Download determination of acceptable closing time scatter and residual flux

ISBN 978-0-620-44584-9
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
DETERMINATION OF ACCEPTABLE CLOSING TIME SCATTER AND
RESIDUAL FLUX MEASUREMENT UNCERTAINTY FOR
CONTROLLED SWITCHING OF TRANSFORMERS
A. Ebner1*
High Voltage Laboratory, Swiss Federal Institute of Technology Zurich, Switzerland
*Email: [email protected]
1
Abstract: Theoretically, controlled switching taking into account the residual flux is able to fully
eliminate inrush currents. Due to non-idealities in the field (closing time scatter, residual flux
measurement uncertainty) that significantly affect the performance of controlled switching, inrush
currents of 1.0 pu must be tolerated. To calculate the maximum acceptable tolerances of both nonidealities in this case, systematic energisation studies are carried out using a topological correct
transformer model and the “Delayed Closing” strategy. The results show that there is a linear
relationship between tolerable closing time scatter and maximum residual flux uncertainty.
Consequently, the required accuracy in the determination of the residual flux can be calculated if
the proposed analysis is carried out and the closing time scatter of the installed circuit breaker is
known.
1.
2.
INTRODUCTION
SIMULATION MODEL
Power transformers of the transmission level wherefore
controlled switching is preferably used are mainly built
as multi-legged transformers with separated windings
([5], [6]). The single-phase units as well as the fivelegged or shell-type units are always equipped with a
delta-winding whereby the phases respectively the legs
are coupled. Hence, they behave similar to the threelegged transformer which is the most representative
configuration and should be used for this analysis.
Besides, the windings of at least one side are starconnected. A transformer that fulfils all these
requirements is chosen for this study and its most
relevant data are listed in Table 1. The magnetising
current and the reserve of the core utilisation of this
transformer are approximately in the lowest third
respectively in the middle of the typical ranges; the
short-circuit impedance lies on the lower border of its
typical range (details see [7]).
Uncontrolled energisation of power transformers can
lead to very high inrush currents whose maximum
values exceed many times the rated current. They can
cause several undesired effects like temporary
overvoltages, a reduced power quality and false
tripping of the network protection schemes ([1]).
Moreover, high inrush currents lead to huge current
forces in the windings that are locally bigger than the
short-circuit current forces ([2]) and possibly reduce
the lifecycle of power transformers.
Several methods to reduce or eliminate these inrush
currents were developed in the last years whereof
“controlled switching taking into account the residual
flux” is the most promising application ([3]). In theory,
the inrush currents can be completely eliminated with
this method. Nevertheless, the algorithm is hardly
deployed in substations (e.g. [4]) because in most cases
additional voltage sensors have to be installed close to
the power transformer to measure the magnetic fluxes.
This significantly increases the costs of controlled
transformer switching.
Table 1: Transformer data
Thus, new methods will be developed to identify the
residual flux with the existing sensor system that does
not allow an exact measurement. The first step in this
process is to calculate the required accuracy for the
determination of the residual flux. Furthermore, the
closing time scatter of the circuit breaker significantly
affects the performance of controlled switching in the
field. Hence, this paper investigates the influence of
closing time scatter and residual flux measurement
uncertainty on the maximum inrush current peak.
Based on the results of these analyses the maximum
acceptable tolerances of the circuit breaker closing time
scatter respectively of the residual flux measurement
uncertainty are calculated.
Pg. 1
Rated values
Power
SR
400
Voltage
UR
16.8/0.42
kV
Current
IR
13.75/550
A
Vector group
Dyn5
Core type
three-legged
kVA
No-load test data (low voltage side)
Current
I0
0.282
%
Losses
912
W
Short-circuit test data (high voltage side)
Short-circuit impedance
ZSC
5.99
Pu
Losses
PSC
6057
W
Resistances
High voltage side (∆)
RHV
10.0244
Ω
Low voltage side (Y)
RLV
1.5782
mΩ
Magnetic data
Reserve of core utilisation
ΦReserve
0.19
pu
P0
Paper G-7
ISBN 978-0-620-44584-9
2.1.
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
floating potentials, numerical capacitances must be
included in the dual magnetic core model. They have to
be chosen small enough so that they do not affect the
results.
Modelling of the transformer
According to [8] and [9] the simulation model of the
power transformer must be correct in the relevant
frequency range from 0.1 Hz to 1 kHz. Within this
range subsequent points must be properly included in
the transformer model:
• Correctness of the winding connection
• Topologically right core model
• Consideration of the hysteresis and the
saturation behaviour of the magnetic core
• Modelling of the leakage inductances
• Possibility to set residual flux values
The capacitive behaviour of the transformer can be
neglected because its influence is irrelevant for the
inrush analyses.
2.2.
Model of the other components
For a worst case analysis the effects of the grid and the
line between the circuit breaker and the transformer
must not be modelled because they cause additional
damping. Considering these elements would be
equivalent with an increased winding resistance
respectively leakage inductance that diminishes the
inrush current peaks. Hence, the grid is modelled as an
ideal three-phase voltage source. The circuit breakers
are ideal time-controlled switches without prestrike
characteristics because it can be assumed that this
effect is compensated by the controller in the field.
An excellent overview of different transformer models
for frequencies up to some kHz can be found in [10].
Only the topology-based model ([11]) is able to fulfil
all requirements mentioned above and has to be used in
this study. Figure 1 shows the complete model in
EMTP-ATP where the transformer is located on the
right side. The winding resistances Rp are separated
from the dual magnetic core by ideal transformers. The
magnetic core model consists in its simplest form of
three nonlinear, hysteretic inductances of type “96
pseudo-nonlinear hysteretic inductor” (LmA, LmB and
LmC) as well as the linear leakage inductances Lsh that
have to be placed in the dual magnetic core too due to
their origin. A partition of the leakage inductance in a
part facing towards the primary side and in a part
facing towards the secondary side is not necessary
because the transformer will only be switched under
no-load conditions. An important requirement for the
model is a simple parameterisation which can be
achieved by using the type-96 elements. They just need
the major loop of the magnetisation curve that can be
identified easily. Besides, the residual flux value of
these elements can be assigned prior to the simulation
start. Due to the fact that EMTP-ATP cannot deal with
2.3.
Controller modules
In principle only one simulation can be done at once in
EMTP-ATP. For the systematic analyses where the
deviations will be varied regularly a lot of simulations
with different combinations of residual fluxes and
closing times are needed. Thus, controller modules
were implemented in MATLAB that vary the closing
times and the residual flux values, start the simulations
and analyse the current waveforms. A more detailed
description of these modules can be found in [12]. The
residual flux patterns for the three-phase analyses were
chosen to be symmetrical sine curves that agree very
well with the experimental results in [12]:
⎡ ⎛
2 ⎞⎤
cos ⎜ ω0 ⋅ t − π ⎟ ⎥
⎢
⎡ Φ Res ,U ⎤
3 ⎠
⎢ ⎝
⎥
⎢
⎥
Φ
=
0.6
⋅
cos
⋅
pu
ω
t
⎢
(
) ⎥
0
⎢ Res ,V ⎥
⎢
⎥
⎢⎣ Φ Res ,W ⎥⎦
⎢ cos ⎛ ω ⋅ t − 4 π ⎞ ⎥
0
⎜
⎟
⎢⎣ ⎝
3 ⎠ ⎥⎦
(1)
Figure 1: Simulation model
Pg. 2
Paper G-7
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
ISBN 978-0-620-44584-9
3.
Figure 3. The curves begin at different points because
the maximum residual flux value of 0.987 pu cannot be
exceeded (residual flux value of the major loop). For
positive deviations some numerical problems occur
during the simulations (vertical lines) but they do not
significantly affect the results. In this case, the width of
the area without inrush currents is independent of the
residual flux value and all curves are congruent. Thus,
the maximum inrush current peak depends only on the
residual flux deviation but not on the residual flux
value. Again, the results can be reduced to the curve
with zero residual flux in phase V. If no inrush currents
are allowed a maximum uncertainty in the residual flux
determination of ±0.21 pu can be tolerated. Due to the
damping effects of the winding resistances and the
hysteresis losses this value is slightly higher than the
theoretical value that is equal to the reserve of the core
utilisation (0.19 pu).
RESULTS IF NO INRUSH CURRENTS ARE
TOLERATED
The closing time scatter and the residual flux
measurement uncertainty occur both together in real
substations. To easier analyse the results, the effects of
the deviations are investigated separately. Thus, on the
one hand a configuration with real circuit breakers and
ideal residual flux measurement and on the other hand
a configuration with ideal circuit breakers and real
residual flux measurement is evaluated. Here, only the
energisation process of the first phase will be
investigated which is always the centre phase V.
3.1.
Acceptable closing time scatter
Absolute Value of Inrush Current Peak [pu]
5
Φ
Res,V
Absolute Value of Inrush Current Peak [pu]
Figure 2 shows the results for a configuration with real
circuit breaker and ideal residual flux measurement
whereas the closing time scatter is varied from -5 ms to
+5 ms and the residual flux in the centre leg ΦRes,V lies
in the range of [-0.6 … 0.0] pu. Analogue results arise
for positive residual flux values in phase V wherefore
they do not need to be discussed. In Figure 2 it can be
seen that for a certain closing time deviation the
maximum inrush current peak for the positive
deviation is always higher than that for the negative
one. Furthermore, the width of the region without
inrush currents marginally depends on the residual flux
value. The smallest region without inrush currents is
marked by the curve with zero residual flux in phase V
that has to be consulted for the maximum tolerable
closing time scatter independent of the residual flux
value. This finally leads to a maximum closing time
scatter of ±0.67 ms if the residual flux measurement is
ideal.
3
3.3.
= 0 pu
-3
-2
-1
0
1
2
3
Deviation from ideal Closing Time [ms]
4
5
Figure 2: Maximum value of inrush current depending
on the closing time deviation and der residual flux for
the energisation of the first phase
3.2.
= 0 pu
= -0.1 pu
= -0.2 pu
= -0.3 pu
= -0.4 pu
= -0.5 pu
= -0.6 pu
2.5
2
1.5
1
0.5
-0.8
-0.6 -0.4 -0.2
0
0.2 0.4 0.6
Deviation from ideal Residual Flux [pu]
0.8
1
Interdependence of the deviations
According to [12] the analyses of first phase
energisation are sufficient in this case and lead to the
most stringent conditions for the acceptable tolerances.
As said before, both deviations occur together in real
substations. Thus, a combined approach has to be
developed that includes both deviations. If for example
only 50 % of the tolerable closing time scatter is used
by the circuit breaker according to Figure 1, the other
50 % can be used for the uncertainty in the residual
flux measurement (Figure 3). Consequently, there is a
linear relationship between the tolerable closing time
deviation and the residual flux deviation. The two
special cases discussed above mark the extreme
positions of this approach. With these results Figure 4
can be plotted that shows the desired relationship.
Typical closing time scatter of circuit breakers that are
used for controlled switching reaches values of ±0.5 ms
to ±1.0 ms ([13]). Even with these very precise circuit
breakers controlled switching of transformers without
inrush currents is not always possible. Therefore, it is
hardly realisable in the field. The toleration of a certain
inrush current is necessary for a successful application
in the field.
1
-4
Res,V
Figure 3: Maximum value of inrush current depending
on the residual flux deviation and the residual flux for
the energisation of the first phase
2
0
-5
Φ
3
0
-1
= -0.1 pu
= -0.2 pu
= -0.3 pu
= -0.4 pu
= -0.5 pu
= -0.6 pu
4
3.5
Tolerable residual flux measurement
uncertainty
Analogue to the analysis of the closing time scatter the
effect of residual flux deviations has to be evaluated as
well. Hereby, an ideal circuit breaker without closing
time deviation and a real residual flux measurement are
emulated. The optimal closing time is calculated based
on the residual flux value in the legend of Figure 3;
afterwards, the residual flux value in the transformer
core will be changed according to the abscissa in
Pg. 3
Paper G-7
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
Residual Flux Measurement Uncertainty [pu]
ISBN 978-0-620-44584-9
For the calculation of the maximum residual flux
measurement uncertainty, Figure 3 is reused. The
maximum residual flux measurement uncertainty is
marked by the intersection point of the curves with the
1.0 pu line which amounts to ±0.465 pu for the
400 kVA transformer.
0.25
0.2
0.15
0.1
With these two values the corresponding plot to Figure
4 can be drawn (Figure 5). Now, controlled switching
can be applied to this power transformer if circuit
breakers are installed that are suitable for controlled
switching. In worst case, a circuit breaker with a
closing time scatter of ±1.0 ms is utilised. Under these
circumstances a residual flux measurement uncertainty
of up to ±0.15 pu can be admitted.
0.05
0
0
0.1
0.2
0.3
0.4
0.5
Closing Time Scatter [ms]
0.6
0.7
4.
Residual Flux Measurement Uncertainty [pu]
Figure 4: Maximum acceptable residual flux
uncertainty depending on the closing time scatter of the
circuit breaker if no inrush current is allowed
RESULTS IF AN INRUSH CURRENT OF
1 PU IS PERMITTED
0.5
0.4
In the present case an inrush current peak of 1.0 pu is
tolerated so that realistic requirements for the
acceptable deviations can be found. If transient inrush
currents occur during the energisation of a three-phase
transformer, the core was driven into saturation. Hence,
different dynamic magnetic flux waveforms occur after
first phase energisation in the other two phases
compared to the behaviour in chapter 3. Therefore, the
“Delayed Closing” strategy which is the preferred
algorithm for controlled switching in the field has to be
verified again.
Figure 5: Maximum acceptable residual flux
uncertainty depending on the closing time scatter of the
circuit breaker if an inrush current of 1.0 pu is tolerated
4.1.
4.2.
Energisation of the first phase
Once again, the effects of both deviations are analysed
separately as already done in chapter 3. Thereby, the
results of Figure 2 and Figure 3 can be used again
because they are just interpreted with different
conditions. The toleration sector is not anymore limited
by the general occurrence of inrush currents as in
chapter 3 but newly by the 1.0 pu line. Hence, this
leads to wider regions for the tolerances and thus less
demanding requirements emerge for the circuit breaker
as well as mainly for the residual flux measurement
device.
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
Closing Time Scatter [ms]
1.2
1.4
Acceptable closing time deviation for second
and third phase energisation if the “Delayed
Closing” strategy is used
The fact that first phase energisation is sufficient to
calculate the tolerances according to chapter 3.3 is not
any longer valid in this case because the first phase will
be energised with 1.0 pu inrush current in worst case.
Therefore, the systematic study for second and third
phase energisation using the “Delayed Closing”
strategy has to be carried out with the simulation model
in Figure 1. With this strategy, these phases are
energised independently of their residual flux values.
Consequently, only the bearable closing time scatter
The results of Figure 2 show that the negative closing
time deviation of a certain residual flux value is bigger
than the positive one for a maximum inrush current
peak of 1.0 pu. Thereof, the smaller value has to be
chosen because the closing time scatter of the circuit
breaker is symmetrical in both directions. Due to the
fact that the curves for positive deviations are identical
for different residual fluxes up to approximately 1.5 pu
inrush current, the tolerable closing time scatter is
independent of the residual flux pattern again. In the
present case the maximum closing time scatter
amounts to ±1.5 ms. In comparison with the results of
chapter 3, the value can be increased by more than
100 % if an inrush current of 1.0 pu is tolerated.
1.15
Closing Time Scatter [ms]
1.1
4 Periods
4.5 Periods
1.05
1
0.95
0.9
0.85
0.8
0.75
-0.6
-0.4
-0.2
0
0.2
Residual Flux in Phase V [pu]
0.4
0.6
Figure 6: Tolerable closing time scatter for second and
third phase energisation using “Delayed Closing” and a
maximum inrush current peak of 1.0 pu in all phases
Pg. 4
Paper G-7
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
ISBN 978-0-620-44584-9
has to be investigated in this case. Thereby, the first
phase is energised so that the inrush current peak is
exactly 1.0 pu. Possibly, the dynamic magnetic fluxes
of the two other phases have not yet reached their
steady-state course after a delay of 4 periods
(energisation instant of the second and third phase).
Thus, the residual flux pattern could influence the
results and has to be considered in this study.
1
Phase U
Phase V
Phase W
Magnetic Flux [pu]
0.5
0
-0.5
By tolerating a maximum inrush current peak of 1.0 pu
in the second and third phase as well, the acceptable
tolerances of the closing time scatter after a delay of 4
periods are displayed by the solid line in Figure 6. It
can be seen that the acceptable tolerances are different
for negative and positive residual flux values in phase
V. This indicates that the dynamic magnetic fluxes
have not yet reached their steady-state course which is
confirmed by Figure 7. The dynamic magnetic fluxes
have assimilated after one to two periods as in the case
of optimal first phase energisation without inrush
currents (Figure 8) but they still possess a significant
offset due to small damping in the system. This offset
influences the acceptable closing time scatter as shown
in Figure 6 (solid line). An increased delay of 6 to 8
periods will not improve the results. The maximum
closing time scatter for positive residual fluxes in phase
V can only be raised to 1.1 ms if the delay is adjusted
to 4.5 periods (dotted line in Figure 6).
1
5.
-1
40
60
80
Time [ms]
100
120
60
80
Time [ms]
100
120
140
CONCLUSIONS
It has been shown that controlled switching of
transformers without inrush currents is hardly possible
in the field. This originates from the non-idealities of
the circuit breaker (closing time scatter) and of the
device for the residual flux determination
(measurement uncertainty). Thus, an inrush current of
1.0 pu must be accepted to get realistic tolerances for
these non-idealities. It was demonstrated that – for this
case as well – the systematic studies of first phase
energisation with zero residual flux in phase V are
sufficient to determine the tolerances if the “Delayed
Closing” strategy is used. Furthermore, it can be
concluded that there is a linear relationship between the
acceptable closing time scatter of the circuit breaker
and the uncertainty of the device that determines the
residual flux.
-0.5
20
40
This paper presented a new transformer model based
on the principle of duality that fulfils all important
requirements for the energisation studies of threelegged power transformers. Furthermore, controller
modules were used to systematically vary the closing
time scatter as well as the residual flux measurement
uncertainty. The interpretation of these results finally
leads to the maximum acceptable tolerances for the
closing time scatter of the circuit breaker and for the
uncertainty of the residual flux measurement device
that are important parameters for the implementation of
controlled transformer switching in the field.
0
-1.5
0
20
Figure 8: Waveforms of the magnetic fluxes after
energisation of the first phase without inrush current
for biggest flux asymmetry in phases U and W
Phase U
Phase V
Phase W
0.5
Magnetic Flux [pu]
-1
0
140
Figure 7: Waveforms of the magnetic fluxes after
energisation of the first phase with an inrush current of
1.0 pu for biggest flux asymmetry in phases U and W
The maximum acceptable closing time scatter for the
second and third phase amounts to ±1.1 ms that is
smaller than the value of the first phase (±1.5 ms).
Because this value is higher than the maximum closing
time scatter of circuit breakers that are used for
controlled switching (±1.0 ms) and the whole tolerance
for second and third phase switching can be used for
the closing time deviation, the tolerances calculated
with the results of the first phase energisation studies
are still sufficient.
A representative three-legged 400 kVA transformer
with star-connected windings was analysed adopting
the methods discussed above. Using circuit breakers
that are suitable for controlled switching the maximum
residual flux uncertainty amounts to ±0.15 pu in worst
case. Hence, new methods to determine the residual
fluxes of this power transformer with the existing
sensor system should be able to identify the residual
fluxes at least with this accuracy.
Pg. 5
Paper G-7
ISBN 978-0-620-44584-9
6.
Proceedings of the 16th International Symposium on High Voltage Engineering
c 2009 SAIEE, Innes House, Johannesburg
Copyright °
[6] J. Taylor, D. J. Bornebroek, “Main Transformer
Arrangements and related Matters in Generating
Stations – Experience and Practices adopted by
various Utilities in the Countries represented by
the Members of Study Committee 23,” Electra, no.
82, pp. 87–108, May 1982.
[7] A. Ebner, “Remanenzflussbestimmung für das
kontrollierte Einschalten von Transformatoren”,
Ph.D. thesis at ETH Zurich, to be published, 2009.
[8] CIGRE WG33.02, “Guidelines for Representation
of Network Elements when Calculating
Transients”, CIGRE Brochure no. 39, 1990.
[9] IEEE WG 15.08.09, “Modeling and Analysis of
System Transients Using Digital Programs”, IEEE
catalogue no. 99TP133-0, 1998.
[10]J. A. Martinez, B. A. Mork, “Transformer
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[12]A. Ebner, “Controlled Switching of Transformers Effects of Closing Time Scatter and Residual Flux
Uncertainty”, Universities Power Engineering
Conference 2008 (UPEC 2008), September 2008.
[13]A. C. Carvalho, W. Hofbauer, P. Högg, K.
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ACKNOWLEDGMENTS
The author would like to thank Mr. Zinnbauer from
SGB Starkstrom-Gerätebau GmbH for the interesting
discussions and for providing the data of the
transformer used in this study.
7.
REFERENCES
[1] A. Ebner, “Begrenzung von transienten
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kontrolliertes
Schalten
von
Leistungstransformatoren“,
FKH-/VSE-Fachtagung
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„Überspannungen
und
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