Thickness dependence of physical properties of PLD-

When only a phasor solution (no transient simulation) is to occur, then a branch may be described by steady-state phasor admittances. These phasor admittances are represented by the branch admittance matrix [Y].

Matrix [Y] has a row and a column for each node at each end of the branch.

Hence a 3-phase branch has a 6x6 branch admittance matrix [Y]. More generally, a N-phase circuit will have a 2Nx2N [Y] matrix.

The "CASCADED PI" case is the only data generator currently available to retrieve the branch admittance matrix [Y]. To see this matrix in the output, we need a DIAGNOSTIC card (column 26, with minimum value = 3) in the input of the CASCADED PI case. Beware, since the output is not immediately in the correct input format for phasor branch [Y] usage.

For steady state solution, the PHASOR BRANCH option dealt with in this section is an alternative for the CASCADED PI option (of section IV.F.). Like for CASCADED PI, some important limitations exist:

- the phasor branch solution uses the long-line equivalent (not the nominal PI-equivalent). Hence, the model is only valid at one specific frequency.

Accordingly, only steady state calculations (TMAX_0 on miscellaneous data card) at that specific frequency are honored. The frequency of the type 14-sources should have the same value as the frequency for which the phasor branch [Y] has been calculated.

- the user can only obtain phasor results at the line terminals, not at the interconnection points.

- when using the CASCADED PI case as a data generator, two runs are necessary:

the first run results in the creation of the branch admittance matrix. The second run results in the steady state calculation. On the other hand, CASCADED PI alone was capable to give you this steady state result in one run.

The steady state solution of a case will be the same, whether the final branch admittance input will be generated by the CASCADED PI representation or directly represented by the phasor branch [Y] representation. This is logical, because the branch admittance matrix [Y] will be resolved in the CASCADED PI solution too. There can be a little difference in the output results depending on whether the solution is obtained by the CASCADED PI feature or by the phasor

branch [Y] feature. The reason for this is the numerical accuracy of the matrix [Y] representation. The CASCADED PI feature has the greatest accuracy, since the matrix [Y] is calculated at high precision, during the solution process. The phasor branch option on the other hand will be less accurate since it uses a lower precision for the input format of the phasor branch admittance.

Card format

Again, two different formats exist: . normal format ($VINTAGE, 0)

. high precision format ($VINTAGE,1) The card format to input the phasor admittances basically is the same format as used in section IV.C. (type 51,52,53). But the meaning of the parameters is entirely different. The only way the program recognizes the difference between a mutually coupled RL input and a phasor branch admittance input is the unnamed extra phases for the extra rows of the branch admittance matrix.

NORMAL CARD FORMAT ($VINTAGE, 0)

The same format as in section IV.C. will apply here.

2345678901234567890123456789012345678901234567890123456789012345678901234567890

ITYPE: Specifies N phases by numbering 51, 52, 53, ...50+2*N in this field. N is limited up to 20. In case of 3 phases, the numbering will be:

51,52,53,54,55,56, since there are 6 rows. Continuation cards must have blank ITYPE fields. See also remark 4.

BUS1, BUS2: Terminal node names of the elements in the phase, indicated by the ITYPE field. Nodes may be grounded (indicated by blank field name) if desired. In case of 3 phases, there will be 6 cards to be specified, but only the first three cards will contain the node names. See also remark 4. This is the only difference between the ordinary type 51,52,53 element of section IV.C. and the phasor branch admittance discussed in this section.

BUS3, BUS4: Equally to mutually coupled RLC branches, referencing can be used here. The same rules must be taken into account as typing only the node names of the first phase of the reference set in the same sequence.

TR, TX: These fields are occupied with the phasor branch admittance values (TR contains the real part, TX contains the imaginary part), expressed in mho and calculated at the frequency for which the steady state calculation will be performed. When the CASCADED PI feature was used as data generator, this frequency has the value FREQCS.

Unlike previous cases, XOPT always should be put equal to 1/(2π), in order to avoid scaling. The value of COPT has no importance for type 51,52,53 cards.

note:

TR and TX are the table headers, as obtained by the data generator (CASCADED PI-feature, using DIAGNOSTIC output in overlay 3 (=column 26). The minimum value for IPRSUP(3) = 3).

Remarks

1) Matrices [TR] and [TX] are symmetric, so only need to be specified on and below the diagonal. When one card is not sufficient to specify all TR-TX values, then continuation cards are used, with columns 1-26 left blank. The only way the program recognize the difference between a mutually coupled RL input (type 51,52,53) and the phasor branch [Y] input is the unnamed extra phases for the extra rows of the matrix. The following format applies for a 3-phase case:

a) for $VINTAGE, 0:

b) for $VINTAGE, 1:

2) There is no branch current output possible for this branch type. However, the branch voltage can be obtained on the first two phases (column 80 is not being used).

3) There must be added two $UNITS cards.

a) The first one "$UNITS, .1591549431, 0." is mandatory whenever [Y] input is used, so loading [Y] into List-3 tables TR and TX (see diagnostic output) has been done without any scaling. In this first $UNITS card XOPT must than be equal to .1591549431 = [Equation: 1 over [2pi]], since the scaling factor should be unity. COPT can be anything, since it will not be used.

b) The second "$UNITS, -1., -1." card is needed to restore the previous values

Following is an extract of the critical portion: TR-TX table.

Rows 1 through IT of List-3 parameters.

ROW TR TX R C 1 0.4844477034482824E-08 0.1228112151516649E-03 0.0000000000000000E+00 0.0000000000000000E+00 2 -0.1296675793838051E-06 -0.2242269695795113E-04 0.0000000000000000E+00 0.0000000000000000E+00 3 0.9441753227445476E-02 -0.2573990023024946E-01 0.0000000000000000E+00 0.0000000000000000E+00 4 0.4361450614869273E-07 -0.1462537283219131E-04 0.0000000000000000E+00 0.0000000000000000E+00 5 -0.8463238089378199E-02 0.1672909357448652E-01 0.0000000000000000E+00 0.0000000000000000E+00 6 0.1659497249358986E-01 -0.4747597790440687E-01 0.0000000000000000E+00 0.0000000000000000E+00 7 -0.1496688542217182E-06 -0.9426424775643807E-05 0.0000000000000000E+00 0.0000000000000000E+00 8 0.1871363082120123E-01 -0.5030148893415707E-01 0.0000000000000000E+00 0.0000000000000000E+00 9 -0.1445905414197019E-01 0.2409757560660085E-01 0.0000000000000000E+00 0.0000000000000000E+00 10 0.4631483359447570E-01 -0.1156116986463779E-01 0.0000000000000000E+00 0.0000000000000000E+00 11 0.1496046015179719E-05 0.6458965458057214E-05 0.0000000000000000E+00 0.0000000000000000E+00 12 -0.1680598538619227E-01 0.5971717826772237E-01 0.0000000000000000E+00 0.0000000000000000E+00 13 0.1897469864840810E-01 -0.4245555564293230E-01 0.0000000000000000E+00 0.0000000000000000E+00 14 -0.3271457520858705E-01 0.3047566556753915E-01 0.0000000000000000E+00 0.0000000000000000E+00 15 0.3607139971436178E-01 -0.6062044468394332E-01 0.0000000000000000E+00 0.0000000000000000E+00 16 0.1189890175137276E-05 0.4485645277231421E-05 0.0000000000000000E+00 0.0000000000000000E+00 17 0.2094153349533659E-02 -0.2062689282010267E-01 0.0000000000000000E+00 0.0000000000000000E+00 18 -0.2240686269477380E-02 0.3689527878049555E-01 0.0000000000000000E+00 0.0000000000000000E+00 19 0.3661437796623669E-02 -0.6532394073363741E-01 0.0000000000000000E+00 0.0000000000000000E+00 20 -0.2258503629330589E-04 0.2742503620833940E-01 0.0000000000000000E+00 0.0000000000000000E+00 21 0.4854082846355038E-02 0.9939308070334987E-02 0.0000000000000000E+00 0.0000000000000000E+00

Using branch admittance as input: C New XOPT, COPT = 1.59154943E-01 0.00000000E+00 |$UNITS, .1591549431, 0.0,

C 1st of coupled R-L. 4.80000E-09 1.22811E-04 |51RA1 GA1 4

C 1.200E-06 4.486E-06 2.090E-03-2.063E-02-2.200E-03|56 1

C 3.660E-03-6.532E-02-2.000E-05 2.742E-02 4.850E-03| . C New XOPT, COPT = 6.00000000E+01 0.00000000E+00 |$UNITS, 60., 0.0, { Restore $UNITS, .1591549431, 0.0, { Ensures no scaling of [Y] in mhos. XOPT = 1/(2*Pi) 51RA1 GA1 4.8E-9 1.22811E-04 { 1st row of 6x6 [Y] in mhos $UNITS, 60., 0.0, { Restore original values; "CIMAGE" ends scaling XUNITS = 1. BLANK card ending branch cards C From bus name | Names of all adjacent busses. C C End injection: -42.47495983067 -106.9773628 -6888.835943954 -0.6822873 PRINTER PLOT BLANK card ending non-existent plot cards BEGIN NEW DATA CASE C 2nd of 3 subcases uses identical data to the first, only in wide format. C Answers are identical because precision of the data has not been increased. 0.0 0.0 60. { Note XOPT = 60 here --- never actually used 1 1

$UNITS, .1591549431, 0.0, { Ensures no scaling of [Y] in mhos. XOPT = 1/(2*Pi) $VINTAGE, 1, { Switch to alternate, wide format in with R-L are read as R-L-C 51RA1 GA1 4.8E-9 1.22811E-04 { R, L, C as 3E16.0 $UNITS, 60., 0.0, { Restore original values; "CIMAGE" ends scaling XUNITS = 1. $VINTAGE, 0, { Done inputing [Y], so return to original, old formats

BLANK card ending non-existent output requests

C Total network loss P-loss by summing injections = 9.326316227367E+03 C End injection: -12.96755041034 44.410354381177 -6429.033843309 9422.7669408263 C End injection: -42.47495983067 -106.9773628 -6888.835943954 -0.6822873 PRINTER PLOT BLANK card ending non-existent plot cards

BEGIN NEW DATA CASE

BLANK card ending all subcases

Remarks:

1) TR-TX table manually should be put in the proper input format described in this section (IV.G).

2) Although the type 51,52,53 data are preceeded by a $UNITS card, data are only valid for the frequency for which they are created (value FREQCS = 60 Hz in DCPRINT25). So only type 14 - sources at that very frequency are allowed.

Furthermore, only Steady state calculations at the same frequency are allowed.