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Hamzehbahmani, Hamed (2019) 'An experimental approach for condition monitoring of magnetic cores with

grain oriented electrical steels.', IEEE transactions on instrumentation and measurement. .

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 An Experimental Approach for Condition Monitoring of
Magnetic Cores with Grain Oriented Electrical Steels
Hamed Hamzehbahmani, Senior member, IEEE
Department of Engineering, Durham University, Durham, DH1 3LE, UK
Abstract- This paper proposes a new approach to an old
challenge in the magnetic cores of power transformers and
other magnetic devices with grain oriented electrical steels. The
main aim of this paper is to evaluate effects of inter-laminar faults
of different configurations on dynamic performance and dynamic
energy losses of the magnetic cores with grain oriented silicon
steels. In the relevant studies, artificial short circuits of different
configurations were applied between the laminations of stacks of
four Epstein size laminations of 3 % grain oriented silicon steel.
The results showed that, inter-laminar fault evaluation and core
quality assessment can be effectively done by interpreting the
dynamic hysteresis loops of the cores.
Index Terms: Condition monitoring, transformer core, soft magnetic
material, dynamic hysteresis loop, magnetic loss, dynamic modelling.
(a)
I. INTRODUCTION

E lectrical steels are key materials for magnetic cores of

reactors, transformers and electrical machines. Quality of
the magnetic cores are determined by electrical and
magnetic properties of the magnetic materials, coating of the
laminations which determine the inter-laminar resistance
between the laminations, clamping pressure, manufacturing
processes, etc. Key amongst these are manufacturing processes
which have direct impacts on properties of the materials and
hence normal operation of the magnetic cores and related
devices [1-7]. (b) (c)
Magnetic and electric properties of the individual laminations Fig 1 Perspective view of a three-phase three-limb transformer core with
and the assembled cores can be deteriorated by manufacturing ILFs (a) Overall view (b) ILF between bolt hole and yoke and (c) ILF on two
processes, e.g. cutting, punching, stamping and welding, as a sides of the limb
result of mechanical and thermal residual stress [7].
Additionally, punching and cutting could lead to microscopic
edge burrs around the punched holes or at the cut edge, and can
cause low inter-laminar resistance, electrical contact and hence
inter-laminar fault (ILF) between the laminations [2], [8-12].
ILF leads to circulating eddy currents between the defective
laminations, which cause hot spot and extra localised power loss
at the defective zone. A few faults may not create high ILF
currents; but with several faults, the induced fault currents could
be large and cause excessive local heating in the damaged area
[5-6]. Though a large number of ILF could result in catastrophic
breakdown, the machine can still be in operation with a small
number of ILF, but with higher power loss and hence lower
efficiency. Local power losses and hot spots in the magnetic (a)
cores, could expedite the degradation of the coating material of
the laminations and result in deterioration of the core at early
stages. Therefore, condition monitoring of the magnetic cores to
identify any ILF should be planned at an early stage before it
progresses to machine breakdown. Examples of ILF in a three-
phase three-limb transformer core are shown in Fig 1. Side view (b)
of a stack of grain oriented (GO) 3 % silicon steel laminations Fig 2 A stack of 3 % grain oriented silicon steel with ILF between two
with ILF between two laminations is shown in Fig 2 [1]. laminations [1]

1
 ILF detection and condition monitoring of the magnetic cores 𝜕𝐵𝑧 (𝑥, 𝑡) 𝜕 2 𝐻𝑧 (𝑥, 𝑡)
have been an active area of research and interesting topic for =𝜌 (1)
𝜕𝑡 𝜕𝑥 2
designers and manufacturers of the electrical steels and
laminated magnetic cores. In this regards, practical methods which links the flux density 𝐵𝑧 (𝑥, 𝑡) and the field strength
have been introduced and successfully employed to evaluate ILF 𝐻𝑧 (𝑥, 𝑡) in a thin ferromagnetic lamination of resistivity ρ. It
of rotating machines [4-12] and transformers [13-16], and other should be noted that (1) is a Maxwell equation describing
magnetic devices with laminated cores. An overall review of diffusion process in a spatially homogeneous medium.
these methods is performed in [1].
Electrical steels are characterised by the relative permeability
and specific power loss in W/kg or total energy loss in J/m3
during one magnetising cycle. Data sheets from the steel
manufacturers typically report the specific loss figure of the
materials measured at power frequencies, 50 Hz or 60 Hz, for
selected peak flux densities. Specific power loss published in the
data sheets of the material, however, do not count for the
geometry of the magnetic cores, and degradation of the material
due to manufacturing processes. Furthermore, it is well
distinguished that low inter-laminar resistance in the clamped
magnetic cores due to, for example, edge burr or damage on the
surface coating has a significant impact on the local and overall
power loss of the magnetic cores [15-16]. Therefore, designers
of the electrical machines and transformers usually find
considerable deviation between the measurements of single
lamination and overall power losses measured from the
assembled cores. Fig 3 Single strip lamination under time varying magnetic field
The main aim of this paper is to evaluate magnetic cores of
GO materials by measuring and interpreting the Static Due to the approximate homogeneous nature of Non-Oriented
Hysteresis Loop (SHL) and Dynamic Hysteresis Loop (DHL) of (NO) steels, (1) can be implemented to characterise NO steels,
the core. The measurements were performed on stacks of four with reasonable accuracy [20]. However, loss calculation of GO
Epstein size laminations of GO silicon steel subjected to steels by means of (1) results in a significant discrepancy with
artificial ILF of different configurations. A new approach has the measured values. Numerical solution of (1) has been
been also developed to reproduce DHLs of the samples under modified to characterise GO steels, by taking into account an
sinusoidal induction with magnetising frequency of 50 Hz and accurate static hysteresis model, skin effect and correction
peak flux densities of 1.3 T, 1.5 T and 1.7 T. This method can factors [24]. Although the achievements are somehow
be used to evaluate the impacts of typical ILFs on the dynamic satisfactory, but due to inhomogeneous nature and grain
performance and dynamic energy loss of power transformers structure of the GO materials, the developed models based on
and other magnetic devices with GO materials. (1) cannot be extended for all types of GO steels, especially for
high frequency magnetisations and high permeability materials.
II. THEORETICAL BASE An alternative approach to evaluate the magnetisation process
Magnetising process of the magnetic materials can be analysed of GO materials is thin sheet model, which is based on the
by means of the hysteresis phenomenon. The area surrounded statistical energy loss separation principle [17]. In this approach,
by the hysteresis loop represents the total energy loss per unit the total energy loss 𝑊𝑡𝑜𝑡 , is separated into three components,
volume for one magnetising cycle, in J/m3 per cycle. Accurate hysteresis loss 𝑊ℎ𝑦𝑠 , classical eddy current loss 𝑊𝑒𝑑𝑑𝑦 , and
measurements of SHL and DHL, is an adequate technique of anomalous loss or excess loss 𝑊𝑒𝑥𝑐 [17]:
loss evaluation of magnetic materials over a wide range of 𝑊𝑡𝑜𝑡 = 𝑊ℎ𝑦𝑠 + 𝑊𝑒𝑑𝑑𝑦 + 𝑊𝑒𝑥𝑐 (2)
magnetisation. However in these analyses, different approaches
might be applied for different materials. In this regard, analytical Energy loss calculation and separation can be performed based
methods have been developed to reproduce DHLs of the on the static and dynamic hysteresis loops of the material, and
materials for energy loss prediction and separation [17-23]. therefore, loss separation of (2), can be interpreted as magnetic
A perspective view of a single lamination of thickness d field separation:
subjected to flux density 𝐵(𝑡) applied in rolling direction (z-
direction) is shown in Fig 3. If eddy current loops are assumed 𝐻(𝑡) = 𝐻ℎ𝑦𝑠 + 𝐻𝑒𝑑𝑑𝑦 + 𝐻𝑒𝑥𝑐 (3)
to be large enough along the y-direction, the field problem
where 𝐻(𝑡) is the magnetic field at the surface of the lamination,
becomes one dimensional and the magnetisation process of the
𝐻ℎ𝑦𝑠 is hysteresis field, 𝐻𝑒𝑑𝑑𝑦 is eddy current field, and 𝐻𝑒𝑥𝑐 is
material can be evaluated for z-component of the magnetic flux
density 𝐵𝑧 (𝑥, 𝑡) by numerical solution of the well-known 1-D excess field. Using the dynamic models of 𝐻𝑒𝑑𝑑𝑦 and 𝐻𝑒𝑥𝑐 , (3)
diffusion equation [20]: led to the well-known thin sheet model and is expressed as [19]:

2
 𝑑 2 𝑑𝐵 𝑑𝐵 𝛼 laminations. Based on a study performed in [2], lead-free solder
𝐻(𝑡) = 𝐻ℎ𝑦𝑠 (𝐵) + + 𝑔(𝐵)𝛿 | | (4) was found as an effective material to reproduce effect of ILF in
12𝜌 𝑑𝑡 𝑑𝑡
clamped magnetic cores. Side view and top view of one the
where 𝐻ℎ𝑦𝑠 (𝐵) is the hysteresis field, d is thickness of the artificial faults is shown in Figs 4-a and 4-b, respectively.
material and 𝛿 = 𝑠𝑖𝑔𝑛(𝑑𝐵 ⁄𝑑𝑡 ) is directional parameter for Perspective view of the samples are shown in Fig 5.
ascending (𝑑𝐵 ⁄𝑑𝑡 > 0) and descending (𝑑𝐵 ⁄𝑑𝑡 < 0)
hysteresis branches. The exponent 𝛼 determines the frequency
law of the excess loss component calculated by (4) under
sinusoidal induction. 𝑔(𝐵) is an important function which
control shape of the dynamic hysteresis loop. Accuracy of the
calculated loss depends on the accuracy of the dynamic
hysteresis loop, reproduced by the dynamic model of (4), which
mainly depends on the hysteresis field 𝐻ℎ𝑦𝑠 (𝐵) and
function 𝑔(𝐵). Examples of calculating 𝑔(𝐵) for some (a)
commercial materials are provided in [21]. Recent publications
show high accuracy of model (4) in characterisation of GO steels
[19-20], and some high silicon NO steels [18].
Energy loss separation can be also interpreted by separating
the total energy loss into hysteresis and dynamic components. In
this method, both classical eddy-current and excess fields are
interpreted as dynamic field, and hence loss separation and field
separation can be expressed as [25]: (b)
Fig 4 Artificial fault applied on the samples (a) side view and (b) top view
𝑊𝑡𝑜𝑡 = 𝑊ℎ𝑦𝑠 + 𝑊𝑑𝑦𝑛 (5)
𝐻(𝑡) = 𝐻ℎ𝑦𝑠 (𝐵) + 𝐻𝑑𝑦𝑛 (𝑡) (6)

where 𝐻ℎ𝑦𝑠 (𝐵) is the hysteresis field and 𝑊ℎ𝑦𝑠 is the area of the
static, or quasi-static hysteresis loop. Based on the two terms
energy loss, a dynamic model is proposed in [20] for GO
materials as follow: (a)

𝑑𝐵 𝛼𝑑𝑦𝑛 (𝐵𝑝𝑘 )
𝐻(𝑡) = 𝐻ℎ𝑦𝑠 (𝐵) + 𝑔𝑑𝑦𝑛 (𝐵)𝛿 | | (7)
𝑑𝑡
where 𝑔𝑑𝑦𝑛 (𝐵) and 𝛼𝑑𝑦𝑛 (𝐵𝑝𝑘 ) differ from 𝑔(𝐵) and 𝛼 in (4).
This model shows a good accuracy to reproduce the DHL of GO
materials and hence energy loss calculation [20, 21]. It should (b)
be noted that, accuracy of the model (7) to reproduce the DHL,
energy loss prediction and energy loss separation depends on the
accuracy of the measured or calculated hysteresis field 𝐻ℎ𝑦𝑠 (𝐵)
and the designed functions for 𝑔𝑑𝑦𝑛 (𝐵) and 𝛼𝑑𝑦𝑛 (𝐵𝑝𝑘 ).
It has been shown that ILFs have significant impacts on the
dynamic behaviour of the magnetic cores [26]. Therefore, in this
paper model (7) was implemented to reproduce the DHLs of (c)
stacks of laminations of GO steels, subjected to ILFs.
III. EXPERIMENTAL SET-UP AND SAMPLE PREPARATION
Epstein size laminations (30 mm × 305 mm) with standard
grades of M105-30P CGO 3 % SiFe (thickness 𝑑 = 0.3 mm and
resistivity 𝜌 = 0.461 μΩm) were provided by Cogent Power
Ltd. Stacks of four laminations were prepared to model different (d)
types of ILFs. The stacks were labelled as: Pack # 1, Stack of Fig 5 Perspective view of stacks of four laminations (a) without ILF
laminations with no ILF; Pack # 2, ILFs at three step-like points; (pack # 1); and with ILFs (b) at three step-like points (pack # 2) (c) one set
point (pack # 3) and (d) at three set points (pack # 4)
Pack # 3, ILFs at one set point and Pack # 4, ILFs at three set
points. Similar to the previous work [2], partial artificial faults Electrical steels are usually characterised at flux densities
of 10 mm wide and ~500 µm thick were applied between the close to the knee of the B-H curve. Electrical steel manufactures

3
also provide the specific power loss of the materials typically at that, even a few ILFs under power frequency magnetisation and
peak flux densities of 1.5 T and 1.7 T, and power frequency of a low flux density of 1.3 T, could lead to critical hot spot in the
50 Hz or 60 Hz. Furthermore it has been shown that, at each magnetic cores. This shows the importance of the ILFs in quality
particular frequency, ILF problems become more crucial at of the magnetic cores. More analysis on the bulk power loss of
higher flux densities [2]. In this work a standard double yoke the samples over a wide range of frequency and flux density is
single strip tester (SST) was used to magnetise the samples provided in [2].
under sinusoidal induction at peak flux densities of 1.3 T, 1.5 T 1.8
and 1.7 T and magnetising frequency of 50 Hz. The measuring
system conforms to the British standard BS EN 10280:2007.
1.2
This system shows good reproducibility of measurements for a
wide range of frequency and flux density. The reproducibility of
this system is characterised by a relative standard deviation of 0.6

Flux density, B (T)

1 % for GO materials and of 2 % for NO materials [27]. More
detail of the experimental setup is available in [24].
0.0
IV. EXPERIMENTAL RESULTS
SHL, DHL and total energy losses of the samples were
measured and analysed for quality assessment purposes. DHL -0.6
and total energy loss of pack # 1, with no ILF, represent the
nominal qualities of the material. A comparison between the Pack # 1
-1.2
DHLs of the specimens at peak flux densities of 1.7 T, 1.5 T and Pack # 2
1.3 T are shown in Fig 6. The most evident feature of the DHLs Pack # 3
of Fig 6 is the change in the hysteresis loop shapes and Pack # 4
-1.8
significant increase in the loop area for different types of ILFs. -100 -50 0 50 100
As stated earlier, with increasing ILFs the induced ILF currents Magnetic field strength, H (A/m)
increase which result in larger loop area in the DHLs and hence
(a)
higher energy loss. However, the experimental results showed
1.6 1.5
that SHLs of the samples are almost indistinguishable from each
other. Therefore it could be concluded that, the ILFs have a
significant impact on the dynamic energy losses, while their 1.0
impact on the hysteresis energy losses is negligible. This reflects
a unique property of the hysteresis phenomenon in energy loss 0.8
evaluation, which can be implemented in the characterisation of 0.5
Flux density, B (T)

Flux density, B (T)

the magnetic cores of transformers, electrical machines and
other magnetic devices with laminated cores. This is a powerful
technique in core quality assessment and can provide a 0.0 0.0
meaningful comparison between magnetic properties of the
magnetic cores subjected to different types of ILFs.
Total energy loss of the samples versus peak flux density are -0.5
shown in Fig 7. Total energy loss of each pack was measured -0.8
three times at each flux density with repeatability of better than Pack # 1 Pack # 1
-1.0
0.3 %. Experimental results presented in this paper are the Pack # 2 Pack # 2
average of three measurements. The estimated uncertainty of the Pack # 3 Pack # 3
measurements are shown by error bars [28]. The measured Pack # 4 Pack # 4
-1.6 -1.5
values lie within the upper and lower limits of the error bars. The 0 50 100 0 50 100
extra energy loss caused by the ILFs on pack # 2 to pack # 4 H (A/m) H (A/m)
were calculated as the difference between the energy loss of (b) (c)
each pack and that of pack # 1; the results are shown in Fig 8. Fig 6 DHL of the samples under sinusoidal induction at frequency of 50 Hz
The results show that, the lowest increase in total energy loss is and peak flux densities of (a) Bpk=1.7 T (b) Bpk=1.5 T and (c) Bpk=1.3 T
15.1 % for pack # 2 at peak flux density of 1.3 T. Under the
same magnetising condition, percentage increase in the total From (5) the area between the static and dynamic hysteresis
energy loss of pack # 4 is 66.6 %. The highest loss increase was loops, corresponding to the second term of model (7), represents
observed for pack # 4 at peak flux density of 1.7 T, which is the dynamic energy loss per cycle (𝑊𝑑𝑦𝑛 ). The dynamic energy
76.6 %. In the IEEE standard 62.2-2004 [29] it is recommended loss per cycle was calculated for each sample for the range of
that ILFs, which result in 5 % increase in total core loss (or result flux densities. Ratio of the dynamic energy loss to the total
in a hot spot 10° C above the ambient after 2 hours test), should energy loss was also calculated. The results are shown in Figs 9-
be identified as critical fault. The experimental results showed a and 9-b, respectively.

4
 Fig 9 shows that for pack # 1, with no ILF, the dynamic energy 0.64 − 1.7 < 𝐵 < −0.5
loss counts for about 50 % of the total energy loss, for all flux
densities. However, dynamic energy losses are increased to 0.60 − 0.08 𝐵 − 0.5 < 𝐵 < 0.7
about 55 %, 65 % and 72 % for pack # 2, pack # 3 and pack # 4, 𝑔𝑑𝑦𝑛2 (𝐵) = (9)
respectively. This proves the initial conclusion that, ILFs have a 0.55 0.7 < 𝐵 < 1.4
direct impact on the dynamic energy loss of the magnetic cores.
350 { −25.3 + 12𝐵(3 − 𝐵) 1.4 < 𝐵 < 1.7
Total energy loss, Wtot (J/m3 per cycle)

Pack # 4 Pack # 3 𝑔𝑑𝑦𝑛3 (𝐵) =

300 0.75 − 1.7 < 𝐵 < 0.3
Pack # 2 Pack # 1
250 (10)
0.72 − 0.18𝐵(𝐵 − 1.4) 0.3 < 𝐵 < 1.4
200
{ −13.4 − 7.4𝐵(𝐵 − 2.8) 1.4 < 𝐵 < 1.7
150
𝑔𝑑𝑦𝑛4 (𝐵) =
100
0.65(1 + 0.1 𝐵2 ) − 1.7 < 𝐵 < −1.0
50
0.98 + 0.11𝐵(𝐵 + 3.3) − 1.0 < 𝐵 < 0.4 (11)
0
1.2 1.3 1.4 1.5 1.6 1.7 1.8
0.87 − 0.66𝐵(𝐵 − 1.4) 0.4 < 𝐵 < 1.4
Peak flux density, Bpk (T)

Fig 7 Total energy loss of the samples { −12.4 − 7.3𝐵(𝐵 − 2.7) 1.4 < 𝐵 < 1.7

150 Dynamic energy loss, Wdyn (J/m3 per cycle) 250

Extra energy loss, Wext (J/m3 per cycle)

Pack # 4 Pack # 4 Pack # 3

125 Pack # 3 Pack # 2 Pack # 1
200
Pack # 2
100
150
75
100
50

25 50

0 0
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Peak flux density, Bpk (T) Peak flux density, Bpk (T)
Fig 8 Extra energy losses of pack # 2 to pack # 4
(a)
V. MODELLING RESULTS 100
Pack # 1 Pack # 2 Pack # 3 Pack # 4
DHLs of the samples were reproduced using model (7). Based
on a trial-and-error method, it was found that a constant
75
exponent of 𝛼𝑑𝑦𝑛 (𝐵𝑝𝑘 ) = 0.57 is acceptable for all samples and
flux densities. Function 𝑔𝑑𝑦𝑛 (𝐵) was constructed for each
Wdyn/Wtot (%)

portion of the measured DHLs to coincide the calculated and 50

measured loops. Due to the distinct shape of the DHLs of
pack # 2 to pack # 4, function 𝑔𝑑𝑦𝑛 (𝐵) was found considerably
different, and more complicated, than that for pack # 1. The 25
following computational functions for 𝑔𝑑𝑦𝑛 (𝐵) were found
acceptable at a peak flux density of Bpk=1.7 T for pack # 1 to
pack # 4, respectively. 0
2) 1.3 1.5 1.7
0.5(1 + 0.2 𝐵 − 1.7 < 𝐵 < 0
Peak flux density, Bpk (T)
𝑔𝑑𝑦𝑛1 (𝐵) = { (8)
(b)
0.46 − 0.18𝐵 0 < 𝐵 < 1.7 Fig 9 (a) Dynamic energy loss of the samples (b) Ratio of the dynamic
energy loss to the total energy loss

5
 The measured and calculated DHLs of pack # 1 to pack # 4 Fig 11 shows that the calculated DHLs coincide with the
under sinusoidal induction at magnetising frequency of 50 Hz measured loops for the range of measured flux density. Total
and a peak flux density of Bpk=1.7 T are shown in Figs 10-a to energy losses per cycle from the modelled and measured DHLs
10-d, respectively. For comparison, the measured SHLs of the were calculated for all samples and flux densities. A comparison
samples, which represents the hysteresis energy loss, are shown between the results and the percentage difference between the
for each sample. values are shown in Figs 12-a and 12-b, respectively.
1.8 1.8 1.8 1.8

1.2 1.2 1.2 1.2

0.6 0.6 0.6 0.6

Flux density, B (T)

Flux density, B (T)

Flux density, B (T)

Flux density, B (T)

0.0 0.0 0.0 0.0

-0.6 -0.6 -0.6 -0.6

-1.2 -1.2 SHL -1.2 -1.2

SHL
Meas. Meas. Meas. Meas.
Model (7) Model (7) Model (7) Model (7)
-1.8 -1.8 -1.8 -1.8
0 50 100 0 50 100 0 50 100 0 50 100
H (A/m) H (A/m) H (A/m) H (A/m)
(a) (b) (a) (b)
1.8 1.8 1.8
1.8

1.2 1.2 1.2

1.2

0.6 0.6 0.6

0.6

Flux density, B (T)

Flux density, B (T)
Flux density, B (T)

Flux density, B (T)

0.0 0.0 0.0 0.0

-0.6 -0.6 -0.6 -0.6

-1.2 -1.2 -1.2 -1.2

SHL SHL
Meas. Meas. Meas. Meas.
Model (7) Model (7) Model (7) Model (7)
-1.8 -1.8 -1.8 -1.8
0 50 100 0 50 100 0 50 100 0 50 100
H (A/m) H (A/m) H (A/m) H (A/m)
(c) (d) (c) (d)
Fig 10 Comparison between the measured and modelled DHLs at peak flux Fig 11 Comparison between the measured and modelled DHL at
density of Bpk=1.7 T (a) pack # 1 (b) pack # 2 (c) pack # 3 and (d) pack # 4 magnetising frequency of 50 Hz and peak flux densities of 1.3 T, 1.5 T and
1.7 T (a) pack # 1 (b) pack # 2 (c) pack # 3 and (d) pack # 4
As can be seen from Fig 10, model (7) grants a fairly accurate
basis to calculate the DHLs of the samples by which the total Fig 12 shows a close agreement between the calculated and
energy loss can be calculated. The same procedure as for peak measured losses, with a maximum difference of less than 4 %
flux density of Bpk=1.7 T was implemented to calculate the for all flux densities, as shown in Fig 12-b. Therefore the
DHLs at peak flux densities of Bpk=1.3 T, Bpk=1.5 T. A developed models, based on the two terms model of (7), show a
comparison between the calculated and measured DHLs at fairly accurate and reliable technique to reproduce the DHLs of
magnetising frequency of 50 Hz and peak flux densities of magnetic cores subjected to ILFs, and hence for energy loss
Bpk=1.3 T, Bpk=1.5 T and Bpk=1.7 T are shown in Figs 11-a to calculations and core quality assessment purposes.
11-d, respectively.

6
 For the designer of the electrical machines and transformers, additional measurements on the SHLs. This is an effective
it is of high importance to develop strategic skills and technique to monitor the overall condition of the magnetic cores.
knowledge to safeguard the magnetic cores against ILFs at the A new analytical approach was also developed to reproduce
design stage. The developed model can provide a reliable figure the DHLs of the magnetic cores with ILFs. The accuracy of the
of effects of typical ILFs on the magnetising processes, energy method was validated on stacks of four laminations subjected to
loss and energy loss components of magnetic cores with GO different kinds of ILFs. A close agreement, with a maximum
materials. difference of less than 4 %, was found between the calculated
350 energy loss obtained from the developed approach and bulk
Measurement
measurements. The developed models can be implemented to
Total energy loss, Wtot (J/m3 per cycle)

300 Calculation evaluate typical ILFs on the hysteresis performance and total
energy loss of magnetic cores of real power transformers and
250
other magnetic devices with GO material.
Pack # 4
200 ACKNOWLEDGMENT
150
The author is grateful to Cogent Power Ltd. for providing the
Pack # 3 electrical steel sheets, and Wolfson centre for magnetics at
100 Cardiff University for the experimental work.
Pack # 2
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BIOGRAPHY
H. Hamzehbahmani received the BEng and MEng
degrees in electrical engineering in 2005 and 2007,
respectively; and PhD degree in electrical engineering
from Cardiff University, UK in 2014. Between 2005 and
2010 he worked on distribution networks and HV
substations as a consultant engineer. Following his PhD
he was appointed as a research associate at Cardiff
University in the field of earthing systems for HVAC and
HVDC systems. From 2016 to 2018 he was a lecturer in electrical engineering
with Ulster University in UK. He is currently an assistant professor in electrical
engineering at Durham University. His main research interest includes magnetic
materials and applications, power loss analysis and condition monitoring of
transformers and electrical machines, high frequency and transient response
analysis of earthing systems, earthing design of HVDC networks.