Cexc is the excess loss coefficient.
The excess losses in (7) are still based on empirical factors from curve fitting. But a theory
and statistical model to determine Cexc mathematically is presented in [13,14]. In this model,
the excess loss part is described by a physical function in terms of the active magnetic
objects and the domain wall motion (Bertotti’s statistical model):
Cexc =
S V0 σ G
where S is the cross sectional area of the lamination sample, G ≈ 0.136 a dimensionless
coefficient of the eddy current damping and σ the electric conductivity of the lamination.
The factor V0 characterizes the statistical distribution of the local coercive fields and takes
into account the grain size [15]. It has to be noted that this loss separation does not hold if
the skin effect is not negligible [16]. A recent study on the properties of the coefficients is
presented in [17].
In electrical machines, the iron losses in the tooth tips and in the intersection areas between
the teeth and the yoke are mainly caused by rotational flux densities. In the previous mentioned loss models, iron losses due to rotational flux densities are not taken into account.
However, there are several approaches investigating this phenomena [18–22]. The iron
losses are separated by their magnetizing processes. This means that the losses caused
by linear magnetization, rotational magnetization and higher harmonics are added up to
determine the total iron losses [23]:
pFe = C1 pa + C2 prot + C3 phf
where pa are the losses caused by linear magnetization, prot the losses caused by rotational
magnetization and phf the losses caused by higher harmonics. Cx are empirical material
and geometric dependent factors determined by measurements and curve fittings.
In the middle of the teeth and in the middle of the yoke, the magnetization is linear only.
It is therefore depending on the machine geometry if the rotational losses account for a
significant part of the total iron losses and if the separation model by the magnetization
process can give better results.
A quite new approach to combine the loss separation model (7) with the rotational loss
separation model is presented by introducing a rotational loss factor due to rotational magnetization in the former equation [24]:
pFe = a2 B̂ 2 f + (a1 + a4 B̂ a3 )B̂ 2 f 2
where a1 = Cec and a2 = Chyst (1 + (r − 1)(Bmin /Bmax )), with r the rotational hysteresis
factor and Bmin and Bmax the minimum and maximum values of B(t) over one period. The
factor a4 and the exponent a3 are used to get an accurate representation of the iron losses at
large flux densities by introducing a higher power of B . Thus, they are called high order loss
factors. Further, a3 is depending on the lamination thickness. The excess loss term Cexc is
negligible compared to the other terms in this model and thus not regarded in (10) [24].
It should be mentioned that the history of the flux density waveform is not taken into account
in the discussed Steinmetz equation models and in the loss separation models. But the
described hysteresis models in the next section do this.
2.3 Hysteresis models
Mathematical hysteresis models simulate the used BH -hysteresis loop due to the applied
flux density in electrical steel sheets. Since the shape and inner area of the BH -hysteresis
loop is proportional to the iron losses, they can be applied to determine losses in electrical
machines e.g. in FEM simulations. Hysteresis models require more measurement and
material data of the used electrical steel sheets but also give better results in terms of
accuracy and allow more complex simulations compared to the simpler Steinmetz models.
The most wide spread hysteresis models are the Preisach model [25,26] and Jiles/Atherton
model [27], and they are still the base for further mathematical hysteresis models [28]. More
information and a comparison between these two is presented in [29, 30]. Since a detailed
description of these models is beyond the scope of this paper, the reader is referred to
relevant literature [26].
Some applicable improved and modified hysteresis models are amongst others the dynamic
Preisach model, the Magnetodynamic Viscosity Based model, the Loss Surface model, the
Friction Like Hysteresis model and the Energy Based Hysteresis model.
The dynamic Preisach model extends the classical Preisach model by introducing a rate
dependent factor for each elementary rectangular loop of the hysteresis model [26,31,32]. It
takes the delay time of the induction B(t) behind the magnetic field H(t) into account. Thus,
it is possible to regard the enlargement of the hysteresis loop with increasing frequency.
The Magnetodynamic Viscosity based model [33] is similar and also based on a static (rateindependent) Preisach hysteresis model. But it uses a viscous type differential equation
for describing the delay time between the induction B(t) and the magnetic field H(t). This
differential equation determines the shape of the dynamic part of the loop and the dynamics
of the model to take the excess losses into account.
2.4 Iron loss models in FEM software
Next to the standard loss separation model described in (7), most commercial FEM software
packages offer in addition different more advanced models to determine iron losses from
electro-magnetic simulations. The software JMAG1 uses a frequency separation approach
to determine iron losses from the electro-magnetic simulation results (post processing) [34].
The eddy current losses are determined by
pec =
" N
b(|Bl |, fl )fl2
where n is the number of elements, Bl the magnetic flux density at the frequency order
l after a Fourier transformation, and b(|Bl |, fl ) is determined by the frequency separation
method [34]. To compute the hysteresis losses from a time series data of magnetic flux
density, the number and size of hysteresis loops can be obtained. The hysteresis losses
are determined by
physt =
a(|Bj |)
where Bj is the amplitude of the j th hysteresis loop, nloop the number of loops, f the basic
frequency and a(|Bj |) is the coefficient of magnetic flux density which is determined from
the frequency separation method
= a(B) + b(B,f )f
A dynamic and scalar post-processing hysteresis model, the Loss Surface model, is presented in [35] and implemented in the FEM software Flux2 . The magnetic field H is determined as a characteristic surface function
S = H B,
= Hstat (B) + Hdyn
separated into a static and a dynamic part. B is the magnetic flux density and dB/dt its
rate of change. The model connects the magnetic field H on the sheet surface with the flux
density B in the thickness of the sheet. The static part is modeled by the classical (static)
Preisach model (rate-independent), which is determined by measurements of the major
loop and first order reversal curves. The dynamic part is modeled by two linear analytical
equations describing the low and high values of the flux density derivatives after subtracting
Hstat .
Another implementation of hysteresis modeling in FEM software which focuses on a simple
material data input approach is presented in [36] and implemented in the FEM software
Opera3 [37]. Here, the given non-linear BH -curve is used directly in the electro-magnetic
FEM calculations to determine the magnetic field and flux distribution as well as the hysteresis and eddy current losses. In this process, also the history of the magnetization in
each element is taken into account.
Finally, a possible implementation of the dynamic Preisach model into FEM software for
iron loss determination in electrical machines is presented in [38, 39].
JMAG is a registered trademark of the JSOL Corporation, Japan
Flux is a registered trademark of the CEDRAT Group, France.
Opera is the software package from Cobham Technical Services, UK
3 A Loss Separation Approach to Determine Iron Losses
in Induction Machines
In electrical machines, the complex geometry and the combined use of different materials
complicates the subdivision of the total losses into well defined categories. However, existing international standards have been developed to define the different loss components.
For small to medium sized industrial induction machines, the ruling ones are IEC 60034-2-1
and IEEE-112. A comparative study of these two standards is reported in [40]. This section
presents results from measurements of iron losses on a small three-phase induction machine, rated 11 kW, used for pump applications. In the following, the iron losses are defined
according to IEC-60034-2-1 [41].
3.1 Distribution of losses at rated power
At rated output power, the total losses in the studied machine can be subdivided into different components, according to Figure 2. As expected for a small induction machine, most of
the losses occur in the stator winding. However, for this machine, the second largest component is the iron losses. These losses are defined indirectly from a set of measurements
performed under no-load conditions, referred to as a no-load test.
Stator winding losses
Iron losses
Rotor winding losses
Stray-load losses
Friction and windage losses
Figure 2: Distribution of the total losses at rated power for the studied 11 kW induction machine.
3.2 No-load test
In order to stabilize the no-load losses, the machine is operated at rated voltage and frequency until thermal equilibrium is reached. That is, according to the standard, when the
no-load input power varies by 3 % or less, when measured at two successive 30 minutes
intervals. Secondly, measurements are performed for a minimum value of seven different
voltage levels, including rated voltage. The voltage being distributed between 20 % and
125 % of rated voltage. Quantities to be measured are; three-phase average stator current,
average stator voltage, and input power. In order to minimize the temperature variations
during the readings, the measurements shall be taken in descending order of voltage, as
quickly as possible. Finally, after the lowest voltage readings, the stator winding resistance
is measured.
As the mechanical output power is zero, the measured input power equals the total losses in
the machine. Figure 3 shows the total no-load losses P0 , and the stator winding losses Ps ,
in the investigated induction machine as a function of the terminal voltage. Here, the stator
winding losses are determined from the measured average line current and the measured
winding resistance. At no-load, the studied induction machine is designed to operate close
to or within the saturated region of the electrical steel. This, however, is common practice
in machine design reducing the cost and the weight of machine. As a result, the no-load
losses increase rapidly when the voltage exceeds the rating.
Total no-load losses P0
Winding losses Ps
Power [W]
Voltage [p.u.]
Figure 3: Measured no-load losses at rated frequency as a function of voltage.
3.3 Segregation of no-load losses
The total losses in the machine consists of stator winding losses (also called stator copper
losses or Joule losses), iron losses, PFe , and friction and windage losses, Pfw . The standard
defines a separation approach for the determination of the iron losses. Subtracting the
winding losses from the total losses gives the so called "constant losses", according to
Equation 15. These losses, i.e. the sum of the iron losses and the friction and windage
losses, are shown as a function of the voltage squared in Figure 4a. Therefore, a linear
behavior is obtained within the region where magnetic saturation is not present. For the
points not affected by saturation, a straight line is extrapolated to zero voltage, the intercept
with the zero voltage axis defines the friction and windage losses.
Pc = P0 − Ps = PFe + Pfw .
The iron losses are obtained by subtracting the friction and windage losses from the constant losses. According to the standard, a curve defining the iron losses as a function of
the voltage shall be developed as shown in Figure 4b. In the present IEC-standard, the iron
losses are considered to be load dependent, taking the resistive voltage drop over the stator
winding into account. In other words; an increased load results in increased current, hence,
the voltage drop over the stator winding increases, reducing the magnetizing voltage. As a
result, the iron losses are reduced. However, this effect is mostly visible on small machines
having a large stator resistance.
Power [W]
Power [W]
Calculated from measurements
Linear approximation
Voltage squared [p.u.]
(a) Constant losses, Pc , as a function of voltage
Calculated from measurements
Curve fit
Voltage [p.u.]
(b) Iron losses, PFe as a function of voltage.
Figure 4: Determination of friction and windage losses (a) and iron losses (b) from measurements.
3.4 Issues related to the loss separation approach
In the loss separation approach described above, the stator winding resistance is a crucial
factor for an accurate determination of the iron losses. According to the standard used, this
resistance is measured at the end of the no-load test. However, depending on the duration
of the test, the winding resistance may vary between the different operating points. A better
result would be obtained if the winding resistance was measured directly on-line for each
operating point. Such a monitoring technique is presented in [42].
During the no-load test, it is obvious that the machine must operate without load, i.e. the
rotor current being zero. However, due to friction losses in the bearings and windage losses
along the rotor surface, the machine is loaded to some extent, introducing additional losses
in the rotor circuit. This effect is usually small but the iron losses calculated from the no-load
test still depends upon the friction and windage losses. This effect can be reduced by using
high efficient bearings, resulting in a more accurate determination of the iron losses.
In an induction machine, parasitic effects such as airgap space harmonics created by the
stator and rotor slotting give rise to additional losses, referred to as stray losses. When
the machine is loaded, the standard defines these losses as stray-load losses. At no-load,
however, the definition of the iron losses includes the stray no-load losses.
The existing standard procedures for measuring iron losses in electrical machines are
adapted for a simplified and standardized testing in industry. The iron losses obtained
for such a test include several other sources of losses. As a result, the losses calculated by
the use of traditional iron loss modeling will most likely seem to be underestimated.
4 Thermal Measurements to Investigate Iron Losses
In this method, first an accurate lumped parameter (LP) thermal model of an electrical
machine is derived. Then, iron losses are calculated based on the derived thermal model
and temperature measurements in the steady state.
4.1 Lumped parameter thermal model of a permanent-magnet
assisted synchronous reluctance machine (PMaSRM)
LP thermal analysis and numerical methods are the major approaches used to model thermal effects in electric machinery [43]. The LP model represents a simplification, where
spatially distributed fields are approximated as a number of single scalars. Thereby, a thermal analysis can be carried out, providing fast results with reasonable accuracy provided
that the LP network is chosen with care.
Using LP thermal models of different parts of the PMaSRM described here, the LP thermal
model of the machine is first implemented, and then solved using the software Portunus4 .
The complete thermal model, including the housing water jacket, is illustrated in Figure 5.
Figure 5: Complete LP thermal model of the PMaSRM. The abbreviations used are reported
in Table 1. Loss sources are indicated as dots. The bold highlighted words also
represent temperature sensor locations in the experimental setup.
To model the convective heat transfer from the stator housing to the coolant, the analytical
formulations in [44, 45] and [46] are used. Also, the convective heat transfers from the end
winding, shaft, and rotor to the end space are modeled analytically [47]. The LP thermal
model representing the winding inserted in the slot is described in details in [48] where
the copper and impregnation filling the slot is divided into a number of concentric ellipses.
Based on the proposed elliptical model, a multi-layer structure of the winding thermal model
Portunus is a registered trademark of the CEDRAT Group, France.
Table 1: Abbreviations used in Figure 5.
Sl-Wl Slot wall
St-Br Stator bore
Stator yoke
End cap
Stator tooth
End space
Wnd Winding
E-Wnd End winding
is developed. For the rotor, it is assumed that surfaces normal to the radial direction are
isothermals. Such an approximate “radial geometry" and corresponding LP thermal model
are illustrated in [49]. The LP thermal models of the remaining parts of the PMaSRM can
be found in [50–54].
In addition to the thermal resistances that can be calculated using analytical and numerical
methods, there are a few thermal resistances that are difficult to estimate without experimental data available for model calibration. These resistances represent the contact resistance between the stator back and stator housing and the contact resistance between the
rotor yoke and the shaft. The exact values of these thermal resistances depend on several
factors, e.g. the manufacturing process, the size of machine and the used materials. Here,
these resistances are first pre-estimated according to [55] and then calibrated using data
from experimental tests.
4.2 Experimental setup
To obtain a good estimation of the produced iron losses and to calibrate the derived thermal
model, temperatures of the stator, winding, coolant, and rotor should be monitored accurately. In this regard, twelve two-wire PT100 resistance temperature detectors (RTDs) are
placed inside the winding and stator, and 3 RTDs are located in the rotor body. Also, two
four-wire RTDs are used to measure temperatures of the inlet and outlet coolant.
The temperature sensors mounted in the rotor are connected to the measurement setup using a slip-ring unit mounted on the rotor shaft. The experimental setup is shown in Figure 6.
4.3 Comparison between the FEM and experimental results
The FEM software JMAG is used to compute the iron losses. Figure 7 shows the resulting
iron loss density distribution in the stator and the rotor laminations for two operating points.
In Figure 7a), the PMaSRM operates at rated speed (1500 rpm) and an average torque of
108 Nm and in Figure 7b), the PMaSRM rotates in the field weakening range (3000 rpm and
72 Nm). The used steel laminations are M250-35A.
A comparison between the calculated iron losses from FEM, as described above, and
the calculated iron losses from the temperature measurements and the developed thermal
model shows that the FEM results underestimate the produced iron losses in the studied
Figure 6: Experimental setup. The front hoses carry inlet and outlet water for the water
Figure 7: Resulting iron loss density distributions (W/m3 ): a) 1500 rpm, 108 Nm; b) 3000 rpm,
72 Nm.
PMaSRM by up to 60 %. Using the 2D FEM computed iron losses as an input to the LP thermal model yielded in a temperature deviation between the LP model and the corresponding
experimental results of 3 ◦C to 6 ◦C. The main reason for this deviation between the experimental and simulation results can be attributed to the influence of the manufacturing
process on the produced iron losses and the accuracy of the adopted iron loss models.
5 Magnetic Material Characterization to Determine Iron
Determining iron losses directly from electro-magnetic measurements is typically carried
out for whole cores of small electrical machines and parts of larger machines. It is possible
to analyze different parts separately, e.g. the stator and the rotor core or the stator teeth and
stator yoke. The Epstein frame is normally used for testing the magnetic properties of laminated materials of a fixed size and the preferred choice for comparable measurements [56].
However, the preferred test for solid or small and special shaped materials uses sample
parts machined into ring shape specimens, following the testing method described in IEC
60404-6 [57]. The rings are wound with a primary winding for the excitation of the core
and a secondary winding for voltage measurements. The primary winding is supplied by
either a sinusoidal current or a sinusoidal voltage and the flux in the ring core is obtained by
Specific iron loss (W/kg)
Magnetic flux density B (peak value) (T)
Figure 8: Wound stator ring cores for magnetic measurements.
Magnetic field strength H (peak value) (A/m)
(a) BH measurement curves for a peak flux density of 1.1 T
Magnetic flux density B (peak value) (T)
(b) Specific iron losses over the flux density
Figure 9: Measurement results of the welded and taped ring cores at 50 Hz.
integration of the voltage across the secondary winding. In the used setup a National Instruments CompactRIO system is used for the control and acquiring measurement results. The
iron losses in the ring cores are determined by a Yokogawa WT3000 power meter. This test
method is applied in an industrial project for small slot-less permanent magnet synchronous
machine stator cores and passive parts of a large synchronous generator in the megawatt
range, as described in the following.
5.1 Iron loss characterization of small permanent magnet machines
The study of the small slot-less permanent magnet synchronous machine stator cores focuses on the influence of the welding process during manufacturing. The cores are made
from low-loss and thin electrical steel sheets produced by Cogent Surahammars Bruk AB
(NO20). Each core is 64.5 mm long and has an outer and inner diameter of 31 mm and 23.2
mm, respectively. They are investigated before and after the welding process. The cores
from before the welding process are wound and tightly pressed together by insulation tape.
Four of the cores are shown in Figure 8. The flux density and magnetic field strengths
measurement results for the welded and taped ring cores at 50 Hz are shown in Figure 9a.
The increase of iron losses due to the welding process for different flux density peak values
at 50 Hz is shown in Figure 9b.
It can be seen that the welding process during manufacturing of the stator ring core deteriorates the magnetic properties of the material significantly. The shape of the BH -curve is
changing and the specific iron losses are increased for the welded cores. Further results
will be published at the International Conference on Electrical Machines 2012 in Marseille.
5.2 Magnetic characterization of solid materials
Inactive parts of a large electrical machine (synchronous generator) are investigated in a
similar way as the ring core test in order to determine the hysteresis loop (for hysteresis
losses) and conductivity (for eddy current losses).
The tested solid material is a construction steel used for supporting the stator stacking
(end rings of the investigated synchronous machine). The position of the end ring in the
machine is shown in Figure 10. Even if the material is not used in the main flux path of the
End ring
Stator core
Figure 10: Location of the end rings at the stator core made of lamination packages and
separated by cooling ducts.
machine, it is subject to a time varying magnetic field caused by leakage flux in the end
region. Therefore, knowing its magnetic characteristics is important when trying to chase
down the unaccounted losses measured in real machines.
Figure 11 shows the measured BH -curves for the tested material at different excitation
levels with sinusoidal current supply. Figure 11a represents the results obtained at a frequency of 0.1 Hz, i.e. DC and Figure 11b shows the results measured at a frequency of
50 Hz. Already at 50 Hz, the eddy currents in the material are pronounced and its’ effect
is to counteract the excitation field which leads to an increased magnetizing field to reach
a given level of flux. This in turn, forces the hysteresis curve to take the elliptical form as
shown in Figure 11b.
Loss measurements at 50 Hz are shown in Figure 12. The flux density was varied from
0.2 T to 1.45 T and the active power was measured. The iron losses are proportional to the
square of the flux density. At 1.45 T they reach 85 W/kg. As the tested material is solid, the
eddy current losses are dominant.
5.3 Measurements of stator iron loss - core flux test
This test reveals any hot spots in the stator core of large electrical machines (i.e. MW
range) after manufacturing and determines the iron losses in the yoke with a flux in the
peripheral direction. Iron loss in the teeth is omitted as the flux path is in the yoke only.
0.1 Hz
1000 2000 3000
-3000 -2000 -1000
Magnetic field strength H (peak value) (A/m)
(a) BH -curve for the stator end ring at 0.1 Hz and
varying excitation field.
Magnetic flux density B (peak value) (T)
Magnetic flux density B (peak value) (T)
50 Hz
1000 2000 3000
-3000 -2000 -1000
Magnetic field strength H (peak value) (A/m)
(b) BH -curve for the stator end ring at 50 Hz and
varying excitation field.
Figure 11: BH -curves for the solid test sample representing the stator end ring.
Specific iron loss (W/kg)
50 Hz
Magnetic flux density B (peak value) (T)
Figure 12: Measured iron loss at different flux densities.
The test is described in detail in [58]. It is performed before the stator is wound. A primary
loop, consisting of a few turns is wound around the stator back and a secondary loop or
measuring loop consisting of one or a few turns is also wound around the stator back.
A current in the primary loop excites the stator core and the flux is calculated from the
measured voltage in the secondary loop. The secondary voltage and primary current are
used to calculate the power loss due to iron loss.
The core is then analyzed with a thermal camera to locate hot spots in the core surface.
The hot spots are positions where excessive loss is produced, which is reflected in the
temperature. The standard defines a hot spot as a point where the temperature exceeds
5 ◦C from the average surface temperature. A found hot spot is an indication that there is
electrical contact between two (or several) stator laminations which has created a closed
path for eddy currents. The increased iron losses associated to a hot spot may not be
significant at a global level but locally hot spots may have disastrous effects, therefore, a
local investigation is done using infra-red camera pictures. Figure 13a shows a thermal
image of a stator during a core flux test. The temperature along the line Li1 is shown in
Figure 13b. The results from this particular test show that no hot spots were found.
(a) Thermal image of a stator during core-flux test.
(b) Temperature along line Li1 shown in 13a
Figure 13: Results from a core-flux test on a healthy stator.
6 Conclusion
Nowadays, machine designers and system engineers have the possibility to choose from
a wide range of more or less complex iron loss simulation models for electrical machines.
Several often used models were presented and described in more detail in this paper to give
the reader a more comprehensive understanding and help choosing a suitable model. Different measurement methods used in ongoing research projects were described, illustrating
advantages and disadvantages that can be expected from these methods.
The standardized procedures for measuring iron losses in electrical machines are adapted
for a simplified testing in industry. These standards are important for comparability and repeatability of test results. However, it is shown that the iron losses obtained from a standard
induction machine test using the loss separation approach also include other sources of
losses. The same yields for the approaches based on direct temperature measurements.
These are independent of uncertain parameters, e.g. the magnetization curve and frequency characteristics of the used materials. However, subtracting different loss sources
in electrical machines is still a challenging research area for these methods. On the other
hand, methods to determine iron losses in electrical machines by magnetic property measurements, i.e. measuring the magnetic field and flux density in different parts of a machine,
can give accurate results locally. The challenge in this approach is to investigate and apply
the correct flux density distributions in the studied local parts of the machine.
One of the major problems is still the discrepancy between simulations and measurements
of iron losses due to the influencing factors from the manufacturing process, i.e. cutting
and punching as well as welding. The simulation models underestimate in general the
iron losses in electrical machines. However, one solution might be to combine numerical
simulation results of field and flux density distributions with loss measurement results of
local geometry parts. In this way more accurate results could be achieved.
The authors would like to thank the Swedish Center of Excellence in Electrical Power Engineering (EKC2) for financial support as well as the companies Bevi AB, ABB Motors, ABB
Machines, Atlas Copco Tools AB, and Motor Design Ltd for the collaboration and support in
the presented projects.
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