pglib_case5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MathOptInterface"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PowerModels, Gurobi, Ipopt, JuMP, COSMO, Mosek, MosekTools, MathOptInterface\n",
    "const MOI = MathOptInterface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"../pglib-opf/api/pglib_opf_case5_pjm__api.m\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = \"../pglib-opf/api/pglib_opf_case5_pjm__api.m\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m[info | PowerModels]: extending matpower format with data: areas 1x3\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 4: [4000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 1: [1400.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 5: [1000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 2: [1500.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 3: [3000.0, 0.0]\u001b[39m\n",
      "\n",
      "******************************************************************************\n",
      "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
      " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
      "         For more information visit http://projects.coin-or.org/Ipopt\n",
      "******************************************************************************\n",
      "\n",
      "This is Ipopt version 3.13.2, running with linear solver mumps.\n",
      "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:      299\n",
      "Number of nonzeros in inequality constraint Jacobian.:      140\n",
      "Number of nonzeros in Lagrangian Hessian.............:      236\n",
      "\n",
      "Total number of variables............................:       44\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:       44\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:       35\n",
      "Total number of inequality constraints...............:       34\n",
      "        inequality constraints with only lower bounds:       11\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:       23\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  1.0899989e+02 1.07e+01 2.88e+01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  5.9119686e+03 9.66e+00 6.77e+01  -1.0 7.73e+00    -  1.83e-03 1.01e-01h  3\n",
      "   2  6.2328296e+03 9.32e+00 6.52e+01  -1.0 1.48e+01    -  8.17e-02 3.45e-02h  1\n",
      "   3  7.4370217e+03 9.04e+00 6.19e+01  -1.0 1.42e+01    -  3.71e-01 3.01e-02h  1\n",
      "   4  1.3363069e+04 7.76e+00 5.28e+01  -1.0 1.50e+01    -  1.93e-01 1.42e-01h  2\n",
      "   5  2.2556856e+04 6.07e+00 3.75e+01  -1.0 1.46e+01    -  6.43e-01 2.17e-01h  1\n",
      "   6  2.5210189e+04 5.75e+00 3.92e+01  -1.0 1.73e+01    -  1.32e-01 5.39e-02h  1\n",
      "   7  4.7638008e+04 3.02e+00 7.23e+01  -1.0 1.34e+01    -  3.14e-03 4.75e-01H  1\n",
      "   8  5.2229622e+04 2.45e+00 3.62e+01  -1.0 9.93e+00    -  5.75e-01 1.87e-01h  1\n",
      "   9  6.6204413e+04 7.42e-01 1.63e+01  -1.0 1.01e+01    -  4.26e-01 6.97e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  6.7733420e+04 5.57e-01 2.19e+01  -1.0 5.84e+00    -  1.00e+00 2.50e-01h  1\n",
      "  11  6.8153747e+04 5.09e-01 5.30e+01  -1.0 1.57e+01    -  1.57e-01 8.56e-02h  1\n",
      "  12  6.8587773e+04 4.65e-01 4.54e+01  -1.0 9.80e+00    -  3.67e-02 8.55e-02h  3\n",
      "  13  6.9838167e+04 3.41e-01 3.34e+01  -1.0 3.68e+00    -  2.36e-01 2.67e-01h  1\n",
      "  14  6.9881411e+04 3.37e-01 4.38e+01  -1.0 2.54e+01    -  1.41e-01 1.26e-02h  3\n",
      "  15  6.9927630e+04 3.32e-01 2.27e+02  -1.0 2.49e+01    -  3.69e-01 1.32e-02h  4\n",
      "  16  7.0074240e+04 3.22e-01 2.08e+02  -1.0 1.11e+01    -  4.63e-03 3.15e-02h  4\n",
      "  17  7.2606437e+04 1.67e-01 9.30e+01  -1.0 7.28e+00    -  1.19e-01 4.81e-01H  1\n",
      "  18  7.4168950e+04 1.15e-01 4.28e+01  -1.0 2.90e+00    -  4.94e-01 5.23e-01h  1\n",
      "  19  7.4794786e+04 1.41e-01 3.96e+01  -1.0 3.55e+00    -  1.00e+00 4.42e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20  7.4959122e+04 1.10e-01 1.35e+02  -1.0 5.94e-01    -  1.00e+00 2.13e-01h  1\n",
      "  21  7.5039554e+04 1.01e-01 2.55e+01  -1.0 1.06e+00    -  5.29e-02 1.05e-01h  1\n",
      "  22  7.6060431e+04 5.36e-02 2.66e+01  -1.0 1.52e+00    -  5.46e-01 1.00e+00h  1\n",
      "  23  7.6159035e+04 3.43e-02 2.31e+01  -1.0 7.32e-01    -  2.70e-01 3.74e-01h  1\n",
      "  24  7.6176293e+04 3.11e-02 7.14e+01  -1.0 3.82e+00    -  2.64e-01 9.21e-02f  4\n",
      "  25  7.6382854e+04 2.03e-03 3.93e+02  -1.0 2.55e+00    -  2.66e-01 9.14e-01H  1\n",
      "  26  7.6438016e+04 5.16e-04 1.64e+01  -1.0 6.91e+00    -  6.77e-01 1.00e+00H  1\n",
      "  27  7.6420756e+04 1.11e-04 4.54e+00  -1.0 7.89e-01    -  1.00e+00 1.00e+00F  1\n",
      "  28  7.6415914e+04 2.32e-04 6.30e-02  -1.0 3.69e-01    -  1.00e+00 1.00e+00h  1\n",
      "  29  7.6378303e+04 2.12e-03 5.41e-01  -2.5 1.63e+00    -  9.10e-01 9.70e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30  7.6378264e+04 7.23e-05 1.60e-01  -2.5 7.53e-01    -  1.00e+00 1.00e+00h  1\n",
      "  31  7.6378324e+04 6.71e-07 1.18e-03  -2.5 7.24e-02    -  1.00e+00 1.00e+00h  1\n",
      "  32  7.6377455e+04 7.59e-07 7.56e-03  -3.8 6.86e-02    -  1.00e+00 9.96e-01h  1\n",
      "  33  7.6377459e+04 2.43e-10 1.12e-06  -3.8 2.57e-04    -  1.00e+00 1.00e+00f  1\n",
      "  34  7.6377412e+04 2.13e-09 1.81e-06  -5.7 3.73e-03    -  1.00e+00 1.00e+00f  1\n",
      "In iteration 34, 1 Slack too small, adjusting variable bound\n",
      "  35  7.6377411e+04 2.89e-10 2.31e+00  -8.6 4.51e-05    -  1.00e+00 8.64e-01h  1\n",
      "  36  7.6377411e+04 6.78e-14 1.55e-09  -8.6 6.31e-06    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 36\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.9094352758069265e+03    7.6377411032277058e+04\n",
      "Dual infeasibility......:   1.5455343393977472e-09    6.1821373575909888e-08\n",
      "Constraint violation....:   2.1926366654938087e-14    6.7834626804597065e-14\n",
      "Complementarity.........:   4.1522991760337718e-09    1.6609196704135087e-07\n",
      "Overall NLP error.......:   4.1522991760337718e-09    1.6609196704135087e-07\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 71\n",
      "Number of objective gradient evaluations             = 37\n",
      "Number of equality constraint evaluations            = 71\n",
      "Number of inequality constraint evaluations          = 71\n",
      "Number of equality constraint Jacobian evaluations   = 37\n",
      "Number of inequality constraint Jacobian evaluations = 37\n",
      "Number of Lagrangian Hessian evaluations             = 36\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      1.750\n",
      "Total CPU secs in NLP function evaluations           =      0.667\n",
      "\n",
      "EXIT: Optimal Solution Found.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 2.79459\n",
       "  \"optimizer\"          => \"Ipopt\"\n",
       "  \"termination_status\" => LOCALLY_SOLVED\n",
       "  \"dual_status\"        => FEASIBLE_POINT\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 76377.4\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100.0,\"branch\"=>Dict{Stri…\n",
       "  \"objective_lb\"       => -Inf"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ipopt_rec = run_opf(file, ACRPowerModel, Ipopt.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m[info | PowerModels]: extending matpower format with data: areas 1x3\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 4: [4000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 1: [1400.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 5: [1000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 2: [1500.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 3: [3000.0, 0.0]\u001b[39m\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: MathOptInterface.VariablePrimalStart() is not supported by MathOptInterface.Bridges.LazyBridgeOptimizer{MosekModel}. This information will be discarded.\n",
      "└ @ MathOptInterface.Utilities /home/weiqizhang/.julia/packages/MathOptInterface/RmalA/src/Utilities/copy.jl:140\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 196             \n",
      "  Cones                  : 12              \n",
      "  Scalar variables       : 115             \n",
      "  Matrix variables       : 3               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer started.\n",
      "Presolve started.\n",
      "Linear dependency checker started.\n",
      "Linear dependency checker terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 22\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - number                 : 9               \n",
      "Presolve terminated. Time: 0.00    \n",
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 196             \n",
      "  Cones                  : 12              \n",
      "  Scalar variables       : 115             \n",
      "  Matrix variables       : 3               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 4               \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 104\n",
      "Optimizer  - Cones                  : 13\n",
      "Optimizer  - Scalar variables       : 72                conic                  : 39              \n",
      "Optimizer  - Semi-definite variables: 3                 scalarized             : 63              \n",
      "Factor     - setup time             : 0.00              dense det. time        : 0.00            \n",
      "Factor     - ML order time          : 0.00              GP order time          : 0.00            \n",
      "Factor     - nonzeros before factor : 1605              after factor           : 2251            \n",
      "Factor     - dense dim.             : 0                 flops                  : 6.61e+04        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   9.7e+00  4.0e+03  4.8e+01  0.00e+00   6.718000000e+04   6.713312000e+04   1.0e+00  0.01  \n",
      "1   1.2e+00  5.1e+02  1.7e+01  -1.00e+00  6.522605932e+04   6.518612647e+04   1.3e-01  0.02  \n",
      "2   4.5e-01  1.8e+02  9.8e+00  -9.68e-01  6.237358037e+04   6.234830420e+04   4.6e-02  0.02  \n",
      "3   3.0e-01  1.2e+02  7.2e+00  -7.22e-01  6.249435418e+04   6.247753925e+04   3.0e-02  0.02  \n",
      "4   1.5e-01  6.0e+01  3.9e+00  -5.46e-01  6.162933651e+04   6.162720743e+04   1.5e-02  0.02  \n",
      "5   1.3e-01  5.3e+01  3.8e+00  -5.15e-01  6.192544246e+04   6.192727304e+04   1.3e-02  0.02  \n",
      "6   5.0e-02  2.0e+01  1.4e+00  -2.74e-01  6.214837394e+04   6.215997896e+04   5.1e-03  0.02  \n",
      "7   1.7e-02  7.0e+00  3.5e-01  2.28e-01   6.299479123e+04   6.300335188e+04   1.7e-03  0.02  \n",
      "8   8.7e-03  3.6e+00  1.6e-01  5.68e-01   6.338024578e+04   6.338780710e+04   8.9e-04  0.02  \n",
      "9   6.6e-03  2.7e+00  1.8e-01  -2.41e-01  6.359197801e+04   6.361473230e+04   6.8e-04  0.02  \n",
      "10  3.9e-03  1.6e+00  1.0e-01  -1.55e-01  6.450980978e+04   6.453321502e+04   4.0e-04  0.02  \n",
      "11  2.0e-03  8.2e-01  4.3e-02  4.50e-01   6.560894383e+04   6.562479837e+04   2.0e-04  0.02  \n",
      "12  1.7e-03  7.0e-01  4.1e-02  5.97e-02   6.581645902e+04   6.583697017e+04   1.7e-04  0.02  \n",
      "13  1.5e-03  6.1e-01  3.0e-02  2.13e-01   6.620559059e+04   6.621971941e+04   1.5e-04  0.02  \n",
      "14  1.2e-03  4.9e-01  2.5e-02  3.00e-01   6.654626671e+04   6.656109831e+04   1.2e-04  0.02  \n",
      "15  8.6e-04  3.5e-01  1.7e-02  3.38e-01   6.701601143e+04   6.703022708e+04   8.9e-05  0.02  \n",
      "16  6.5e-04  2.7e-01  1.4e-02  2.26e-01   6.734611657e+04   6.736242788e+04   6.7e-05  0.02  \n",
      "17  3.3e-04  1.3e-01  6.9e-03  2.39e-01   6.829983847e+04   6.831671357e+04   3.4e-05  0.02  \n",
      "18  1.9e-04  7.8e-02  4.4e-03  -1.90e-01  6.923179083e+04   6.925213075e+04   2.0e-05  0.02  \n",
      "19  1.3e-04  5.2e-02  2.8e-03  3.69e-01   6.993680657e+04   6.995674597e+04   1.3e-05  0.02  \n",
      "20  9.0e-05  3.7e-02  1.9e-03  6.62e-02   7.068353858e+04   7.070095108e+04   9.2e-06  0.02  \n",
      "21  8.0e-05  3.3e-02  1.6e-03  4.16e-01   7.092777900e+04   7.094388211e+04   8.2e-06  0.03  \n",
      "22  4.6e-05  1.9e-02  8.2e-04  4.25e-01   7.186644876e+04   7.187878829e+04   4.8e-06  0.03  \n",
      "23  1.8e-05  7.5e-03  2.6e-04  5.83e-01   7.297934959e+04   7.298738498e+04   1.9e-06  0.03  \n",
      "24  8.2e-06  3.4e-03  1.0e-04  6.10e-01   7.353986491e+04   7.354619084e+04   8.4e-07  0.03  \n",
      "25  3.5e-06  1.5e-03  4.4e-05  2.66e-01   7.401192902e+04   7.401828514e+04   3.6e-07  0.03  \n",
      "26  1.6e-06  6.4e-04  2.0e-05  1.96e-01   7.444466251e+04   7.445144407e+04   1.6e-07  0.03  \n",
      "27  4.5e-07  1.9e-04  5.2e-06  2.28e-01   7.506708047e+04   7.507243998e+04   4.7e-08  0.03  \n",
      "28  2.3e-07  9.3e-05  2.4e-06  3.14e-01   7.537392078e+04   7.537837507e+04   2.3e-08  0.03  \n",
      "29  7.3e-08  3.0e-05  5.8e-07  4.17e-01   7.576769001e+04   7.577030019e+04   7.5e-09  0.03  \n",
      "30  2.7e-08  1.1e-05  1.5e-07  5.32e-01   7.598576462e+04   7.598711631e+04   2.8e-09  0.03  \n",
      "31  2.2e-08  2.3e-06  1.5e-08  9.79e-01   7.612279702e+04   7.612308947e+04   5.9e-10  0.03  \n",
      "32  1.5e-08  1.1e-07  1.6e-10  9.90e-01   7.616062052e+04   7.616063543e+04   2.8e-11  0.03  \n",
      "33  1.5e-08  1.1e-07  1.6e-10  1.00e+00   7.616062052e+04   7.616063543e+04   2.8e-11  0.03  \n",
      "34  1.4e-08  8.2e-08  1.1e-10  1.00e+00   7.616103846e+04   7.616105001e+04   2.1e-11  0.03  \n",
      "35  1.4e-08  8.2e-08  1.1e-10  1.00e+00   7.616103846e+04   7.616105001e+04   2.1e-11  0.03  \n",
      "Optimizer terminated. Time: 0.04    \n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 0.0397069\n",
       "  \"optimizer\"          => \"Mosek\"\n",
       "  \"termination_status\" => SLOW_PROGRESS\n",
       "  \"dual_status\"        => UNKNOWN_RESULT_STATUS\n",
       "  \"primal_status\"      => UNKNOWN_RESULT_STATUS\n",
       "  \"objective\"          => 76161.0\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100.0,\"branch\"=>Dict{Stri…\n",
       "  \"objective_lb\"       => 0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mosek_sdp = run_opf(file, SparseSDPWRMPowerModel, Mosek.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m[info | PowerModels]: extending matpower format with data: areas 1x3\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 4: [4000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 1: [1400.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 5: [1000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 2: [1500.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 3: [3000.0, 0.0]\u001b[39m\n",
      "Academic license - for non-commercial use only\n",
      "Academic license - for non-commercial use only\n",
      "Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)\n",
      "Optimize a model with 58 rows, 51 columns and 190 nonzeros\n",
      "Model fingerprint: 0x96995137\n",
      "Model has 18 quadratic constraints\n",
      "Coefficient statistics:\n",
      "  Matrix range     [6e-01, 2e+02]\n",
      "  QMatrix range    [1e+00, 1e+00]\n",
      "  Objective range  [1e+03, 4e+03]\n",
      "  Bounds range     [6e-01, 1e+01]\n",
      "  RHS range        [3e-01, 1e+01]\n",
      "  QRHS range       [6e+00, 2e+01]\n",
      "Presolve removed 0 rows and 1 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 154 rows, 74 columns, 309 nonzeros\n",
      "Presolved model has 18 second-order cone constraints\n",
      "Ordering time: 0.00s\n",
      "\n",
      "Barrier statistics:\n",
      " AA' NZ     : 1.283e+03\n",
      " Factor NZ  : 2.010e+03\n",
      " Factor Ops : 3.034e+04 (less than 1 second per iteration)\n",
      " Threads    : 1\n",
      "\n",
      "                  Objective                Residual\n",
      "Iter       Primal          Dual         Primal    Dual     Compl     Time\n",
      "   0   3.64003539e+05  5.07619991e+04  1.76e+01 9.07e+02  6.87e+03     0s\n",
      "   1   1.13443339e+05 -4.46549792e+04  2.32e+00 9.98e-04  1.16e+03     0s\n",
      "   2   8.26753190e+04  3.72411394e+04  7.42e-01 1.25e-04  2.77e+02     0s\n",
      "   3   6.91758379e+04  5.73721512e+04  2.05e-01 1.02e-05  6.29e+01     0s\n",
      "   4   6.80270191e+04  6.38069408e+04  1.22e-01 2.48e-06  2.67e+01     0s\n",
      "   5   6.78258520e+04  6.69980765e+04  6.30e-02 3.63e-07  9.98e+00     0s\n",
      "   6   6.79806302e+04  6.79785827e+04  4.84e-02 2.41e-07  7.38e+00     0s\n",
      "   7   6.80153804e+04  6.93374464e+04  4.61e-02 2.07e-07  6.42e+00     0s\n",
      "   8   6.81589823e+04  7.03385751e+04  4.34e-02 1.94e-07  5.81e+00     0s\n",
      "   9   6.85195603e+04  7.10527636e+04  3.84e-02 1.79e-07  4.97e+00     0s\n",
      "  10   6.86188798e+04  7.14808404e+04  3.74e-02 1.74e-07  4.79e+00     0s\n",
      "  11   6.91142315e+04  7.09321968e+04  3.47e-02 1.70e-07  6.23e+00     0s\n",
      "  12   6.99998936e+04  7.16141984e+04  2.71e-02 1.26e-07  6.12e+00     0s\n",
      "  13   7.14560291e+04  7.16936570e+04  1.59e-02 8.53e-08  7.27e+00     0s\n",
      "  14   7.18581314e+04  7.29311789e+04  1.17e-02 6.44e-08  2.66e+00     0s\n",
      "  15   7.22901840e+04  7.30687280e+04  8.04e-03 1.71e-07  2.10e+00     0s\n",
      "  16   7.30917368e+04  7.32152357e+04  1.36e-03 2.19e-08  3.90e-01     0s\n",
      "  17   7.31674575e+04  7.32347857e+04  7.31e-04 2.53e-08  2.02e-01     0s\n",
      "  18   7.32210218e+04  7.32457895e+04  2.90e-04 5.36e-07  8.59e-02     0s\n",
      "  19   7.32506209e+04  7.32538856e+04  4.57e-05 1.57e-06  1.56e-02     0s\n",
      "  20   7.32547986e+04  7.32550469e+04  6.23e-06 2.40e-05  3.10e-03     0s\n",
      "  21   7.32554222e+04  7.32554315e+04  3.50e-07 9.98e-07  1.97e-04     0s\n",
      "  22   7.32554526e+04  7.32554584e+04  5.83e-08 1.45e-08  1.08e-05     0s\n",
      "  23   7.32554582e+04  7.32554588e+04  5.62e-09 6.02e-08  9.00e-07     0s\n",
      "\n",
      "Barrier solved model in 23 iterations and 0.01 seconds\n",
      "Optimal objective 7.32554582e+04\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 0.0132072\n",
       "  \"optimizer\"          => \"Gurobi\"\n",
       "  \"termination_status\" => OPTIMAL\n",
       "  \"dual_status\"        => NO_SOLUTION\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 73255.5\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100.0,\"branch\"=>Dict{Stri…\n",
       "  \"objective_lb\"       => -Inf"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grb_soc = run_opf(file, SOCWRPowerModel, Gurobi.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m[info | PowerModels]: extending matpower format with data: areas 1x3\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 4: [4000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 1: [1400.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 5: [1000.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 2: [1500.0, 0.0]\u001b[39m\n",
      "\u001b[32m[info | PowerModels]: removing 1 cost terms from generator 3: [3000.0, 0.0]\u001b[39m\n",
      "Min 4000 0_pg[4] + 1500 0_pg[2] + 3000 0_pg[3] + 1000 0_pg[5] + 1400 0_pg[1]\n",
      "Subject to\n",
      " 0_vi[4] = 0.0\n",
      " 0_p[(6, 4, 5)] + 0_p[(2, 4, 1)] + 0_p[(5, 4, 3)] - 0_pg[4] = -10.748800000000001\n",
      " 0_q[(6, 4, 5)] + 0_q[(2, 4, 1)] + 0_q[(5, 4, 3)] - 0_qg[4] = -1.3147\n",
      " 0_p[(4, 2, 3)] + 0_p[(1, 2, 1)] = -8.0616\n",
      " 0_q[(4, 2, 3)] + 0_q[(1, 2, 1)] = -0.9861\n",
      " 0_p[(5, 3, 4)] + 0_p[(4, 3, 2)] - 0_pg[3] = -8.0616\n",
      " 0_q[(5, 3, 4)] + 0_q[(4, 3, 2)] - 0_qg[3] = -0.9861\n",
      " 0_p[(3, 5, 1)] + 0_p[(6, 5, 4)] - 0_pg[5] = 0.0\n",
      " 0_q[(3, 5, 1)] + 0_q[(6, 5, 4)] - 0_qg[5] = 0.0\n",
      " 0_p[(2, 1, 4)] + 0_p[(3, 1, 5)] + 0_p[(1, 1, 2)] - 0_pg[2] - 0_pg[1] = 0.0\n",
      " 0_q[(2, 1, 4)] + 0_q[(3, 1, 5)] + 0_q[(1, 1, 2)] - 0_qg[2] - 0_qg[1] = 0.0\n",
      " -9.167583425009166 0_vr[2]² - 9.167583425009166 0_vi[2]² + 9.167583425009166 0_vr[2]*0_vr[3] + 9.167583425009166 0_vi[2]*0_vi[3] - 91.67583425009167 0_vi[2]*0_vr[3] + 91.67583425009167 0_vi[3]*0_vr[2] + 0_p[(4, 2, 3)] = 0.0\n",
      " -91.66657425009167 0_vr[2]² - 91.66657425009167 0_vi[2]² + 91.67583425009167 0_vr[2]*0_vr[3] + 91.67583425009167 0_vi[2]*0_vi[3] + 9.167583425009166 0_vi[2]*0_vr[3] - 9.167583425009166 0_vi[3]*0_vr[2] + 0_q[(4, 2, 3)] = 0.0\n",
      " -9.167583425009166 0_vr[3]² - 9.167583425009166 0_vi[3]² + 9.167583425009166 0_vr[2]*0_vr[3] + 9.167583425009166 0_vi[2]*0_vi[3] + 91.67583425009167 0_vi[2]*0_vr[3] - 91.67583425009167 0_vr[2]*0_vi[3] + 0_p[(4, 3, 2)] = 0.0\n",
      " -91.66657425009167 0_vr[3]² - 91.66657425009167 0_vi[3]² + 91.67583425009167 0_vr[2]*0_vr[3] + 91.67583425009167 0_vi[2]*0_vi[3] - 9.167583425009166 0_vi[2]*0_vr[3] + 9.167583425009166 0_vr[2]*0_vi[3] + 0_q[(4, 3, 2)] = 0.0\n",
      " -3.2569046378322044 0_vr[1]² - 3.2569046378322044 0_vi[1]² + 3.2569046378322044 0_vr[1]*0_vr[4] + 3.2569046378322044 0_vi[1]*0_vi[4] - 32.56904637832204 0_vi[1]*0_vr[4] + 32.56904637832204 0_vi[4]*0_vr[1] + 0_p[(2, 1, 4)] = 0.0\n",
      " -32.56575637832204 0_vr[1]² - 32.56575637832204 0_vi[1]² + 32.56904637832204 0_vr[1]*0_vr[4] + 32.56904637832204 0_vi[1]*0_vi[4] + 3.2569046378322044 0_vi[1]*0_vr[4] - 3.2569046378322044 0_vi[4]*0_vr[1] + 0_q[(2, 1, 4)] = 0.0\n",
      " -3.2569046378322044 0_vr[4]² - 3.2569046378322044 0_vi[4]² + 3.2569046378322044 0_vr[1]*0_vr[4] + 3.2569046378322044 0_vi[1]*0_vi[4] + 32.56904637832204 0_vi[1]*0_vr[4] - 32.56904637832204 0_vr[1]*0_vi[4] + 0_p[(2, 4, 1)] = 0.0\n",
      " -32.56575637832204 0_vr[4]² - 32.56575637832204 0_vi[4]² + 32.56904637832204 0_vr[1]*0_vr[4] + 32.56904637832204 0_vi[1]*0_vi[4] - 3.2569046378322044 0_vi[1]*0_vr[4] + 3.2569046378322044 0_vr[1]*0_vi[4] + 0_q[(2, 4, 1)] = 0.0\n",
      " -15.470297029702971 0_vr[1]² - 15.470297029702971 0_vi[1]² + 15.470297029702971 0_vr[1]*0_vr[5] + 15.470297029702971 0_vi[1]*0_vi[5] - 154.7029702970297 0_vi[1]*0_vr[5] + 154.7029702970297 0_vi[5]*0_vr[1] + 0_p[(3, 1, 5)] = 0.0\n",
      " -154.68734029702972 0_vr[1]² - 154.68734029702972 0_vi[1]² + 154.7029702970297 0_vr[1]*0_vr[5] + 154.7029702970297 0_vi[1]*0_vi[5] + 15.470297029702971 0_vi[1]*0_vr[5] - 15.470297029702971 0_vi[5]*0_vr[1] + 0_q[(3, 1, 5)] = 0.0\n",
      " -15.470297029702971 0_vr[5]² - 15.470297029702971 0_vi[5]² + 15.470297029702971 0_vr[1]*0_vr[5] + 15.470297029702971 0_vi[1]*0_vi[5] + 154.7029702970297 0_vi[1]*0_vr[5] - 154.7029702970297 0_vr[1]*0_vi[5] + 0_p[(3, 5, 1)] = 0.0\n",
      " -154.68734029702972 0_vr[5]² - 154.68734029702972 0_vi[5]² + 154.7029702970297 0_vr[1]*0_vr[5] + 154.7029702970297 0_vi[1]*0_vi[5] - 15.470297029702971 0_vi[1]*0_vr[5] + 15.470297029702971 0_vr[1]*0_vi[5] + 0_q[(3, 5, 1)] = 0.0\n",
      " -3.3336667000033335 0_vr[3]² - 3.3336667000033335 0_vi[3]² + 3.3336667000033335 0_vr[3]*0_vr[4] + 3.3336667000033335 0_vi[3]*0_vi[4] - 33.33666700003334 0_vi[3]*0_vr[4] + 33.33666700003334 0_vi[4]*0_vr[3] + 0_p[(5, 3, 4)] = 0.0\n",
      " -33.33329700003334 0_vr[3]² - 33.33329700003334 0_vi[3]² + 33.33666700003334 0_vr[3]*0_vr[4] + 33.33666700003334 0_vi[3]*0_vi[4] + 3.3336667000033335 0_vi[3]*0_vr[4] - 3.3336667000033335 0_vi[4]*0_vr[3] + 0_q[(5, 3, 4)] = 0.0\n",
      " -3.3336667000033335 0_vr[4]² - 3.3336667000033335 0_vi[4]² + 3.3336667000033335 0_vr[3]*0_vr[4] + 3.3336667000033335 0_vi[3]*0_vi[4] + 33.33666700003334 0_vi[3]*0_vr[4] - 33.33666700003334 0_vr[3]*0_vi[4] + 0_p[(5, 4, 3)] = 0.0\n",
      " -33.33329700003334 0_vr[4]² - 33.33329700003334 0_vi[4]² + 33.33666700003334 0_vr[3]*0_vr[4] + 33.33666700003334 0_vi[3]*0_vi[4] - 3.3336667000033335 0_vi[3]*0_vr[4] + 3.3336667000033335 0_vr[3]*0_vi[4] + 0_q[(5, 4, 3)] = 0.0\n",
      " -3.3336667000033335 0_vr[4]² - 3.3336667000033335 0_vi[4]² + 3.3336667000033335 0_vr[4]*0_vr[5] + 3.3336667000033335 0_vi[4]*0_vi[5] - 33.33666700003334 0_vi[4]*0_vr[5] + 33.33666700003334 0_vi[5]*0_vr[4] + 0_p[(6, 4, 5)] = 0.0\n",
      " -33.33329700003334 0_vr[4]² - 33.33329700003334 0_vi[4]² + 33.33666700003334 0_vr[4]*0_vr[5] + 33.33666700003334 0_vi[4]*0_vi[5] + 3.3336667000033335 0_vi[4]*0_vr[5] - 3.3336667000033335 0_vi[5]*0_vr[4] + 0_q[(6, 4, 5)] = 0.0\n",
      " -3.3336667000033335 0_vr[5]² - 3.3336667000033335 0_vi[5]² + 3.3336667000033335 0_vr[4]*0_vr[5] + 3.3336667000033335 0_vi[4]*0_vi[5] + 33.33666700003334 0_vi[4]*0_vr[5] - 33.33666700003334 0_vr[4]*0_vi[5] + 0_p[(6, 5, 4)] = 0.0\n",
      " -33.33329700003334 0_vr[5]² - 33.33329700003334 0_vi[5]² + 33.33666700003334 0_vr[4]*0_vr[5] + 33.33666700003334 0_vi[4]*0_vi[5] - 3.3336667000033335 0_vi[4]*0_vr[5] + 3.3336667000033335 0_vr[4]*0_vi[5] + 0_q[(6, 5, 4)] = 0.0\n",
      " -3.5234840209999647 0_vr[1]² - 3.5234840209999647 0_vi[1]² + 3.5234840209999647 0_vr[1]*0_vr[2] + 3.5234840209999647 0_vi[1]*0_vi[2] - 35.234840209999646 0_vi[1]*0_vr[2] + 35.234840209999646 0_vi[2]*0_vr[1] + 0_p[(1, 1, 2)] = 0.0\n",
      " -35.231280209999646 0_vr[1]² - 35.231280209999646 0_vi[1]² + 35.234840209999646 0_vr[1]*0_vr[2] + 35.234840209999646 0_vi[1]*0_vi[2] + 3.5234840209999647 0_vi[1]*0_vr[2] - 3.5234840209999647 0_vi[2]*0_vr[1] + 0_q[(1, 1, 2)] = 0.0\n",
      " -3.5234840209999647 0_vr[2]² - 3.5234840209999647 0_vi[2]² + 3.5234840209999647 0_vr[1]*0_vr[2] + 3.5234840209999647 0_vi[1]*0_vi[2] + 35.234840209999646 0_vi[1]*0_vr[2] - 35.234840209999646 0_vr[1]*0_vi[2] + 0_p[(1, 2, 1)] = 0.0\n",
      " -35.231280209999646 0_vr[2]² - 35.231280209999646 0_vi[2]² + 35.234840209999646 0_vr[1]*0_vr[2] + 35.234840209999646 0_vi[1]*0_vi[2] - 3.5234840209999647 0_vi[1]*0_vr[2] + 3.5234840209999647 0_vr[1]*0_vi[2] + 0_q[(1, 2, 1)] = 0.0\n",
      " -0_vr[4]² - 0_vi[4]² ≥ -1.2100000000000002\n",
      " -0_vr[2]² - 0_vi[2]² ≥ -1.2100000000000002\n",
      " -0_vr[3]² - 0_vi[3]² ≥ -1.2100000000000002\n",
      " -0_vr[5]² - 0_vi[5]² ≥ -1.2100000000000002\n",
      " -0_vr[1]² - 0_vi[1]² ≥ -1.2100000000000002\n",
      " 0_vi[2]*0_vr[3] - 0_vi[3]*0_vr[2] + 0.5773502691896257 0_vr[2]*0_vr[3] + 0.5773502691896257 0_vi[2]*0_vi[3] ≥ 0.0\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] + 0.5773502691896257 0_vr[1]*0_vr[4] + 0.5773502691896257 0_vi[1]*0_vi[4] ≥ 0.0\n",
      " 0_vi[1]*0_vr[5] - 0_vi[5]*0_vr[1] + 0.5773502691896257 0_vr[1]*0_vr[5] + 0.5773502691896257 0_vi[1]*0_vi[5] ≥ 0.0\n",
      " 0_vi[3]*0_vr[4] - 0_vi[4]*0_vr[3] + 0.5773502691896257 0_vr[3]*0_vr[4] + 0.5773502691896257 0_vi[3]*0_vi[4] ≥ 0.0\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] + 0.5773502691896257 0_vr[4]*0_vr[5] + 0.5773502691896257 0_vi[4]*0_vi[5] ≥ 0.0\n",
      " 0_vi[1]*0_vr[2] - 0_vi[2]*0_vr[1] + 0.5773502691896257 0_vr[1]*0_vr[2] + 0.5773502691896257 0_vi[1]*0_vi[2] ≥ 0.0\n",
      " -0_vr[4]² - 0_vi[4]² ≤ -0.81\n",
      " -0_vr[2]² - 0_vi[2]² ≤ -0.81\n",
      " -0_vr[3]² - 0_vi[3]² ≤ -0.81\n",
      " -0_vr[5]² - 0_vi[5]² ≤ -0.81\n",
      " -0_vr[1]² - 0_vi[1]² ≤ -0.81\n",
      " 0_vi[2]*0_vr[3] - 0_vi[3]*0_vr[2] - 0.5773502691896257 0_vr[2]*0_vr[3] - 0.5773502691896257 0_vi[2]*0_vi[3] ≤ 0.0\n",
      " 0_p[(4, 2, 3)]² + 0_q[(4, 2, 3)]² ≤ 18.147599999999997\n",
      " 0_p[(4, 3, 2)]² + 0_q[(4, 3, 2)]² ≤ 18.147599999999997\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] - 0.5773502691896257 0_vr[1]*0_vr[4] - 0.5773502691896257 0_vi[1]*0_vi[4] ≤ 0.0\n",
      " 0_p[(2, 1, 4)]² + 0_q[(2, 1, 4)]² ≤ 18.147599999999997\n",
      " 0_p[(2, 4, 1)]² + 0_q[(2, 4, 1)]² ≤ 18.147599999999997\n",
      " 0_vi[1]*0_vr[5] - 0_vi[5]*0_vr[1] - 0.5773502691896257 0_vr[1]*0_vr[5] - 0.5773502691896257 0_vi[1]*0_vi[5] ≤ 0.0\n",
      " 0_p[(3, 1, 5)]² + 0_q[(3, 1, 5)]² ≤ 18.147599999999997\n",
      " 0_p[(3, 5, 1)]² + 0_q[(3, 5, 1)]² ≤ 18.147599999999997\n",
      " 0_vi[3]*0_vr[4] - 0_vi[4]*0_vr[3] - 0.5773502691896257 0_vr[3]*0_vr[4] - 0.5773502691896257 0_vi[3]*0_vi[4] ≤ 0.0\n",
      " 0_p[(5, 3, 4)]² + 0_q[(5, 3, 4)]² ≤ 18.147599999999997\n",
      " 0_p[(5, 4, 3)]² + 0_q[(5, 4, 3)]² ≤ 18.147599999999997\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] - 0.5773502691896257 0_vr[4]*0_vr[5] - 0.5773502691896257 0_vi[4]*0_vi[5] ≤ 0.0\n",
      " 0_p[(6, 4, 5)]² + 0_q[(6, 4, 5)]² ≤ 5.76\n",
      " 0_p[(6, 5, 4)]² + 0_q[(6, 5, 4)]² ≤ 5.76\n",
      " 0_vi[1]*0_vr[2] - 0_vi[2]*0_vr[1] - 0.5773502691896257 0_vr[1]*0_vr[2] - 0.5773502691896257 0_vi[1]*0_vi[2] ≤ 0.0\n",
      " 0_p[(1, 1, 2)]² + 0_q[(1, 1, 2)]² ≤ 16.0\n",
      " 0_p[(1, 2, 1)]² + 0_q[(1, 2, 1)]² ≤ 16.0\n",
      " 0_vr[4] ≥ -1.1\n",
      " 0_vr[2] ≥ -1.1\n",
      " 0_vr[3] ≥ -1.1\n",
      " 0_vr[5] ≥ -1.1\n",
      " 0_vr[1] ≥ -1.1\n",
      " 0_vi[4] ≥ -1.1\n",
      " 0_vi[2] ≥ -1.1\n",
      " 0_vi[3] ≥ -1.1\n",
      " 0_vi[5] ≥ -1.1\n",
      " 0_vi[1] ≥ -1.1\n",
      " 0_pg[4] ≥ 0.0\n",
      " 0_pg[2] ≥ 0.0\n",
      " 0_pg[3] ≥ 0.0\n",
      " 0_pg[5] ≥ 0.0\n",
      " 0_pg[1] ≥ 0.0\n",
      " 0_qg[4] ≥ -5.86\n",
      " 0_qg[2] ≥ -1.776\n",
      " 0_qg[3] ≥ -5.75\n",
      " 0_qg[5] ≥ -4.5\n",
      " 0_qg[1] ≥ -1.776\n",
      " 0_p[(4, 2, 3)] ≥ -4.26\n",
      " 0_p[(2, 1, 4)] ≥ -4.26\n",
      " 0_p[(3, 1, 5)] ≥ -4.26\n",
      " 0_p[(5, 3, 4)] ≥ -4.26\n",
      " 0_p[(6, 4, 5)] ≥ -2.4\n",
      " 0_p[(1, 1, 2)] ≥ -4.0\n",
      " 0_p[(4, 3, 2)] ≥ -4.26\n",
      " 0_p[(2, 4, 1)] ≥ -4.26\n",
      " 0_p[(3, 5, 1)] ≥ -4.26\n",
      " 0_p[(5, 4, 3)] ≥ -4.26\n",
      " 0_p[(6, 5, 4)] ≥ -2.4\n",
      " 0_p[(1, 2, 1)] ≥ -4.0\n",
      " 0_q[(4, 2, 3)] ≥ -4.26\n",
      " 0_q[(2, 1, 4)] ≥ -4.26\n",
      " 0_q[(3, 1, 5)] ≥ -4.26\n",
      " 0_q[(5, 3, 4)] ≥ -4.26\n",
      " 0_q[(6, 4, 5)] ≥ -2.4\n",
      " 0_q[(1, 1, 2)] ≥ -4.0\n",
      " 0_q[(4, 3, 2)] ≥ -4.26\n",
      " 0_q[(2, 4, 1)] ≥ -4.26\n",
      " 0_q[(3, 5, 1)] ≥ -4.26\n",
      " 0_q[(5, 4, 3)] ≥ -4.26\n",
      " 0_q[(6, 5, 4)] ≥ -2.4\n",
      " 0_q[(1, 2, 1)] ≥ -4.0\n",
      " 0_vr[4] ≤ 1.1\n",
      " 0_vr[2] ≤ 1.1\n",
      " 0_vr[3] ≤ 1.1\n",
      " 0_vr[5] ≤ 1.1\n",
      " 0_vr[1] ≤ 1.1\n",
      " 0_vi[4] ≤ 1.1\n",
      " 0_vi[2] ≤ 1.1\n",
      " 0_vi[3] ≤ 1.1\n",
      " 0_vi[5] ≤ 1.1\n",
      " 0_vi[1] ≤ 1.1\n",
      " 0_pg[4] ≤ 11.72\n",
      " 0_pg[2] ≤ 3.41\n",
      " 0_pg[3] ≤ 11.5\n",
      " 0_pg[5] ≤ 2.92\n",
      " 0_pg[1] ≤ 2.22\n",
      " 0_qg[4] ≤ 5.86\n",
      " 0_qg[2] ≤ 1.776\n",
      " 0_qg[3] ≤ 5.75\n",
      " 0_qg[5] ≤ 4.5\n",
      " 0_qg[1] ≤ 1.776\n",
      " 0_p[(4, 2, 3)] ≤ 4.26\n",
      " 0_p[(2, 1, 4)] ≤ 4.26\n",
      " 0_p[(3, 1, 5)] ≤ 4.26\n",
      " 0_p[(5, 3, 4)] ≤ 4.26\n",
      " 0_p[(6, 4, 5)] ≤ 2.4\n",
      " 0_p[(1, 1, 2)] ≤ 4.0\n",
      " 0_p[(4, 3, 2)] ≤ 4.26\n",
      " 0_p[(2, 4, 1)] ≤ 4.26\n",
      " 0_p[(3, 5, 1)] ≤ 4.26\n",
      " 0_p[(5, 4, 3)] ≤ 4.26\n",
      " 0_p[(6, 5, 4)] ≤ 2.4\n",
      " 0_p[(1, 2, 1)] ≤ 4.0\n",
      " 0_q[(4, 2, 3)] ≤ 4.26\n",
      " 0_q[(2, 1, 4)] ≤ 4.26\n",
      " 0_q[(3, 1, 5)] ≤ 4.26\n",
      " 0_q[(5, 3, 4)] ≤ 4.26\n",
      " 0_q[(6, 4, 5)] ≤ 2.4\n",
      " 0_q[(1, 1, 2)] ≤ 4.0\n",
      " 0_q[(4, 3, 2)] ≤ 4.26\n",
      " 0_q[(2, 4, 1)] ≤ 4.26\n",
      " 0_q[(3, 5, 1)] ≤ 4.26\n",
      " 0_q[(5, 4, 3)] ≤ 4.26\n",
      " 0_q[(6, 5, 4)] ≤ 2.4\n",
      " 0_q[(1, 2, 1)] ≤ 4.0\n"
     ]
    }
   ],
   "source": [
    "pm = instantiate_model(file, ACRPowerModel, PowerModels.build_opf)\n",
    "print(pm.model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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