Download Demagnetisation of CT cores under exposure of operating currents

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Demagnetisation of CT cores under
exposure of operating currents
by Dr. Fred Steinhauser, Omicron
Saturated CT cores and their behavior during fault conditions have been and still are an important topic for protection engineers, in particular
when fault currents with transient components occur. Many papers have been written and presented about this. Typically, the CT cores contain
some residual magnetism when the current flow is interrupted. Especially at reclosing, this residual magnetism may cause undesired effects.
In this context, the question "How will the
magnetisation in the CT develop when
power is restored and the CT is exposed to
normal operating currents?" is frequently
raised. Surprisingly, the answer is often
based on opinion, it is even said this may
be a "matter of philosophy". Statements
like "some say the saturation level remains
there forever, some say it will go away
over time" can be heard. Much of what
is said is based on assumptions, models
and simulations. But for engineers, there
must be a better way than relying "on
philosophy". The recognised method is to
look for plain facts and align them with
proven theories. For this paper, systematic
measurements have been made to put
some light on this matter.
Fig. 1: Injecting current on the secondary winding
of the CT for magnetising the core.
Practical implications
Measuring residual flux can be a
cumbersome procedure [6]. In the
past, it was hardly feasible to perform a
large number of such measurements in
reasonable time. Also, for establishing a
relationship between a measured residual
flux and the conditions that caused this
residual flux, the full previous history (the
anamnesis) of the CT must be known.
Even if the fault records were available for
some arbitrary cases of saturated CTs, this
is not a systematic approach for reliably
determining a correlation of effects.
Another problem is that the established
methods for determining the residual flux
result also in a destruction of the residual
flux [3]. It is not possible to resume the
test at the most recent point. Thus, every
single measurement has to start from the
de-magnetised state, first bringing the
CT into a defined state of magnetisation
(applying a defined residual flux). Then,
some other condition which may alter
the residual flux may be applied. Then,
this residual flux is to be measured. Each
of the steps involved must be performed
with adequate precision and repeatability.
Modern test equipment allows for precise
application of the test quantities for
each of these steps and performing the
measurements in reasonable time to make
a systematic series of tests feasible.
Establishing a defined magnetisation
The first step for performing measurements
with residual magnetism is to apply a
Fig. 2: Magnetisation along the initial magnetisation
curve and the hysteresis curve.
Fig. 3: Setup for measuring the residual flux.
defined initial magnetisation to the CT
core. It is assumed that we start with a
demagnetised core. In our case, this
condition is fulfilled without further efforts,
since the measurement device for the
residual flux leaves the core demagnetized
after the measurement.
Then, a DC current is applied as shown
in Fig. 1. The primary side of the CT is an
open circuit, so the injected current equals
the excitation current through the main
inductance of the CT. As its magnitude is
increased, the magnetisation will develop
along the initial magnetisation curve.
This residual flux is then measured. This
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can be conveniently achieved with a test
set with dedicated residual magnetism
measurement features as shown in Fig. 3.
Since the values scatter slightly from
measurement to measurement, some
averaging has to be applied to get reliable
values. Fig. 4 shows how the residual
magnetism depends on the excitation
current applied for magnetising the core.
Using this method, it is possible to establish
a well defined magnetisation of the core
as a starting condition for the tests. To
make the results more independent from
the actual ratings of the specific CTs, the
quantities are normalised. The currents are
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Fig. 4: Residual flux vs. magnetisation current.
Fig. 5: Equivalent circuit of the CT with burden.
Fig. 6: Reduction of the residual magnetism
when applying nominal current.
referred to the kneepoint current I k, which
is the exciting current at the knee point
voltage. The residual flux Q res is referred
to the saturation flux Q s and expressed
as the residual magnetism. The residual
magnetism is defined as :
‫ܯ‬௥ = 100% ή ܳ௥௘௫ /ܳ௦
(1)
The reference values I k and Q s used
here are those obtained according
to IEC 60044-1 [1]. These values are
measured under special conditions and
var y depending on the standard and
method used for determining them. But the
actual standard which is used to determine
these reference values is not so crucial;
some other values would just lead to a
different scaling of the diagrams, leaving
the essence of the statements unaffected.
Demagnetisation
The goal of this work is to investigate how
the magnetisation of the saturated core
is affected by normal operating currents.
Therefore, conditions as under nominal
currents shall be applied.
Applying nominal currents at the primary
side is difficult. While it might be feasible
for steady state conditions, it is not possible
to produce such currents with the dynamic
behavior as required for the following
tests, e.g. for a defined time or even for
a defined number of cycles. The current
further modifying the magnetisation
of the core is again applied on the
secondary side as shown in Fig. 1 for the
magnetisation. As the primary side is an
open circuit, the current injected equals
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the magnetisation current through the
main inductance L m
Estimating the nominal current
Fig. 5 shows the circumstances in the
loaded CT at nominal conditions. The
secondar y current flows through the
secondar y CT impedances and the
burden, producing a voltage drop U m,nom
which occurs at the main inductance.
With the total secondary impedance
ܼ௦ = ݆߱‫ܮ‬ఙ,௦ + ܴௌ + ܼ஻
(2)
the magnitude of the magnetisation
current at a given burden ZB can be easily
calculated:
‫ܫ‬௠,௡௢௠ = ‫ܫ‬௦,௡௢௠ ή
ܼௌ
߱‫ܮ‬௠
Fig. 7: Reduction of the residual magnetism at different frequencies.
(3)
As it has to be expected for a reasonable
CT, this is a fairly small current, only a few
percent of the knee-point current. In reality,
this means only a few milliamperes.
Demagnetisation with injected current
The current source injects a sinusoidal
current into the secondar y winding. As
long the compliance voltage of the current
source is not exceeded, the voltage
adapts to the load impedance and the
current is kept constant. As the secondary
impedances are almost negligible
compared to the impedance of the main
inductance, the voltage measured at the
terminals is almost identical to the voltage
at the main inductance and according to
hysteresis curve. It must be noted that this
injection of a defined current is different
from the procedures described in most
standards, such as IEC 60044-1, where a
sinusoidal voltage is applied and a current
with potentially non-sinusoidal waveform
is obtained.
Fig. 8: Voltages (top and middle trace) and current (bottom trace)
when applying nominal current to the magnetised CT.
This current Im,nom was now applied to the
CT for a few seconds and the remaining
residual magnetism was measured. It
was significantly reduced from the value
established through the magnetisation. This
was a first finding, but further measurements
with longer exposure time of the nominal
current showed the same result, the
residual magnetism did not drop further.
Consequently, the exposure time was
reduced until a change of the measured
residual magnetism could be observed.
It turned out that the time interval to be
considered is less than 1 s or only a few
cycles.
Fig. 6 shows how the residual magnetism
develops under the application of a
current of about nominal magnitude.
The process is more or less completed
after about 20 cycles and the residual
magnetism is roughly reduced to half of
the initial value. This result could be used to
get to an answer to the question raised in
the motivation. And as in most cases, the
extremes (stays forever / goes away) do not
apply and the actual circumstances might
depend on many other parameters which
were not considered in the measurement.
The insight summarised in Fig. 6 is not
Fig. 9: Magnetisation changing during the first
cycle at a frequency of 10 Hz.
unique and not new. There are several
publications [2, 3, 4], one of them dating
back almost 70 years that describe similar
findings. Some of these statements shall be
briefly reviewed here.
Reference [2] contains a statement, called
a hypothesis, which nicely resembles what
was concluded above: "This residual flux
remains in the current transformer core
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practically undiminished unless the circuit
is loaded, in which case it is decreased
gradually but not usually removed entirely."
It describes one specific case where a CT
was magnetied to a certain value and
then exposed to a current of 5 A for 24
hours.
After this, the residual flux had been
reduced to about 31% of the initial
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magnetisation. At the time when this experiment was made,
it would have been probably ver y difficult to find out that
the same reduction would have occurred most likely after 24
cycles and not only after 24 hours. Reference [3] displays some
oscillographic recordings which indicate that most of the change
of the residual magnetism takes place in a few dozen cycles.
Reference [4] states that under the flow of rated current the
residual flux in CTs is reduced to 60% to 70% of the remanent
flux within a few seconds. So far, the measurements and results
described are just in line with the state of the art.
Frequency dependency of the effect
For the measurements described above it was implicitly
assumed and therefore not explicitly mentioned that the
current applied for changing the magnetisation of the core had
nominal frequency, in this case 50 Hz. But it turns out that the
reduction of the magnetisation is essentially more significant if
the frequency of this current is lowered. Fig. 7 shows how the
residual magnetism develops for different frequencies of the
applied current.
The initial magnetisation was established with I mag = 2I k, so the
yellow curve (for 50 Hz) is identical to the lower curve in Fig. 6.
The residual magnetism is already heavily reduced at 20 Hz
(red curve), and it is essentially removed at 10 Hz after only 5 to
10 cycles (blue curve). The observed differences in the levels
of the residual flux are remarkable. Obviously, the magnetic
properties of the core material are very differently involved at
the different frequencies.
A further attempt to visualise this is to look at the voltages that
occur at the CT when the current is applied. The current is
injected from a current source, imposing the sinusoidal waveform
of the current. Any influence from the core material will become
visible in the waveform of the voltage. Recorded waveforms from
two cases are shown in Fig. 8. The lower (yellow) trace shows
the injected current. As explained above, it is sinusoidal and the
burst contains exactly five cycles.
The special scaling axes in Fig. 8 must be kept in mind. The
horizontal axis shows the angle (Tt), giving the same distance
for a cycle independent of frequency. As the frequencies are
different by a factor of 5, the voltage ranges are also different
and not to scale.
The upper (red) trace is the voltage at 50 Hz. After the first cycle,
the waveform is close to sinusoidal, not showing much of a visible
effect from the hysteresis of the core material. The middle (blue)
trace is the voltage at 10 Hz. Its waveform is visibly affected
from the hysteresis. The first cycle at 10 Hz is where the largest
change in the residual magnetism occurs. This is illustrated in
Fig. 9 in detail.
By performing an integration of the voltage and appropriate
scaling, the approximate course of the residual magnetism over
the applied current can be constructed. The current value on
the horizontal axis is referred to I max, which is the peak value of
the sinusoidal current applied. During the positive half wave of
the current, the magnetisation curve describes a small hysteresis
loop superimposed to the remanence point established by the
initial magnetization. At the end of the positive half wave, the
magnetization is more or less back where it started off when the
current was applied.
During the negative half wave, the magnetisation is heavily
eroded as long the magnitude of the current is increasing. But
even when the current moves back toward zero after reaching its
maximum value, the magnetization becomes further decreased
until the positive zero crossing of the voltage takes place.
An attempt for an explanation
So, why can such different behaviour be observed at frequencies
not higher than the rated frequency? Or is the rated frequency
already a "considerably high" frequency when it comes to the
demagnetizing effect of a magnetic field caused by a rated
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of the magnetic material from the outer
field. The effects of the eddy-currents
become essential when the frequency of
the outer field is approaching the Wolman
frequency:
݂௪ =
Fig. 10: Locus of the complex permeability (solid:
measurement; dashed: calculation) [7].
current? This thought shall be further pursued
and some reasoning shall be given. One
approach is reference [7] that does not
aim at the magnetic polarisation issue, but
focuses on the frequency dependency of
the permeability instead.
The key point is that this paper gives
insight how the magnetic field penetrates
magnetic sheet metals as used for
transformer cores. It is well known that
eddy-currents occur when a magnetic
material is exposed to a changing outer
magnetic field. These eddy-currents build
by themselves a magnetic field that is
opposed to the outer field. By doing so,
the eddy-currents shield the inner portions
4
‫݌‬
ή
ߨ ߤ஺ ݀ଶ
(4)
The formula applies for sheet metals, where
D is the specific resistance of the material,
d is the thickness of the sheet, and A is
the "overall initial permeability" which is
used throughout the calculations in the
mentioned paper. This Wolman frequency
can assume surprisingly low values. For
typical materials and thicknesses of the
laminated core material, it can be as
low as only a few hundred Hertz or even
below. Fig. 10 from [7] shows the locus
of the complex permeability [8, 9] as
a function of frequency for a chromepermalloy sheet metal. The frequency
is referred to the Wolman frequency.
The vertical axis represents the inductive
component, while the horizontal axis
represents the resistive component. The
resistive component is connected to the
eddy-current losses. Reference [7] is very
challenging, containing more than 50
numbered equations for mathematically
encompassing the effects. Fig. 11 shows
the local permeability over the cross
section of the sheet metal.
On the surface, the local permeability is
zero and increases when going deeper
into the material. The local permeability
is essentially affected by the outer field
only within a certain depth of about the
value S, which characterises where the
local permeability reaches the value
of the overall initial permeability. The
permeability remains at high levels in a
large inner portion of the sheet, because it
is effectively shielded by the eddy-currents
and not exposed to the outer field.
In the case of an outer field resulting from
an operating current in a CT, this inner
portion of the core material is not involved
in the demagnetisation process and
remains magnetised at its former level.
The value of S is inversely proportional to
f 2. So for lower values of f, S increases and
more of the material becomes involved
in the demagnetisation process, which
would explain the effects shown in Fig. 7
and Fig. 8. Thus, even when the sheets in a
laminated transformer core are obviously
thin enough for reducing the eddy-current
losses to an acceptable level, the sheets
may still appear to be thick when it comes
to the penetration by an outer field of rated
frequency.
Conclusions
Referring to the question raised in the
motivation section, a rough answer can be
given: The magnetisation of a saturated CT
core exposed to normal operating currents
will neither "remain there forever", nor will
it completely "go away over time". The
actual degree of the demagnetisation
due to operating currents depends on
several parameters, which were not all
investigated in detail.
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Fig. 11: Local permeability over the cross section
of a 36% Nickel-Iron sheet of thickness dE [7].
Given the observed speed of the
demagnetisation (only a few cycles
in some cases), it might be realistic
that saturation effects will be quickly
diminished in a CT core at reclosing after
successful fault clearing. The explanations
and conclusions given above could
be verified by systematic repetition
of the measurements with other CTs,
preferably with the exact knowledge of
the construction.
There is the question if the use of thinner sheet
metals in the core yields in more effective
demagnetisation due to operating currents
and better recovery after saturation. This
could be investigated by comparing
CTs with cores with different lamination
thickness at otherwise identical data. This
approach may collide with a statement
from reference [5] that points out that
"the eddy current loss in a laminated core
may increase if the lamination thickness
is reduced". The overall optimum for the
technical compromise may depend on
how important an improvement of the
recovery behaviour is regarded compared
to other properties of a CT.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
IEC 60044-1, Instrument transformers – Part1:
Current transformers. Ed. 1.2, IEC, Geneva
2003.
HT Seeley: “The Effect of Current- Transformer
Residual Magnetism on Balanced-Current or
Differential Relays.” AIEE Trans., Vol. 62, April
1943.
RG Bruce, and A Wright: “Remanent Flux
inCurrent-Transformer Cores.” Proc. IEE, Vol.
113, No. 5, May 1966.
J Dickert, et al: “Investigation on the Behaviour
of the Remanence Level of Protective Current
Transformers”. MEPS'06, Wroclaw 2006.
SK Mukerji, et al: “ Eddy C u r r e n t s in
Laminated Rectangular Cores.” Progress In
Electromagnetics Research, PIER 83, 2008
M Pfannenstiel: Residual magnetism of
current transformers, OMICRON ITMF, 2010.
R Feldtkeller: Permeabilität und Wirbelströme
in Blechkernen bei sehr hohen Frequenzen.
Frequenz, Band 3/1949 Nr.4.
R Boll, Weichmagnetische Werkstoffe.
Vacuumschmelze GmbH. 4th Edition, 1980.
L Michalowsky, J Schneider: Magnettechnik.
Vulkan-Verlag GmbH. 3rd Edition, 2006.
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