Propagation of Overvoltages in the Form of Impulse, Chopped and Oscillating Waveforms in Transformer Windings

energies
Article
Propagation of Overvoltages in the Form of Impulse,
Chopped and Oscillating Waveforms in Transformer
Windings—Time and Frequency Domain Approach
Marek Florkowski , Jakub Furgał and Maciej Kuniewski *
Department of Electrical and Power Engineering, AGH University of Science and Technology,
al. Mickiewicza 30, 30-059 Kraków, Poland; [email protected] (M.F.); [email protected] (J.F.)
* Correspondence: [email protected]
Received: 26 November 2019; Accepted: 5 January 2020; Published: 8 January 2020
Abstract: This paper describes a comparison of overvoltage propagation in transformer windings.
Expanding and evolving electrical networks comprise various classes of transient waveforms, related
to network reconfigurations, failure stages and switching phenomena, including new sources based on
power electronics devices. In particular, the integration of renewable energy sources—mainly solar and
wind—as well as expanding charging and energy storage infrastructure for electric cars in smart cities
results in network flexibility manifested by switching phenomena and transients propagation, both
impulse and oscillating. Those external transients, having a magnitude below the applied protection
level may have still a considerable effect on winding electrical insulation in transformers, mainly
due to internal resonance phenomena, which have been the root cause of many transformer failures.
Such cases might occur if the frequency content of the incoming waveform matches the resonance
zones of the winding frequency characteristic. Due to this coincidence, the measurements were
performed both in time and frequency domain, applying various classes of transients, representing
impulse, chopped (time to chopping from 1 µs to 50 µs) and oscillating overvoltages. An additional
novelty was a superposition of a full lighting impulse with an oscillating component in the form of a
modulated wavelet. The comparison of propagation of those waveforms along the winding length
as well as a transfer case between high and low voltage windings were analyzed. The presented
mapping of overvoltage prone zones along the winding length can contribute to transformer design
optimization, development of novel diagnostic methodology, improved protection concepts and the
proper design of modern networks.
Keywords: transformer windings; lightning; chopped; oscillating impulse; overvoltages; modulated
wavelet; non-standard voltage waveforms
1. Introduction
Reliability of electric power systems, on both transmission and distribution levels, is an actual
research topic [1–12]. Transformers play a crucial role in electrical networks and belong to the
class of equipment which is not quickly replaceable. The subject of the presented research is the
propagation of overvoltages in the form of impulse, chopped and oscillating waveforms in transformer
windings, considered both in the time and frequency domain. The experiments were performed on
a distribution transformer exposed during normal operational conditions to several surge stresses
in the form of full and chopped lightning as well as switching phenomena. On the other hand, the
integration of renewable energy sources, such as solar and wind, and expanding charging and energy
storage infrastructure for electric cars results in network reconfiguration and the immanently related
propagation of transients, both impulse and oscillating, originating in power electronics devices.
Energies 2020, 13, 304; doi:10.3390/en13020304
www.mdpi.com/journal/energies
Energies 2020, 13, 304
2 of 16
Hence, transformers are subjected to the non-standardized fast transients such as resonant
oscillations, which may lead to the dangerous amplification of overvoltages inside the windings [3,13].
Proper transformer grounding should also be not neglected, which in case of lightning, may result in a
higher total impedance and can lead to higher transformer terminal voltages than those computed by
ideal grounding [14].
The frequency domain view allowed for the determination of the bands in the spectrum prone
to resonances. If the incoming transient has a frequency content related to the resonance frequency zone,
then the overvoltage amplification inside a winding might occur. Such cases are analyzed in the paper for
various classes of the waveforms. The amplification or attenuation of overvoltages are analyzed along
the transformer winding and also from the high voltage (HV) winding to low voltage (LV) side transfer
perspective. Such tests of voltage exposure and overvoltage propagation allow a check of transformer
immunity and are related to both distribution and power units. In the case of power transformers,
standards [15–19] also require compliance with tests based on tail chopped lightning impulse. This kind
of extended testing is recommended in configurations where the transformer is protected by a spark-gap
or is operating in connection to a gas insulated substation. Power transformer units for a grid above
170 kV are checked routinely applying chopped lightning impulse, usually with a time delay to
chopping in the range 3 µs and 10 µs [15,16,20]. Presented measurements were conducted both for a
full impulse and chopped one, with the time delay to chopping from 1 µs up to 50 µs.
Another class of transient stresses is addressed by a rectangular impulse with a variable rise time,
reflecting the behavior of power equipment in response to protection devices such as surge arresters.
Above tests are complemented by a superimposed configuration of waveform composed of a full lighting
impulse with an oscillating component, named a modulated wavelet. Such a waveform might mimic,
for example, the oscillating packet appearing at the transformer terminals, propagated by the re-strikes
in circuit breakers. According to the design principles, the peak values of transient overvoltages at
transformer clamps are constrained by the installed protective devices to the level suggested by the
insulation coordination [1,7,21,22]. Those values are much higher than the maximum nominal voltage,
thus the incoming transient containing the oscillating component below the protection level may form
overvoltages inside the insulation system of high voltage equipment caused by internal resonance in
the windings despite the applied surge arresters. Particularly some switching transients, generated
in gas insulated substations, during power making or breaking in lines supplying the transformers,
ground faults or network reconfigurations, including those originated form power electronics, having
oscillating character may cause high amplitude internal overvoltages. The amplitude of the overvoltage
depends on the network topology, attenuation conditions and duration of the oscillating components.
Transformer windings form a complex distributed resistive-inductive-capacitive (RLC) network,
reflecting various internal resonances. Hence, the internal overvoltages recorded along the winding
height may vary from the proportionally attenuated incoming external transients [3,23–27]. For this
reason, study on internal transient waveforms in transformers, subjected to standard and non-standard
excitations, including superimposed waveforms containing oscillating components, are important for
the development of more reliable transformers.
In this context, the mapping of overvoltage prone zones along the winding length can contribute
to the development of proper diagnostic methodology, improved protection concepts and the proper
design of modern networks.
2. Characteristic of Voltage Waveforms Applied to Transformer Winding
In order to achieve a holistic view of test transformer response to various overvoltages, the
following voltage stimulus, graphically illustrated in Table 1, have been applied:
(a)
(b)
(c)
(d)
full lighting impulse,
chopped lighting impulse,
rectangular impulse with a variable risetime,
modulated wavelet, i.e., superposition of a full lighting impulse with an oscillating component.
The lightning impulse waveform Ul can be described by the following double exponential
function:
function:
(1)
𝑈 (𝑡) = 𝑈 [exp(−𝑡/𝜏 ) − exp(−𝑡/𝜏 )]
𝑈 (𝑡) = 𝑈 [exp(−𝑡/𝜏 ) − exp(−𝑡/𝜏 )]
(1)
(1)
) − magnitude.
𝑈 (𝑡)constant
= 𝑈 [exp(−𝑡/𝜏
exp(−𝑡/𝜏 )] For example, in high voltage testing,
where τ1 and τ2 define a time
and U1 the
1 and τ22 define a time constant and U11 the magnitude. For example, in high voltage testing,
where
τ
1
for
the standard
impulse
1.2/50
µsU
the
time constants correspond to τ1 = 0.405 µs and τ2 =
where
τ1 and τ2 lightning
define a time
constant
and
1 the magnitude. For example, in high voltage testing,
for
the
lightning impulse 1.2/50 µs the time constants correspond to τ11 = 0.405 µs and τ322 of
=
68.2
µs.standard
Energies
13, 304
for 2020,
the
standard
lightning impulse 1.2/50 µs the time constants correspond to τ1 = 0.405 µs and τ2 =16
68.2 µs.
68.2 µs.
Table 1. Characteristic of voltage waveforms applied to transformer windings.
Table1.1.Characteristic
Characteristicof
of voltage
voltage waveforms applied
to transformer
windings.
Table
windings.
Table 1. Characteristic
of voltagewaveforms
waveformsapplied
applied to
to transformer
transformer windings.
(a) Full lighting impulse
(a)
Full lighting
impulse
t(a)
f—Front
time
Fulllighting
lighting
impulse
(a)
Full
impulse
tttfff—Front
time
tt—Front
—Time
to
half
of
wave tail
time
f—Front time
ttttt—Time
tohalf
halfofofwave
wave
—Time to
tailtail
tt—Time to half of wave
tail
(b) Chopped lighting impulse
(b)
Chopped lighting impulse
T(b)
c—Time delay to chopping
Chopped
lighting
impulse
Chopped
lighting
impulse
T(b)
cc —Time delay to chopping
c—Collapse time
c
—Time
delay
to
chopping
TtT
—Time
delay
to
chopping
c
ttcc—Collapse
time
time
c—Collapse
time
ct—Collapse
(c) Rectangular impulse with a variable
(c)
Rectangular impulse with a variable
risetime
(c) Rectangular impulse with a variable
(c) Rectangular impulse with a variable risetime
risetime
t0—Initial time
trisetime
—Initial time
tt0001—Initial
oftime
risetime
—Initial
time
t1t0—End
—End
of
risetime
ttt11r—End
of
risetime
—Rise
time
—Rise
time
rt1—End of risetime
trr—Rise time
tr—Rise time
(d) Superposition of full lighting impulse with
(d)
Superposition
of
fulllighting
lightingimpulse
impulse
with
oscillating
component
(d)
Superposition
ofoffull
with
(d) Superposition
full lighting
impulse
with
oscillating
component
oscillating
component
toscillating
f—Front time
component
—Front time
tttfff—Front
time
t—Time to half of wave tail
f—Front time
tttt—Time
to half of wave tail
ttt—Time
to halfand
of wave
tail of oscillating
,, ttw2—Initial
end
time
tw1t—Time
to half
ofend
wave
tail
tw1
and
time
of oscillating packet
w2 —Initial
w1, tw2
w2—Initial and end time of oscillating
w1
tω
packet
oscillating
packet
tww1—Frequency
, tw2—Initialofand
end time
of oscillating
packet
ωpacket
w—Frequency of oscillating packet
ωww—Frequency of oscillating packet
ωw—Frequency of oscillating packet
In order to design the chopped impulse Ucl (Figure 1a), the inverted and shifted lightning
Special attention was paid to the propagation
of those overvoltages along the high and low
In order
design
the chopped
impulse Uclcl (Figure 1a), the inverted and shifted lightning
waveform
U-lsto
is
add
(Figure
1b):
In
order
to
design
the
chopped
impulse
U
cl (Figure 1a), the inverted and shifted lightning
voltage
windings
as well as to the inter winding transfer case, while applying the stimulus between
-ls is add (Figure 1b):
waveform U-ls
(
)
(
)
U-ls is add
(Figure
(𝑡)1b):
𝑈ground.
] − exp[ −
]
for t ≥ Tc
= −𝑈 exp[ −
the waveform
winding terminal
and
(2)
(
)
(
)
(𝑡)
(
) − exp[ − (
)
𝑈
exp[
−
]
]
for
=
−𝑈
t
≥
T
(2)
c
c
The lightning impulse𝑈waveform
exponential function:
(𝑡) = −𝑈 Uexp[
l can−be described
] − exp[ −by the] following
for t double
≥ Tc
(2)
𝑈 (𝑡) = 0
for t < Tc
(𝑡)==U01 [exp(−t/τ1 ) − exp(−t/τ2 )]
for t < Tcc
U𝑈𝑈
(1)
l (t) (𝑡)
= 0
for t < Tc
Delay of chopping Tc can be tuned in a broad range—in the presented paper,
up to 50 µs. In this
ofτ chopping
cc can
be tuned
inthe
a broad
range—in
presented
paper,
up
to 50 µs.
In this
way,Delay
a1 and
chopped
lightning
impulse
on
and
on thethe
tail
is created.
collapse
time
c isfor
where
τDelay
define
aT
time
constant
and
the magnitude.
For
example,
inThe
high
voltage
testing,
of2 chopping
be tuned
inU
a 1front
broad
range—in
the
presented
paper,
up
to 50 µs.
In tthis
Tc can
c is
way,
a
chopped
lightning
impulse
on
the
front
and
on
the
tail
is
created.
The
collapse
time
t
c
tolightning
be about
0.1 µs. impulse
Thus,
lightning
impulse
the
UThe
cl_tail,collapse
shown
way,
a chopped
lightning
the
front
and oncorrespond
the tail on
is created.
tc isµs.
theassumed
standard
impulse
1.2/50the
µsonchopped
the
time
constants
to τtail
µs
and τin
=Figure
68.2
1 = 0.405
2time
cl_tail, shown in Figure
assumed
toby
bedescribed
about 0.1by
µs.equation:
Thus, the chopped lightning impulse on the tail Ucl_tail
1a,
can
be
assumed
be design
about 0.1
Thus, theimpulse
choppedUlightning
impulse
oninverted
the tail Uand
cl_tail, shown
Figure
In ordertoto
theµs.chopped
1a), the
shiftedinlightning
cl (Figure
1a, can be by described by equation:
1a, can be
by equation:
waveform
U-lsbyisdescribed
add (Figure
1b):
(3)
𝑈 _ (𝑡) = 𝑈 (𝑡) + 𝑈 (𝑡)
(𝑡)
(𝑡)
(𝑡)
(3)
𝑈
=
𝑈
+
𝑈
_
𝑈 _ (𝑡) = 𝑈 (𝑡) + 𝑈 (𝑡) (3)
(t−T )
(t−T )
U−ls (t) = −U2 exp[− τ3 c ] − exp[− τ4 c ] for t ≥ Tc
(2)
U−ls (t) = 0
for t < Tc
Delay of chopping Tc can be tuned in a broad range—in the presented paper, up to 50 µs.
In this way, a chopped lightning impulse on the front and on the tail is created. The collapse time
tc is assumed to be about 0.1 µs. Thus, the chopped lightning impulse on the tail Ucl_tail , shown in
Figure 1a, can be by described by equation:
Ucl_tail (t) = Ul (t) + U−ls (t)
(3)
𝑈 (𝑡) = −𝑈 exp[ −
(
)

] sin [ (𝑡 − 𝑇 − 𝑡 )]
for t ≥ Tc + tc
𝑈 (𝑡) = 0
for
(6)
t < Tc + t c
where U4, τα and ω are, respectively, the values of the magnitude, damping time constant and
4 of 16
oscillation frequency.
Energies 2020, 13, 304
Figure 1. Illustrative formation of chopped impulse: (a) tail chopped impulse, (b) composition of
Figure 1. Illustrative formation of chopped impulse: (a) tail chopped impulse, (b) composition of
component pulses for tail chopped impulse, (c) front chopped impulse, (d) composition of component
component pulses for tail chopped impulse, (c) front chopped impulse, (d) composition of component
pulses for front chopped impulse.
pulses for front chopped impulse.
To design the impulse chopped on the front before reaching the prospective peak, the additional
To illustrate
and1d)
to isquantify
spectralbydensity
of full and
chopped lightning impulses, the
waveform
Uh (Figure
needed,the
described
the following
equation:
frequency analysis was performed (Figure 2), using the above presented methodology. It was based
on two time-shifted pulses having inverted
to achieve
(t−T −t ) voltage waveform with desired front
(t−T −tpolarity
)
Uh (t) = −U3 exp[− τc5 c ] − exp[− τc6 c ] for t ≥ Tc + tc
(4)
time and delayed chopping moment.
(
)
U
t
=
0
for
t
<
T
+
t
c
c
h
The chopping time significantly influences the spectral content compared with the full lightning
impulse voltage, i.e., the shorter the time to chopping, the spectrum is broader but simultaneously
Hence, for chopped lightning impulse on the front Ucl_front , the superposition of full lightning
impulse Ul , inverted and shifted one U-ls and additional waveform Uh is performed, as presented in
Figure 1c,d and given by the expression:
Ucl_ f ront (t) = Ul (t) + U−ls (t) + Uh (t)
(5)
When decaying oscillations Udh follow the impulse fall at the chopping point, at a time moment
t = Tc + tc , the corresponding waveform component may be represented by the following expression:
(t−Tc −tc )
(
)]
Udh (t) = −U4 exp[−
]
sin
[
ω
t
−
T
−
t
for t ≥ Tc + tc
c
c
τ
Udh (t) = 0
for t < Tc + tc
(6)
where U4 , τα and ω are, respectively, the values of the magnitude, damping time constant and
oscillation frequency.
To illustrate and to quantify the spectral density of full and chopped lightning impulses, the
frequency analysis was performed (Figure 2), using the above presented methodology. It was based on
two time-shifted pulses having inverted polarity to achieve voltage waveform with desired front time
and delayed chopping moment.
Energies 2020, 13, x FOR PEER REVIEW
5 of 16
the energy spectral density lower. This effect might have a significant implication in the case of
internal
transients
Energies
2020,
13, 304 occurring along windings lengths, while performing chopped and full lightning
5 of 16
probe.
Figure
Spectral content
content of
of chopped
chopped and
and full
full lightning
Figure 2.
2. Spectral
lightning impulse
impulse (FLI).
(FLI). Delay
Delay time
time to
to chopping
chopping
respectively:
(1)
0.8
µs,
(2)
2
µs,
(3)
2
µs,
(4)
6
µs,
(5)
10
µs,
(6)
20
µs,
(7)
FLI.
respectively: (1) 0.8 µs, (2) 2 µs, (3) 2 µs, (4) 6 µs, (5) 10 µs, (6) 20 µs, (7) FLI.
The chopping time significantly influences the spectral content compared with the full lightning
Another applied waveform was a rectangular impulse with a variable risetime tr calculated
impulse voltage, i.e., the shorter the time to chopping, the spectrum is broader but simultaneously the
between 10% and 90% of voltage slope magnitude U5. In the presented model, a rectangular impulse
energy spectral density lower. This effect might have a significant implication in the case of internal
rise time is initiated at time t0 and lasts until time moment t1 with a slope β. Such a waveform can be
transients occurring along windings lengths, while performing chopped and full lightning probe.
described by the following expression:
Another applied waveform was a rectangular impulse with a variable risetime tr calculated
𝑓𝑜𝑟 𝑡 < 𝑡
0
between 10% and 90% of voltage slope magnitude
U . In the presented model, a rectangular impulse
𝑓𝑜𝑟5 𝑡 > 𝑡 𝑎𝑛𝑑 𝑡 < 𝑡
𝑈 (𝑡) = 𝑡
(7)
rise time is initiated at time t0 and lasts until
𝑈 time moment
𝑓𝑜𝑟 𝑡 >t1𝑡 with a slope β. Such a waveform can be
described by the following expression:
The last case of a stimulus waveform Ulw presented in this paper refers to the superposition of a
 component Uw, appearing at time moment tw1 and lasting until
full lighting impulse Ul with oscillating

0
f or t < t0



tw2. Such a waveform with superimposed
wavelet
can
expression:
Ur ( t ) = 
(7)
βt
f or be
t >represented
t0 and t < tby
1


 U
f
or
t
>
t
5
𝑈 (𝑡) = 𝑈 + 𝑈 = 𝑈 + 𝑈 exp( −(𝑡
− 𝑡 ) /𝜏 ) sin [  1 (𝑡 − 𝑡 )]
for tw1 < t < tw2
(8)
The(𝑡)last
case of a stimulusfor
waveform
Ulw tpresented
in this paper refers to the superposition of a
𝑈
t < tw1 and
> tw2
=𝑈
full lighting impulse Ul with oscillating component Uw , appearing at time moment tw1 and lasting
where τw and ωw are the width and frequency of the oscillating packet.
until tw2 . Such a waveform with superimposed wavelet can be represented by expression:
3. Measurement Setup and Test Object
Ulw (t) = Ul + Uw = Ul + U6 exp(− t − tw1 )2 /τw sin[ωw (t − tw1 )]
for tw1 < t < tw2
(8)
The measurement on transformer
windings
were
performed,
both
time
Ulw (t) = Ul
for t in
< tw1
andand
t > tfrequency
w2
domain, in a setup presented in Figure 3. The lightning voltage pulses were generated by a lightning
where
ωwmaximum
are the width
and frequency
of the
packet.
stroke τunit
with
amplitude
300 V. The
testoscillating
waveforms
with oscillating component as well
w and
as the measurements in frequency domain from 20 Hz to 2 MHz were performed using
3.
Measurementfunction
Setup and
Test Object
programmable
generator
Tektronix type AFG310 with maximum output voltage 20 V. It is
important
to notice thaton
the
magnitudewindings
of the generated
voltage waveforms
used
experiments
does
The measurement
transformer
were performed,
both in time
andinfrequency
domain,
not
have
a
practical
impact
on
measurement
results.
The
influence
of
the
ferromagnetic
transformer
in a setup presented in Figure 3. The lightning voltage pulses were generated by a lightning stroke
core with
in themaximum
analysis of
transients300
is often
subject
of discussion.
The contentious
issueas
concerns
the
unit
amplitude
V. Thea test
waveforms
with oscillating
component
well as the
cutoff frequencyinoffrequency
transformer
core impact.
to the
investigations
by Wilcox
measurements
domain
from 20Usually,
Hz to 2referring
MHz were
performed
using done
programmable
[28], in a generator
frequency Tektronix
range above
several
dozens
kHz, the impact
the core20
is V.
neglected.
Hence, to
in
function
type
AFG310
withofmaximum
outputofvoltage
It is important
this high
frequency
band, the
can be
treatedwaveforms
as linear objects
the magnitudes
applied
notice
that
the magnitude
of windings
the generated
voltage
used and
in experiments
doesofnot
have
stimuli
do not
influence the measurements.
For the acquisition
of the overvoltage
waveforms,
avoltage
practical
impact
on measurement
results. The influence
of the ferromagnetic
transformer
core in
an oscilloscope
Tektronixismodel
wasofused
as in the
configuration
in Figure
The
the
analysis of transients
often a784D
subject
discussion.
The
contentious shown
issue concerns
the3a.
cutoff
frequency of
characteristics
of the
windings
were
obtained
in the
computer controlled
configuration.
frequency
transformer core
impact.
Usually,
referring
to the
investigations
done by Wilcox
[28], in a
The
generator
was
programmed
to
yield
the
sweep
in
predefined
frequency
range
(up
to
2
MHz)
and
frequency range above several dozens of kHz, the impact of the core is neglected. Hence, in this high
frequency band, the windings can be treated as linear objects and the magnitudes of applied voltage
stimuli do not influence the measurements. For the acquisition of the overvoltage waveforms, an
Energies 2020, 13, 304
6 of 16
Energies 2020, 13,
x FOR PEER
REVIEW
6 of 16
oscilloscope
Tektronix
model
784D was used as in the configuration shown in Figure 3a. The frequency
characteristics of the windings were obtained in the computer controlled configuration. The generator
the programmed
corresponding
response
was in
acquired
by frequency
an oscilloscope.
Both
programmable
function
was
to yield
the sweep
predefined
range (up
to 2 the
MHz)
and the corresponding
generator
and
the
scope
acting
as
a
recorder
were
linked
with
a
control
computer
by
GPIB-USB.
The
response was acquired by an oscilloscope. Both the programmable function generator and the scope
controlasand
analysiswere
software
was
developed
incomputer
LabView™by
environment
Nationaland
Instruments
acting
a recorder
linked
with
a control
GPIB-USB.from
The control
analysis
[3,10,26,29].
software was developed in LabView™ environment from National Instruments [3,10,26,29].
Figure 3. Measurement setup: (a) time domain measurements of overvoltages along transformer
windings, (b) frequency domain and combined waveform measurements.
Figure 3. Measurement setup: (a) time domain measurements of overvoltages along transformer
windings,
(b) frequency
domain
andpaper
combined
measurements.
All
experiments
presented
in this
werewaveform
performed
on the test transformer 20 kVA 15/0.4 kV.
The rated and design parameters of the experimental unit are shown in Table 2. This kind of distribution
All experiments
presented
in thisto
paper
performed
on the test
transformer
20 kVA
transformer
was selected
on purpose
test awere
variety
of overvoltage
waveforms.
Such
a unit15/0.4
can
kV.
The
rated
and
design
parameters
of
the
experimental
unit
are
shown
in
Table
2.
This
kind
of
be subjected to both full lightning and chopped lightning stroke as well as to transients containing
distribution
transformer
was
selected
on
purpose
to
test
a
variety
of
overvoltage
waveforms.
Such
a superimposed oscillating component due to switching operations in the network. The systema
unit can be subjected
to both
full lightning
and chopped
lightning
strokeofasconnected
well as torenewable
transients
reconfigurations
will occur
increasingly
frequently
in the grid
as a result
containing and
a superimposed
oscillating
due infrastructure
to switching operations
in the network. The
generation
expanding charging
andcomponent
energy storage
for e-mobility.
system reconfigurations will occur increasingly frequently in the grid as a result of connected
renewable generationTable
and 2.expanding
charging
and energy
storage
Experimental
transformer
rated and
designinfrastructure
parameters. for e-mobility.
Parameter
Valueparameters.
Table 2. Experimental
transformer rated and design
Sr , (kVA)
Parameter
UrHV ,S(kV)
r, (kVA)
UrLV ,U
(kV)
rHV, (kV)
number of electrical
phases
UrLV, (kV)
number
Uz , of
(%)electrical phases
Uz, (%)
∆PFe , (kW)
ΔPFe, (kW)
∆Pk , (kW)
ΔPk, (kW)
I0 , (%)
I0, (%)
number
of turns
in the in
coilthe coil
number
of turns
number
of coils
number
of coils
winding
height
l, (mm)
winding
height
l, (mm)
internal
coil diameter
do, (mm)
internal
coil diameter
do , (mm)
externat
coil
diameter
di, (mm)
externat coil diameter di , (mm)
coil width h, (mm)
coil width h, (mm)
20
Value
15
20
0.4
15
3
0.4
3
4.2
4.2
0.11
0.11
0.53
0.53
2.8
2.8
810
810
44
280
280
157
157
205
205
25
25
The research was focused on the analysis of overvoltages occurring inside transformer high and
The
research
was focused
analysis of
overvoltages
transformer
highwere
and
low voltage
windings
as wellon
asthe
transferred
from
HV to LVoccurring
side. Theinside
ground
overvoltages
low
voltage
windings
as
well
as
transferred
from
HV
to
LV
side.
The
ground
overvoltages
were
measured along the HV winding, at tap x/l denoted as follows: x/l = 0 (corresponds to the clamp of
the phase L1), x/l = 0.2, x/l = 0.3, x/l = 0.7), applying various stimuli waveforms from the terminal side.
The access to the internal winding structure was possible through additional taps installed inside in
the winding. Due to the paper limitations, certain characteristic tap positions were selected to the
Energies 2020, 13, 304
7 of 16
Energies 2020, 13, x FOR PEER REVIEW
7 of 16
measured along the HV winding, at tap x/l denoted as follows: x/l = 0 (corresponds to the clamp of
the
phase L1), x/l = 0.2, x/l = 0.3, x/l = 0.7), applying various stimuli waveforms from the terminal side.
visualization of the voltage distributions along the windings. For evaluation purposes, both the
The access to the internal winding structure was possible through additional taps installed inside
frequency and time relationships ko of internal overvoltages in the transformer winding are calculated
in the winding. Due to the paper limitations, certain characteristic tap positions were selected to
using following expression:
the visualization of the voltage distributions along the windings. For evaluation purposes, both the
u
frequency and time relationships ko of internal overvoltages
in the transformer winding are calculated
ko = x / l
(9)
u0- max
using following expression:
ux/l
ko =
(9)
where:
u0− max
u x/l—measurement at tap x/l along the winding,
where:
u0-max—magnitude of external stimulus applied at winding clamps (tap x/l = 0 and x/l = 1.0).
ux/l —measurement
at tap
x/l along the
winding,
The distributions
of maximum
internal
winding overvoltages ko-max is obtained according to the
u0- max —magnitude of external stimulus applied at winding clamps (tap x/l = 0 and x/l = 1.0).
relationship:
The distributions of maximum internal winding
overvoltages ko- max is obtained according to
ux / l max
−
=
k
(10)
the relationship:
o− max
uux/l
0- max
− max
ko− max =
(10)
u0− max
where:
u x/—lmaximum value obtained for measurement at tap x/l along the winding,
where:
u0-max—highest magnitude of external stimulus applied at winding clamps (tap x/l = 0 and x/l =
ux/ l —maximum value obtained for measurement at tap x/l along the winding,
1.0).
u0- max —highest magnitude of external stimulus applied at winding clamps (tap x/l = 0 and x/l = 1.0).
4. Overvoltages in Frequency Domain
4. Overvoltages in Frequency Domain
Determination of the winding broadband characteristics in a frequency domain allows the
Determination of the winding broadband characteristics in a frequency domain allows the
determination of sensitive zones and resonance frequencies [3,10,12,29]. It is well suited for analysis
determination of sensitive zones and resonance frequencies [3,10,12,29]. It is well suited for analysis of
of the response of a transformer winding to an excitation in form of an oscillating packet of
the response of a transformer winding to an excitation in form of an oscillating packet of overvoltage
overvoltage occurring in an electrical network. The normalized frequency characteristics of
occurring in an electrical network. The normalized frequency characteristics of overvoltages along the
overvoltages along the windings are presented in Figure 4. Depending on the excitation spectral
windings are presented in Figure 4. Depending on the excitation spectral content match with these
content match with these characteristics, the stress on electrical insulation systems is obtained. From
characteristics, the stress on electrical insulation systems is obtained. From the plot one can notice
the plot one can notice characteristic frequencies, for which sinusoidal excitations are strongly
characteristic frequencies, for which sinusoidal excitations are strongly amplified inside the winding.
amplified inside the winding. Those frequencies may fit with spectrum of incoming external
Those frequencies may fit with spectrum of incoming external overvoltages. For example (Figure 4),
overvoltages. For example (Figure 4), the overvoltage ratio in case of HV winding at frequency 12
the overvoltage ratio in case of HV winding at frequency 12 kHz equals to 3.4 p.u. Analysis confirms,
kHz equals to 3.4 p.u. Analysis confirms, that excitation waveforms having oscillating wavelet may
that excitation waveforms having oscillating wavelet may undergo amplification inside transformer
undergo amplification inside transformer winding because of resonance phenomena, especially if the
winding because of resonance phenomena, especially if the frequencies of the applied voltage are
frequencies of the applied voltage are matching the self frequencies of the transformer winding.
matching the self frequencies of the transformer winding.
Figure 4.
4. Frequency
Frequency characteristic
characteristic of
of terminal
terminal overvoltages
overvoltages and
and for
for point
point in
in half
half of
of windings
windings and
and
Figure
ground: (a)—HV windings, (b)—LV windings.
ground: (a)—HV windings, (b)—LV windings.
From the frequency characteristics of overvoltages in HV and LV experimental transformer
From the frequency characteristics of overvoltages in HV and LV experimental transformer
windings (Figure 4), one can notice, that sinusoidal voltages at resonance frequencies propagated in
windings (Figure 4), one can notice, that sinusoidal voltages at resonance frequencies propagated in
transformer undergo amplification inside the windings. For example, in HV windings oscillating
overvoltages reach maximum for following frequencies 0.65 kHz, 13.1 kHz, 36.7 kHz and 51 kHz and
in LV windings for frequencies: 0.64 kHz, 8.7 kHz, 107 kHz and 0.85 MHz. If the resonant frequencies
Energies 2020, 13, 304
8 of 16
Energies 2020, 13, x FOR PEER REVIEW
8 of 16
transformer undergo amplification inside the windings. For example, in HV windings oscillating
Energies 2020, 13,
x FOR
PEER REVIEW
8 ofin16
overvoltages
reach
maximum
for following frequencies 0.65 kHz, 13.1 kHz, 36.7 kHz and 51 kHz and
of the transformer is larger, then the probability of multiplication of internal overvoltages in
LV windings for frequencies: 0.64 kHz, 8.7 kHz, 107 kHz and 0.85 MHz. If the resonant frequencies of
transformers
is greater.
It was also observed
that maximal
values of oscillating
in
of transformer
the transformer
is larger,
the probability
of multiplication
of internal overvoltages
overvoltages
the
is larger,
then thethen
probability
of multiplication
of internal overvoltages
in
transformersin
windings
occurs,
practically
for
the
same
frequencies,
for
all
phases.
is also
greater.
It wasthat
also
observed
that of
maximal
values
of oscillating
overvoltages
in
istransformers
greater. It was
observed
maximal
values
oscillating
overvoltages
in windings
occurs,
In
turn,
an
interesting
case
is
a
transfer
characteristic
i.e.,
stimuli
on
HV
winding
side
and
windings for
occurs,
practically
for thefor
same
for all phases.
practically
the same
frequencies,
all frequencies,
phases.
response
measured
at LV winding,
as
presented
in Figure 5. i.e.,
Illustration of
to LV transfer
In
turn,
an
interesting
case
is
a
transfer
characteristic
on the
HVHV
winding
side and
In turn, an interesting case is a transfer characteristic i.e., stimuli stimuli
on HV winding
side
and response
characteristic
of
overvoltages
for
injecting
the
signal
at
HV
terminal
of
phase
A
and
recording
response at
measured
at LV
winding, as
presented
in Figure of
5. the
Illustration
the HV
to LV transfer
measured
LV winding,
as presented
in Figure
5. Illustration
HV to LVof
transfer
characteristic
of
response
at LV of
winding
phase “a”
isinjecting
shown inthe
Figure
5a,atwhile
an
analogous
case reflecting
HV-LV
characteristic
overvoltages
for
signal
HV
terminal
of
phase
A
and
overvoltages for injecting the signal at HV terminal of phase A and recording response at LV recording
winding
winding
phase
is shown
in Figure
5b.
response
LVC-c
winding
phase
“a” isan
shown
in Figure
while an
analogous
case
reflecting
HV-LV
phase
“a” isatshown
in Figure
5a, while
analogous
case 5a,
reflecting
HV-LV
winding
phase
C-c is shown
phase C-c is shown in Figure 5b.
inwinding
Figure 5b.
(a)
(b)
(a)
(b) (x = 1.00) and for point
Figure 5. Transfer frequency
characteristic of overvoltages at winding terminal
in
half of windingsfrequency
and ground (x = 0.50): of
(a) injection HVatwindings
phase A,(xresponse
LV for
winding
Figure
Figure5.5.Transfer
Transfer frequencycharacteristic
characteristic ofovervoltages
overvoltages atwinding
windingterminal
terminal (x= =1.00)
1.00)and
and forpoint
point
phase
“a”,
(b)
injection
HV
winding
phase
C,
response
LV
winding
phase
“c”.
ininhalf
halfofofwindings
windingsand
andground
ground(x(x==0.50):
0.50):(a)
(a)injection
injectionHV
HVwindings
windingsphase
phaseA,
A,response
responseLV
LVwinding
winding
phase
phase
“c”.
phase“a”,
“a”,(b)
(b)injection
injectionHV
HVwinding
windingphase
phaseC,C,response
responseLV
LVwinding
winding
phase
“c”.
5. Propagation of Different Waveforms in Transformer Windings in Time Domain
5. Propagation of Different Waveforms in Transformer Windings in Time Domain
5. Propagation
ofrecorded
DifferentinWaveforms
in of
Transformer
Windings
Domain
Overvoltages
various parts
a transformer
windingin
inTime
response
to different stimuli
Overvoltages
recorded
in
various
parts
of
a
transformer
winding
in
response
stimuli
waveforms
are presented
in this
section.parts of a transformer winding in responsetotodifferent
Overvoltages
recorded
in various
different stimuli
waveforms are presented in this section.
waveforms are presented in this section.
5.1. Full Lightning Voltage Impulse
5.1. Full Lightning Voltage Impulse
5.1. Overvoltages
Full Lightning measured
Voltage Impulse
between selected points x/l of both HV and LV winding and ground
Overvoltages
measured
between
selected
points x/linofFigure
both HV
LV winding
and ground
duringOvervoltages
the full lightning
impulse
u0(t)
are presented
6a,and
whereas
the corresponding
measured between
selected
points x/l of both HV
and
LV winding
and ground
during the full
lightning
impulse
u0shown
(t) are presented
in Figure
6a, whereas
the
corresponding
differences
differences
of
inter
taps
ratios
are
in
Figure
6b.
The
magnitude
of
the
waveform
is
normalized
during the full lightning impulse u0(t) are presented in Figure 6a, whereas the corresponding
of
inter
taps
ratios
are
shown
in
Figure
6b.
The
magnitude
of
the
waveform
is
normalized
with
respect
with
respect of
tointer
maximal
value are
of the
full in
lightning
impulse
accordingof
tothe
formula
(9). The
response
differences
taps ratios
shown
Figure 6b.
The magnitude
waveform
is normalized
to maximal
value of overvoltages
the full lightning
impulse
according
to formula
(9).
The response
shapes
internal
shapes
of internal
arethe
different
comparing
to the
excitation
applied
at The
theofexternal
with respect
to maximal value of
full lightning
impulse
according
to formula
(9).
response
overvoltages
are
different
comparing
to
the
excitation
applied
at
the
external
transformer
clamps
of one
transformer
clamps of
one phase. For
the tap
x/lexcitation
= 0.3 in theapplied
HV winding,
can
shapes of internal
overvoltages
are example,
different taking
comparing
to atthe
at the one
external
phase.
For
example,
taking
the
tap
at
x/l
=
0.3
in
the
HV
winding,
one
can
recalculate
the
magnitude
of
recalculate
the
magnitude
of
corresponding
lightning
impulse,
which
results
in
1.04
p.u,
and
exceeds
transformer clamps of one phase. For example, taking the tap at x/l = 0.3 in the HV winding, one can
corresponding
lightning
which results in 1.04 p.u, and exceeds the impulse peak value.
the
impulse the
peak
value. impulse,
recalculate
magnitude
of corresponding lightning impulse, which results in 1.04 p.u, and exceeds
the impulse peak value.
(a)
(b)
(a) of
(b)
(a)(a)
HV
winding:
(1)(1)
x/l x/l
= 0,
x/l =
(3) x/l
0.3,
Figure 6. Measurement
Measurement
ofovervoltages
overvoltagesatattap
tapx/lx/linin
HV
winding:
= (2)
0, (2)
x/l0.2,
= 0.2,
(3)=x/l
=
(4)
0.7= and
(b) corresponding
overvoltage
differences:
1—u
,
2—u
,
3—u
.
0.3,x/l
(4)=x/l
0.7 and
(b) corresponding
overvoltage
differences:
1—u
0-0.2
,
2—u
0.2-0.3
,
3—u
0.3-0.7
.
0-0.2
0.3-0.7
Figure 6. Measurement of overvoltages at tap x/l in (a) HV winding:
(1) 0.2-0.3
x/l = 0, (2) x/l
= 0.2, (3) x/l =
0.3, (4) x/l = 0.7 and (b) corresponding overvoltage differences: 1—u 0-0.2, 2—u 0.2-0.3, 3—u 0.3-0.7.
Energies 2020, 13, 304
9 of 16
5.2. Chopped Lightning Voltage Impulse
Energies 2020, 13, x FOR PEER REVIEW
9 of 16
Overvoltages recorded in HV winding of 20 kVA transformer, excited by a lightning voltage
5.2. Chopped Lightning Voltage Impulse
impulse, were
performed in a broad chopping time delay scope. The lightning impulse was chopped
Overvoltages
in The
HV winding
of 20 kVA
transformer,
excited bytaps
a lightning
after time tu from 1 µs uprecorded
to 50 µs.
waveforms
measured
at selected
x/l in avoltage
HV winding in
impulse, were performed in a broad chopping time delay scope. The lightning impulse was chopped
response to the tail chopped lightning voltage impulse, with various chopping time delays: 2 µs, 5 µs,
after time tu from 1 µs up to 50 µs. The waveforms measured at selected taps x/l in a HV winding in
Energies
2020, 13,in
x FOR PEER 7A
REVIEW corresponding overvoltage differences in Figure 7B.
9 of 16 maximal
and 10 µs, are
shown
response
to the Figure
tail choppedand
lightning voltage impulse, with various chopping time delays: 2 µs,The
5
µs, and 10 overvoltages
µs, are shown inobtained
Figure 7A and
correspondingat
overvoltage
differences
in Figure 7B.
The
values of chopped
in
transformer
selected
taps
x/l
depend
on
time
delay to
5.2. Chopped Lightning Voltage Impulse
values of chopped overvoltages obtained in transformer at selected taps x/l depend on time
chopping tmaximal
u . Increased time tu leads to amplification of inter-winding overvoltages. Thus, time delay
in HV
winding
kVA transformer,
excited by overvoltages.
a lightning voltage
delayOvervoltages
to chopping recorded
tu. Increased
time
tu leadsofto20
amplification
of inter-winding
Thus,
tu has largetime
influence
on
longitudinal
overvoltage
can be
highlighted
especially in a
impulse,
were
performed
in a broad
timeenhancement.
delay scope.enhancement.
The In
lightning
impulse
chopped
delay
tu has
large influence
onchopping
longitudinal
overvoltage
In
can bewas
highlighted
winding region
being
a1 µs
proximity
toThe
the
after time
tin
u from
up
to 50being
µs.
at selected
taps x/l in a HV winding in
especially
a in
winding
region
in waveforms
a transformer
proximity measured
to theterminals.
transformer
terminals.
response to the tail chopped lightning voltage impulse, with various chopping time delays: 2 µs, 5
µs, and 10 µs, are shown in Figure 7A and corresponding overvoltage differences in Figure 7B. The
maximal values of chopped overvoltages obtained in transformer at selected taps x/l depend on time
delay to chopping tu. Increased time tu leads to amplification of inter-winding overvoltages. Thus,
time delay tu has large influence on longitudinal overvoltage enhancement. In can be highlighted
especially in a winding region being in a proximity to the transformer terminals.
(A)
(B)
Figure 7. Measurement
of overvoltages
applying tail
lightning
impulse
(A) in HV(A)
winding
Figure 7. Measurement
of overvoltages
applying
tailchopped
chopped
lightning
impulse
in HV winding
at tap (1) x/l = 0, (2) x/l = 0.2, (3) x/l = 0.3, (4) x/l = 0.7 and (B) corresponding overvoltage differences:
at tap (1) x/l = 0, (2) x/l = 0.2, (3) x/l = 0.3, (4) x/l = 0.7 and (B) corresponding overvoltage differences:
(1) u 0-0.2, (2) u 0.2-0.3, (3) u 0.3-0.7. Time delay to chopping tu: (a) 2 µs, (b) 5 µs, (c) 10 µs.
(1) u 0-0.2 , (2) u 0.2-0.3 , (3) u 0.3-0.7 . Time delay to chopping tu : (a) 2 µs, (b) 5 µs, (c) 10 µs.
The above measurements lead to the plot shown in Figure 8 representing overvoltages ko-max =
(A) and ground as well as gradients of overvoltages
(B)
f(x/l) between
selected points
in HV winding kofo-max = f(x/l)
The above
measurements
lead
to the plot shown in Figure 8 representing
overvoltages
transformer
excited
by
both
full
and
chopped
lightning
voltage
impulse
employing
time
delay of
tu in
Figure
7. Measurement
of overvoltages
tail chopped
lightning impulsein
(A)HV
in HV
winding
between selected
points
and ground
as well applying
as gradients
of overvoltages
winding
transformer
the range
upx/l
to=50
µs.
at tapfrom
(1) x/l1=µs
0, (2)
0.2,
(3) x/l = 0.3, (4) x/l = 0.7 and (B) corresponding overvoltage differences:
excited by both(1)full
and
chopped
lightning
voltage
impulse
employing
time
delay
t
in
the
range from
u
u 0-0.2, (2) u 0.2-0.3, (3) u 0.3-0.7. Time delay to chopping tu: (a) 2 µs, (b) 5 µs, (c) 10 µs.
1 µs up to 50 µs.
The above
measurements
lead to thetoplot
in Figure winding
8 representing
overvoltages
ko-maxto
= Figure 8b
The chopped
voltage
impulse applied
theshown
transformer
results
according
f(x/l) between selected points and ground as well as gradients of overvoltages in HV winding of
in the enhanced gradients, stressing the winding electrical insulation system, especially in a proximity
transformer excited by both full and chopped lightning voltage impulse employing time delay tu in
to the transformer
clamps
the range from
1 µs [6,7].
up to 50 µs.
Figure 8. (a) Maximal values of overvoltages and (b) overvoltage gradient for full (FLI) and chopped
lightning impulse, with time to chopping: (1) 1 µs, (2) 2 µs, (3) 4 µs, (4) 6 µs, (5) 10 µs, (6) 20 µs, (7) 30 µs,
(8) 50 µs, (9) FLI.
lightning impulse, with time to chopping: (1) 1 µs, (2) 2 µs, (3) 4 µs, (4) 6 µs, (5) 10 µs, (6) 20 µs, (7) 30
µs, (8) 50 µs, (9) FLI.
The chopped voltage impulse applied to the transformer winding results according to Figure 8b
Energies
13, 304 gradients, stressing the winding electrical insulation system, especially10in
of 16
in
the 2020,
enhanced
a
proximity to the transformer clamps [6,7].
5.3. Rectangular
Rectangular Voltage
Voltage Impulse
Impulse
5.3.
In this
this part,
measured in
in the
winding, excited
excited by
by aa rectangular
In
part, transients
transients measured
the transformer
transformer winding,
rectangular impulse
impulse
applied
at
HV
clamp
(tap
x/l
=
0
and
x/l
=
1.0)
are
presented
in
Figure
9.
applied at HV clamp (tap x/l = 0 and x/l = 1.0) are presented in Figure 9.
Figure 9.
Overvoltages excited
excited by
by rectangular
rectangular impulse
impulse in
in the
0, (2)
Figure
9. Overvoltages
the HV
HV winding
winding at
at tap:
tap: (1)
(1) x/l
x/l =
= 0,
(2) x/l
x/l =
=
0.2,
(3)
x/l
=
0.3,
(4)
x/l
=
0.7.
0.2, (3) x/l = 0.3, (4) x/l = 0.7.
Overvoltages generated inside the windings contain oscillatory components with a resonance
frequency equal to 13.1 kHz. The magnitude manifests great variability, i.e., overvoltages measured at
Overvoltages
generated
the windings
containcomparing
oscillatorytocomponents
resonance
tap x/l
= 0.3 along the
windinginside
are roughly
1.3 amplified
the impulse with
crest avalue
at the
frequency
equal
to
13.1
kHz.
The
magnitude
manifests
great
variability,
i.e.,
overvoltages
measured
transformer clamp. Due to the relatively low self frequencies of HV windings, overvoltages are not
at
tap x/l to
= 0.3
theof
winding
are roughly
amplified
to the
impulse
value at
sensitive
the along
rise time
the applied
impulse,1.3
ranging
from comparing
10 ns to several
hundred
ofcrest
nanoseconds.
the
transformer
clamp.
Due
to
the
relatively
low
self
frequencies
of
HV
windings,
overvoltages
are
In turn, overvoltages generated inside the LV transformer windings in response to the rectangular
not
sensitive
to the
rise time
of the
applied
ranging
from 10 to
nsnotice,
to several
hundredthe
of
voltage
impulse
strongly
depend
on rise
timeimpulse,
(Figure 10).
It is possible
for example,
nanoseconds.
In
turn,
overvoltages
generated
inside
the
LV
transformer
windings
in
response
to
the
overvoltage coefficient kiLV for voltage U0.5c in the LV winding of phase “c” for a rise time of 10 ns is
rectangular
impulse
strongly
depend
on rise
time (Figure
10). Itk is possible
to notice, for
about 3.3 butvoltage
for a rise
time 100
ns is about
1.6. The
overvoltage
coefficient
iLV of transient voltage Ua
example,
the
overvoltage
coefficient
k
iLV for voltage U0.5c in the LV winding of phase “c” for a rise time
at the terminal of phase “a” for rise time 10 ns reach about 1.95 but for rise time of 100 ns is equal only
of
to 10
0.7.ns is about 3.3 but for a rise time 100 ns is about 1.6. The overvoltage coefficient kiLV of transient
voltage Ua at the terminal of phase “a” for rise time 10 ns reach about 1.95 but for rise time of 100 ns
is equal only to 0.7.
Figure 10. Overvoltages measured in transformer LV windings in response. to rectangular voltage
impulse with different rise times: (a) 10 ns, (b) 100 ns.
Figure 10. Overvoltages measured in transformer LV windings in response. to rectangular voltage
5.4. Lightning
Voltage Impulse with Superimposed Oscilating Wavelet
impulse with different rise times: (a) 10 ns, (b) 100 ns.
Another class of stimulus is created by superimposed waveforms. Such an approach allows
5.4.
Lightning
Voltage
Impulse
with Superimposed
Wavelet winding, which result from the
analysis of the
internal
overvoltages
generatedOscilating
in the transformer
resonance
phenomenon
at impulse
voltagebywith
superimposed
oscillating
component,
in theallows
form
Another
class of stimulus
is created
superimposed
waveforms.
Such
an approach
of a wavelet.
the resultant
waveform
contains
aperiodic part
as a lightning
voltage
surge
analysis
of theThus
internal
overvoltages
generated
in theantransformer
winding,
which result
from
the
and an oscillating wavelet. The oscillating frequency of the wavelet has been adjusted to the winding
resonance frequencies obtained from frequency characteristics presented in Figure 4. An exemplary
case of HV winding response to a lightning voltage impulse with superimposed oscillating wavelet
tuned to 8.3 kHz, 13.1 kHz and 108 kHz is shown in Figure 11. One may notice the amplification of
the oscillating components related to winding resonance frequencies (8.3 kHz and 13.1 kHz) inside
the winding. Simultaneously overvoltages in HV windings have greater values than those generated
resonance frequencies obtained from frequency characteristics presented in Figure 4. An exemplary
case of HV winding response to a lightning voltage impulse with superimposed oscillating wavelet
tuned to 8.3 kHz, 13.1 kHz and 108 kHz is shown in Figure 11. One may notice the amplification of
the oscillating components related to winding resonance frequencies (8.3 kHz and 13.1 kHz) inside
Energies 2020, 13, 304
11 of 16
the winding.
Simultaneously overvoltages in HV windings have greater values than those
generated
during action just of the lightning impulse. However, overvoltages shown in Figure 11c, excited by
duringimpulse
action justcontaining
of the lightning
impulse. However,
overvoltages
shown in Figure
11c, excited
the
the lightning
oscillating
component
with frequency
108 kHz
are notbyamplified
in
lightning impulse containing oscillating component with frequency 108 kHz are not amplified in the
the LV winding. The wavelet frequency in this case is not matching the sharp winding resonance
LV winding. The wavelet frequency in this case is not matching the sharp winding resonance peak at
peak at 107
kHz.
107 kHz.
Figure 11. Response of the HV windings to lightning impulse containing oscillating components with
frequency:
(a) 8.3
kHz,HV
(b) 13.1
kHz, (c)to
108
kHz.
Figure 11.
Response
of the
windings
lightning
impulse containing oscillating components with
frequency: (a) 8.3 kHz, (b) 13.1 kHz, (c) 108 kHz.
Similar measurement have been performed on LV winding, adjusting the wavelet frequency to
the resonances in frequency characteristic (Figure 4), i.e., 107 kHz, 0.85 MHz. The results presented
Similar
measurement
havestrong
been amplification
performed of
onthe
LVoscillating
winding,
adjusting in
the
frequency
to
in Figure
12 also indicated
overvoltages
LVwavelet
windings,
for
example in
in the
case of frequency
0.85 MHz,
the overvoltage
voltage
U0.5c
is equal
to 3.4
the resonances
frequency
characteristic
(Figure
4), i.e., coefficient
107 kHz,for
0.85
MHz.
The
results
presented
and
for
voltage
U
is
about
1.5.
Analyzing
the
de-tuned
case,
overvoltages
generated
in
HV
winding
a
in Figure 12 also indicated
strong amplification of the oscillating overvoltages in LV windings, for
excited by the lightning impulse containing oscillating wavelet having frequency 14.6 kHz (Figure 12c)
example in the case of frequency 0.85 MHz, the overvoltage coefficient for voltage U0.5c is equal to 3.4
are significantly smaller than for cases of resonance frequencies.
and for voltage Ua is about 1.5. Analyzing the de-tuned case, overvoltages generated in HV winding
excited by the lightning impulse containing oscillating wavelet having frequency 14.6 kHz (Figure
12c) are significantly smaller than for cases of resonance frequencies.
Energies 2020, 13, 304
12 of 16
Energies 2020, 13, x FOR PEER REVIEW
12 of 16
Figure 12. Response of the LV windings to lightning impulse containing oscillating wavelet. with
Figure
12. Response of the LV windings to lightning impulse containing oscillating wavelet. with
frequency: (a) 107 kHz, (b) 0.85 MHz (c) 14.6 kHz.
frequency: (a) 107 kHz, (b) 0.85 MHz (c) 14.6 kHz.
6. Assessment of Overvoltages in Transformer Windings
6. Assessment of Overvoltages in Transformer Windings
The various applied excitation have different frequency ranges, both narrow- and broad-band.
Thus
observedapplied
transient
overvoltages
different
responses,
applying
testing and
voltages
and
The various
excitation
havemanifest
different
frequency
ranges,
both narrowbroad-band.
waveforms,
which
might
occur
during
transformer
operation
in
a
network.
As
a
reference
of
transformer
Thus observed transient overvoltages manifest different responses, applying testing voltages and
testing, the
full lightning
impulse
was accepted.
Poweroperation
grid transients
reflected
waveforms,
which
might occur
during
transformer
in awere
network.
Asbyaswitching
reference of
and oscillating waveforms. Both cases revealed relevant distinctions of maximum overvoltages along
transformer testing, the full lightning impulse was accepted. Power grid transients were reflected by
the winding. As an assessment factor the Time Domain Severity Factor (TDSF) was used. The TDSF is
switching and oscillating waveforms. Both cases revealed relevant distinctions of maximum
evaluated according to the following expression [21,22]:
overvoltages along the winding. As an assessment factor the Time Domain Severity Factor (TDSF) was
Ux/l max
used. The TDSF is evaluated according to the following
expression [21,22]:
TDSF =
where:
Ux/l maxtest
U
TDSF= x / l max
Ux / l maxtest
(11)
(11)
Ux/lmax —highest magnitude of overvoltages occurring at tap x/l during network operation,
where:
U
—highest
magnitude
overvoltages
occurringatattap
tapx/lx/lduring
excitednetwork
by reference
voltage impulse.
Ux/lmax
x/l maxtest
—highest
magnitude
of of
overvoltages
occurring
operation,
Ux/l max test—highest magnitude of overvoltages occurring at tap x/l excited by reference voltage impulse.
The TDSF obtained for the experimental transformer was evaluated taking the maximum values
of overvoltages yielded by testing with the standard full lightning impulse with crest value Utest = 95
kV [15]. The protection of the unit in a grid operation was considered, assuming two models of surge
arresters, having different tripping and time to disconnection parameters. In the first case, the
Energies 2020, 13, 304
13 of 16
The TDSF obtained for the experimental transformer was evaluated taking the maximum
values of overvoltages yielded by testing with the standard full lightning impulse with crest value
Utest = 95 kV [15]. The protection of the unit in a grid operation was considered, assuming two models
of surge arresters, having different tripping and time to disconnection parameters. In the first case, the
transformer
has
been
protected
12ofkV,
Energies
2020, 13,
x FOR
PEER
REVIEWby a surge arrester model SA1 rated for continuous voltage Uc =13
16
whereas the latter one is protected by model SA2 working at Uc = 18 kV. Both surge arresters are
applied in the distinctive network operating modes, i.e., SA1 in 15 kV topologies with automatic
disconnection of short circuits current to ground, whilst the model SA2 refers to the networks without
automatic ground fault clearing
clearing [21,22,30].
[21,22,30]. The
Therated
ratedsurge
surgearrester
arrester parameters
parameters are following: for
for SA1
SA1
lightning protection level is U
Ulplp == 42
sp =
42 kV
kV and
and switching one is Usp
=31.1
31.1kV
kVand
and for
for SA2
SA2 respectively
Ulplp ==63
63kV
kVand
and U
Uspsp==46.7
46.7kV
kV[30].
[30].The
Thedependencies,
dependencies,of
ofthe
theassessment
assessment factor
factor TDSF
TDSF == f(x/l)
f(x/l) for
for HV
winding of experimental
experimental transformer
transformer rated
rated 20
20 kVA
kVA 15/0.4 kV, were calculated and are illustrated in
Figure 13.
Figure 13.
13. Assessment
Assessment factor
factor TDSF
TDSF ==f(x/l)
f(x/l)for
forHV
HVwinding
winding excited
excited by
by standard
standard full
full lightning
lightning impulse
impulse
Figure
U
=
95
kV
of
experimental
transformer
protected
by
two
models
of
surge
arresters:
(a)
U
12 kV
kV
c
test
Utest = 95 kV of experimental transformer protected by two models of surge arresters: (a) Uc == 12
(SA1),
(b)
U
=
18
kV
(SA2);
1—standard
full
lightning
impulse,
2—sinusoidal
wavelet
with
resonance
c
(SA1), (b) Uc = 18 kV (SA2); 1—standard full lightning impulse, 2—sinusoidal wavelet with resonance
frequency 13.1
13.1 kHz,
kHz, 3—rectangular
frequency
3—rectangular impulse.
impulse.
The tabular summary of results of maximum overvoltages obtained for test transformer exposed to
The tabular summary of results of maximum overvoltages obtained for test transformer exposed
various stresses is presented in Table 3. One can notice, that overvoltages recorded at internal winding
to various stresses is presented in Table 3. One can notice, that overvoltages recorded at internal
taps of transformer, in certain waveform cases, surpass magnitudes obtained at standard lightning
winding taps of transformer, in certain waveform cases, surpass magnitudes obtained at standard
voltage impulse tests. Maximum internal overvoltages are recorded for a sinusoidal oscillating
lightning voltage impulse tests. Maximum internal overvoltages are recorded for a sinusoidal
component with the frequency matching the resonant frequency of transformer. For example, at the
oscillating component with the frequency matching the resonant frequency of transformer. For
winding tap x/l = 0.7, the response to excitation of 95 kV standard lightning voltage impulse test equals
example, at the winding tap x/l = 0.7, the response to excitation of 95 kV standard lightning voltage
to 84.6 kV.
impulse test equals to 84.6 kV.
A comparison of both cases of installed protective devices SA1 and SA2 provide quantitative
illustration
transientofovervoltage
effects.waveforms
In the case
of a network
equipped
with SA1,
Table 3.of
Comparison
an impact of various
on overvoltages
in transformer
windings.
with an automatic restoration after ground fault occurrence and transient excitation in the form
Reference
Test
the wavelet having the oscillating
frequency
13.1 kHz Overvoltages
(matching oneinof
the transformer
winding
Network
Operation
Overvoltages
resonance frequencies), the measured overvoltage at the same tap was 102.6 kV. While for the
Rectangular
Sinusoidal Oscillating
experimental
connected
to a network
Windingtransformer
Lightning
Impulse
95 kV without automatic restoration after a ground fault
Impulse
Component
occurrence,
with SA2 device, the overvoltage at tap x/l = 0.7, in the response
to excitation
Positionprotected
x/l
duration: Tens of
duration: Milliseconds
Microseconds
(kV)
Network with Automatic Fault Clearing (SA1 Uc = 12 kV)
Energies 2020, 13, 304
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containing the same wavelet with transformer resonant frequency, is equal to 154.1 kV. Such an
analysis reflects the transformer winding sensitive zones with respect to waveform frequency content.
As an extension of the presented work, further investigations on transformers with different winding
topologies and voltage levels are planned. Such an approach could lead to scalable and more general
methodology for assessment of overvoltages representing impulse, chopped and oscillating waveforms.
Table 3. Comparison of an impact of various waveforms on overvoltages in transformer windings.
Reference Test Overvoltages
Winding Position x/l
Lightning Impulse 95 kV
Overvoltages in Network Operation
Rectangular Impulse
duration: Tens of Microseconds
Sinusoidal Oscillating Component
duration: Milliseconds
(kV)
Network with Automatic Fault Clearing (SA1 Uc = 12 kV)
0
0.18
0.33
0.67
95.0
95.0
102.6
84.6
42.0
53.3
59.2
45.4
31.1
48.2
78.4
102.6
Network without Automatic Fault Clearing (SA2 Uc = 18 kV)
0
0.18
0.33
0.67
95.0
95.0
102.6
84.6
63.0
80.0
88.8
68.0
46.7
72.4
117.7
154.1
7. Conclusions
This paper reports about propagation of various waveforms of overvoltages inside transformer
winding stressing the electric insulation system. Especially highlighted are overvoltage exposures in
response to a lightning voltage impulse, rectangular one and impulse containing sinusoidal oscillating
component. The experiments were performed on a distribution transformer, which can be subjected in
real operating conditions to such stresses in an electric network. The transformer insulation between
windings and ground is exposed to the largest maximal of overvoltages during the tests with full
lightning voltage impulses. The application of chopped lightning impulses, with a variable delay time
to chopping does not increase the recorded transients. However, chopped lightning voltage impulses
result in an enhancement of the overvoltage gradients in the electrical insulation, especially localized
close to the transformer clamps. It was observed that excitation with the lightning voltage impulses
chopped on tail, with a delay time above 6 µs, does not cause an increase of overvoltage impact
in experimental winding. It was noticed that attention should be paid to overvoltages containing
oscillating component, especially those having the frequency close to one of the winding resonance
frequencies. Knowledge of these effects broadens the knowledge about transformer immunity tests and
recommendations for new designs, resistant to new classes of transients and overvoltages occurring in
resilient power grid.
Author Contributions: All authors cooperated fully and equally at all stages of the presented research and during
the preparation of the article. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
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article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).