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Instance acopf_caseactivsg70k_qcqp

AC Optimal Power Flow: Given an undirected network, where at every node electric power is generated or demanded and edges model transmission lines, the goal is to minimize the cost of power generation subject to network demand, the nonlinear physics of power flows, and operational constraints. Synthetic US power system model

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	16439499.83000000 p1 ( gdx sol ) (infeas: 4e-09)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.00000000 (ANTIGONE) 7621342.97200000 (GUROBI) 7621342.96200000 (SCIP)
Referencesⓘ	Bienstock, Daniel and Villagra, Matias, Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF, Tech. Rep., 2024. Hua Wei, H. Sasaki, J. Kubokawa, R. Yokoyama, An interior point nonlinear programming for optimal power flow problems with a novel data structure. In Proceedings of the 20th International Conference on Power Industry Computer Applications, 1997, 134-141. Carpentier, J. L., Contribution a l'Etude du Dispatching Economique, Bulletin de la Societe Francoise des Electriciens, 8, 1962, 431-447. Birchfield, Adam B., Xu, Ti, Gegner, Kathleen M., Shetye, Komal S., and Overbye, Thomas J., Grid Structural Characteristics as Validation Criteria for Synthetic Networks, IEEE Transactions on Power Systems, 32:4, 2017, 3258-3265. Birchfield, Adam B., Xu, Ti, and Overbye, Thomas J., Power Flow Convergence and Reactive Power Planning in the Creation of Large Synthetic Grids, IEEE Transactions on Power Systems, 33:6, 2018, 6667-6674.
Applicationⓘ	Electricity Networks
Added to libraryⓘ	04 Mar 2024
Problem typeⓘ	QCQP
#Variablesⓘ	900023
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	418897
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	4430
#Nonlinear Nonzeros in Objectiveⓘ	4429
#Constraintsⓘ	1016476
#Linear Constraintsⓘ	632828
#Quadratic Constraintsⓘ	383648
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	3434923
#Nonlinear Nonzeros in Jacobianⓘ	1120124
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	1085441
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	418897
#Blocks in Hessian of Lagrangianⓘ	278898
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	140000
Average blocksize in Hessian of Lagrangianⓘ	1.501972
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.9238e-04
Maximal coefficientⓘ	3.3927e+06
Infeasibility of initial pointⓘ	6.75e+04
Sparsity Hessian of Lagrangianⓘ

---

$offlisting
*
* Equation counts
*     Total        E        G        L        N        X        C        B
*   1016477   879243        0   137234        0        0        0        0
*
* Variable counts
*                  x        b        i      s1s      s2s       sc       si
*     Total     cont   binary  integer     sos1     sos2    scont     sint
*    900024   900024        0        0        0        0        0        0
* FX 133499
*
* Nonzero counts
*     Total    const       NL
*   3439354  2314801  1124553

* Solve m using RMIQCP minimizing objvar;

Variables
    objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,
    x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39,
    x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56,x57,x58,
    x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,
    x78,x79,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,
    x97,x98,x99,x100,x101,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,
    x112,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,
    x127,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,
    x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155,x156,
    x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168,x169,x170,x171,
    x172,x173,x174,x175,x176,x177,x178,x179,x180,x181,x182,x183,x184,x185,x186,
    x187,x188,x189,x190,x191,x192,x193,x194,x195,x196,x197,x198,x199,x200,x201,
    x202,x203,x204,x205,x206,x207,x208,x209,x210,x211,x212,x213,x214,x215,x216,
    x217,x218,x219,x220,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231,
    x232,x233,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244,x245,x246,
    x247,x248,x249,x250,x251,x252,x253,x254,x255,x256,x257,x258,x259,x260,x261,
    x262,x263,x264,x265,x266,x267,x268,x269,x270,x271,x272,x273,x274,x275,x276,
    x277,x278,x279,x280,x281,x282,x283,x284,x285,x286,x287,x288,x289,x290,x291,
    x292,x293,x294,x295,x296,x297,x298,x299,x300,x301,x302,x303,x304,x305,x306,
    x307,x308,x309,x310,x311,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,
    x322,x323,x324,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335,x336,
    x337,x338,x339,x340,x341,x342,x343,x344,x345,x346,x347,x348,x349,x350,x351,
    x352,x353,x354,x355,x356,x357,x358,x359,x360,x361,x362,x363,x364,x365,x366,
    x367,x368,x369,x370,x371,x372,x373,x374,x375,x376,x377,x378,x379,x380,x381,
    x382,x383,x384,x385,x386,x387,x388,x389,x390,x391,x392,x393,x394,x395,x396,
    x397,x398,x399,x400,x401,x402,x403,x404,x405,x406,x407,x408,x409,x410,x411,
    x412,x413,x414,x415,x416,x417,x418,x419,x420,x421,x422,x423,x424,x425,x426,
    x427,x428,x429,x430,x431,x432,x433,x434,x435,x436,x437,x438,x439,x440,x441,
    x442,x443,x444,x445,x446,x447,x448,x449,x450,x451,x452,x453,x454,x455,x456,
    x457,x458,x459,x460,x461,x462,x463,x464,x465,x466,x467,x468,x469,x470,x471,
    x472,x473,x474,x475,x476,x477,x478,x479,x480,x481,x482,x483,x484,x485,x486,
    x487,x488,x489,x490,x491,x492,x493,x494,x495,x496,x497,x498,x499,x500,x501,
    x502,x503,x504,x505,x506,x507,x508,x509,x510,x511,x512,x513,x514,x515,x516,
    x517,x518,x519,x520,x521,x522,x523,x524,x525,x526,x527,x528,x529,x530,x531,
    x532,x533,x534,x535,x536,x537,x538,x539,x540,x541,x542,x543,x544,x545,x546,
    x547,x548,x549,x550,x551,x552,x553,x554,x555,x556,x557,x558,x559,x560,x561,
    x562,x563,x564,x565,x566,x567,x568,x569,x570,x571,x572,x573,x574,x575,x576,
    x577,x578,x579,x580,x581,x582,x583,x584,x585,x586,x587,x588,x589,x590,x591,
    x592,x593,x594,x595,x596,x597,x598,x599,x600,x601,x602,x603,x604,x605,x606,
    x607,x608,x609,x610,x611,x612,x613,x614,x615,x616,x617,x618,x619,x620,x621,
    x622,x623,x624,x625,x626,x627,x628,x629,x630,x631,x632,x633,x634,x635,x636,
    x637,x638,x639,x640,x641,x642,x643,x644,x645,x646,x647,x648,x649,x650,x651,
    x652,x653,x654,x655,x656,x657,x658,x659,x660,x661,x662,x663,x664,x665,x666,
    x667,x668,x669,x670,x671,x672,x673,x674,x675,x676,x677,x678,x679,x680,x681,
    x682,x683,x684,x685,x686,x687,x688,x689,x690,x691,x692,x693,x694,x695,x696,
    x697,x698,x699,x700,x701,x702,x703,x704,x705,x706,x707,x708,x709,x710,x711,
    x712,x713,x714,x715,x716,x717,x718,x719,x720,x721,x722,x723,x724,x725,x726,
    x727,x728,x729,x730,x731,x732,x733,x734,x735,x736,x737,x738,x739,x740,x741,
    x742,x743,x744,x745,x746,x747,x748,x749,x750,x751,x752,x753,x754,x755,x756,
    x757,x758,x759,x760,x761,x762,x763,x764,x765,x766,x767,x768,x769,x770,x771,
    x772,x773,x774,x775,x776,x777,x778,x779,x780,x781,x782,x783,x784,x785,x786,
    x787,x788,x789,x790,x791,x792,x793,x794,x795,x796,x797,x798,x799,x800,x801,
    x802,x803,x804,x805,x806,x807,x808,x809,x810,x811,x812,x813,x814,x815,x816,
    x817,x818,x819,x820,x821,x822,x823,x824,x825,x826,x827,x828,x829,x830,x831,
    x832,x833,x834,x835,x836,x837,x838,x839,x840,x841,x842,x843,x844,x845,x846,
    x847,x848,x849,x850,x851,x852,x853,x854,x855,x856,x857,x858,x859,x860,x861,
    x862,x863,x864,x865,x866,x867,x868,x869,x870,x871,x872,x873,x874,x875,x876,
    x877,x878,x879,x880,x881,x882,x883,x884,x885,x886,x887,x888,x889,x890,x891,
    x892,x893,x894,x895,x896,x897,x898,x899,x900,x901,x902,x903,x904,x905,x906,
    x907,x908,x909,x910,x911,x912,x913,x914,x915,x916,x917,x918,x919,x920,x921,
    x922,x923,x924,x925,x926,x927,x928,x929,x930,x931,x932,x933,x934,x935,x936,
    x937,x938,x939,x940,x941,x942,x943,x944,x945,x946,x947,x948,x949,x950,x951,
    x952,x953,x954,x955,x956,x957,x958,x959,x960,x961,x962,x963,x964,x965,x966,
    x967,x968,x969,x970,x971,x972,x973,x974,x975,x976,x977,x978,x979,x980,x981,
    x982,x983,x984,x985,x986,x987,x988,x989,x990,x991,x992,x993,x994,x995,x996,
    x997,x998,x999,x1000,x1001,x1002,x1003,x1004,x1005,x1006,x1007,x1008,x1009,
    x1010,x1011,x1012,x1013,x1014,x1015,x1016,x1017,x1018,x1019,x1020,x1021,
    x1022,x1023,x1024,x1025,x1026,x1027,x1028,x1029,x1030,x1031,x1032,x1033,
    x1034,x1035,x1036,x1037,x1038,x1039,x1040,x1041,x1042,x1043,x1044,x1045,
    x1046,x1047,x1048,x1049,x1050,x1051,x1052,x1053,x1054,x1055,x1056,x1057,
    x1058,x1059,x1060,x1061,x1062,x1063,x1064,x1065,x1066,x1067,x1068,x1069,
    x1070,x1071,x1072,x1073,x1074,x1075,x1076,x1077,x1078,x1079,x1080,x1081,
    x1082,x1083,x1084,x1085,x1086,x1087,x1088,x1089,x1090,x1091,x1092,x1093,
    x1094,x1095,x1096,x1097,x1098,x1099,x1100,x1101,x1102,x1103,x1104,x1105,
    x1106,x1107,x1108,x1109,x1110,x1111,x1112,x1113,x1114,x1115,x1116,x1117,
    x1118,x1119,x1120,x1121,x1122,x1123,x1124,x1125,x1126,x1127,x1128,x1129,
    x1130,x1131,x1132,x1133,x1134,x1135,x1136,x1137,x1138,x1139,x1140,x1141,
    x1142,x1143,x1144,x1145,x1146,x1147,x1148,x1149,x1150,x1151,x1152,x1153,
    x1154,x1155,x1156,x1157,x1158,x1159,x1160,x1161,x1162,x1163,x1164,x1165,
    x1166,x1167,x1168,x1169,x1170,x1171,x1172,x1173,x1174,x1175,x1176,x1177,
    x1178,x1179,x1180,x1181,x1182,x1183,x1184,x1185,x1186,x1187,x1188,x1189,
    x1190,x1191,x1192,x1193,x1194,x1195,x1196,x1197,x1198,x1199,x1200,x1201,
    x1202,x1203,x1204,x1205,x1206,x1207,x1208,x1209,x1210,x1211,x1212,x1213,
    x1214,x1215,x1216,x1217,x1218,x1219,x1220,x1221,x1222,x1223,x1224,x1225,
    x1226,x1227,x1228,x1229,x1230,x1231,x1232,x1233,x1234,x1235,x1236,x1237,
    x1238,x1239,x1240,x1241,x1242,x1243,x1244,x1245,x1246,x1247,x1248,x1249,
    x1250,x1251,x1252,x1253,x1254,x1255,x1256,x1257,x1258,x1259,x1260,x1261,
    x1262,x1263,x1264,x1265,x1266,x1267,x1268,x1269,x1270,x1271,x1272,x1273,
    x1274,x1275,x1276,x1277,x1278,x1279,x1280,x1281,x1282,x1283,x1284,x1285,
    x1286,x1287,x1288,x1289,x1290,x1291,x1292,x1293,x1294,x1295,x1296,x1297,
    x1298,x1299,x1300,x1301,x1302,x1303,x1304,x1305,x1306,x1307,x1308,x1309,
    x1310,x1311,x1312,x1313,x1314,x1315,x1316,x1317,x1318,x1319,x1320,x1321,
    x1322,x1323,x1324,x1325,x1326,x1327,x1328,x1329,x1330,x1331,x1332,x1333,
    x1334,x1335,x1336,x1337,x1338,x1339,x1340,x1341,x1342,x1343,x1344,x1345,
    x1346,x1347,x1348,x1349,x1350,x1351,x1352,x1353,x1354,x1355,x1356,x1357,
    x1358,x1359,x1360,x1361,x1362,x1363,x1364,x1365,x1366,x1367,x1368,x1369,
    x1370,x1371,x1372,x1373,x1374,x1375,x1376,x1377,x1378,x1379,x1380,x1381,
    x1382,x1383,x1384,x1385,x1386,x1387,x1388,x1389,x1390,x1391,x1392,x1393,
    x1394,x1395,x1396,x1397,x1398,x1399,x1400,x1401,x1402,x1403,x1404,x1405,
    x1406,x1407,x1408,x1409,x1410,x1411,x1412,x1413,x1414,x1415,x1416,x1417,
    x1418,x1419,x1420,x1421,x1422,x1423,x1424,x1425,x1426,x1427,x1428,x1429,
    x1430,x1431,x1432,x1433,x1434,x1435,x1436,x1437,x1438,x1439,x1440,x1441,
    x1442,x1443,x1444,x1445,x1446,x1447,x1448,x1449,x1450,x1451,x1452,x1453,
    x1454,x1455,x1456,x1457,x1458,x1459,x1460,x1461,x1462,x1463,x1464,x1465,
    x1466,x1467,x1468,x1469,x1470,x1471,x1472,x1473,x1474,x1475,x1476,x1477,
    x1478,x1479,x1480,x1481,x1482,x1483,x1484,x1485,x1486,x1487,x1488,x1489,
    x1490,x1491,x1492,x1493,x1494,x1495,x1496,x1497,x1498,x1499,x1500,x1501,
    x1502,x1503,x1504,x1505,x1506,x1507,x1508,x1509,x1510,x1511,x1512,x1513,
    x1514,x1515,x1516,x1517,x1518,x1519,x1520,x1521,x1522,x1523,x1524,x1525,
    x1526,x1527,x1528,x1529,x1530,x1531,x1532,x1533,x1534,x1535,x1536,x1537,
    x1538,x1539,x1540,x1541,x1542,x1543,x1544,x1545,x1546,x1547,x1548,x1549,
    x1550,x1551,x1552,x1553,x1554,x1555,x1556,x1557,x1558,x1559,x1560,x1561,
    x1562,x1563,x1564,x1565,x1566,x1567,x1568,x1569,x1570,x1571,x1572,x1573,
    x1574,x1575,x1576,x1577,x1578,x1579,x1580,x1581,x1582,x1583,x1584,x1585,
    x1586,x1587,x1588,x1589,x1590,x1591,x1592,x1593,x1594,x1595,x1596,x1597,
    x1598,x1599,x1600,x1601,x1602,x1603,x1604,x1605,x1606,x1607,x1608,x1609,
    x1610,x1611,x1612,x1613,x1614,x1615,x1616,x1617,x1618,x1619,x1620,x1621,
    x1622,x1623,x1624,x1625,x1626,x1627,x1628,x1629,x1630,x1631,x1632,x1633,
    x1634,x1635,x1636,x1637,x1638,x1639,x1640,x1641,x1642,x1643,x1644,x1645,
    x1646,x1647,x1648,x1649,x1650,x1651,x1652,x1653,x1654,x1655,x1656,x1657,
    x1658,x1659,x1660,x1661,x1662,x1663,x1664,x1665,x1666,x1667,x1668,x1669,
    x1670,x1671,x1672,x1673,x1674,x1675,x1676,x1677,x1678,x1679,x1680,x1681,
    x1682,x1683,x1684,x1685,x1686,x1687,x1688,x1689,x1690,x1691,x1692,x1693,
    x1694,x1695,x1696,x1697,x1698,x1699,x1700,x1701,x1702,x1703,x1704,x1705,
    x1706,x1707,x1708,x1709,x1710,x1711,x1712,x1713,x1714,x1715,x1716,x1717,
    x1718,x1719,x1720,x1721,x1722,x1723,x1724,x1725,x1726,x1727,x1728,x1729,
    x1730,x1731,x1732,x1733,x1734,x1735,x1736,x1737,x1738,x1739,x1740,x1741,
    x1742,x1743,x1744,x1745,x1746,x1747,x1748,x1749,x1750,x1751,x1752,x1753,
    x1754,x1755,x1756,x1757,x1758,x1759,x1760,x1761,x1762,x1763,x1764,x1765,
    x1766,x1767,x1768,x1769,x1770,x1771,x1772,x1773,x1774,x1775,x1776,x1777,
    x1778,x1779,x1780,x1781,x1782,x1783,x1784,x1785,x1786,x1787,x1788,x1789,
    x1790,x1791,x1792,x1793,x1794,x1795,x1796,x1797,x1798,x1799,x1800,x1801,
    x1802,x1803,x1804,x1805,x1806,x1807,x1808,x1809,x1810,x1811,x1812,x1813,
    x1814,x1815,x1816,x1817,x1818,x1819,x1820,x1821,x1822,x1823,x1824,x1825,
    x1826,x1827,x1828,x1829,x1830,x1831,x1832,x1833,x1834,x1835,x1836,x1837,
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    x248904,x248905,x248906,x248907,x248908,x248909,x248910,x248911,x248912,
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    x250065,x250066,x250067,x250068,x250069,x250070,x250071,x250072,x250073,
    x250074,x250075,x250076,x250077,x250078,x250079,x250080,x250081,x250082,
    x250083,x250084,x250085,x250086,x250087,x250088,x250089,x250090,x250091,
    x250092,x250093,x250094,x250095,x250096,x250097,x250098,x250099,x250100,
    x250101,x250102,x250103,x250104,x250105,x250106,x250107,x250108,x250109,
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    x250119,x250120,x250121,x250122,x250123,x250124,x250125,x250126,x250127,
    x250128,x250129,x250130,x250131,x250132,x250133,x250134,x250135,x250136,
    x250137,x250138,x250139,x250140,x250141,x250142,x250143,x250144,x250145,
    x250146,x250147,x250148,x250149,x250150,x250151,x250152,x250153,x250154,
    x250155,x250156,x250157,x250158,x250159,x250160,x250161,x250162,x250163,
    x250164,x250165,x250166,x250167,x250168,x250169,x250170,x250171,x250172,
    x250173,x250174,x250175,x250176,x250177,x250178,x250179,x250180,x250181,
    x250182,x250183,x250184,x250185,x250186,x250187,x250188,x250189,x250190,
    x250191,x250192,x250193,x250194,x250195,x250196,x250197,x250198,x250199,
    x250200,x250201,x250202,x250203,x250204,x250205,x250206,x250207,x250208,
    x250209,x250210,x250211,x250212,x250213,x250214,x250215,x250216,x250217,
    x250218,x250219,x250220,x250221,x250222,x250223,x250224,x250225,x250226,
    x250227,x250228,x250229,x250230,x250231,x250232,x250233,x250234,x250235,
    x250236,x250237,x250238,x250239,x250240,x250241,x250242,x250243,x250244,
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