arc rogers
TRANSCRIPT
-
7/22/2019 Arc Rogers
1/20
Modeling of Free-Air Arcs
Two practicle free-air arc models have been developed for use with EMTP. The models
have been used to match the voltage versus current curves of several measured arcs and
have proven useful as components of larger system models.
The basic model consists of a zinc oxide component in shunt with an inductor for energy
storage. A shunt resistor is connected across the ZnO component to adjust the slope and
shape of the arc voltage versus current curve. A switch is used to initiate the fault and to
terminate the fault current when the arc extinguishes. A voltage versus current arc curve
is generated by driving the basic model with a current source.
To create a model from measured field data, the measured V-I arc curve can be plotted
and overlayed on a curve produced with the model. Then the model's parameters can be
adjusted until the best achievable match is made. For the basic model, five variables are
involved in this procedure: the ZnO reference voltage, the ZnO exponent, the resistance,
the inductance, and the magnitude of the current source.
The advanced model adds a damped capacitor and shunt resistor in parallel with the basic
model. These additional components allow modeling of complex arc curves which cross
over near the origin. With the extra parameters, matching a model to specific field data
is more laborious than with the basic model.
However, by understanding the effect that each component has on the shape of the arc
curve, a model can be produced with just a few iterations.
MODELING OF FREE-AIR ARCS
Will Rogers - EOHC
Two practicle models have been developed for modeling free-air arcs in EMTP cases.
For the simpler model, a five step process has been defined to aid in matching the
parameters to measured arc voltages and currents. For the more complex model, several
test cases are given that demonstrate the effect of the
parameters on the arc curve shape and provide guidance on how to use the model.
Finally, examples are included which demonstrate the use of these models to match
actual measured data.
February 3, 1994
-
7/22/2019 Arc Rogers
2/20
ARC MODELING - EXPLAINATION OF THE BASIC MODEL
The following report outlines a general procedure for building an EMTP model of a free-
air arc. The basic model consists of the following components (Fig. 1):
I. Zn0 component: i=(v/K)^ALPHA II. Resistor
III. Inductor
/ ARCIS ______/ _________ ARCZ1 | | | SWITCH _____|_____ | | | | | | | Z R | ZnO _Z_/ R RESISTOR
| / Z R CURRENT [^] | | SOURCE | | | | |_________| | | ARCZ2 | | | L | L INDUCTOR | L | | | | GROUND |_________________| | V
FIGURE 1. BASIC MODEL
In addition, a current source is used to excite the model when adjusting parameters to
match the model's response to measured data. Note that the current source will not
usually be included with with the model when it is substituted into a larger EMTP case.
The basic model has the following parameters for the purpose of matching data:
I. K=Vref of ZnO
II. ALPHA=Exponent of ZnO
III. R=Resistance Value IV. L=Inductance Value
V. Amplitude of Current Source
These five independent parameters can be used to match five quantities in the model to
five quantities in the measured data. However, ALPHA and K are interdependent,
necessitating an iterative process to achieve optimal matching.
Four cardinal point can be defined on the curve of an arbitrary, free-air arc (Fig. 2).
Note that this model can only represent a simple, closed curve with four inflection points.
The cardinal points are as follows:
-
7/22/2019 Arc Rogers
3/20
I. Voltage at Current = 0
II. Current at Voltage = 0
III. Voltage at Maximum Current
IV. Current at Maximum Voltage
Because the entire curve can be arbitarily scaled, one current, Iarb, and one voltage,
Varb, can be likewise arbitrarily chosen. Then all points are measured relative to this
coordinate pair. Thus, the four cardinal points havesix independent quantities. If Iarb=0
and Varb=0, then the six quantities are:
I. V at I=0 IV. I at Vmax
II. I at V=0 V. Imax
III. Vmax VI. V at Imax
Since it has been shown that there are only five independent parameters of the model, it
follows logically that any five quantaties can be matched, but not more than five.
The four cardinal points defined above are present in both the first and third quadrants.
The arc curve to be modeled may not be symmetric; however, the unsymmetry is due to
time-varying parameters and measurement error, both of which are not accounted for in
the model. Finding a close match to the datapoints in one quadrant is generally the best that can be accomplished.
-
7/22/2019 Arc Rogers
4/20
-
7/22/2019 Arc Rogers
5/20
Step 3. Vmax - (V @ Imax)
Measure the difference between Vmax and V at Imax on the data. Adjust ALPHA so
that the model matches this parameter. Note that changes in K will have a weak but
noticable affect on this measurement. (See Figure 4).
-
7/22/2019 Arc Rogers
6/20
Step 4. I @ V=0
Set the Current at V=0 by adjusting the resistance, R. (See Figure 5).
Step 5. V at Imax and Vmax
Match V at Imax be adjusting K. Varying K affects step 3 slightly; however, the ideal is
to match both Vmax and V at Imax. The current at Vmax cannot be matched without
affecting the other parameters already set. (See Figure 6).
-
7/22/2019 Arc Rogers
7/20
AN EXAMPLE OF MATCHING THE BASIC MODEL'S
PARAMETERS TO MEASURED DATA
- TWO APPROACHES -
The first step in matching the model to the data is to condition the raw, measured data.
The appendix gives a sample command file for Randy's Plotter that accomplishes this
task. Also contained in the appendix is a sample data case that contains examples of the
basic and advanced models.
Figure 7 shows a curve generated by following the five step method previously outlined.The cardinal points are matched fairly accurately considering the inherent limitations of
the model as described previously. An iteration of the five step method would yield a
slightly better match of the cardinal points.
-
7/22/2019 Arc Rogers
8/20
Figure 8 shows a curve arrived at by attempting to match the overall shape of the
measured curve rather than just a few cardinal points. The interdependence of the model
parameters as show in figures 3 through 6 should be kept in mind.
This method is less mechanical than simply matching cardinal points but may yield a
more satisfactory model since it tends to minimize the overall error.
-
7/22/2019 Arc Rogers
9/20
ARC MODELING - EXPLAINATION OF THE ADVANCED
MODEL
The advanced model consists of six components and a current source (Figure. 9) and has
the following eight parameters:
I. K=Vref of ZnO
II. ALPHA=Exponent of ZnO
III. R=Resistance value across ZnO
IV. L=Inductance value
V. C=Capacitance value
VI. Rc=Capacitor damping resistance
VII. Rs=Shunt resistance
VIII. Amplitude of Current Source
/ ARCIS ______/ ______________ ARCZ1 | SWITCH | | __________|_____________________________ | | | | | | | | | | | Z R | | | ZnO _Z_/ R R ===== C | | / Z R | | CURRENT [^] | | | | SOURCE | | | | R | |_________| | R Rs | | ARCZ2 | R | | | | | L R | | L L R Rc | | L R | | | | | | | | | GROUND |_________________|____________________|____________| | V
FIGURE 9. ADVANCED MODEL
The discussion of cardinal points given for the basic model is equally valid for theadvanced model; however, the advanced model will generally be used with more
complex arc curves which have additional characteristics that must be modeled. For
many observed arcs, the I-V curves exhibit either pinching off or crossing over of the
curve near the origin (see Figure 10).
-
7/22/2019 Arc Rogers
10/20
Pinch-off
The current from the source is divided between the multiple paths to ground. One path
contains the inductor which stores energy. Let us assume the other path is a simple
resistor and that there is no capacitance. See figure 9 for clarity. As the current from the
source decreases, the ZnO impedance will increase, thus forcing more current through
the non-inductive shunt path and less through the inductor. The voltage across the arc a
I=0 is due to stored energy in the inductor ( V=L di/dt). Since current is shuntedthrough a non-inductive path, the voltage at I=0 will be less than if all the source current
had been forced through the inductor. When the current increases, the ZnO impedance
becomes rapidly less, increasing the proportion of source current flowing into the
inductor.
When the current from the source is high, the ZnO impedance vanishes compared to R
and Rs and thus the current through the inductor is high so the energy stored is large
which opens up the curve.
When the current from the source is low, the ZnO impedance is very high compared to Rand thus the current is divided between R and Rs. If Rs is small compared to R, then
there will be little current flowing into the inductor and thus the curve will be narrow.
Cross-over
A capacitive shunt branch around the inductor and ZnO will store energy when the ZnO
impedance is high (i. e. at low values of source current). The voltage across the
capacitor will be of opposite polarity to the inductor voltage and will subtract. If the
capacitance is of the correct magnitude, the curve will exceed the pinched-off point and
the curve will cross over itself. A crossed over curve can only be achieved when the
inductance and capacitance are of proper proportion to one another.
-
7/22/2019 Arc Rogers
11/20
ARC MODELING - USING THE ADVANCED MODEL
The following several pages contain plots which demonstrate the effect of varying each
of the advanced model's parameters one at a time. These plots are intended to serve asexamples to guide the process of building a model to match a paticular set of measured
data. Note that when the capacitance is very large or removed, Rc is functionally
equivalent to Rs. Rs is present only where listed as a parameter in the plot title; all other
cases just use C and Rc.
Effect of the Capacitor
Figures 11 through 15 show the effect of varying the capacitance. Assume the absence
of Rs. As capacitance increases, and thus Xc decreases, the curve is transformed from
the simple curve generated by the basic model in to a fully pinched off curve, then into acrossed over curve. As capacitance continues to increase the cross-over loop collapses
back to a fully pinched off condition and then approaches the partially pinched off curve
formed by the basic model with a shunt resistance. The slope of the curve remains
constant with changes in C and the voltage at maximum source current is a weak
function of C.
-
7/22/2019 Arc Rogers
12/20
-
7/22/2019 Arc Rogers
13/20
-
7/22/2019 Arc Rogers
14/20
and may cause crossover if capacitance is present in the shunt branch. The slope of the
curve remains constant with changes in L and the voltage at maximum source current is a
weak function of inductance. The capacitance that will result in maximum cross-over
changes with inductance. See Figure 16.
The Resistive Components
If the parallel resistance of R and Rc is held constant while the ratio of R to Rc is
changed then the slope of the curve will be maintained and the ratio of capacitive to
inductive energy storage can be set (see Figure 17). Where Rs is present, the slope will
be the parallel combination of R, Rc, and Rs. The effect of Rs is to decrease the amountof energy storage by shunting it away from the energy storing components. (see figure
18). When there only a shunt resistor, Rs, and no shunt capacitive branch, pinching off
of the curve also results in a decrease in total energy when the inductance is constant
(see figure 19).
-
7/22/2019 Arc Rogers
15/20
The ZnO
Alpha affects how sharply the curve bends and should be set early in the model building
process and can then generally be left alone. The voltage reference, K, is most usefull
for setting the final value of the voltage at maximum current (V @ Imax). Usually it will
be adjusted at the beginning of the modeling process to an approximately correct value
and then will be set to its final value after all other parameters are fixed.
Modeling Strategy
The process of building a model to closely match measured data is necessarily an
iterative one. However, by approaching the process in a logical, stepwise fashion, the
-
7/22/2019 Arc Rogers
16/20
model will rapidly converge to the measurements. First, the slope can be set and then the
value of V at Imax. Next, the inductance can be adjusted to set the approximate size of
the curve. Then ALPHA can be set to match the general shape of the measured curve.
The value of C and the ratio of R to Rc then need to be adjusted to achieve the desired
amount of cross-over. Several iterations of these steps may need to be performed,
depending on the desired accuracy of the model. A final value for K is then selected.
Running three or more test models in a single data case and overlaying the results
directly on the measured data helps to quickly hone the model for optimal matching.
Two Modeling Examples
As shown in Figure 20 and Figure 21, two curves that appear similar in the I-V plane can
have different forms in the time domain. The models in Figure 21 and Figure 22 where
achieved after fifteen and thirty-one iterations, respectively, of a three test case modeland represent nearly the closest match achievable with the types of model used. The
model of the curve in Figure 21 uses an advanced model composed of the basic model
plus a damped capacitor in shunt. The model of the curve in Figure 22 uses an advanced
model as shown in Figure 9 which has both a shunt damped capacitor and a shunt
resistor.
-
7/22/2019 Arc Rogers
17/20
-
7/22/2019 Arc Rogers
18/20
! APPENDIX - SAMPLE DATA CONDITIONING FILE
!
! THIS FILE SMOOTHS THE VOLTAGE AND CURRENT DATA
! POINTS FOR THE FAULT ARC
! IT ALSO SETS THE AXIS SCALES AND SHIFTS THE TIME
!
SET UNITS/BASE=UNITY!
! SMOOTH THE ARC VOLTAGE WITH LOW-PASS, ZERO-PHASE-SHIFT FILTER
ANALYZE/FILTER=LOW_PASS/BI/TAU=0.5 1 101
!
! GENERATE IDEAL SINE WAVE THAT MATCHES PHASE AND AMPLITUDE OF DATA
ANALYZE/USER=SIN/PAR=(65,160) 1 102
!
! SHIFT TIME BASES OF DATA SO SIMULATION TIME OF MODEL IS DECREASED
ANALYZE/SHIFT_TIME=-170 101 103
ANALYZE/SHIFT_TIME=-170 102 104
!
SET LEVELS/UPPER=6/TR=1
SET LEVELS/UPPER=80/TR=2
SET AXIS/GRID=2/DIVISIONS=12/TR=1
SET AXIS/GRID=4/DIVISIONS=8/TR=2
TIME 122 139
!NAMES 1 /GET=ARC_CURVE.NAMES
TITLE 1 /GET=ARC_CURVE.TITLE
LIST 103 104
DISPLAY/XY
!
C APPENDIX - SAMPLE DATA CASE FOR BASIC MODEL (FIGURE 8)
C
BEGIN NEW DATA CASE
C ==============================================================================
C
C Purpose:
C This data case is used for developing a more accurate arc model based
C on the ZNO component.
C ==============================================================================
C Card to adjust MAXZNO ZNO solution iterations (default 50)
ZO,100.,,,,0.1,3.0,C ==============================================================================
C delT )( TMax )( Xopt )( Copt )(Epsiln)(Tolmat)
20.E-6 .500 60.
10000 5 0 0 0 0 0 1 0 0
C print][ Iplot][Connct][ SSout][Maxout][ Ipun ][MemSav][PL4sav][NEnerg][ Diag ]
C ==============================================================================
C
C ***** SPECIAL FAULT ARC MODEL (Based on ZnO) *****
C 200 OHM RESISTOR IN PARALLEL, 1070 V AT 1 AMP WITH EXPONENT OF 10
C I = (V/1070.)**10 amps (ATP ignores ZnO model below 0.1 pu voltage)
C ZNO SHUNT RESISTANCE ( R )
ARCZ1 ARCZ2 0.100 0
C $DISABLE
92ARCZ1 ARCZ2 5555. 0
2.4500 -1.
1.0 8. .10
9999.C $ENABLE
C ZNO SERIES INDUCTANCE ( R )( L )
ARCZ2 .0250
C ==============================================================================
BLANK ENDS BRANCH
C ==============================================================================
C Fault Switch for 20 kV LL fault test on SVC A to B-phase
ARCIS ARCZ1 -1. 10. 1
C ==============================================================================
BLANK ENDS SWITCH CARDS
C ZNO CURRENT SOURCE
C [NODE]-1( Ampl )( Freq )( Angle )( A1 )( T1 )( T start)( T stop )
14ARCIS -1 65.000 60.0 0.0 -1. 10.
BLANK ENDS SOURCE CARDS
C ==============================================================================
ARCIS
C ==============================================================================
BLANK ENDS OUTPUT
BLANK ENDS PLOT
BLANK ENDING CASE
-
7/22/2019 Arc Rogers
19/20
-
7/22/2019 Arc Rogers
20/20
BLANK ENDS SOURCE CARDS
C ==============================================================================
C ARC VOLTAGE MEASUREMENT
ARCIS BRCIS CRCIS
C ==============================================================================
BLANK ENDS OUTPUT
BLANK ENDS PLOT
BLANK ENDING CASE