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BEGIN NEW DATA CASE
C BENCHMARK DC-55
C Illustration of "AVERAGE OUTPUT" usage, as applied to Hermann's example
C "Remarks on opening action" that is to be found in the Rule Book section
C on switches (page 28a for June, 1984 version). Because of averaging, the
C "hash" that Hermann's photograph documents can no longer be detected.
C Later (2nd and 3rd) subcases are unrelated: simple Type-18 source usage.
C 4th subcase shows an alternative to the first, using damping resistors.
C The 5th of 6 subcases has IDEAL TRANSFORMER (internally, this uses
C the Type-18 source). Solution was wrong prior to correction on 25 Feb 01.
C Finally, the 6th subcase illustrates the RECLOSE feature of switches.
PRINTED NUMBER WIDTH, 13, 2, { Request maximum precision (for 8 output columns)
CHANGE PRINTOUT FREQUENCY
5 5 10 10 90 1 100 10
AVERAGE OUTPUT
.000100 .020
1 1 1 1 1
BUS1 BUS2 .18 0.8 1
BUS3 22100.
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BUS2 BUS3 -1.0 0.0 { Will open on current zero at T = 9.4 msec
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14BUS1 1.0 60. -90.
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C Step Time BUS3 BUS2 BUS1 BUS1
C BUS2
C *** Switch "BUS2 " to "BUS3 " closed before 0.00000000E+00 sec.
C 0 0.0 0.0 0.0 0.0 0.0
C 1 .1E-3 .2634734E-5 .2634734E-5 .0188450913 .0011645523
C 2 .2E-3 .183793E-4 .183793E-4 .0565084941 .0057945482
C
C 93 .0093 .6380267563 .6380267563 -.338677744 .1867579604
C *** Open switch "BUS2 " to "BUS3 " after 9.40000000E-03 sec.
C 94 .0094 .6385842673 .6385842673 -.373892773 .0596618907
C 95 .0095 .638714397 -.442503423 -.408576479 -.00214456
1
C Final step: 200 .02 .6387095451 .944895187 .944895187 .693889E-17
C Variable maxima : .638714397 .944895187 .9998026167 2.665085529
C Times of maxima : .0095 .02 .0042 .0058
C Variable minima : 0.0 -.999644736 -.999644736 -.00214456
C Times of minima : 0.0 .0126 .0126 .0095
PRINTER PLOT
144 3. 0.0 20. BUS1 BUS2 { Axis limits: (-9.996, 9.998)
BLANK card ending plot cards
BEGIN NEW DATA CASE
C Second of 5 subcases is unrelated to the preceding first data subcase.
C Test of Type-18 source (ideal transformer plus ungrounded source). There
C are 3 disconnected subnetworks, each of which contains a single, trivial
C Type-18 source usage. In order of use: 1) Ideal transformer alone (near
C zero source); 2) Ideal transformer with a voltage source shifted by 90
C degrees (so when added to external generator, the total phasor is 1.414
C at an angle of -45 degrees; 3) Ungrounded voltage source alone. There
C is no phasor solution for initial conditions in this 2nd subcase of DC-55
PRINTED NUMBER WIDTH, 12, 2, { Tailor width so easy documentation within 80 cols
CHANGE PRINTOUT FREQUENCY
5 5 20 20
.000100 .024 1.E-12
1 1 1 1 1
PRIM1 GEN 1.E-8 { Create node PRIM1 of unknown voltage }
PRIM2 GEN 1.E-8 { Create node PRIM2 of unknown voltage }
SEC1 0.5 { 1-ohm resistive load on primary trans. 1 }
SEC2 .25 { 1-ohm resistive load on primary trans. 2 }
PRIBOT 1.0 { 1/2 of resistor for ungrounded source }
PRITOPGEN 1.0 { other 1/2 of R for ungrounded source }
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14GEN 1.0 60. -90. { Network's real source is sine wave
C Type-18 ideal transformer has both windings grounded. Primary goes to the
C generator "GEN", while the secondary "SEC" drives a 1-ohm resistive load
11PRIM1 1.E-12 { 1st primary terminal of ideal transformer; near-0 source
18 00 1.414SEC1 { Ratio**2 = 2: step down, primary to secondary
C End 1st transformer. Begin 2nd by adding 1-volt sinusoidal voltage source:
14PRIM2 1.0 60. 0.0 { Add vectors: 1.414 /_-45 degrees
18 00 2.0SEC2 { Ratio=2: step down, primary to secondary
C End 2nd transformer. Begin 3rd device: effectively no transformer (since
C both secondary nodes are grounded); ungrounded voltage source is a battery
C that becomes nonzero only after TSTART = 6.0 msec --- in series with GEN
11PRITOP 1.0 .006
18PRIBOT 1.0 { Ratio is arbitrary since secondary nodes shorted to earth
BLANK card ending source cards
C Step Time 18TYP1 18TYP2 18TYP3 GEN SEC1 SEC2
C 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
C 1 .1E-3 .037701568 -.96159928 .018845091 .037690183 .026655009 -.48079964
C 2 .2E-3 .07534956 -.92183209 .037663403 .075326806 .053272139 -.46091604
C 3 .3E-3 .112890477 -.88075492 .056428192 .112856385 .079813567 -.44037746
18TYP118TYP218TYP3GEN SEC1 SEC2 PRIBOTPRITOP
BLANK card ending selective node voltage output requests
C 240 .024 .368235756 1.29790103 -.31593772 .368124553 .26034268 .648950513
C maxima : 1.0002231 1.41418563 .499960522 .999921044 .707157733 .707092816
C Times max : .0042 .0229 .0042 .0042 .0042 .0229
C minima : -1.0003021 -1.4141856 -1. -1. -.70721357 -.70709282
C Times min : .0125 .0146 .0125 .0125 .0125 .0146
PRINTER PLOT
C Both of the following curves are sinusoids. Curve "A" is pure SIN ( 377t )
C whereas curve "B" is 1.414 * SIN ( 377t - 45 degrees ) for time t > 0.
144 3. 0.0 18. 18TYP118TYP2 { Axis limits: (-1.414, 1.414)
C The following plot drops vertically by 0.5 at 6 msec. Before the drop, it
C is y = 0.5 * SIN ( 377t ); after 6 msec, y = 0.5 * ( SIN ( 377t ) - 1.0 )
144 3. 0.0 24. 18TYP3 { Axis limits: (-1.000, 0.500)
BLANK card ending plot cards
BEGIN NEW DATA CASE
C 3rd of 6 subcases repeats preceding 2nd case only with phasor solution.
C Since transients are identical to preceding subcase (since no dynamics,
C no energy storage), stop after the phasor solution in this subcase. It
C will be noted that the only sinusoidal internal source of Type-18 usage
C (the "14PRIM2" card) has TSTART = -1.0 so present for steady state.
.000100 -1.0 1.E-12 { TMAX < 0 ===> no transients
1 1 1 1 1
PRIM1 GEN 1.E-8 { Create node PRIM1 of unknown voltage }
PRIM2 GEN 1.E-8 { Create node PRIM2 of unknown voltage }
SEC1 0.5 { 1-ohm resistive load on primary trans. 1 }
SEC2 .25 { 1-ohm resistive load on primary trans. 2 }
PRIBOT 1.0 { 1/2 of resistor for ungrounded source }
PRITOPGEN 1.0 { other 1/2 of R for ungrounded source }
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14GEN 1.0 60. -90. { Tstart = -1.0 ---> } -1.0
C Type-18 ideal transformer has both windings grounded. Primary goes to the
C generator "GEN", while the secondary "SEC" drives a 1-ohm resistive load
11PRIM1 1.E-12 { 1st primary terminal of ideal transformer; near-0 source
18 00 1.414SEC1 { Ratio**2 = 2: step down, primary to secondary
C End 1st transformer. Begin 2nd by adding 1-volt sinusoidal voltage source
C that is present in steady state, and which leads GEN by 90 degrees. Adding
C these around the loop (KVL) gives 1.414 at an angle of -135 degrees, note:
14PRIM2 1.0 60. 0.0 -1.0
18 00 2.0SEC2 { Ratio=2: step down, primary to secondary
C End 2nd transformer. Begin 3rd device: effectively no transformer (since
C both secondary nodes are grounded); ungrounded voltage source is a battery
C that becomes nonzero only after TSTART = 6.0 msec --- in series with GEN
11PRITOP 1.0 .006
18PRIBOT 1.0 { Ratio is arbitrary since secondary nodes shorted to earth
C
C Node-K Node-M Vk-magnitude Vm-magnitude Ikm-magnitude Pk (watts)
C name name Vk-degrees Vm-degrees Ikm-degrees Qk (vars)
C
C PRIM1 .99999998999698 1.0 1.0003020856075 -.5001510378007
C GEN -90.0000000 -90.0000000 90.0000000 .2879679111E-24
C
C PRIM2 .99999999 1.0 1.4142135431541 -.4999999814101
C GEN -89.9999994 -90.0000000 44.9999998 -.499999995
C
$WIDTH, 79, { Request narrow output for phasor branch flows: easy to document
BLANK card ending source cards
C PRITOP 0.5 0.0 0.5 .125
C TERRA -90.0000000 0.0 -90.0000000 0.0
C Total network loss P-loss by summing injections = 7.501510357193E-01
C
C node Vk-magnitude Ik-magnitude Pk (watts) MVA (watts)
C name Vk-degrees Ik-degrees Qk (vars) Power factor
C
C GEN 1.0 2.692862873031 1.2501510381699 1.3464314365155
C -90.0000000 -111.7990223 .499999995 0.9284922
C
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PRINTER PLOT
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BEGIN NEW DATA CASE
$WIDTH, 132, { Back to wide output after injections but before outputs read
C 4th of 6 subcases is modification of first. Rather than "AVERAGE OUTPUT"
C to dampen oscillations of the series inductor, a parallel damping resistor
C is used. The resistance value is automatically a function of the time-
C step size thanks to use of the "DELTAT" request (BUS4 field of columns
C 21-26). A theoretical formula for determining nominal damping resistance
C is R = 16 * L [Henry] / dt, and here 16*L = 16 * .8 [mH] = .0128 [Henry].
C The "DIVIDEDELTAT" request of columns 15-26 provides just such scaling.
C Enter the value 16 * L [Henry] in the R-field of columns 27-32.
C Only to produce a nicer (denser) character plot, the time step is halved.
PRINTED NUMBER WIDTH, 13, 2, { Request maximum precision (for 8 output columns)
CHANGE PRINTOUT FREQUENCY
5 5 20 20 185 1 205 5 220 20
.000050 .020
1 1 1 1 1
BUS1 BUS2 .18 0.8 { Series R-L oscillates when opened} 1
BUS3 22100. { Capacitor disconnected by switch
C Damping resistor is extra, placed in parallel with hanging R-L branch:
BUS1 BUS2 DIVIDEDELTAT .0128 { Nominal parallel R-damping is R = 16 * L / dt
C BUS1 BUS4 128. { Equivalent branch would have R = .0128/1.E-4
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BUS2 BUS3 -1.0 0.0 { Will open on current zero at T = 9.4 msec
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14BUS1 1.0 60. -90.
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C Step Time BUS3 BUS2 BUS1 BUS1
C BUS2
C *** Switch "BUS2 " to "BUS3 " closed before 0.00000000E+00 sec.
C 0 0.0 0.0 0.0 0.0 0.0
C 1 .5E-4 .7458368E-6 .7458368E-6 .0188484397 .5856959E-3
C 2 .1E-3 .4300663E-5 .4300663E-5 .0376901827 .002335936
C 3 .15E-3 .1328333E-4 .1328333E-4 .0565185345 .0052368122
C
C 186 .0093 .6386376275 .6386376275 -.356411879 .1216511334
C 187 .00935 .638831863 .638831863 -.373959206 .0578961619
C *** Open switch "BUS2 " to "BUS3 " after 9.40000000E-03 sec.
C 188 .0094 .6388812702 .6388812702 -.391373667 -.006239594
C 189 .00945 .6388696593 -1.50023245 -.408649075 -.004263998
C 190 .0095 .6388696593 .4233815153 -.425779292 .0033170344
C 191 .00955 .6388696593 -1.1033345 -.442758231 -.002580376
C 192 .0096 .6388696593 .0542933726 -.459579861 .0020073173
C 193 .00965 .6388696593 -.875988712 -.476238204 -.001561525
C 194 .0097 .6388696593 -.181754793 -.492727342 .0012147365
1
C 400 .02 .6388696593 .9510565163 .9510565163 .208083E-17
C Variable maxima : .6388812702 .9510565163 .9999802609 2.66459913
C Times of maxima : .0094 .02 .00415 .00575
C Variable minima : 0.0 -1.50023245 -1. -.006239594
C Times of minima : 0.0 .00945 .0125 .0094
PRINTER PLOT { Following plot is of region of oscillation following 9.4 msec
144 .4 9.0 11. BUS1 BUS2 { Axis limits: (-1.500, 0.639)
BLANK card ending plot cards
BEGIN NEW DATA CASE
C 5th of 6 subcases demonstrates a simple Type-18 source that required
C correction on 25 February 2001. The key structure is this: one or more
C (in this case, two) terminal nodes of the Type-18 source that is used to
C represent IDEAL TRANSFORMER has known voltage.
.0001 .0001 { One dT is all it takes to verify voltages now are continuous
1 1 1 1
GENA 1.E7 { High resist. to ground provides connectivity
GENB GENA { 2nd of 3 is the same. Avoid KILL code
LOAD GENA { 3rd of 3 satisfies need for connectivity
IDEAL TRANSFORMER { Internally, ideal transformer is represented as Type-18
1GENA GENB 1.0 { Winding 1 has rated voltage = 1.
2LOAD 1.0 { Winding 2 has same rated voltage
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14GENA 10. 1.0 0.0 -1.0 10.0
14GENB 10. 1.0 -120.0 -1.0 10.0
BLANK card ending sources
GENA GENB LOAD
C Step Time GENA GENB LOAD
C 0 0.0 10. -5. 15.
C 1 .1E-3 9.999998026 -4.99455762 14.99455564
BLANK card ending node voltage outputs
BLANK card ending plot cards
BEGIN NEW DATA CASE
C 6th of 6 subcases illustrates the RECLOSE feature of time-controlled
C switches, which became available 24 December 2001 as should be
C described in some future newsletter story (July, 2002 or later). Data
C comes from the 4th subcase, which provides half of the network. Time
C is extended (doubled, in fact) to allow reclosing of the switch. Using
C old modeling, this is done by means of a second time-controlled switch
C in parallel with the first. Of course, only one switch or the other is
C closed at any one time --- a requirement of switch logic. The same
C solution is obtained using new modeling by a RECLOSE switch. Although
C only two pairs of (T-close and T-open) are illustrated, in fact an
C arbitrary number are allowed. When ATP is done with one (upon opening),
C the next pair will replace the preceding pair. Storage is in List 10, so
C is variably-dimensioned. Time-step size DELTAT has been doubled simply
C to speed simulation. Finally, the source has been rotated 90 degrees to
C speed the action (no need to waste time waiting for the first opening).
PRINTED NUMBER WIDTH, 11, 2, { Request maximum precision (for 8 output columns)
CHANGE PRINTOUT FREQUENCY
5 5 55 1 155 5
.000100 .020
1 1 1 1 1
C Naming is as follows. Keep the original "BUS" names for the original
C data. For the new alternative, replace BUS by GUS. This is for nodes
C numbered 2 and 3. For Node 1 (the voltage source), no copy is required:
BUS1 BUS2 .18 0.8 { Series R-L oscillates when opened} 1
BUS1 GUS2 .18 0.8 { Series R-L oscillates when opened} 1
BUS3 22100. { Capacitor disconnected by switch
GUS3 22100. { Capacitor disconnected by switch
C Damping resistor is extra, placed in parallel with hanging R-L branch:
BUS1 BUS2 DIVIDEDELTAT .0128 { Nominal parallel R-damping is R = 16 * L / dt
BUS1 GUS2 DIVIDEDELTAT .0128 { Nominal parallel R-damping is R = 16 * L / dt
BLANK card ending branch cards
C Switches: < T-close>< T-open > < Request> I
C ______------__________---------- __________ _
BUS2 BUS3 -1.0 0.0 { Will open on current 0 at T = 5.8 msec } 1
BUS2 BUS3 .011 0.0 { Will open on current 0 at T = 14.9 msec }
GUS2 GUS3 -1.0 0.0 RECLOSE 3
.011 0.0 { 2nd pair of T-close and T-open follow 1st
9999. { Bound to terminate last pair of switch T
BLANK card ending switch cards
14BUS1 1.0 60. 0.0
BLANK card ending source cards
BUS1 BUS2 GUS2 { Request for the output of node voltages at these nodes
C First 4 output variables are electric-network voltage differences (upper voltage minus lower voltage);
C Next 4 output variables are branch currents (flowing from the upper node to the lower node);
C Step Time GUS2 BUS1 BUS2 GUS2 BUS2 GUS2 BUS1 BUS1
C GUS3 BUS3 GUS3 BUS2 GUS2
C *** Switch "BUS2 " to "BUS3 " closed before 0.00000000E+00 sec.
C *** Switch "GUS2 " to "GUS3 " closed before 0.00000000E+00 sec.
C 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
C 1 .1E-3 0.0 .99928947 .15737E-3 .15737E-3 .06955678 .06955678 .06175106 .06175106
C 2 .2E-3 0.0 .9971589 .74798E-3 .74798E-3 .19149551 .19149551 .18371105 .18371105
C 3 .3E-3 0.0 .99361131 .00188315 .00188315 .31024774 .31024774 .30249987 .30249987
BLANK card ending node voltage outputs
C 200 .02 .08475006 .30901699 .30902085 .30902085 0.0 0.0 .30129E-7 .30129E-7
C Variable maxima : 1.6703679 .99992104 1.8946387 1.8946387 1.8705409 1.8705409 1.8678888 1.8678888
C Times of maxima : .015 .0167 .015 .015 .0028 .0028 .0028 .0028
C Variable minima : -2.667432 -.999921 -2.354268 -2.354268 0.0 -.8127145 -.8114678 -.8114678
C Times of minima : .0059 .0083 .0059 .0059 0.0 .0128 .0128 .0128
CALCOMP PLOT
144 2. 0.0 20. BUS2 GUS2 { These 2 node voltages should coincide
BLANK card ending plot cards
BEGIN NEW DATA CASE
BLANK
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