Cálculos de PTDF_s.xls

Cálculo de los Factores de Distribución Paper de Rudnick

Datos del Sistema EjemploLíneas Resist. Reactan. Shunt Barras Generac. Carga

l-k l-k l-k l-k MW MW[1-2] 0.02 0.06 0.030 1 80.000 1.000[1-3] 0.08 0.24 0.025 2 53.530 20.000

[2-3] 0.06 0.18 0.020 3 0.000 45.000

[2-4] 0.06 0.18 0.020 4 0.000 40.000[2-5] 0.04 0.12 0.015 5 34.600 60.000[3-4] 0.01 0.03 0.010 Total 168.130 166.000[4-5] 0.08 0.24 0.025

Cálculo de la Zbarra por algoritmo (slack 01)[2] [3] [4] [5]

[2] 0.01686 0.05057 0.01257 0.03771 0.01343 0.04029 0.01571 0.04714[3] 0.01257 0.03771 0.02971 0.08914 0.02629 0.07886 0.01714 0.05143[4] 0.01343 0.04029 0.02629 0.07886 0.03171 0.09514 0.01952 0.05857[5] 0.01571 0.04714 0.01714 0.05143 0.01952 0.05857 0.04365 0.13095

Factores GSDF ó PTDF Datos de los Flujos barra [1] como slack[1] [2] [3] [4] [5]

[1-2] 0 -0.84286 -0.62857 -0.67143 -0.78572 Líneas Flujos Factor Factor[1-3] 0 -0.15714 -0.37143 -0.32857 -0.21429 l-k Dl-k,R Cl-k,R[2-3] 0 0.07143 -0.28571 -0.21429 -0.02381 [1-2] 48.350 0.71762 -0.42646[2-4] 0 0.05714 -0.22857 -0.30476 -0.06349 [1-3] 30.400 0.27494 -0.09312[2-5] 0 0.02857 -0.11429 -0.15238 -0.69841 [2-3] 24.600 0.12847 0.01910[3-4] 0 -0.08571 0.34286 -0.54286 -0.23809 [2-4] 26.200 0.15070 0.00637[4-5] 0 -0.02857 0.11429 0.15238 -0.30159 [2-5] 30.300 0.31485 -0.13417

[3-4] 9.400 0.13220 -0.07762[4-5] -4.650 0.04350 -0.07276

Factores GGDF Factores GLDF[1] [2] [3] [4] [5] [1] [2] [3] [4] [5]

[1-2] 0.71762 -0.12523 0.08905 0.04619 -0.06809 [1-2] -0.42646 0.41639 0.20211 0.24497 0.35925[1-3] 0.27494 0.11780 -0.09649 -0.05363 0.06066 [1-3] -0.09312 0.06403 0.27831 0.23546 0.12117[2-3] 0.12847 0.19990 -0.15724 -0.08581 0.10466 [2-3] 0.01910 -0.05232 0.30482 0.23339 0.04291[2-4] 0.15070 0.20785 -0.07787 -0.15406 0.08721 [2-4] 0.00637 -0.05077 0.23494 0.31113 0.06986[2-5] 0.31485 0.34342 0.20056 0.16247 -0.38356 [2-5] -0.13417 -0.16274 -0.01988 0.01822 0.56425[3-4] 0.13220 0.04648 0.47506 -0.41066 -0.10590 [3-4] -0.07762 0.00809 -0.42048 0.46524 0.16047[4-5] 0.04350 0.01493 0.15779 0.19589 -0.25808 [4-5] -0.07276 -0.04419 -0.18705 -0.22514 0.22882

Cálculo de la Zbarra por algoritmo (slack 01)[1] [3] [4] [5]

[1] 0.01686 0.05056 0.00429 0.01286 0.00343 0.01029 0.00114 0.00343

[3] 0.00429 0.01286 0.02143 0.06429 0.01714 0.05143 0.00571 0.01714[4] 0.00343 0.01029 0.01714 0.05143 0.02171 0.06514 0.00724 0.02171[5] 0.00114 0.00343 0.00571 0.01714 0.00724 0.02171 0.02908 0.08724

Factores GSDF ó PTDF Datos de los Flujos barra [2] como slack

[1] [2] [3] [4] [5][1-2] 0.84262 0 0.21429 0.17143 0.05714 Líneas Flujos Factor Factor[1-3] 0.15708 0 -0.21429 -0.17143 -0.05714 l-k Dl-k,R Cl-k,R[2-3] -0.07143 0 -0.35714 -0.28571 -0.09524 [1-2] 48.050 -0.1269 0.4146[2-4] -0.05714 0 -0.28571 -0.36190 -0.12063 [1-3] 30.300 0.1172 0.0634

[2-5] -0.02857 0 -0.14286 -0.18095 -0.72698 [2-3] 24.600 0.1999 -0.0523[3-4] 0.08571 0 0.42857 -0.45714 -0.15238 [2-4] 26.200 0.2078 -0.0508[4-5] 0.02857 0 0.14286 0.18095 -0.27302 [2-5] 30.300 0.3434 -0.1627

[3-4] 9.400 0.0465 0.0081[4-5] -4.700 0.0146 -0.0445


[1-2] 0.71571 -0.12691 0.08738 0.04452 -0.06976 [1-2] -0.42803 0.41459 0.20030 0.24316 0.35744[1-3] 0.27432 0.11723 -0.09705 -0.05420 0.06009 [1-3] -0.09366 0.06342 0.27771 0.23485 0.12057[2-3] 0.12847 0.19990 -0.15724 -0.08581 0.10466 [2-3] 0.01910 -0.05232 0.30482 0.23339 0.04291[2-4] 0.15070 0.20785 -0.07787 -0.15406 0.08721 [2-4] 0.00637 -0.05077 0.23494 0.31113 0.06986[2-5] 0.31485 0.34342 0.20056 0.16247 -0.38356 [2-5] -0.13417 -0.16274 -0.01988 0.01822 0.56425[3-4] 0.13220 0.04648 0.47505 -0.41066 -0.10590 [3-4] -0.07762 0.00809 -0.42048 0.46523 0.16047[4-5] 0.04321 0.01464 0.15749 0.19559 -0.25838 [4-5] -0.07306 -0.04449 -0.18735 -0.22544 0.22852


Datos del Sistema EjemploLíneas Resist. Reactan. Conduct. Sucept. Shunt Barras Generac. Carga

l-k l-k l-k l-k l-k l-k MW MW[1-2] 0.02 0.06 5.00 -15.00 0.030 1 80.000 1.000[1-3] 0.08 0.24 1.25 -3.75 0.025 2 53.530 20.000[2-3] 0.06 0.18 1.67 -5.00 0.020 3 0.000 45.000[2-4] 0.06 0.18 1.67 -5.00 0.020 4 0.000 40.000[2-5] 0.04 0.12 2.50 -7.50 0.015 5 34.600 60.000[3-4] 0.01 0.03 10.00 -30.00 0.010 Total 168.130 166.000[4-5] 0.08 0.24 1.25 -3.75 0.025

Cálculo de la matriz incidencia (Bf)

[1] [2] [3] [4] [5] Cálculo de la matriz susceptancia (B)[1-2] -15.00 15.00 0 0 0[1-3] -3.75 0 3.75 0 0 [1] [2] [3] [4] [5][2-3] 0 -5.00 5.00 0 0 [1] -18.695 15.00 3.75 0 0[2-4] 0 -5.00 0 5.00 0 [2] 15.00 -32.415 5.00 5.00 7.50[2-5] 0 -7.50 0 0 7.50 [3] 3.75 5.00 -38.695 30.00 0[3-4] 0 0 -30.00 30.00 0 [4] 0 5.00 30.00 -38.695 3.750[4-5] 0 0 0 -3.75 3.75 [5] 0 7.50 0 3.750 -11.21

Transpuesta de la matriz (Bf)

[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] -15 -3.75 0 0 0 0 0[2] 15.000 0.000 -5.000 -5.000 -7.500 0 0[3] 0.000 3.750 5.000 0.000 0.000 -30 0[4] 0.000 0.000 0.000 5.000 0.000 30 -3.75[5] 0.000 0.000 0.000 0.000 7.500 0 3.75

Considerando la barra [1] como slack para hallar los PTDF's

Transpuesta de la matriz (Bf) reducida

[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][2] 15.000 0.000 -5.000 -5.000 -7.500 0.000 0.000[3] 0.000 3.750 5.000 0.000 0.000 -30.00 0.000[4] 0.000 0.000 0.000 5.000 0.000 30.000 -3.750[5] 0.000 0.000 0.000 0.000 7.500 0.000 3.750

Matriz B reducida la referencia Cálculo de B inversa (B-1)

[2] [3] [4] [5] [2] [3] [4] [5][2] -32.415 5.000 5.000 7.500 [2] -0.0568 -0.0427 -0.0456 -0.0532[3] 5.000 -38.695 30.000 0.000 [3] -0.0427 -0.1003 -0.0889 -0.0583[4] 5.000 30.000 -38.695 3.750 [4] -0.0456 -0.0889 -0.1071 -0.0663[5] 7.500 0.000 3.750 -11.210 [5] -0.0532 -0.0583 -0.0663 -0.1470

Producto de (B-1)*(Bf_reducida)

[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][2] -0.8518 -0.1601 0.0705 0.0560 0.0266 -0.087 -0.0287[3] -0.6402 -0.3762 -0.2881 -0.2313 -0.1172 0.3412 0.1149[4] -0.6838 -0.3335 -0.2167 -0.3076 -0.1556 -0.545 0.1529[5] -0.7986 -0.2186 -0.0253 -0.0655 -0.7033 -0.241 -0.3026



[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] -15.000 -3.750 0 0 0 0 0[3] 0 3.750 5.000 0 0 -30.00 0[4] 0 0 0 5.000 0 30.000 -3.750[5] 0 0 0 0 7.500 0 3.750


[1] [3] [4] [5] [1] [3] [4] [5][1] -18.695 3.750 0.000 0.000 [1] -0.0564 -0.0144 -0.0116 -0.0039[3] 3.750 -38.695 30.000 0.000 [3] -0.0144 -0.0719 -0.0576 -0.0193[4] 0.000 30.000 -38.695 3.750 [4] -0.0116 -0.0576 -0.0729 -0.0244[5] 0.000 0.000 3.750 -11.210 [5] -0.0039 -0.0193 -0.0244 -0.0974


[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] 0.845759 0.157342 -0.07213 -0.0578 -0.029 0.086 0.028846[3] 0.216389 -0.2156 -0.359591 -0.28813 -0.14458 0.4288 0.143808[4] 0.173386 -0.17275 -0.28813 -0.36442 -0.18286 -0.4577 0.181882[5] 0.058002 -0.05779 -0.096386 -0.12191 -0.73022 -0.1531 -0.273679

Los PTDF's serán: Datos de los Flujos barra [2] como slack

[1] [2] [3] [4] [5] Líneas Flujos Factor Factor[1-2] 0.84576 0 0.21639 0.17339 0.0580 l-k Dl-k,R Cl-k,R[1-3] 0.15734 0 -0.21560 -0.17275 -0.05779 [1-2] 48.050 -0.1286 0.4160[2-3] -0.07213 0 -0.35959 -0.28813 -0.09639 [1-3] 30.300 0.1172 0.0625[2-4] -0.05780 0 -0.28813 -0.36442 -0.12191 [2-3] 24.600 0.2005 -0.0540[2-5] -0.02900 0 -0.14458 -0.18286 -0.73022 [2-4] 26.200 0.2084 -0.0525[3-4] 0.08601 0 0.42877 -0.45771 -0.15311 [2-5] 30.300 0.3443 -0.1648[4-5] 0.02885 0 0.14381 0.18188 -0.27368 [3-4] 9.400 0.0465 0.0077

[4-5] -4.700 0.0146 -0.0442

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack 02)>


[1-2] 0.71718 -0.12858 0.08781 0.04481 -0.0706 [1-2] -0.42980 0.41596 0.19957 0.24257 0.35796[1-3] 0.27459 0.11724 -0.09835 -0.05551 0.05945 [1-3] -0.09482 0.06252 0.27811 0.23527 0.12031[2-3] 0.12834 0.20047 -0.15912 -0.08766 0.10409 [2-3] 0.01814 -0.05399 0.30560 0.23414 0.04240[2-4] 0.15062 0.20842 -0.07971 -0.15600 0.08651 [2-4] 0.00530 -0.05250 0.23563 0.31192 0.06941[2-5] 0.31529 0.34429 0.19971 0.16143 -0.3859 [2-5] -0.13583 -0.16483 -0.02025 0.01802 0.56538[3-4] 0.13250 0.04650 0.47526 -0.41122 -0.1066 [3-4] -0.07826 0.00774 -0.42103 0.46545 0.16086[4-5] 0.04349 0.01464 0.15845 0.19652 -0.2590 [4-5] -0.07309 -0.04425 -0.18806 -0.22613 0.22943



[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] -15.000 -3.750 0 0 0 0 0[2] 15.000 0 -5.000 -5.000 -7.500 0 0[3] 0 3.750 5 0 0 -30.00 0[5] 0 0 0 0 7.500 0 3.750


[1] [2] [3] [5] [1] [2] [3] [5][1] -18.695 15.000 3.750 0.000 [1] -0.10674 -0.06179 -0.01833 -0.04134[2] 15.000 -32.415 5.000 7.500 [2] -0.06179 -0.07315 -0.01544 -0.04894[3] 3.750 5.000 -38.695 0.000 [3] -0.01833 -0.01544 -0.02961 -0.01033[5] 0.000 7.500 0.000 -11.210 [5] -0.04134 -0.04894 -0.01033 -0.12195


[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] 0.67432 0.33155 0.21729 0.30893 0.15336 0.5498 -0.15501[2] -0.17040 0.17380 0.28853 0.36573 0.18156 0.4632 -0.18352[3] 0.04333 -0.04232 -0.07088 0.07720 0.03832 0.8884 -0.03874[5] -0.11401 0.11628 0.19304 0.24469 -0.5476 0.3099 -0.45730


[1] [2] [3] [4] [5] Líneas Flujos Factor Factor[1-2] 0.67432 -0.17040 0.04333 0 -0.1140 l-k Dl-k,R Cl-k,R[1-3] 0.33155 0.17380 -0.04232 0 0.11628 [1-2] 48.05 0.04265 0.24353[2-3] 0.21729 0.28853 -0.07088 0 0.19304 [1-3] 30.30 -0.05680 0.236022[2-4] 0.30893 0.36573 0.07720 0 0.24469 [2-3] 24.50 -0.08926 0.234223[2-5] 0.15336 0.18156 0.03832 0 -0.5476 [2-4] 26.10 -0.15855 0.312522[3-4] 0.54984 0.46318 0.88843 0 0.30989 [2-5] 30.10 0.16094 0.016594[4-5] -0.15501 -0.18352 -0.03874 0 -0.4573 [3-4] 9.20 -0.41815 0.467386

[4-5] -4.50 0.19953 -0.22594

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack-referencia 04)>


[1-2] 0.71697 -0.12775 0.08598 0.04265 -0.0714 -0.43079 0.41393 0.20020 0.24353 0.35754[1-3] 0.27474 0.11699 -0.09913 -0.05680 0.05948 -0.09552 0.06222 0.27835 0.23602 0.11974[2-3] 0.12803 0.19927 -0.16013 -0.08926 0.10378 0.01694 -0.05431 0.30510 0.23422 0.04118[2-4] 0.15037 0.20717 -0.08136 -0.15855 0.08613 0.00359 -0.05321 0.23533 0.31252 0.06783[2-5] 0.31430 0.34250 0.19926 0.16094 -0.3866 -0.13677 -0.16496 -0.02173 0.01659 0.56417[3-4] 0.13169 0.04503 0.47028 -0.41815 -0.1083 -0.08246 0.00421 -0.42104 0.46739 0.15750[4-5] 0.04452 0.01602 0.16080 0.19953 -0.2578 -0.07093 -0.04243 -0.18721 -0.22594 0.23136


[2] [3] [4] [5] Líneas Flujos Factor Factor

[1-2] -0.85176 -0.64021 -0.68381 -0.79861 l-k Dl-k,R Cl-k,R[1-3] -0.16005 -0.37615 -0.33350 -0.21865 [1-2] 48.350 0.7231 -0.4383[2-3] 0.07051 -0.28814 -0.21673 -0.02532 [1-3] 30.350 0.2765 -0.0978[2-4] 0.05598 -0.23126 -0.30762 -0.06545 [2-3] 24.600 0.1291 0.0172[2-5] 0.02657 -0.11719 -0.15558 -0.70331 [2-4] 26.200 0.1515 0.0041[3-4] -0.08719 0.34123 -0.54534 -0.24076 [2-5] 30.300 0.3165 -0.1377[4-5] -0.02870 0.11485 0.15293 -0.30257 [3-4] 9.400 0.1332 -0.0798

[4-5] -4.650 0.0437 -0.0728

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper Rudnick (slack 01)>

Los factores PTDF o GSDF, GGDF y GLDF se muestran a continuación, barra slack 01

Factores PTDF o GSDF[1] [2] [3] [4] [5]

[1-2] 0 -0.85176 -0.64021 -0.68381 -0.79861[1-3] 0 -0.16005 -0.37615 -0.33350 -0.21865[2-3] 0 0.07051 -0.28814 -0.21673 -0.02532[2-4] 0 0.05598 -0.23126 -0.30762 -0.06545[2-5] 0 0.02657 -0.11719 -0.15558 -0.70331[3-4] 0 -0.08719 0.34123 -0.54534 -0.24076[4-5] 0 -0.02870 0.11485 0.15293 -0.30257

Factores GGDF[1] [2] [3] [4] [5]

[1-2] 0.72311 -0.12865 0.08290 0.03930 -0.07550[1-3] 0.27647 0.11642 -0.09969 -0.05703 0.05782[2-3] 0.12908 0.19959 -0.15906 -0.08766 0.10375[2-4] 0.15148 0.20746 -0.07979 -0.15615 0.08603[2-5] 0.31649 0.34307 0.19931 0.16091 -0.38682[3-4] 0.13322 0.04603 0.47444 -0.41212 -0.10755[4-5] 0.04375 0.01505 0.15860 0.19667 -0.25882

Factores GLDF[1] [2] [3] [4] [5]

[1-2] -0.43834 0.41342 0.20188 0.24547 0.36028[1-3] -0.09781 0.06224 0.27834 0.23569 0.12083[2-3] 0.01720 -0.05331 0.30534 0.23393 0.04253[2-4] 0.00410 -0.05188 0.23537 0.31172 0.06955[2-5] -0.13773 -0.16431 -0.02055 0.01785 0.56558[3-4] -0.07981 0.00738 -0.42104 0.46553 0.16096[4-5] -0.07285 -0.04415 -0.18770 -0.22577 0.22972



[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] -15.00 -3.75 0 0 0 0 0[2] 15.00 0 -5.00 -5.00 -7.50 0 0[4] 0 0 0 5.00 0 30.00 -3.75[5] 0 0 0 0 7.50 0 3.75


[1] [2] [4] [5] [1] [2] [4] [5][1] -18.695 15.00 0 0 [1] -0.1000 -0.0579 -0.0116 -0.0426[2] 15.00 -32.415 5.00 7.50 [2] -0.0579 -0.0722 -0.0145 -0.0531[4] 0 5.00 -38.695 3.750 [4] -0.0116 -0.0145 -0.0296 -0.0196[5] 0 7.50 3.750 -11.210 [5] -0.0426 -0.0531 -0.0196 -0.1313


[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] 0.630677 0.374821 0.289535 0.231467 0.11460 -0.3484 -0.1163[2] -0.21397 0.217151 0.360857 0.288485 0.142826 -0.4342 -0.1450[4] -0.04291 0.043551 0.072372 -0.07569 -0.03837 -0.8884 0.0376[5] -0.15751 0.159853 0.26564 0.16769 -0.58632 -0.5877 -0.4189

Los PTDF's serán: Datos de Flujos barra [3] como slack

[1] [2] [3] [4] [5] Líneas Flujos Factor Factor[1-2] 0.630677 -0.21397 0 -0.04291 -0.15751 l-k Dl-k,R Cl-k,R[1-3] 0.374821 0.217151 0 0.043551 0.159853 [1-2] 48.00 0.08594 0.1999[2-3] 0.289535 0.360857 0 0.072372 0.26564 [1-3] 30.30 -0.1002 0.2792[2-4] 0.231467 0.288485 0 -0.07569 0.16769 [2-3] 24.50 -0.1616 0.3063[2-5] 0.11460 0.142826 0 -0.03837 -0.58632 [2-4] 26.05 -0.0816 0.2355[3-4] -0.34841 -0.43423 0 -0.88836 -0.58770 [2-5] 30.10 0.19969 -0.0219[4-5] -0.11630 -0.14495 0 0.037583 -0.41893 [3-4] 9.70 0.48267 -0.4225

[4-5] -4.50 0.16094 -0.1876

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack_refer 03)>


[1-2] 0.71662 -0.12803 0.08594 0.04303 -0.07157 -0.4308 0.4139 0.1999 0.2428 0.3574

[1-3] 0.27466 0.11699 -0.10016 -0.05661 0.05969 -0.0956 0.0621 0.2792 0.2357 0.1194

[2-3] 0.12793 0.19925 -0.16160 -0.08923 0.10404 0.0167 -0.0546 0.3063 0.2339 0.0406

[2-4] 0.14991 0.20693 -0.08156 -0.15724 0.08613 0.0040 -0.0530 0.2355 0.3111 0.0678

[2-5] 0.31428 0.34251 0.19969 0.16132 -0.38663 -0.1365 -0.1648 -0.0219 0.0164 0.5644

[3-4] 0.13426 0.04844 0.48267 -0.40569 -0.10503 -0.0741 0.0118 -0.4225 0.4659 0.1652

[4-5] 0.04464 0.01599 0.16094 0.19852 -0.25799 -0.0713 -0.0427 -0.1876 -0.2252 0.2313



[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] -15.00 -3.750 0 0 0 0 0[2] 15.00 0 -5.00 -5.00 -7.50 0 0[3] 0 3.750 5.00 0 0 -30.0 0[4] 0 0 0 5 0 30.0 -3.75


[1] [2] [3] [4] [1] [2] [3] [4][1] -18.695 15.000 3.750 0.000 [1] -0.1483 -0.0954 -0.0909 -0.0828[2] 15.000 -32.415 5.000 5.000 [2] -0.0954 -0.0989 -0.0800 -0.0748[3] 3.750 5.000 -38.695 30.000 [3] -0.0909 -0.0800 -0.1329 -0.1134[4] 0.000 5.000 30.000 -38.695 [4] -0.0828 -0.0748 -0.1134 -0.1234


[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] 0.79296 0.21519 0.02260 0.06306 0.71541 0.2428 0.3104[2] -0.05234 0.05759 0.09423 0.12026 0.74158 0.1562 0.2806[3] 0.16254 -0.15754 -0.26424 -0.16665 0.60024 0.5855 0.4251[4] 0.11925 -0.11470 -0.19269 -0.24288 0.56118 -0.3012 0.4628


[1] [2] [3] [4] [5] Líneas Flujos Factor Factor[1-2] 0.79296 -0.05234 0.16254 0.11925 0 l-k Dl-k,R Cl-k,R[1-3] 0.21519 0.05759 -0.15754 -0.11470 0 [1-2] 48.05 -0.0749 0.36073[2-3] 0.02260 0.09423 -0.26424 -0.19269 0 [1-3] 30.30 0.0595 0.12042[2-4] 0.06306 0.12026 -0.16665 -0.24288 0 [2-3] 24.60 0.1056 0.04162[2-5] 0.71541 0.74158 0.60024 0.56118 0 [2-4] 26.15 0.0872 0.0687[3-4] 0.24279 0.15621 0.58552 -0.30116 0 [2-5] 30.00 -0.3981 0.57232[4-5] 0.31041 0.28059 0.42511 0.46275 0 [3-4] 9.30 -0.1099 0.16247

[4-5] -4.80 -0.2656 0.23351

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack-ref 05)>


[1-2] 0.71811 -0.12719 0.08769 0.04440 -0.07485 -0.4322 0.4131 0.1982 0.2415 0.3607[1-3] 0.27468 0.11708 -0.09805 -0.05521 0.05949 -0.0948 0.0628 0.2780 0.2351 0.1204[2-3] 0.12816 0.19979 -0.15868 -0.08713 0.10556 0.0190 -0.0526 0.3059 0.2343 0.0416[2-4] 0.15030 0.20750 -0.07941 -0.15564 0.08724 0.0056 -0.0516 0.2353 0.3116 0.0687[2-5] 0.31733 0.34350 0.20216 0.16310 -0.39808 -0.1431 -0.1693 -0.0279 0.0111 0.5723[3-4] 0.13284 0.04627 0.47558 -0.41110 -0.10995 -0.0803 0.0063 -0.4231 0.4636 0.1625[4-5] 0.04482 0.01501 0.15952 0.19717 -0.26558 -0.0769 -0.0471 -0.1916 -0.2292 0.2335


Datos del Sistema Ejemplo Cálculo de la Ybarra Ybarra = G + j B G BLíneas Resist. Reactan. Conduct. Sucept. Shunt [1] [2] [3] [4] [5]

l-k l-k l-k l-k l-k l-k [1] 6.2500 -18.6950 -5.0000 15.0000 -1.2500 3.7500 0.0000 0.0000 0.0000 0.0000

[1-2] 0.02 0.06 5.00 -15.00 0.030 [2] -5.0000 15.0000 10.8333 -32.4150 -1.6667 5.0000 -1.6667 5.0000 -2.5000 7.5000

[1-3] 0.08 0.24 1.25 -3.75 0.025 [3] -1.2500 3.7500 -1.6667 5.0000 12.9167 -38.6950 -10.0000 30.0000 0.0000 0.0000

[2-3] 0.06 0.18 1.67 -5.00 0.020 [4] 0.0000 0.0000 -1.6667 5.0000 -10.0000 30.0000 12.9167 -38.6950 -1.2500 3.7500

[2-4] 0.06 0.18 1.67 -5.00 0.020 [5] 0.0000 0.0000 -2.5000 7.5000 0.0000 0.0000 -1.2500 3.7500 3.7500 -11.2100[2-5] 0.04 0.12 2.50 -7.50 0.015

[3-4] 0.01 0.03 10.00 -30.00 0.010 Matriz jacobiana incidencia de flujos (Jf)[4-5] 0.08 0.24 1.25 -3.75 0.025 [1] [2] [3] [4] [5] [1] [2] [3] [4] [5]

[1-2] 5.00 -5.00 0 0 0 15.00 -15.00 0 0 0

Barras Generac. Carga [1-3] 1.25 0 -1.25 0 0 3.75 0 -3.75 0 0MW MW [2-3] 0 1.6667 -1.6667 0 0 0 5.00 -5.00 0 0

1 80.000 1.000 [2-4] 0 1.6667 0 -1.6667 0 0 5.00 0 -5.00 02 53.530 20.000 [2-5] 0 2.50 0 0 -2.50 0 7.50 0 0 -7.503 0.000 45.000 [3-4] 0 0 10.00 -10.00 0 0 0 30.00 -30.00 04 0.000 40.000 [4-5] 0 0 0 1.25 -1.25 0 0 0 3.75 -3.755 34.600 60.000 [1-2] 15.00 -15.00 0 0 0 -5.00 5.00 0 0 0

Total 168.130 166.000 [1-3] 3.75 0.00 -3.75 0 0 -1.25 0 1.25 0 0[2-3] 0 5.00 -5.00 0 0 0 -1.6667 1.6667 0 0[2-4] 0 5.00 0 -5.00 0 0 -1.6667 0 1.6667 0[2-5] 0 7.50 0 0 -7.50 0 -2.50 0 0 2.50[3-4] 0 0 30.00 -30.00 0 0 0 -10.00 10.00 0

Transpuesta de la matriz incidencia (Jf) [4-5] 0 0 0 3.75 -3.75 0 0 0 -1.25 1.25

[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5] [1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5][1] 5 1.25 0 0 0 0 0 15 3.75 0 0 0 0 0[2] -5 0 1.666667 1.666667 2.5 0 0 -15 0 5 5 7.5 0 0[3] 0 -1.25 -1.66667 0.00 0 10 0 0 -3.75 -5 0 0 30 0[4] 0 0 0 -1.67 0 -10 1.25 0 0 0 -5 0 -30 3.75[5] 0 0 0 0 -2.5 0 -1.25 0 0 0 0 -7.5 0 -3.75[1] 15 3.75 0 0 0 0 0 -5 -1.25 0 0 0 0 0[2] -15 0 5 5 7.5 0 0 5 0 -1.66667 -1.66667 -2.5 0 0[3] 0 -3.75 -5 0 0 30 0 0 1.25 1.666667 0 0 -10 0[4] 0 0 0 -5 0 -30 3.75 0 0 0 1.666667 0 10 -1.25[5] 0 0 0 0 -7.5 0 -3.75 0 0 0 0 2.5 0 1.25

Producto de (J-1)*(Jf_reducida)[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5] [1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5]

[2] -0.8591 -0.16245 0.06976 0.05502 0.02492 -0.08841 -0.02881 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[3] -0.6498 -0.38004 -0.29012 -0.23347 -0.11958 0.33988 0.11531 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[4] -0.6940 -0.33755 -0.21874 -0.30997 -0.15822 -0.54738 0.15337 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[5] -0.8092 -0.22224 -0.02658 -0.06707 -0.70732 -0.24295 -0.30336 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[2] 0.00540 0.00177 0.00056 0.00071 0.00122 0.00090 0.00008 -0.84286 -0.15714 0.07143 0.05714 0.02857 -0.08571 -0.02857[3] 0.00708 0.00287 0.00147 0.00163 0.00177 0.00099 -0.00034 -0.62857 -0.37143 -0.28571 -0.22857 -0.11429 0.34286 0.11429[4] 0.00752 0.00299 0.00148 0.00174 0.00195 0.00151 -0.00033 -0.67143 -0.32857 -0.21429 -0.30476 -0.15238 -0.54286 0.15238[5] 0.00784 0.00265 0.00092 0.00119 0.00297 0.00162 0.00059 -0.78571 -0.21429 -0.02381 -0.06349 -0.69841 -0.23810 -0.30159

Transpuesta del producto (J-1)*(Jf_reducida) Los PTDF's serán[2] [3] [4] [5] [2] [3] [4] [5] [1] [2] [3] [4] [5]

[1-2] -0.85907 -0.64980 -0.69400 -0.80922 0.005403 0.007076 0.007525 0.007837 [1-2] 0 -0.85366 -0.64272 -0.68648 -0.80139[1-3] -0.16245 -0.38004 -0.33755 -0.22224 0.001769 0.00287 0.002994 0.002652 [1-3] 0 -0.16068 -0.37717 -0.33456 -0.21959[2-3] 0.069755 -0.29012 -0.21874 -0.02658 0.000558 0.001468 0.001484 0.000923 [2-3] 0 0.07031 -0.28865 -0.21725 -0.02566[2-4] 0.05502 -0.23347 -0.30997 -0.06707 0.000707 0.001634 0.001736 0.001193 [2-4] 0 0.05573 -0.23184 -0.30823 -0.06588[2-5] 0.024921 -0.11958 -0.15822 -0.70732 0.001217 0.001765 0.001946 0.002969 [2-5] 0 0.02614 -0.11782 -0.15627 -0.70435[3-4] -0.08841 0.339875 -0.54738 -0.24295 0.000897 0.000994 0.001508 0.001619 [3-4] 0 -0.08751 0.34087 -0.54587 -0.24133[4-5] -0.02881 0.115314 0.153368 -0.30336 7.79E-05 -0.00034 -0.00033 0.000589 [4-5] 0 -0.02873 0.11497 0.15304 -0.30277[1-2] 0 0 0 0 -0.84286 -0.62857 -0.67143 -0.78571[1-3] 0 0 0 0 -0.15714 -0.37143 -0.32857 -0.21429 Datos de los Flujos barra [1] como slack[2-3] 0 0 0 0 0.071429 -0.28571 -0.21429 -0.02381 Líneas Flujos Factor Factor[2-4] 0 0 0 0 0.057143 -0.22857 -0.30476 -0.06349 l-k Dl-k,R Cl-k,R

[2-5] 0 0 0 0 0.028571 -0.11429 -0.15238 -0.69841 [1-2] 48.35 0.7243 -0.4409[3-4] 0 0 0 0 -0.08571 0.342857 -0.54286 -0.2381 [1-3] 30.40 0.2772 -0.0985[4-5] 0 0 0 0 -0.02857 0.114286 0.152381 -0.30159 [2-3] 24.60 0.1292 0.0168

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper Rudnick (slack 01)> [2-4] 26.20 0.1516 0.0036[2-5] 30.30 0.3168 -0.1385

Factores GGDF Factores GLDF [3-4] 9.40 0.1334 -0.0803[1] [2] [3] [4] [5] [1] [2] [3] [4] [5] [4-5] -4.65 0.0438 -0.0729

[1-2] 0.72429 -0.12937 0.08156 0.03781 -0.07710 [1-2] -0.44089 0.41277 0.20183 0.24559 0.36049[1-3] 0.27716 0.11648 -0.10001 -0.05740 0.05757 [1-3] -0.09846 0.06222 0.27871 0.23610 0.12113[2-3] 0.12921 0.19952 -0.15944 -0.08805 0.10355 [2-3] 0.01679 -0.05352 0.30544 0.23405 0.04245[2-4] 0.15165 0.20737 -0.08019 -0.15659 0.08577 [2-4] 0.00361 -0.05211 0.23545 0.31185 0.06949[2-5] 0.31685 0.34298 0.19903 0.16057 -0.38750 [2-5] -0.13850 -0.16464 -0.02068 0.01777 0.56585[3-4] 0.13344 0.04593 0.47430 -0.41244 -0.10790 [3-4] -0.08028 0.00723 -0.42115 0.46560 0.16106[4-5] 0.04380 0.01507 0.15877 0.19684 -0.25897 [4-5] -0.07286 -0.04414 -0.18783 -0.22590 0.22990


[1-2] 0.63238 -0.21370 -0.04295 -0.15779 -0.00127 -0.00020 0.00003 0.00022 [1-2] 0.63111 -0.21389 0 -0.04292 -0.15758[1-3] 0.37759 0.21949 0.04412 0.16207 -0.00205 -0.00174 -0.00042 -0.00164 [1-3] 0.37554 0.21776 0 0.04370 0.16043[2-3] 0.29266 0.36389 0.07314 0.26870 -0.00231 -0.00225 -0.00057 -0.00226 [2-3] 0.29034 0.36164 0 0.07257 0.26643[2-4] 0.23383 0.29075 -0.07527 0.16983 -0.00175 -0.00168 -0.00031 -0.00158 [2-4] 0.23208 0.28907 0 -0.07558 0.16825[2-5] 0.11484 0.14279 -0.03859 -0.58810 -0.00019 0.00002 0.00016 0.00132 [2-5] 0.11466 0.14282 0 -0.03842 -0.58677[3-4] -0.35295 -0.43886 -0.89050 -0.59320 0.00337 0.00343 0.00160 0.00408 [3-4] -0.34959 -0.43543 0 -0.88891 -0.58912[4-5] -0.11795 -0.14666 0.03716 -0.42142 0.00122 0.00127 0.00031 0.00185 [4-5] -0.11673 -0.14540 0 0.03747 -0.41957[1-2] 0.00000 0.00000 0.00000 0.00000 0.62857 -0.21429 -0.04286 -0.15714[1-3] 0.00000 0.00000 0.00000 0.00000 0.37143 0.21429 0.04286 0.15714 Datos de los Flujos barra [3] como slack[2-3] 0.00000 0.00000 0.00000 0.00000 0.28571 0.35714 0.07143 0.26190 Líneas Flujos Factor Factor[2-4] 0.00000 0.00000 0.00000 0.00000 0.22857 0.28571 -0.07619 0.16508 l-k Dl-k,R Cl-k,R[2-5] 0.00000 0.00000 0.00000 0.00000 0.11429 0.14286 -0.03810 -0.58413 [1-2] 48.00 0.08573 0.19989[3-4] 0.00000 0.00000 0.00000 0.00000 -0.34286 -0.42857 -0.88571 -0.58095 [1-3] 30.30 -0.10082 0.27954[4-5] 0.00000 0.00000 0.00000 0.00000 -0.11429 -0.14286 0.03810 -0.41587 [2-3] 24.50 -0.16240 0.30670

[2-4] 26.05 -0.08215 0.23575

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack_refer 03)> [2-5] 30.10 0.19976 -0.02212[3-4] 9.70 0.48391 -0.42326

Factores GGDF Factores GLDF [4-5] -4.50 0.16141 -0.18795[1] [2] [3] [4] [5] [1] [2] [3] [4] [5]

[1-2] 0.71684 -0.12817 0.08573 0.04280 -0.07185 [1-2] -0.43122 0.41378 0.19989 0.24281 0.35747[1-3] 0.27472 0.11694 -0.10082 -0.05712 0.05961 [1-3] -0.09599 0.06179 0.27954 0.23585 0.11911[2-3] 0.12794 0.19924 -0.16240 -0.08983 0.10403 [2-3] 0.01635 -0.05494 0.30670 0.23413 0.04027[2-4] 0.14993 0.20692 -0.08215 -0.15773 0.08610 [2-4] 0.00367 -0.05332 0.23575 0.31133 0.06751[2-5] 0.31441 0.34257 0.19976 0.16133 -0.38702 [2-5] -0.13678 -0.16494 -0.02212 0.01630 0.56465[3-4] 0.13432 0.04848 0.48391 -0.40500 -0.10521 [3-4] -0.07368 0.01217 -0.42326 0.46564 0.16586[4-5] 0.04468 0.01602 0.16141 0.19889 -0.25816 [4-5] -0.07122 -0.04256 -0.18795 -0.22542 0.23162

Cálculo de la matriz jacobiana (J)[1] [2] [3] [4] [5] [1] [2] [3] [4] [5]

[1] 6.25 -5.00 -1.25 0 0 18.750 -15.00 -3.75 0 0

[2] -5.00 10.8333 -1.6667 -1.6667 -2.50 -15 32.50 -5.00 -5.00 -7.50

[3] -1.25 -1.66667 12.9167 -10.00 0 -3.75 -5 38.750 -30.00 0

[4] 0 -1.66667 -10 12.9167 -1.25 0 -5 -30 38.750 -3.75

[5] 0 -2.50 0 -1.25 3.75 0 -7.5 0 -3.75 11.250

[1] 18.640 -15.00 -3.75 0.00 0.00 -6.25 5.00 1.25 0.00 0.00

[2] -15 32.330 -5.00 -5.00 -7.50 5 -10.8333 1.6667 1.6667 2.5000[3] -3.75 -5 38.640 -30.00 0.00 1.25 1.666667 -12.9167 10.00 0.00

[4] 0 -5 -30 38.640 -3.75 0 1.666667 10 -12.9167 1.25[5] 0 -7.5 0 -3.75 11.170 0 2.5 0 1.25 -3.75


Transpuesta de la matriz incidencia (Jf) reducida[1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5] [1-2] [1-3] [2-3] [2-4] [2-5] [3-4] [4-5]

[2] -5 0 1.66667 1.66667 2.5 0 0 -15 0 5 5 7.5 0 0[3] 0 -1.25 -1.6667 0 0 10 0 0 -3.75 -5 0 0 30 0[4] 0 0 0 -1.6667 0 -10 1.25 0 0 0 -5 0 -30 3.75

[5] 0 0 0 0 -2.5 0 -1.25 0 0 0 0 -7.5 0 -3.75[2] -15 0 5 5 7.5 0 0 5 0 -1.6667 -1.6667 -2.5 0 0[3] 0 -3.75 -5 0 0 30 0 0 1.25 1.66667 0 0 -10 0[4] 0 0 0 -5 0 -30 3.75 0 0 0 1.66667 0 10 -1.25[5] 0 0 0 0 -7.5 0 -3.75 0 0 0 0 2.5 0 1.25

Matriz J reducida la referencia Cálculo de la matriz J inversa (J-1)[2] [3] [4] [5] [2] [3] [4] [5] [2] [3] [4] [5] [2] [3] [4] [5]

[2] 10.8333 -1.6667 -1.6667 -2.5000 32.50 -5.00 -5.00 -7.50 [2] 0.01718 0.01300 0.01388 0.01618 0.05154 0.03899 0.04164 0.04855[3] -1.6667 12.9167 -10.000 0.0000 -5.00 38.75 -30.00 0.00 [3] 0.01300 0.03040 0.02700 0.01778 0.03899 0.09121 0.08101 0.05334[4] -1.6667 -10.0000 12.9167 -1.2500 -5.00 -30.00 38.75 -3.75 [4] 0.01388 0.02700 0.03248 0.02021 0.04164 0.08101 0.09743 0.06063[5] -2.5000 0.0000 -1.2500 3.7500 -7.50 0.00 -3.75 11.25 [5] 0.01618 0.01778 0.02021 0.04448 0.04855 0.05334 0.06063 0.13343[2] 32.330 -5.000 -5.000 -7.500 -10.8333 1.6667 1.6667 2.5000 [2] 0.05046 0.03757 0.04014 0.04699 -0.01718 -0.01300 -0.01388 -0.01618[3] -5.000 38.640 -30.000 0.000 1.6667 -12.9167 10.0000 0.0000 [3] 0.03757 0.08891 0.07862 0.05122 -0.01300 -0.03040 -0.02700 -0.01778[4] -5.000 -30.000 38.640 -3.750 1.6667 10.0000 -12.9167 1.2500 [4] 0.04014 0.07862 0.09489 0.05834 -0.01388 -0.02700 -0.03248 -0.02021[5] -7.500 0.000 -3.750 11.170 2.5000 0.0000 1.2500 -3.7500 [5] 0.04699 0.05122 0.05834 0.13068 -0.01618 -0.01778 -0.02021 -0.04448



[1] 5 1.25 0 0 0 0 0 15 3.75 0 0 0 0 0[3] 0 -1.25 -1.66667 0 0 10 0 0 -3.75 -5 0 0 30 0[4] 0 0 0 -1.66667 0 -10 1.25 0 0 0 -5 0 -30 3.75[5] 0 0 0 0 -2.5 0 -1.25 0 0 0 0 -7.5 0 -3.75[1] 15 3.750 0 0 0 0 0 -5 -1.25 0 0 0 0 0[3] 0 -3.750 -5 0 0 30 0 0 1.25 1.666667 0 0 -10 0[4] 0 0 0 -5 0 -30 3.75 0 0 0 1.666667 0 10 -1.25

[5] 0 0 0 0 -7.5 0 -3.75 0 0 0 0 2.5 0 1.25


[1] 6.25 -1.25 0.00 0 18.75 -3.75 0.00 0.00 [1] 0.01696 0.00436 0.00350 0.00117 0.05089 0.01309 0.01050 0.00352[3] -1.25 12.9167 -10.00 0 -3.75 38.750 -30.000 0.000 [3] 0.00436 0.02169 0.01741 0.00584 0.01309 0.06508 0.05222 0.01752[4] 0 -10.0000 12.9167 -1.2500 0 -30.000 38.750 -3.750 [4] 0.00350 0.01741 0.02199 0.00738 0.01050 0.05222 0.06596 0.02213[5] 0 0.0000 -1.2500 3.7500 0 0.000 -3.750 11.250 [5] 0.00117 0.00584 0.00738 0.02931 0.00352 0.01752 0.02213 0.08794[1] 18.640 -3.75 0 0 -6.25 1.25 0.00 0.00 [1] 0.05054 0.01283 0.01026 0.00342 -0.01696 -0.00436 -0.00350 -0.00117[3] -3.75 38.64 -30.00 0.00 1.25 -12.9167 10.00 0 [3] 0.01283 0.06420 0.05134 0.01710 -0.00436 -0.02169 -0.01741 -0.00584[4] 0 -30.00 38.64 -3.75 0 10.0000 -12.9167 1.2500 [4] 0.01026 0.05134 0.06505 0.02167 -0.00350 -0.01741 -0.02199 -0.00738[5] 0 0.00 -3.75 11.17 0 0.0000 1.2500 -3.7500 [5] 0.00342 0.01710 0.02167 0.08716 -0.00117 -0.00584 -0.00738 -0.02931


[1] 0.84810 0.15750 -0.07270 -0.05833 -0.02935 0.08624 0.02907 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[3] 0.21810 -0.21666 -0.36158 -0.29009 -0.14598 0.42892 0.14458 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[4] 0.17498 -0.17382 -0.29009 -0.36645 -0.18441 -0.45817 0.18264 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

[5] 0.05870 -0.05831 -0.09732 -0.12294 -0.73283 -0.15371 -0.27421 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[1] -0.00175 -0.00012 0.00042 0.00039 0.00026 -0.00018 -0.00017 0.84286 0.15714 -0.07143 -0.05714 -0.02857 0.08571 0.02857[3] -0.00127 0.00079 0.00148 0.00146 0.00104 -0.00012 -0.00057 0.21429 -0.21429 -0.35714 -0.28571 -0.14286 0.42857 0.14286[4] -0.00118 0.00080 0.00146 0.00152 0.00115 0.00034 -0.00056 0.17143 -0.17143 -0.28571 -0.36190 -0.18095 -0.45714 0.18095[5] -0.00052 0.00039 0.00069 0.00077 0.00195 0.00044 0.00040 0.05714 -0.05714 -0.09524 -0.12063 -0.72698 -0.15238 -0.27302


[1-2] 0.84810 0.21810 0.17498 0.05870 -0.00175 -0.00127 -0.00118 -0.00052 [1-2] 0.84635 0 0.21683 0.17379 0.05818

[1-3] 0.15750 -0.21666 -0.17382 -0.05831 -0.00012 0.00079 0.00080 0.00039 [1-3] 0.15738 0 -0.21587 -0.17302 -0.05792

[2-3] -0.07270 -0.36158 -0.29009 -0.09732 0.00042 0.00148 0.00146 0.00069 [2-3] -0.07228 0 -0.36010 -0.28863 -0.09663

[2-4] -0.05833 -0.29009 -0.36645 -0.12294 0.00039 0.00146 0.00152 0.00077 [2-4] -0.05793 0 -0.28863 -0.36494 -0.12217

[2-5] -0.02935 -0.14598 -0.18441 -0.73283 0.00026 0.00104 0.00115 0.00195 [2-5] -0.02909 0 -0.14494 -0.18325 -0.73088

[3-4] 0.08624 0.42892 -0.45817 -0.15371 -0.00018 -0.00012 0.00034 0.00044 [3-4] 0.08606 0 0.42881 -0.45783 -0.15326

[4-5] 0.02907 0.14458 0.18264 -0.27421 -0.00017 -0.00057 -0.00056 0.00040 [4-5] 0.02890 0 0.14400 0.18207 -0.27381[1-2] 0.00000 0.00000 0.00000 0.00000 0.84286 0.21429 0.17143 0.05714

[1-3] 0.00000 0.00000 0.00000 0.00000 0.15714 -0.21429 -0.17143 -0.05714 Datos de los Flujos barra [2] como slack[2-3] 0.00000 0.00000 0.00000 0.00000 -0.07143 -0.35714 -0.28571 -0.09524 Líneas Flujos Factor Factor[2-4] 0.00000 0.00000 0.00000 0.00000 -0.05714 -0.28571 -0.36190 -0.12063 l-k Dl-k,R Cl-k,R

[2-5] 0.00000 0.00000 0.00000 0.00000 -0.02857 -0.14286 -0.18095 -0.72698 [1-2] 48.05 -0.12890 0.41624[3-4] 0.00000 0.00000 0.00000 0.00000 0.08571 0.42857 -0.45714 -0.15238 [1-3] 30.30 0.11725 0.06233

[4-5] 0.00000 0.00000 0.00000 0.00000 0.02857 0.14286 0.18095 -0.27302 [2-3] 24.60 0.20059 -0.05433[2-4] 26.20 0.20854 -0.05286

Nota: El flujo de potencia se ejecutó en el programa PowerWorld 6.0 <Paper de Rudnick (slack 02)> [2-5] 30.30 0.34447 -0.16527[3-4] 9.40 0.04650 0.00767[4-5] -4.70 0.01464 -0.04420


[1-2] 0.71746 -0.12890 0.08793 0.04490 -0.07071 [1-2] -0.43011 0.41624 0.19942 0.24245 0.35806[1-3] 0.27463 0.11725 -0.09861 -0.05577 0.05933 [1-3] -0.09505 0.06233 0.27820 0.23536 0.12025[2-3] 0.12831 0.20059 -0.15951 -0.08804 0.10396 [2-3] 0.01794 -0.05433 0.30576 0.23430 0.04229

[2-4] 0.15061 0.20854 -0.08009 -0.15640 0.08637 [2-4] 0.00508 -0.05286 0.23578 0.31208 0.06931

[2-5] 0.31538 0.34447 0.19953 0.16121 -0.38641 [2-5] -0.13618 -0.16527 -0.02033 0.01799 0.56561[3-4] 0.13256 0.04650 0.47530 -0.41133 -0.10677 [3-4] -0.07839 0.00767 -0.42114 0.46550 0.16094[4-5] 0.04354 0.01464 0.15865 0.19672 -0.25917 [4-5] -0.07310 -0.04420 -0.18820 -0.22627 0.22962



[1] 5 1.25 0 0 0 0 0 15 3.75 0 0 0 0 0[2] -5 0 1.666667 1.666667 2.5 0 0 -15 0 5 5 7.5 0 0[4] 0 0 0 -1.66667 0 -10 1.25 0 0 0 -5 0 -30 3.75[5] 0 0 0 0 -2.5 0 -1.25 0 0 0 0 -7.5 0 -3.75[1] 15 3.75 0 0 0 0 0 -5 -1.25 0 0 0 0 0[2] -15 0 5 5 7.5 0 0 5 0 -1.66667 -1.66667 -2.5 0 0[4] 0 0 0 -5.0000 0 -30.00 3.7500 0 0 0 1.6667 0 10.00 -1.25

[5] 0 0 0 0 -7.5000 0 -3.7500 0 0 0 0 2.50 0 1.25


[1] 6.2500 -5.0000 0.0000 0.0000 18.7500 -15.0000 0.0000 0.0000 [1] 0.03021 0.01756 0.00353 0.01297 0.09062 0.05268 0.01059 0.03890[2] -5.0000 10.8333 -1.6667 -2.5000 -15.0000 32.5000 -5.0000 -7.5000 [2] 0.01756 0.02183 0.00439 0.01612 0.05268 0.06550 0.01317 0.04837[4] 0.0000 -1.6667 12.9167 -1.2500 0.0000 -5.0000 38.7500 -3.7500 [4] 0.00353 0.00439 0.00891 0.00593 0.01059 0.01317 0.02672 0.01780[5] 0.0000 -2.5000 -1.2500 3.7500 0.0000 -7.5000 -3.7500 11.2500 [5] 0.01297 0.01612 0.00593 0.03965 0.03890 0.04837 0.01780 0.11894[1] 18.6400 -15.0000 0.0000 0.0000 -6.2500 5.0000 0.0000 0.0000 [1] 0.08898 0.05129 0.01025 0.03758 -0.03021 -0.01756 -0.00353 -0.01297[2] -15.0000 32.3300 -5.0000 -7.5000 5.0000 -10.8333 1.6667 2.5000 [2] 0.05129 0.06415 0.01282 0.04701 -0.01756 -0.02183 -0.00439 -0.01612[4] 0.0000 -5.0000 38.6400 -3.7500 0.0000 1.6667 -12.9167 1.2500 [4] 0.01025 0.01282 0.02656 0.01739 -0.00353 -0.00439 -0.00891 -0.00593[5] 0.0000 -7.5000 -3.7500 11.1700 0.0000 2.5000 1.2500 -3.7500 [5] 0.03758 0.04701 0.01739 0.11705 -0.01297 -0.01612 -0.00593 -0.03965


[1] 0.63238 0.37759 0.29266 0.23383 0.11484 -0.35295 -0.11795 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[2] -0.21370 0.21949 0.36389 0.29075 0.14279 -0.43886 -0.14666 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[4] -0.04295 0.04412 0.07314 -0.07527 -0.03859 -0.89050 0.03716 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

[5] -0.15779 0.16207 0.26870 0.16983 -0.58810 -0.59320 -0.42142 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000[1] -0.00127 -0.00205 -0.00231 -0.00175 -0.00019 0.00337 0.00122 0.62857 0.37143 0.28571 0.22857 0.11429 -0.34286 -0.11429[2] -0.00020 -0.00174 -0.00225 -0.00168 0.00002 0.00343 0.00127 -0.21429 0.21429 0.35714 0.28571 0.14286 -0.42857 -0.14286[4] 0.00003 -0.00042 -0.00057 -0.00031 0.00016 0.00160 0.00031 -0.04286 0.04286 0.07143 -0.07619 -0.03810 -0.88571 0.03810[5] 0.00022 -0.00164 -0.00226 -0.00158 0.00132 0.00408 0.00185 -0.15714 0.15714 0.26190 0.16508 -0.58413 -0.58095 -0.41587

Cálculos de PTDF_s.xls

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Transcript of Cálculos de PTDF_s.xls