Download User Instructions of Noda Setup in ATP

User Instructions of Noda Setup in ATP
Taku Noda and Akihiro Ametani
Original manuscript was prepared in March 1997 and revised by A. Ametani in July 1998
1
INTRODUCTION
The importance of more precisely simulating transmission-line transients is increasing due to
the economical incentive of using more accurate modeling in design as well as protection studies. For
switching, fault, and fault-clearing surge studies, the most important and also the most difficult part of
the simulation is the inclusion of the frequency dependence of a transmission line. The frequency
dependence of modal propagation has been investigated widely, and the results are already installed in
EMTP as WEIGHTING [1], SEMLYEN SETUP [2], AMETANI SETUP [3], HAUER SETUP [4],
and JMARTI SETUP [5]. But all of them only take into account the frequency dependence of the
modal propagation and ignore the frequency dependence of the modal-transformation matrices (hereafter
those models are referred to modal-domain line models), although the frequency dependence of the
matrices can be significant in many cases.
The modal-domain line models successfully reproduce the modal-domain frequency dependence. Nevertheless, when the frequency dependence of the modal-transformation matrices is heavy, the
use of constant modal-transformation matrices causes an error.
The inclusion of the frequency-
dependent modal-transformation matrices can be achieved by either applying convolution to the matrices
[6,7] or direct phase-domain approaches [8-11]. The practical implementation of the transformationmatrix convolution could be complicated in terms of eigenvalue tracing by mode crossing (at some
frequency, two or more eigenvalues become equal) [12]. On the other hand, the direct phase-domain
approaches avoid the modal transformation itself, but the application of recursive convolution to a
phase-domain response is difficult because of the time-domain discontinuities of the response due to
modal traveling-time differences.
The NODA SETUP is one of the direct phase-domain approaches developed by the author
[10]. The line model uses an ARMA (AutoRegressive Moving-Average) model for the time-domain
realization of the phase-domain convolution, and the phase-domain discontinuous response is accurately
1
reproduced by the ARMA model, taking advantage of the one-sample-delay nature of the Z-operator. In
ref. [11], further improvements to the line model are made. The improvement to convolution allows
each ARMA model to use its own time step interfacing with the external circuit by a linear interpolation
technique, and thus the model is designated as IARMA (interpolated ARMA) model. A steady-state
initialization method is also developed in the reference in order to make possible such as fault
calculations. The matrix stability conditions presented in ref. [11] is not yet installed in the present
version of the NODA SETUP, because it requires more investigation for the accurate evaluation of
eigenvalues.
In the following, the usage of the NODA SETUP is illustrated using an example : 500-kV
horizontal overhead line.
2
FREQUENCY-DOMAIN FITTING
A. Overview
The modeling of a transmission line (overhead lines and cables) using the NODA SETUP
requires the following two steps :
1)
Calculation of the frequency-dependent line constants of the transmission line, hereafter referred to
“frequency data”, using CABLE PARAMETERS or LINE CONSTANTS supporting routine in
ATP. The result is written in .AFT file (ARMAFIT file). Note that CABLE CONSTANTS
cannot be used to make the .AFT file.
2)
Fitting the frequency data (stored in .AFT file) with IARMA models for the time-domain
realization of the frequency dependence. This procedure is performed by an independent fitting
program ARMAFIT. The result is written in .PCH file (punch-out file).
It should be noted that another line-constants calculation program can be used, because
ARMAFIT is independent of ATP. This is important, because a certain transmission-line configuration,
which is not supported neither by CABLE PARAMETERS nor LINE CONSTANTS, can be fitted
using ARMAFIT, if the frequency data is prepared in .AFT file by a user-made line-constants
calculation program. The format of .AFT file is illustrated in Section 2-C.
In order to use the line model for a transient simulation, the name of .PCH file has to be
2
specified in a branch card in an ATP data case unlike other line models. (On the other hand, using other
line models such as SEMLYEN SETUP, JMARTI SETUP, and so on, .PCH file has to be pasted in a
data case) Because the .PCH file remains outside of the data case, the .PCH file can be used by other
data cases by simply specifying the file name.
B. Example
A 500-kV single-circuit overhead line (Azumi Trunk of the Tokyo Electric Power Co.) is used
to illustrate the usage of the NODA SETUP. As shown in Fig. 1, each of the ground wires is a single
conductor ACSR 120, and each of the phase wires is a bundle of 4 conductors ACSR 240 of which the
separation is 0.4 m.
Three phase wires and two ground wires are horizontally arranged and
untransposed, and the line length is 83 km. Fig. 2 illustrates an actual test circuit where the receivingend voltages were measured in case of switching as shown in Fig. 3 [13]. For this switching-surge
simulation, the impedance and admittance matrices are reduced from 5 by 5 to 3 by 3 assuming zero
voltages, because the voltages on the ground wires are not interested. Thus, the line is treated as a
three-phase line. Fig. 4 shows the frequency dependence of the first-column elements of the voltage
modal-transformation matrix A. Because the magnitude of A11 and A31 elements vary more than 10 %,
the proposed phase-domain model is advantageous than model-domain models. A switching-surge
simulation corresponding to Fig. 2 is carried out in Chapter 3.
22 m
GW
GW ACSR 120
14 m
35 m
25 m
a
b
c
ACSR 240
×4
sep. = 0.4 m
line length = 83 km
earth resistivity = 200 Ω m
Fig. 1 500-kV single-circuit untransposed horizontal overhead line
(Azumi trunk of the Tokyo Electric Power Co.)
3
415 Ω
83 km
a
b
1 p.u.
c
Fig. 2 Actual test circuit of switching surge
Fig. 3 Measured switching transients of receiving-end voltages
1
0.9
0.8
0.7
0.6
0.5 1
10
magnitude of A11 and A31,
when A21 is normalized to unity
102
103
104
frequency [Hz]
105
106
Fig. 4 First column elements of voltage transformation matrix A
4
C. Calculation of Frequency Data using ATP
The following data case HORIZ-LC.DAT calculates the frequency data of the example line
and writes them into file HORIZ.AFT, using ATP. It uses the CABLE PARAMETERS supporting
routine.
BEGIN NEW DATA CASE
{ HORIZ-LC.DAT }
C 500-kV Single-Circuit Horizontal Line (see HORIZ.DAT for transients)
C
type "ARMAFIT HORIZ.AFT -pHORIZ.PCH" on command prompt for fitting
NODA SETUP { Request IARMA model fitter (ARMAFIT). No printout of F-scan
HORIZ.AFT
{ Output file name (blank requests use of default TAKUNODA.CCC)
HOMOGENEOUS LINE { keyword for homogeneous line
-1.
{ time step (if negative, optimum time step is selected)
4 16
{ min and max orders for voltage deformation matrix [H]
1 12
{ min and max orders for char. admittance matrix [Y0]
1. .5 1. 3
{ error constants: EpsA, EpsM1, EpsM2 in percent, and Nitr
1, 3
{ pair(s) of phases having symmetry
NODA SETUP END
{ Bound of fitter data; begin CABLE PARAMETERS data
CABLE CONSTANTS
CABLE PARAMETERS
1
0
1
0
1
0
0
3
2
4
1
11.20E-03 4.800E-03 8.050E-03 3.450E-03
0.4
4.0855E-08
1.04.5103E-08
1.0
25.
12.5
-14.
25.
12.5
0.0
25.
12.5
14.
35.
17.5
-11.
35.
17.5
11.
200.
1.
6
20
83.E3 { 1st f. card for f. scan
200.
10.E6
83.E3 { 2nd f. card to determine v
BLANK
BLANK
BEGIN NEW DATA CASE
BLANK
First comes keyword BEGIN NEW DATA CASE as usual, and keyword NODA SETUP follows. The
next line specifies the name of .AFT file to which the frequency data is written, and HORIZ.AFT is
specified in the present example. Then, keyword HOMOGENEOUS LINE follows. Lines enclosed by
keywords HOMOGENEOUS LINE and NODA SETUP END are simply copied into the .AFT file, and
those lines are fitting parameters. HOMOGENEOUS LINE declares that the present transmission line is
simulated by a homogeneous line model. Other line models, for example CORONA LINE to include
corona branches, would be added in the future, but only the homogeneous line model is supported for
now. (If keyword KIZILCAY F-DEPENDENT is specified here, the frequency characteristic of an
admittance element can be modeled as an ARMA model or as a Laplace s-function model to be used as
a KIZILCAY F-DEPENDENT element in a branch card of an ATP data case, although the format of
the following parameters and data is different.) The next five lines are fitting parameters section in
which parameters are placed using a free format separated by space ‘ ’ or comma ‘,’. There is no
distinction between space and comma, and contiguous space or comma are treated as one separator.
5
The first line of the fitting parameters section specifies a time step, with which all the ARMA models in
the line model, is synthesized.
If a negative value is specified, then an appropriate time step is
automatically determined by ARMAFIT using the following equation :
∆t =
1
2 ×10
log10 f max + ( log10 f max − log10 f min )/( N − 1)
,
where fmin : lowest frequency, fmax : highest frequency, N : number of total frequency points of the
frequency scan, and fmin = 1 Hz, fmax = 1 MHz, N = 120 in case of the present example. The meaning
of the above equation is that the time step is determined by the sampling theorem using a frequency
which is a little higher than the highest frequency. The second line of the fitting parameters section
specifies the minimum and maximum orders Nmin, Nmax of the ARMA models which represent the
elements of the propagation-function matrix H(jω). The third line specifies those of the characteristicadmittance matrix Y0(jω). From author’s experience, Nmin = 4 and Nmax = 16 is recommended for the
propagation-function matrix. And Nmin = 1 and Nmax = 12 is recommended for the characteristicadmittance matrix, because each element of the characteristic-admittance matrix has smoother
frequency characteristics than the propagation-function matrix. If desired fitting accuracy cannot be
obtained, the maximum order may be increased by user for achieving better fitting. In the fourth line,
the values of error tolerances εA, εM1, εM2, and Nitr are specified. The description of the error tolerances
is :
εA
: error tolerance in the stage of least-square fitting in %
εM1
: error tolerance for detecting modal traveling timings in %
εM2
: error tolerance for detecting dominant modes in each phase response in %
Nitr
: maximum iteration steps in the stage of nonlinear improvement
The author recommends εA = 3 %, εM1 = 0.5 %, εM2 = 1 %, and Nitr= 3 as in the example. ARMAFIT
uses a linearized least-squares method presented in refs. [10, 14, 15] for the fitting, and the stage of a
nonlinear improvement using the Newton-Raphson iteration is added purposing a better result. The
Newton-Raphson iteration improves the solution obtained by the least-squares method. It is important
that if the iteration does not converge, Nitr should be set to 0. The fifth line specifies the symmetry
information of line configuration. In the example line, phases 1 and 3 (a and c) are symmetrical with a
reference line which is usually the tower supporting the wires. If there are more than two pairs of
symmetrical phases, for example, specify “1,4
2,5
3,6” when phases 1 and 4, 2 and 5, 3 and
6 are symmetrical phases. If there is no symmetry in the line configuration, keyword NO SYMMETRY
6
is placed here. The symmetry information is used to reduce the number of fitting. Because the
proposed line model is a phase-domain model, the computation time of the frequency-dependence
synthesis is in proportional to n2 (n : number of conductors). Thus, the reduction of the fitting time is
important, although the linearized least-squares fitting method is quite fast.
Next comes a standard CABLE PARAMETERS case describing the line configuration, which
has two frequency cards. The first frequency card determines the range of frequency logarithmically
scanned for the subsequent frequency-domain fitting using ARMAFIT. In the example, from 1 Hz to 1
MHz with 20 points per a decade. The second frequency card specifies a frequency at which the
velocity of all the natural modes of propagation are determined. Usually, a value which is higher than
the highest frequency of the frequency scan is appropriate. Finally comes BEGIN NEW DATA CASE
and BLANK to terminate the ATP execution.
D. Format of .AFT File
Executing ATP with the above data case HORIZ-LC.DAT gives a disk file HORIZ.AFT
shown below. The lines between keywords HOMOGENEOUS LINE and NODA SETUP END in
the .DAT file are simply copied into the first part of the .AFT file as mentioned in the previous section.
HOMOGENEOUS LINE { keyword for homogeneous line
{ HORIZ.AFT }
-1.
{ time step (if negative, optimum time step is selected)
4 16
{ min and max orders for voltage deformation matrix [H]
1 12
{ min and max orders for char. admittance matrix [Y0]
1. .5 1. 3
{ error constants: EpsA, EpsM1, EpsM2 in percent, and Nitr
1, 3
{ pair(s) of phases having symmetry
C
============ End data for fitter. Begin F-scan output for fitter.
3 { NG above DO 890 of NEWCBL
8.3000000000000000E+04 { DIST above DO 890 of NEWCBL
C
============== Begin data for next frequency of F-scan.
1.0000000000000000E+00 { FREQ upon exit from PRCON
C
---Next comes CZCHAR for JNC = 3
1.1483624297072260E-03
8.3286203848444986E-04 ... { End row 1
-8.0649434426595086E-05 -1.9393906464409792E-04 ... { End row 2
-3.2559956812689386E-05 -1.3353667417340801E-04 ... { End row 3
C
---Next comes AI for JNC = 3
-3.5477094314368024E-01 -3.2288262662208501E-02 ... { End row 1
3.5530613970561342E-01 -2.5739096571082504E-02 ... { End row 2
-5.0000000000000022E-01
5.5099579897649624E-18 ... { End row 3
C
---Next comes A for JNC = 3
-4.9447986717851772E-01 -6.6953373809247194E-02 ... { End row 1
9.9738635894709371E-01 -7.2252688436203208E-02 ... { End row 2
-4.9447986717851800E-01 -6.6953373809246999E-02 ... { End row 3
C
---Next comes vector QN.
3.3816076572349785E-08
3.9995235127918691E-08 ...
...
2ND FREQUENCY CARD. SAME OUTPUT FOR IT FOLLOWS:
C
============== Begin data for next frequency of F-scan.
1.0000000000000000E+07 { FREQ upon exit from PRCON
C
---Next comes CZCHAR for JNC = 3
3.4766404870108167E-03
1.1568967262196594E-05 ... { End row
7
1
-4.6285596552050965E-04
7.1894505011143260E-06
-1.1362460182818989E-04
3.5753455568815521E-06
C
---Next comes AI for JNC = 3
3.5333941127383395E-01 -1.0177101506049404E-03
-4.9999999999999889E-01
1.4325890054917487E-15
-3.5333907665528164E-01 -1.1279191848317151E-03
C
---Next comes A for JNC = 3
8.7852428469030430E-01 -1.7127878532396993E-03
9.9999490505719602E-01
3.1921559563152751E-03
8.7852428469031174E-01 -1.7127878532326984E-03
C
---Next comes vector QN.
1.7341030197062220E-03
2.1145674635292447E-01
...
...
{ End row
{ End row
2
3
...
...
...
{ End row
{ End row
{ End row
1
2
3
...
...
...
{ End row
{ End row
{ End row
1
2
3
...
The next two lines are the number of conductors n and the line length l. In the present
example, n = 3 (the ground wires are eliminated using a matrix manipulation assuming zero voltages),
and l = 83 km. In the next part, N sets of line constants are provided, where N is the total number of
frequencies of the frequency scan :
(1) frequency
(2) characteristic-admittance matrix Y0
(3) inverse of voltage transformation matrix A− 1
(4) voltage transformation matrix A
(5) propagation constant γ
Frequency comes on the first line of each set. Then, characteristic-admittance matrix Y0, inverse of
voltage transformation matrix A− 1, and voltage transformation matrix A are provided in the following
matrix form :
x11real
x11imag
x12real
x12imag
.....
x1n real
x1n imag
x21real
x21imag
x22real
x22imag
.....
x2n real
x2n imag
xn1real
xn1imag
.....
xn2real
xn2imag
.....
xnn real
xnn imag
where n is the number of conductors, and xij is the (i, j) element of matrix X. At last, propagation
constant γis provided in the following vector form :
γ
1real
γ
1imag
γ
2real
γ
2imag
.....
γ
n real
γ
n imag
where γi is the i-th element of vector γ
. After N sets of the above line constants, keyword 2ND
FREQUENCY CARD.
SAME OUTPUT FOR IT FOLLOWS: comes to declare that the same set
of line constants follows in order to calculate the velocity of the natural modes of propagation.
E. Fitting using ARMAFIT
In order to perform fitting of the frequency data prepared in .AFT file, an independent
program ARMAFIT is used.
As mentioned earlier, ARMAFIT can also be used to fit the given
8
frequency characteristic of an admittance element with an ARMA model or with a Laplace s-function
model, and the identified model can be used as a KIZILCAY F-DEPENDENT element in a branch
card in an ATP data case. The instructions for this use may be provided as separate user instructions.
ARMAFIT
is an MS-DOS application.
To execute ARMAFIT, type as follows on a
command line :
C:>ARMAFIT F_NAME.AFT
F_NAME.AFT is the file name containing the frequency data. If the file name is TEMP.AFT, it can be
omitted as :
C:>ARMAFIT
Files TEMP.PCH and TEMP.AGF are created by the execution. TEMP.PCH contains the fitting
results, i.e. the coefficients of the identified ARMA models of the transmission line, and it is used in
subsequent transient calculations. TEMP.AGF (ARMAFIT graph file) contains information used by a
small plotting program PGVGA to show the graphs of the fitting results. If file name TEMP.PCH is not
desired, -p option can be used to specify the name as :
C:>ARMAFIT F_NAME.AFT -pF_NAME.PCH
In the present example,
C:>ARMAFIT HORIZ.AFT -pHORIZ.PCH
may be appropriate. HORIZ.PCH is created instead of TEMP.PCH. If one needs more information
during the fitting, she/he can modify the debugging level of the execution using -d option. Bigger value
provides more information, and the default is zero. To execute the present example with debugging
level 2, type :
C:>ARMAFIT HORIZ.AFT -pHORIZ.pch -d2
To modify file name TEMP.AGF, -g option can be used in the same manner as the -p option.
In order to visualize the fitting results using PGVGA, .AGF file has to be converted into .PG
file that can be read by PGVGA. For this purpose, a small converter program AGF2PG is used.
To
convert F_NAME.AGF to F_NAME.PG, type as :
C:>AGF2PG F_NAME.AGF > F_NAME.PG
And the results can be shown by typing as :
C:>PGVGA F_NAME
If TEMP.AGF is always used, batch file G.BAT is prepared to simplify the above two steps into one
9
step. Typing as
C:>G
is equivalent to the following two steps :
C:>AGF2PG TEMP.AGF > TEMP.PG
C:>PGVGA TEMP
Other command line options : -t to request transformation matrices output, -s to request step
responses are available. -? option invokes the following help screen :
usage : ARMAFIT [file name] [options]
[file name] : specifies input file name, when TEMP.AFT is not desired
[options]
-d<n>
: requests n-th level debugging mode: 0-3
-p<file name> : specifies the name of punch-out file,
when 'TEMP.PCH' is not desired
-g<file name> : specifies the name of ARMAFIT graph file,
when 'TEMP.AGF' is not desired
-t
: requests transformation-matrices output
(valid for the NODA SETUP line model)
-s<Tmax>
: requests step response of each ARMA
model ( 0 < t < Tmax: end time )
-?
: prints this help
F. Format of .PCH File
File HORIZ.PCH created from HORIZ.AFT using ARMAFIT is shown below. If one
prepares another fitting program, this section would help, or otherwise can be skipped. The first line is
the same as the first line of .AFT file. In the present example, HOMOGENEOUS LINE. The second
line specifies the number of conductors and the simulation time step. If the simulation time step is
negative, each ARMA element uses its own time step. If positive, all the ARMA elements have to use
the same value. Then, the identified ARMA coefficients of the elements of the propagation-function
matrix H(jω) and of the characteristic-admittance matrix Y0(jω) follow. First comes H(jω), and then
Y0(jω) next. The element order is (1,1), ..., (1,n), (2,1), ..., (2,n), (3,1), ..., (3,n),..., (n,n) for H(jω), and
(1,1), (1,2), ..., (1,n), (2,2), ..., (2,n), (3,3), ..., (3,n), ..., (n,n) for Y0(jω) considering the symmetry of
Y0(jω).
C PUNCH-OUT FILE GENERATED BY ARMAFIT (NODA SETUP)
C
HOMOGENEOUS LINE
3 -1.00000E+00 { number of phase, simulation time step
C
C *** VOLTAGE DEFORMATION MATRIX [H]
C
10
{HORIZ.PCH}
C
PHASE (1,1)
4.46050E-07
2.77671E-04 { time step, minimum traveling time
13 { optimum order
0
1.159827456617948E-02
1.000000000000000E+00
1
3.595321963155144E-02 -4.981616631738193E+00
2 -3.025769143023499E-01
1.100358764129312E+01
3
6.961972292452843E-01 -1.423961716325489E+01
4 -8.513947268404801E-01
1.177294404866907E+01
5
6.317563569520553E-01 -6.091515973705507E+00
6 -2.780167317768813E-01
1.512039923121173E+00
7
5.648610354705126E-02
4.237318112541313E-01
53
8.256802868730861E-04 -8.341824081458369E-01
54 -4.155159173918327E-03
8.087371458735804E-01
55
8.543141344913702E-03 -5.947718596715662E-01
56 -8.980675645850781E-03
2.956097797044899E-01
57
4.832418232056019E-03 -8.558476654305983E-02
58 -1.067723551040730E-03
1.063894864058851E-02
C
C PHASE (1,2)
4.46050E-07
2.77671E-04 { time step, minimum traveling time
13 { optimum order
0 -2.446174878582950E-02
1.000000000000000E+00
1 -7.012602228324355E-02 -4.109552722838114E+00
2
4.563107912664058E-01
7.171363377533132E+00
3 -7.884415023531451E-01 -7.159300220801263E+00
4
7.090787574874342E-01
4.573510792094408E+00
5 -3.958056542776619E-01 -1.809712407445911E+00
6
1.285954217083908E-01
2.815897615276392E-01
7 -1.515032050643555E-02
1.802002270243410E-01
53
8.431942998029481E-04 -2.726531499251255E-01
54 -3.181426997708536E-04
2.609346961699580E-01
55 -3.119735216863715E-03 -1.740165175780101E-01
56
3.815050576647997E-03
7.035124251642322E-02
57 -1.220089215728256E-03 -1.271507826850998E-02
58 -3.315273403026175E-15
0.000000000000000E+00
C
...
C
PHASE (2,2)
4.46050E-07
2.77671E-04 { time step, minimum traveling time
8 { optimum order
0
4.077414418562324E-02
1.000000000000000E+00
1
2.514698469506246E-01 -1.852088871937162E+00
2 -4.381029810508936E-01
5.926203441950437E-01
4
1.402409273131093E-01
4.502775959949800E-01
5 -2.086972191791472E-02 -3.147828226445844E-01
6
2.649484066606273E-02
1.843576083753680E-01
53
8.063451962296873E-03 -1.007130904982679E-01
54 -1.267264851542401E-02
7.823970342837594E-02
55
4.609021563865146E-03 -3.790355109417610E-02
C
C PHASE (2,3)
SAME AS 2, 1
C
C PHASE (3,1)
SAME AS 1, 3
C
C PHASE (3,2)
SAME AS 1, 2
C
C PHASE (3,3)
SAME AS 1, 1
C
C *** CHARACTERISTIC ADMITTANCE MATRIX [Y0]
C
C PHASE (1,1)
4.46050E-07 { time step
5 { optimum order
0
3.432407053569759E-03
1.000000000000000E+00
11
1
2
3
4
5
-9.477240720144314E-03
5.888979538603486E-03
4.914126439826022E-03
-6.748260262659145E-03
1.989987950812137E-03
-2.750819873944151E+00
1.690222644076477E+00
1.447087899059234E+00
-1.961562935236077E+00
5.750722660538831E-01
PHASE (2,2)
4.46050E-07 { time step
5 { optimum order
0
3.452700899052231E-03
1 -9.409100320835660E-03
2
5.599271989996347E-03
3
5.172670073548110E-03
4 -6.770257398645766E-03
5
1.954714756888454E-03
1.000000000000000E+00
-2.717296116866567E+00
1.602408609808761E+00
1.509493358048324E+00
-1.957027347600902E+00
5.624214966149745E-01
C
...
C
C
C
C PHASE
SAME AS
C
C PHASE
SAME AS
C
C
(2,3)
1, 2
(3,3)
1, 1
For each element of H(jω), the first line contains the time step and the shortest traveling time
of the element. The shortest traveling time is the traveling time of the fastest mode included in the
element, and the value is evaluated at frequency specified by the second frequency card. The second
line is the model order, and then the identified ARMA coefficients follow. For an illustration of the
format of the ARMA coefficients, consider the following ARMA model :
a0 + a1z − 1 + a10 z − 10 + a11z − 11
Hij ( z) =
1 + b1z − 1 + b2 z − 2 + b3 z − 3
The order of the above ARMA model is 3, and the coefficients are specified as follows :
index
numerator coefficients
denominator coefficients
0
a0
1.0
1
a1
b1
10
a10
b2
11
a11
b3
If the frequency characteristics of element Hij is identical to element Hkl, considering the symmetry of
conductor configuration, SAME AS
i, j replaces the above format to avoid duplication.
For each element of Y0(jω), the first line contains the time step. The second line is the model
12
order, and then the identified ARMA coefficients follow in the same manner.
characteristics of element Y0ij is identical to element Y0kl, SAME AS
If the frequency
i, j also replaces the format to
avoid duplication. The above parameters are placed using a free format separated by space ‘ ’ or
comma ‘,’. There is no distinction between space and comma, and contiguous space or comma are
treated as one separator.
3
TIME-DOMAIN SIMULATION
A. Branch Cards in ATP
In order to use a transmission-line model created by the Noda Setup, the name of .PCH file
containing the ARMA coefficients of the line model is specified as :
C -------------------------------------------------------------------C
1
2
3
4
5
6
7
C 34567890123456789012345678901234567890123456789012345678901234567890
C BUS1 BUS2
Noda Line FILE NAME
SHOW X
C --------------------------------------------------------------------1SND1 RCV1
Noda line F_NAME.PCH SHOW 1
{ 1 of n }
-2SND2 RCV2
{ 2 of n }
...
-nSNDn RCVn
{ n of n }
An n-phase transmission line requires n branch cards in the same manner as other line models. The first
column of the branch cards is occupied by minus sign -, and the second column by phase index (1, 2, ...,
n). Specify the two terminal nodes of the branch by 6-character alphanumeric node names using
columns 3 to 8 and 9 to 14. The order of the two pairs of phases follows the rule of CABLE
PARAMETERS or LINE CONSTANTS supporting routine. Only on the first line, keyword Noda
Line is required in columns 25 to 33, and .PCH file is specified using columns 35 to 46. Keyword
SHOW is also required only on the first line in columns 47 to 50, and a digit in column 52 controls the
amount of information printed out on screen. Bigger digit shows more information of the line model.
B. Switching-Surge Calculation
Using the present example, a switching-surge calculation is carried out.
The circuit
configuration is shown in Fig. 2, and corresponding ATP data case HORIZ.DAT is listed below. Fig. 5
shows the calculated results of the receiving-end voltages, and they agree well with the field-test results
shown in Fig. 3.
13
BEGIN NEW DATA CASE
{ HORIZ.DAT }
C 500-kV Single-Circuit Horizontal Line (see HORIZ-LC.DAT for fitting)
0.1E-6 400.E-6
1
1
SRC
SENDA
415.
-1SENDA RECA
Noda line HORIZ.PCH
SHOW 1
{ 1 of 3 }
-2SENDB RECB
{ 2 of 3 }
-3SENDC RECC
{ 3 of 3 }
BLANK
BLANK
11SRC
1.
BLANK
1
BLANK
BEGIN NEW DATA CASE
BLANK
receiving-end voltages in p.u.
1
phase a
0.5
phase b
0
phase c
-0.5
250
300
350
time in microseconds
Fig. 5 Calculated results of switching-surge (NODA SETUP)
14
400
REFERENCES
[1]
W.S. Meyer and H.W. Dommel, “Numerical modeling of frequency-dependent transmission
parameters in an electromagnetic transient program,” IEEE Trans., Power Apparatus and Systems,
Vol. PAS-93, pp.1401-1409, 1974.
[2]
A. Semlyen and A. Dabuleau, “Fast and accurate switching transient calculations on transmission
lines with ground return using recursive convolutions,” IEEE Trans., Power Apparatus and Systems,
Vol. PAS-94 (2), pp.561-571, 1975.
[3]
A. Ametani, “A highly efficient method for calculating transmission line transients,” IEEE Trans.,
Power Apparatus and Systems, Vol. PAS-95 (5), pp.1545-1549, 1976.
[4]
J.F. Hauer, “State-space modeling of transmission line dynamics via nonlinear optimization,” IEEE
Trans., Power Apparatus and Systems, Vol. PAS-100 (12), pp.4918-4925, 1981.
[5]
J.R. Marti, “Accurate modelling of frequency-dependent transmission lines in electromagnetic
transient simulations,” IEEE Trans., Power Apparatus and Systems, Vol. PAS-101 (1), pp.147-155,
1982.
[6]
A. Ametani, “Refraction coefficient method for switching-surge calculations on untransposed
transmission lines (Accurate and approximate inclusion of frequency dependency),” IEEE PES
Summer Meeting, C 73-444-7, 1973.
[7]
L. Marti, “Simulation of transients in underground cables with frequency dependent modal
transformation matrices,” IEEE Trans., Power Delivery, vol. PWD-3 (3), pp.1099-1110, 1988.
[8]
G. Angelidis and A. Semlyen, “Direct Phase-Domain Calculation of Transmission Line Transients
Using Two-Sided Recursions,” IEEE Trans., Power Delivery, Vol. 10, No. 2, pp. 941-949, April
1995.
[9]
B. Gustavsen, J. Sletbak, and T. Henriksen, “Calculation of electromagnetic transients in transmission
cables and lines taking frequency dependent effects accurately into account,” IEEE Trans., Power
Delivery, Vol. 10, No. 2, pp. 1076-1084, April 1995.
[10]
T. Noda, N. Nagaoka, and A. Ametani, “Phase domain modeling of frequency-dependent transmission
lines by means of an ARMA model,” IEEE Trans., Power Delivery, Vol. 11, No. 1, pp. 401-411,
January 1996.
[11]
T. Noda, N. Nagaoka, A. Ametani, “Further Improvements to a Phase-Domain ARMA Line Model in
Terms of Convolution, Steady-State Initialization, and Stability,” IEEE Power Engineering Society
Summer Meeting, Denver, Colorado, USA, 1996. (to be published in IEEE Trans.)
[12]
Tsu-huei Liu and Li Jin-gui, “Call for Help with Rational Function Approximations to FrequencyDependent Transformation Matrices of Cables and Lines,” EMTP News, Leuven EMTP Center,
March, 1988.
[13]
A. Ametani, T. Ono, and A. Honaga, “Surge Propagation on Japanese 500kV Untransposed
Transmission Line,” Proc. IEE, Vol. 121, No.2, 1974.
[14]
T. Noda and N. Nagaoka, “Development of ARMA Models for a Transient Calculation using
Linearized Least-Squares Method,” Trans. IEE of Japan, Vol. 114-B, No. 4, pp. 396-402, 1994.
[15]
T. Noda, “Development of a Transmission-Line Model Considering the Skin and Corona Effects for
Power Systems Transient Analysis,” Ph.D. Thesis submitted to Doshisha University, 1996.
[16]
T. Noda, N. Nagaoka, and A. Ametani, “Fault-Surge Calculations using the Phase-Domain ARMA
Line Model,” Trans. IEE of Japan, Vol. 116-B, No. 11, pp. 1409-1414, 1996.
15