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. BLANK card ending branch cards BUS2 BUS3 -1.0 0.0 { Will open on current zero at T = 9.4 msec BLANK card ending switch cards 14BUS1 1.0 60. -90. BLANK card ending source cards 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 } BLANK card ending branch cards BLANK card ending switch cards 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 } BLANK card ending branch cards BLANK card ending switch cards 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 BLANK card ending selective node voltage output requests PRINTER PLOT BLANK card ending plot cards 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 BLANK card ending branch cards BUS2 BUS3 -1.0 0.0 { Will open on current zero at T = 9.4 msec BLANK card ending switch cards 14BUS1 1.0 60. -90. BLANK card ending source cards 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 BLANK card ending branches BLANK card ending switches 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