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ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013
Inductive Sensor Parameters Important for Partial
Discharge Measurement
Jozef BALOGH, Jaroslav PETRÁŠ∗
Abstract
Monitoring of partial discharge activity in insulation systems of high voltage and very high voltage electric power
devices can be made by galvanic method, but additionally there are alternative methods, such as measurement
by inductive sensors or acoustic method. For inductive indirect method we needed to design linear sensors that
are ideal for partial discharge source localization and toroidal sensors that are used for partial discharge activity
measurement due to their electro-magnetic and geometric parameters. In order to test parameters of these
sensors we had to find a method to measure them. (Parameters of inductive sensors for partial discharge
activity measurement).
Keywords: toroidal sensor, induction sensor, partial discharges
1. Introduction
Partial discharge measurement is one of
the often used methods of insulation system
diagnostics. This method has a fixed place
in the set of diagnostic measurement
methods used for insulation system
condition determination in high voltage
electric power devices [8,10].
We developed inductive sensors for
partial discharge detection and monitoring in
insulation systems which have two different
construction types: linear [1] and toroidal
type [2], [3].
Inductive toroidal sensors are used for
leakage current measuring at frequency of
50 Hz and they are connected into working
grounding of the object under test. They
exploit a current changer function. A signal
from
sensor
winding
on
toroidal
ferromagnetic core is furthermore evaluated
by computer technology.
2. Toroidal sensor principle
A toroidal inductive sensor is designed
with respect to its location and placement,
shape and way of connection into working
grounding circuit of the measured object.
Supposing two current circuits that are
∗
Jozef BALOGH, PhD., TU Košice, FEI, Department of
Electric Power Engineering, Mäsiarska 74, 040 01 Košice,
Slovak Republic, [email protected]
Jaroslav PETRÁŠ, Ing. PhD., TU Košice, FEI, Department
of Electric Power Engineering, Mäsiarska 74, 040 01
Košice, Slovak Republic, [email protected]
electro-magnetically connected (Figure 1),
Figure 1. Inductive toroidal sensor
we can get an equation in ideal case for
output voltage:
u 2 = −i2 .R2 − L2 .
di2
di
+ M 12 . 1
dt
dt
(1)
where R2 and L2 parameters represent
measurable values of effective resistance
and self-inductivity of the coil, and M12
represents common inductivity between
circuits 1 and 2.
Outgoing from real conditions, it is
obvious that the measurement of the current
i1 flowing through the conductor can be
made by measuring u2 voltage on the
clamps of coil with winding number N2
ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, nr. 1, ianuarie-martie 2013
(secondary winding), and on input resistor
Rm of the amplifier (u2=Rm.i2). Because of
exactness of the measurement it is
necessary that the windings were uniformly
placed on the ringlet with the shape of
rectangular cross-sectioned toroid. A
conductor with primary current flowing
through it with unknown value i1 runs
through ringlet hole in arbitrary surface. The
current i1 induces in secondary winding a
voltage u2:
u2 = − M 21. didt1
(2)
This voltage u2 induces in closed
secondary winding a current i2. It must be
noticed that M12 = M21. Voltage u2 is equal to
the sum of i2R2 voltage descent on R2
resistance and on the L2 inductance:
− M 21. didt1 = i2 R2 + L2 . didt2
(3)
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By calculation, we suppose that the
current is only in secondary circuit and we
search for induction flow Ψ1M supplied by
this current which flows trough the surface
delimited by primary circuit. If the secondary
circuit is winded uniformly and relatively
narrowly on the ringlet, each induction line
of the flow Φ induced by current i2 runs
through all the secondary windings. Each
induction line of this flow enlaces once the
conductor of the primary current despite of
complicated shape of the conductor.
In this case, the equation Ψ1Μ=Φ is valid.
As can be found in Kalantarov-Nejman [5],
for toroid with dimensions on Figure 1, the
next equation is valid:
Ψ1 M = Φ =
μ 0μ r
2π
. N 2 i 2 h ln
r2
r1
(8)
where:
By integrating this equation and
supposing that for i1=0 is i2=0 we can get:
- permeability of vacuum (1,256.10-6
H.m-1),
μr – relative permeability of magnetic
core,
N2 - number of secondary windings,
h - toroid height,
r1, r2 - inner and outer radius of the
toroid.
For reciprocal induction coefficient, we
can write [4]:
i2 = − ML221 .i1 = − k .i1
M 12 = M 21 =
Voltage drop on resistor (i2R2), especially
at higher frequencies, is neglectable in
comparison to self induced voltage in
secondary circuit. Therefore:
− M 21. didt1 = L2 . didt2
(4)
(5)
where k is transform coefficient. If we want
to calculate, it we have to know the
coefficient of reciprocal induction M12, which
represents the inductive acting of the first
current circuit on the second circuit. The
coefficient M21 is defined by equation [6]:
M 21 =
Ψ2M
i1
(6)
In order to calculate directly the
reciprocal coefficient of induction M21
according to the equation above we have to
define first the allover flow Ψ2M, which run
through the second circuit with condition
that in the first circuit flows the current i1.
However the complicated shape of the
primary circuit disables the straightforward
calculation of the flow Ψ2M.
In this case, the equation M21=M12 does a
good job for us. The definition of M12 is
according to:
M 12 =
Ψ1 M
i2
(7)
μ0
Ψ1Μ
2π
=
μ 0μ r
2π
. N 2 h ln
r2
r1
(9)
The coefficient of self-induction L2 for
winding of toroid reads:
L2 =
μ 0μ r
2π
.N 22 h ln rr12
(10)
The transform coefficient k can be
expressed in this way:
k=
M 21
L2
=
1
N2
(11)
In general, if the the primary current
conductor runs trough the hole of the ringlet
N1-times, the transform coefficient will be:
k=
N1
N2
(12)
An important attribute of this alignment is
that its transform coefficient does not
depend on the shape of the primary current
conductor.
By application of the knowledge as
mentioned above, we can say that all
conditions for small AC current and pulse
ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013
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current measurement are fulfilled. Inductive
sensor should be connected to the
secondary winding circuit and to the circuit
with high input impedance (Figure 2).
Usually, the signal of partial discharge
activity in insulation cavities has a pulse
character and the amplitude a duration of
this pulse depend on various factors. A
signal emitted from insulation system can be
captured by resonance circuit.
On Figure 4, there is depicted a current
pulse created in insulation material cavity
[6].
Figure 2. Detection circuit with inductive sensor
A low number of windings ensures high
resistance against external noises. From the
mentioned above conditions, it results that:
i2 =
N1
N2
.i1
(13)
If N1=1, then i2 represents N2-times
smaller part of the measured current i1.
For operation in AC electric fields or in
dynamic modes, some magnetic materials
are appropriate with coercive strength
Hc~800 Am-1. They are used for the weakest
magnetic fields and are very easy to
magnetize or demagnetize. They also have
narrow hysteresis loop, high value of initial
and maximal permeability (80 to 100
thousands) and small measured losses.
3. Linear sensor principle
Linear sensor has to be placed into
electromagnetic field of the radiated signal
so that the vector of magnetic induction B
and magnetic intensity H are oriented into
the axis of the sensor (Figure 3).
I
H
B
Figure 4. Current pulse of streamer discharge [7]
This pulse can be captured by above
mentioned circuit (as seen on Figure 5).
Figure 5. Transmitter and receiver of discharge current
pulse signals
We
can
solve
this
situation
mathematically by the help of modeled
circuit and Dirac function.
If we replace the signal transmitter by DC
source that is connected for a short time to
a capacitor C, we can assume that in time
t=0 a source with voltage U0 is connected
(with initial conditions i(0)=0 and charge on
capacitor Q(0)=0.
We can solve the current in circuit in time
t>0.
Voltage has the shape U0δ(t). Then, the
equation for the circuit is:
t
U
L + Ri +
di
dt
1
C
∫ idt = U δ(t )
0
0
Lpi + Ri + Cp1 i = U 0 .1
Figure 3. Linear shaped inductive sensor
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ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, nr. 1, ianuarie-martie 2013
(Lp
2
+ Rp + C1 )i = U 0 p
4. Conclusions
p
i = L ( p 2 U+ R0 pp + 1 ) = UL0
2
( p + 2RL ) + LC1 − 4RL22
L
LC
We assume that:
1
R2
− 2 = ω2
LC 4 L
i = UωL0 ( p+p+aa)2−+aω2 = ωUL
i=
U0
ωL
(e
− at
R
2L
[
p+a
( p+a)2 +ω2
17
=a
− ω1 ( p+aa)ω2 +ω2
]
cos( ω t ) − ωa e − at sin( ω t ) )
These equations result in a current signal
that is dumped with signal envelope e-at, as
can be seen on Figure 6. a).
Economical aspects have forced the
usage of linear sensor type as more
advantageous.
Their
advantage
in
comparison to toroidal type lies in the fact
that we do not have to disconnect the circuit
before measurement by linear sensor type.
Using this type of sensors for partial
discharge measurement can complete the
widely used direct galvanic method. It is
possible to measure the device without
disconnecting it from operation [9].
5. Acknowledgment
We support research
activities in Slovakia /
Project
is co-financed from EU funds. This paper was
developed within the Project "Centrum
excelentnosti integrovaného výskumu a využitia
progresívnych materiálov a technológií v oblasti
automobilovej elektroniky", ITMS 26220120055
6. References
Figure 6. Current signal: a) in resonance circuit; b) signal
spectrum
The current i invokes on amplifier input
voltage drop ΔU with the same signal shape
(Figure 6).
As the condition R2/4L2, 1/LC is usually
fulfilled we can state that the angle velocity
equals to ω ≈ 1 / LC .
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K.:
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ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 61, Nr. 1, ianuarie-martie 2013
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7. Biography
Jozef BALOGH graduated TU
Košice, FEI in 1991.
He received the PhD degree in
2001.
His research interests concern:
partial discharge measurement methods,
overvoltage protection and renewable energy
exploitation.
Jaroslav PETRÁŠ graduated TU
Košice, FEI in 1997.
He received the PhD degree in
2008.
His research interests concern:
partial discharge measurement by acoustic
methods and renewable energy exploitation.