User Instructions of Noda Setup in ATP

Transcription

1 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 INTRODUTION 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 frequencydependent 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

2 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 FREQUENY-DOMAIN FITTING A. Overview The modeling of a transmission line (overhead lines and cables) using the NODA SETUP requires the following two steps : 1) alculation of the frequency-dependent line constants of the transmission line, hereafter referred to frequency data, using ABLE PARAMETERS or LINE ONSTANTS supporting routine in ATP. The result is written in.aft file (ARMAFIT file). Note that ABLE ONSTANTS 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.ph 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 ABLE PARAMETERS nor LINE ONSTANTS, 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-. In order to use the line model for a transient simulation, the name of.ph file has to be 2

3 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,.ph file has to be pasted in a data case) Because the.ph file remains outside of the data case, the.ph 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 o.) is used to illustrate the usage of the NODA SETUP. As shown in Fig. 1, each of the ground wires is a single conductor ASR 120, and each of the phase wires is a bundle of 4 conductors ASR 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 A 11 and A 31 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 hapter 3. GW 14 m 22 m GW ASR m 25 m a b c line length = 83 km earth resistivity = 200 Ω m ASR sep. = 0.4 m Fig kV single-circuit untransposed horizontal overhead line (Azumi trunk of the Tokyo Electric Power o.) 3

4 1 p.u. 415 Ω a b c 83 km Fig. 2 Actual test circuit of switching surge Fig. 3 Measured switching transients of receiving-end voltages magnitude of A 11 and A 31, when A 21 is normalized to unity frequency [Hz] Fig. 4 First column elements of voltage transformation matrix A 4

5 . alculation of Frequency Data using ATP The following data case HORIZ-L.DAT calculates the frequency data of the example line and writes them into file HORIZ.AFT, using ATP. It uses the ABLE PARAMETERS supporting routine. BEGIN NEW DATA ASE { HORIZ-L.DAT } 500-kV Single-ircuit Horizontal Line (see HORIZ.DAT for transients) type "ARMAFIT HORIZ.AFT -phoriz.ph" 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.) 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] { 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 ABLE PARAMETERS data ABLE ONSTANTS ABLE PARAMETERS E E E E E E E3 { 1st f. card for f. scan E6 83.E3 { 2nd f. card to determine v BEGIN NEW DATA ASE First comes keyword BEGIN NEW DATA ASE 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 ORONA LINE to include corona branches, would be added in the future, but only the homogeneous line model is supported for now. (If keyword KIZILAY 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 KIZILAY 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

6 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 : 1 t = f + ( f f ) N log max log max log min /( ), where f min : lowest frequency, f max : highest frequency, N : number of total frequency points of the frequency scan, and f min = 1 Hz, f max = 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 N min, N max of the ARMA models which represent the elements of the propagation-function matrix H(jω). The third line specifies those of the characteristicadmittance matrix Y 0 (jω). From author s experience, N min = 4 and N max = 16 is recommended for the propagation-function matrix. And N min = 1 and N max = 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 ε A, ε M1, ε M2, and N itr are specified. The description of the error tolerances is : ε A : error tolerance in the stage of least-square fitting in % ε M1 : error tolerance for detecting modal traveling timings in % ε M2 : error tolerance for detecting dominant modes in each phase response in % N itr : maximum iteration steps in the stage of nonlinear improvement The author recommends ε A = 3 %, ε M1 = 0.5 %, ε M2 = 1 %, and N itr = 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, N itr 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

7 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 n 2 (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 ABLE 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 ASE and to terminate the ATP execution. D. Format of.aft File Executing ATP with the above data case HORIZ-L.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] { error constants: EpsA, EpsM1, EpsM2 in percent, and Nitr 1, 3 { pair(s) of phases having symmetry ============ End data for fitter. Begin F-scan output for fitter. 3 { NG above DO 890 of NEWBL E+04 { DIST above DO 890 of NEWBL ============== Begin data for next frequency of F-scan E+00 { FREQ upon exit from PRON ---- Next comes ZHAR for JN = E E { End row E E { End row E E { End row Next comes AI for JN = E E { End row E E { End row E E { End row Next comes A for JN = E E { End row E E { End row E E { End row Next comes vector QN E E ND FREQUENY ARD. SAME OUTPUT FOR IT FOLLOWS: ============== Begin data for next frequency of F-scan E+07 { FREQ upon exit from PRON ---- Next comes ZHAR for JN = E E { End row 1 7

8 E E { End row E E { End row Next comes AI for JN = E E { End row E E { End row E E { End row Next comes A for JN = E E { End row E E { End row E E { End row Next comes vector QN E E 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 Y 0 (3) inverse of voltage transformation matrix A 1 (4) voltage transformation matrix A (5) propagation constant g Frequency comes on the first line of each set. Then, characteristic-admittance matrix Y 0, inverse of voltage transformation matrix A 1, and voltage transformation matrix A are provided in the following matrix form : x 11real x 11imag x 12real x 12imag... x 1n real x 1n imag x 21real x 21imag x 22real x 22imag... x 2n real x 2n imag... x n1real x n1imag x n2real x n2imag... x nn real x nn imag where n is the number of conductors, and x ij is the (i, j) element of matrix X. At last, propagation constant gis provided in the following vector form : γ 1real γ 1imag γ 2real γ 2imag... γ n real γ n imag where γ i is the i-th element of vector g. After N sets of the above line constants, keyword 2ND FREQUENY ARD. 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

9 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 KIZILAY 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 : :>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 : :>ARMAFIT Files TEMP.PH and TEMP.AGF are created by the execution. TEMP.PH 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.PH is not desired, -p option can be used to specify the name as : :>ARMAFIT F_NAME.AFT -pf_name.ph In the present example, :>ARMAFIT HORIZ.AFT -phoriz.ph may be appropriate. HORIZ.PH is created instead of TEMP.PH. 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 : :>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 : :>AGF2PG F_NAME.AGF > F_NAME.PG And the results can be shown by typing as : :>PGVGA F_NAME If TEMP.AGF is always used, batch file G.BAT is prepared to simplify the above two steps into one 9

10 step. Typing as :>G is equivalent to the following two steps : :>AGF2PG TEMP.AGF > TEMP.PG :>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.PH' 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.ph File File HORIZ.PH 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 Y 0 (jω) follow. First comes H(jω), and then Y 0 (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 Y 0 (jω) considering the symmetry of Y 0 (jω). PUNH-OUT FILE GENERATED BY ARMAFIT (NODA SETUP) HOMOGENEOUS LINE E+00 { number of phase, simulation time step *** VOLTAGE DEFORMATION MATRIX [H] {HORIZ.PH} 10

11 PHASE (1,1) E E-04 { time step, minimum traveling time 13 { optimum order E E E E E E E E E E E E E E E E E E E E E E E E E E E E-02 PHASE (1,2) E E-04 { time step, minimum traveling time 13 { optimum order E E E E E E E E E E E E E E E E E E E E E E E E E E E E PHASE (2,2) E E-04 { time step, minimum traveling time 8 { optimum order E E E E E E E E E E E E E E E E E E-02 PHASE (2,3) SAME AS 2, 1 PHASE (3,1) SAME AS 1, 3 PHASE (3,2) SAME AS 1, 2 PHASE (3,3) SAME AS 1, 1 *** HARATERISTI ADMITTANE MATRIX [Y0] PHASE (1,1) E-07 { time step 5 { optimum order E E+00 11

12 E E E E E E E E E E PHASE (2,2) E-07 { time step 5 { optimum order E E E E E E E E E E E E-01 PHASE (2,3) SAME AS 1, 2 PHASE (3,3) SAME AS 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 : a a z a z a z Hij ( z ) = b z + b z + b z The order of the above ARMA model is 3, and the coefficients are specified as follows : index numerator coefficients denominator coefficients 0 a a 1 b 1 10 a 10 b 2 11 a 11 b 3 If the frequency characteristics of element H ij is identical to element H kl, considering the symmetry of conductor configuration, SAME AS i, j replaces the above format to avoid duplication. For each element of Y 0 (jω), the first line contains the time step. The second line is the model 12

13 order, and then the identified ARMA coefficients follow in the same manner. If the frequency characteristics of element Y 0ij is identical to element Y 0kl, SAME AS 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 ards in ATP In order to use a transmission-line model created by the Noda Setup, the name of.ph file containing the ARMA coefficients of the line model is specified as : BUS1 BUS2 Noda Line FILE NAME SHOW X SND1 RV1 Noda line F_NAME.PH SHOW 1 { 1 of n } -2SND2 RV2 { 2 of n }... -nsndn RVn { 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 ABLE PARAMETERS or LINE ONSTANTS supporting routine. Only on the first line, keyword Noda Line is required in columns 25 to 33, and.ph 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 alculation 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

14 BEGIN NEW DATA ASE { HORIZ.DAT } 500-kV Single-ircuit Horizontal Line (see HORIZ-L.DAT for fitting) 0.1E E SR SENDA SENDA REA Noda line HORIZ.PH SHOW 1 { 1 of 3 } -2SENDB REB { 2 of 3 } -3SEND RE { 3 of 3 } 11SR 1. 1 BEGIN NEW DATA ASE 1 receiving-end voltages in p.u phase a phase b phase c time in microseconds Fig. 5 alculated results of switching-surge (NODA SETUP) 14

15 REFERENES [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 , [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 , [3] A. Ametani, A highly efficient method for calculating transmission line transients, IEEE Trans., Power Apparatus and Systems, Vol. PAS-95 (5), pp , [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 , [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 , [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, , [7] L. Marti, Simulation of transients in underground cables with frequency dependent modal transformation matrices, IEEE Trans., Power Delivery, vol. PWD-3 (3), pp , [8] G. Angelidis and A. Semlyen, Direct Phase-Domain alculation of Transmission Line Transients Using Two-Sided Recursions, IEEE Trans., Power Delivery, Vol. 10, No. 2, pp , April [9] B. Gustavsen, J. Sletbak, and T. Henriksen, alculation of electromagnetic transients in transmission cables and lines taking frequency dependent effects accurately into account, IEEE Trans., Power Delivery, Vol. 10, No. 2, pp , April [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 , January [11] T. Noda, N. Nagaoka, A. Ametani, Further Improvements to a Phase-Domain ARMA Line Model in Terms of onvolution, Steady-State Initialization, and Stability, IEEE Power Engineering Society Summer Meeting, Denver, olorado, USA, (to be published in IEEE Trans.) [12] Tsu-huei Liu and Li Jin-gui, all for Help with Rational Function Approximations to Frequency- Dependent Transformation Matrices of ables and Lines, EMTP News, Leuven EMTP enter, March, [13] A. Ametani, T. Ono, and A. Honaga, Surge Propagation on Japanese 500kV Untransposed Transmission Line, Proc. IEE, Vol. 121, No.2, [14] T. Noda and N. Nagaoka, Development of ARMA Models for a Transient alculation using Linearized Least-Squares Method, Trans. IEE of Japan, Vol. 114-B, No. 4, pp , [15] T. Noda, Development of a Transmission-Line Model onsidering the Skin and orona Effects for Power Systems Transient Analysis, Ph.D. Thesis submitted to Doshisha University, [16] T. Noda, N. Nagaoka, and A. Ametani, Fault-Surge alculations using the Phase-Domain ARMA Line Model, Trans. IEE of Japan, Vol. 116-B, No. 11, pp ,