ieee9_exp.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": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"case9.m\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = \"case9.m\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\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...:      223\n",
      "Number of nonzeros in inequality constraint Jacobian.:       72\n",
      "Number of nonzeros in Lagrangian Hessian.............:      399\n",
      "\n",
      "Total number of variables............................:       60\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:       51\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:       55\n",
      "Total number of inequality constraints...............:       36\n",
      "        inequality constraints with only lower bounds:        9\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:       27\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  1.2026175e+03 1.25e+00 1.19e+01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  5.3143936e+03 3.18e-02 1.96e+02  -1.0 1.28e+00    -  9.07e-03 1.00e+00H  1\n",
      "   2  5.2973778e+03 8.62e-03 1.37e+02  -1.0 3.76e-01    -  2.69e-01 2.54e-01f  1\n",
      "   3  5.3027282e+03 6.19e-03 5.99e+00  -1.0 1.54e-01    -  9.80e-01 1.00e+00f  1\n",
      "   4  5.2993637e+03 1.76e-03 2.82e-01  -1.0 3.58e-02    -  1.00e+00 1.00e+00h  1\n",
      "   5  5.2972842e+03 4.69e-04 4.38e-02  -1.7 2.27e-02    -  1.00e+00 1.00e+00f  1\n",
      "   6  5.2967159e+03 1.27e-04 6.27e-01  -2.5 1.06e-02    -  1.00e+00 8.02e-01f  1\n",
      "   7  5.2967430e+03 7.33e-06 1.17e-01  -2.5 7.50e-03    -  9.84e-01 1.00e+00f  1\n",
      "   8  5.2967304e+03 4.82e-07 2.25e-04  -2.5 2.03e-03    -  1.00e+00 1.00e+00h  1\n",
      "   9  5.2966898e+03 2.78e-06 1.18e-01  -3.8 3.84e-03    -  1.00e+00 9.30e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  5.2966885e+03 3.39e-07 3.33e-05  -3.8 1.46e-03    -  1.00e+00 1.00e+00f  1\n",
      "  11  5.2966862e+03 4.73e-08 4.64e-06  -5.7 5.15e-04    -  1.00e+00 1.00e+00h  1\n",
      "  12  5.2966862e+03 1.19e-10 1.35e-08  -8.6 2.71e-05    -  1.00e+00 1.00e+00h  1\n",
      "  13  5.2966862e+03 5.55e-15 2.28e-12  -9.0 6.03e-08    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 13\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.0593372404463116e+03    5.2966862022315581e+03\n",
      "Dual infeasibility......:   2.2774185552848070e-12    1.1387092776424035e-11\n",
      "Constraint violation....:   5.5511151231257827e-15    5.5511151231257827e-15\n",
      "Complementarity.........:   9.0917673257049247e-10    4.5458836628524618e-09\n",
      "Overall NLP error.......:   9.0917673257049247e-10    4.5458836628524618e-09\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 15\n",
      "Number of objective gradient evaluations             = 14\n",
      "Number of equality constraint evaluations            = 15\n",
      "Number of inequality constraint evaluations          = 15\n",
      "Number of equality constraint Jacobian evaluations   = 14\n",
      "Number of inequality constraint Jacobian evaluations = 14\n",
      "Number of Lagrangian Hessian evaluations             = 13\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      1.826\n",
      "Total CPU secs in NLP function evaluations           =      1.147\n",
      "\n",
      "EXIT: Optimal Solution Found.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 3.39388\n",
       "  \"optimizer\"          => \"Ipopt\"\n",
       "  \"termination_status\" => LOCALLY_SOLVED\n",
       "  \"dual_status\"        => FEASIBLE_POINT\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5296.69\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\n",
       "  \"objective_lb\"       => -Inf"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ipopt for polar ACOPF\n",
    "ipopt_polar = run_ac_opf(file, Ipopt.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\u001b[39m\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...:      379\n",
      "Number of nonzeros in inequality constraint Jacobian.:      216\n",
      "Number of nonzeros in Lagrangian Hessian.............:      327\n",
      "\n",
      "Total number of variables............................:       60\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:       60\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:       55\n",
      "Total number of inequality constraints...............:       54\n",
      "        inequality constraints with only lower bounds:       18\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:       36\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  1.2026175e+03 1.25e+00 1.19e+01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  5.3150036e+03 8.60e-03 1.94e+02  -1.0 1.28e+00    -  9.07e-03 1.00e+00H  1\n",
      "   2  5.3011028e+03 6.27e-03 9.97e+00  -1.0 2.26e-01    -  7.92e-01 1.00e+00f  1\n",
      "   3  5.3016973e+03 3.14e-04 4.13e-02  -1.0 3.61e-02    -  1.00e+00 1.00e+00h  1\n",
      "   4  5.2974612e+03 7.89e-04 2.64e-01  -2.5 9.27e-02    -  8.48e-01 1.00e+00f  1\n",
      "   5  5.2967853e+03 2.57e-04 7.45e-01  -2.5 3.22e-02    -  1.00e+00 6.68e-01h  1\n",
      "   6  5.2967567e+03 3.32e-05 2.88e-03  -2.5 1.81e-02    -  1.00e+00 1.00e+00h  1\n",
      "   7  5.2967064e+03 1.64e-05 5.81e-01  -3.8 7.16e-03    -  1.00e+00 6.51e-01h  1\n",
      "   8  5.2966887e+03 5.27e-06 1.03e-03  -3.8 5.53e-03    -  1.00e+00 1.00e+00f  1\n",
      "   9  5.2966868e+03 1.42e-06 7.74e-01  -5.7 1.60e-03    -  1.00e+00 7.79e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  5.2966862e+03 4.84e-08 1.91e-05  -5.7 5.47e-04    -  1.00e+00 1.00e+00f  1\n",
      "  11  5.2966862e+03 1.18e-11 7.27e-09  -5.7 8.65e-06    -  1.00e+00 1.00e+00h  1\n",
      "  12  5.2966862e+03 2.32e-11 2.17e-05  -8.6 1.17e-05    -  1.00e+00 9.99e-01h  1\n",
      "  13  5.2966862e+03 4.57e-15 7.48e-10  -8.6 1.43e-08    -  1.00e+00 1.00e+00f  1\n",
      "\n",
      "Number of Iterations....: 13\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.0593372406283074e+03    5.2966862031415367e+03\n",
      "Dual infeasibility......:   7.4813394368433705e-10    3.7406697184216853e-09\n",
      "Constraint violation....:   4.5692616357229099e-15    4.5692616357229099e-15\n",
      "Complementarity.........:   3.3287074301277267e-09    1.6643537150638634e-08\n",
      "Overall NLP error.......:   3.3287074301277267e-09    1.6643537150638634e-08\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 15\n",
      "Number of objective gradient evaluations             = 14\n",
      "Number of equality constraint evaluations            = 15\n",
      "Number of inequality constraint evaluations          = 15\n",
      "Number of equality constraint Jacobian evaluations   = 14\n",
      "Number of inequality constraint Jacobian evaluations = 14\n",
      "Number of Lagrangian Hessian evaluations             = 13\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.014\n",
      "Total CPU secs in NLP function evaluations           =      0.000\n",
      "\n",
      "EXIT: Optimal Solution Found.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 0.146873\n",
       "  \"optimizer\"          => \"Ipopt\"\n",
       "  \"termination_status\" => LOCALLY_SOLVED\n",
       "  \"dual_status\"        => FEASIBLE_POINT\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5296.69\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\n",
       "  \"objective_lb\"       => -Inf"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ipopt for rectangular ACOPF\n",
    "ipopt_rec = run_opf(file, ACRPowerModel, Ipopt.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\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 19 rows, 60 columns and 43 nonzeros\n",
      "Model fingerprint: 0x31a6be54\n",
      "Model has 3 quadratic objective terms\n",
      "Model has 90 quadratic constraints\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  QMatrix range    [1e+00, 2e+01]\n",
      "  QLMatrix range   [1e+00, 1e+00]\n",
      "  Objective range  [1e+02, 5e+02]\n",
      "  QObjective range [2e+03, 2e+03]\n",
      "  Bounds range     [1e-01, 3e+00]\n",
      "  RHS range        [3e-01, 1e+00]\n",
      "  QRHS range       [8e-01, 9e+00]\n",
      "Presolve removed 7 rows and 7 columns\n",
      "\n",
      "Continuous model is non-convex -- solving as a MIP.\n",
      "\n",
      "\n",
      "User MIP start did not produce a new incumbent solution\n",
      "User MIP start violates constraint R1 by 1.000000000\n",
      "\n",
      "Presolve removed 7 rows and 7 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 268 rows, 104 columns, 838 nonzeros\n",
      "Presolved model has 3 quadratic objective terms\n",
      "Presolved model has 26 quadratic constraint(s)\n",
      "Presolved model has 54 bilinear constraint(s)\n",
      "Variable types: 104 continuous, 0 integer (0 binary)\n",
      "\n",
      "Root relaxation: objective 1.188750e+03, 283 iterations, 0.00 seconds\n",
      "Another try with MIP start\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "     0     0 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "     0     0 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "     0     0 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "     0     0 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "     0     2 1188.75000    0   54          - 1188.75000      -     -    0s\n",
      "* 1304   509              81    5590.5726292 2191.91386  60.8%  49.6    0s\n",
      "* 1603   476              71    5409.2667893 2297.09536  57.5%  44.8    0s\n",
      "* 1858   452              79    5407.6831246 2415.16550  55.3%  42.0    1s\n",
      "* 3213   757              73    5407.0516678 3770.92795  30.3%  34.9    1s\n",
      "* 3318   807              75    5406.6336720 3770.92795  30.3%  34.6    1s\n",
      "* 3435   852              75    5406.6185645 3770.92795  30.3%  34.2    1s\n",
      "* 3754   808              63    5349.0352346 3770.92795  29.5%  32.9    1s\n",
      "* 3885   766              64    5324.7730502 3770.92795  29.2%  32.4    1s\n",
      "* 7405  2078              64    5324.5255628 4526.17248  15.0%  27.4    2s\n",
      "* 7548  1996              71    5317.1534563 4526.17248  14.9%  27.3    2s\n",
      "*12171  3100              85    5310.7219424 4686.40730  11.8%  24.2    4s\n",
      " 13472  3581     cutoff   36      5310.72194 4746.31712  10.6%  23.8    5s\n",
      "*18705  4811              77    5308.5623206 4820.38440  9.20%  23.2    6s\n",
      "*19037  4773              78    5303.9600194 4829.88382  8.94%  23.1    6s\n",
      " 29342  6504 infeasible   37      5303.96002 4979.52809  6.12%  22.0   10s\n",
      " 45659  8882     cutoff   33      5303.96002 5087.19402  4.09%  21.0   15s\n",
      "*49961  9307              76    5303.1583404 5102.75753  3.78%  20.8   16s\n",
      " 59336 10661     cutoff   45      5303.15834 5129.70536  3.27%  20.5   20s\n",
      " 69775 12428     cutoff   37      5303.15834 5151.22610  2.86%  20.2   25s\n",
      " 81007 14365     cutoff   50      5303.15834 5164.75471  2.61%  20.0   30s\n",
      "*84669 14842              87    5301.4891005 5168.47320  2.51%  20.0   31s\n",
      "*85391 14963              87    5301.4878609 5168.90835  2.50%  20.0   32s\n",
      "*85392 14963              87    5301.4877727 5168.90835  2.50%  20.0   32s\n",
      " 91565 15761 5284.70132   43   42 5301.48777 5176.62298  2.36%  19.9   35s\n",
      " 104585 17582 5264.22507   37   30 5301.48777 5188.12205  2.14%  19.6   40s\n",
      " 117030 19077     cutoff   44      5301.48777 5197.71045  1.96%  19.4   45s\n",
      "*127493 19600              78    5299.9617950 5204.88384  1.79%  19.3   49s\n",
      "*127494 19598              77    5299.9581374 5204.88384  1.79%  19.3   49s\n",
      "*127497 19596              77    5299.9574619 5204.88384  1.79%  19.3   49s\n",
      " 128561 19746     cutoff   42      5299.95746 5205.68412  1.78%  19.3   50s\n",
      " 142060 20562     cutoff   42      5299.95746 5214.36734  1.61%  19.1   55s\n",
      "*146082 20631              70    5299.5000468 5216.71073  1.56%  19.1   56s\n",
      "*146083 20623              69    5299.4933205 5216.71073  1.56%  19.1   56s\n",
      " 155689 21307     cutoff   47      5299.49332 5221.50999  1.47%  19.0   60s\n",
      " 170275 21864 5248.64294   40   29 5299.49332 5228.64714  1.34%  18.8   65s\n",
      "*180924 22435              72    5299.3104877 5233.20748  1.25%  18.7   68s\n",
      " 184984 22600 5297.37749   40   34 5299.31049 5234.90648  1.22%  18.7   70s\n",
      " 199158 23123     cutoff   49      5299.31049 5240.07132  1.12%  18.6   75s\n",
      " 213708 23732     cutoff   47      5299.31049 5244.72963  1.03%  18.5   80s\n",
      " 227825 24242     cutoff   39      5299.31049 5248.85350  0.95%  18.4   85s\n",
      " 242118 24610     cutoff   49      5299.31049 5252.36728  0.89%  18.3   90s\n",
      "*254149 23429              74    5297.5872373 5255.13922  0.80%  18.2   94s\n",
      " 254677 23383     cutoff   49      5297.58724 5255.34467  0.80%  18.2   95s\n",
      " 268298 23216     cutoff   50      5297.58724 5258.96862  0.73%  18.1  100s\n",
      "*271689 22578              81    5297.0043529 5259.72121  0.70%  18.1  101s\n",
      " 281137 22307     cutoff   48      5297.00435 5262.02620  0.66%  18.1  105s\n",
      "*287339 22157              80    5296.9141551 5263.30818  0.63%  18.0  107s\n",
      "*287340 22153              80    5296.9075930 5263.30818  0.63%  18.0  107s\n",
      " 294288 21878 5295.90191   50   31 5296.90759 5264.88325  0.60%  18.0  110s\n",
      " 309269 21363     cutoff   51      5296.90759 5267.93433  0.55%  17.9  115s\n",
      " 322766 20853     cutoff   44      5296.90759 5270.77427  0.49%  17.8  120s\n",
      " 334666 20091 5273.67878   47   42 5296.90759 5273.02979  0.45%  17.8  125s\n",
      " 347415 19380     cutoff   55      5296.90759 5275.67616  0.40%  17.8  130s\n",
      " 360342 18787 5286.68153   53   38 5296.90759 5277.80046  0.36%  17.7  135s\n",
      " 372436 18000     cutoff   46      5296.90759 5279.60388  0.33%  17.7  140s\n",
      " 384059 17030     cutoff   56      5296.90759 5281.51206  0.29%  17.6  145s\n",
      " 395851 16342     cutoff   48      5296.90759 5283.36797  0.26%  17.5  150s\n",
      " 406768 15478 5289.27997   53   45 5296.90759 5284.97084  0.23%  17.5  155s\n",
      " 417663 14637     cutoff   49      5296.90759 5286.35038  0.20%  17.4  160s\n",
      " 430583 13617     cutoff   48      5296.90759 5287.83923  0.17%  17.3  165s\n",
      "*435721 12851              84    5296.7234291 5288.39117  0.16%  17.3  167s\n",
      "*436871 12726              85    5296.7233224 5288.49419  0.16%  17.3  167s\n",
      " 443992 11948     cutoff   48      5296.72332 5289.38139  0.14%  17.2  170s\n",
      " 453515 10875     cutoff   54      5296.72332 5290.39000  0.12%  17.2  175s\n",
      " 465530  9210 5296.65350   56   41 5296.72332 5291.81729  0.09%  17.1  180s\n",
      "*468400  8766              79    5296.6990861 5292.11579  0.09%  17.1  181s\n",
      "*468403  8758              80    5296.6933054 5292.11579  0.09%  17.1  181s\n",
      " 475286  7980     cutoff   44      5296.69331 5292.84603  0.07%  17.0  185s\n",
      " 484565  6369 5294.34533   59   37 5296.69331 5293.86894  0.05%  17.0  190s\n",
      " 494781  4599 5296.67325   70   42 5296.69331 5294.90439  0.03%  16.9  195s\n",
      " 504933  3653 5296.41184   69   30 5296.69331 5295.65834  0.02%  16.8  200s\n",
      "*505699  3564              79    5296.6758861 5295.66334  0.02%  16.8  200s\n",
      "*505898  3564              81    5296.6757235 5295.66442  0.02%  16.8  200s\n",
      "\n",
      "Explored 516634 nodes (8638431 simplex iterations) in 204.98 seconds\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 10: 5296.68 5296.68 5296.69 ... 5297.59\n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Warning: max constraint violation (1.1811e-05) exceeds tolerance\n",
      "Best objective 5.296675723501e+03, best bound 5.296188557024e+03, gap 0.0092%\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 204.982\n",
       "  \"optimizer\"          => \"Gurobi\"\n",
       "  \"termination_status\" => OPTIMAL\n",
       "  \"dual_status\"        => NO_SOLUTION\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5296.68\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\n",
       "  \"objective_lb\"       => 5296.19"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gurobi nonconvex QP for rectangular ACOPF\n",
    "pm = instantiate_model(file, ACRPowerModel, PowerModels.build_opf)\n",
    "set_optimizer_attribute(pm.model, \"NonConvex\", 2)\n",
    "grb_rec = optimize_model!(pm, optimizer=Gurobi.Optimizer)\n",
    "print(pm.model)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\u001b[39m\n",
      "Min 850.0000000000001 0_pg[2]² + 1225 0_pg[3]² + 1100 0_pg[1]² + 120 0_pg[2] + 100 0_pg[3] + 500 0_pg[1] + 1085\n",
      "Subject to\n",
      " 0_vi[1] = 0.0\n",
      " 0_p[(6, 7, 8)] + 0_p[(5, 7, 6)] = -1.0\n",
      " 0_q[(6, 7, 8)] + 0_q[(5, 7, 6)] = -0.35\n",
      " 0_p[(2, 4, 5)] + 0_p[(9, 4, 9)] + 0_p[(1, 4, 1)] = 0.0\n",
      " 0_q[(2, 4, 5)] + 0_q[(9, 4, 9)] + 0_q[(1, 4, 1)] = 0.0\n",
      " 0_p[(9, 9, 4)] + 0_p[(8, 9, 8)] = -1.25\n",
      " 0_q[(9, 9, 4)] + 0_q[(8, 9, 8)] = -0.5\n",
      " 0_p[(7, 2, 8)] - 0_pg[2] = 0.0\n",
      " 0_q[(7, 2, 8)] - 0_qg[2] = 0.0\n",
      " 0_p[(4, 3, 6)] - 0_pg[3] = 0.0\n",
      " 0_q[(4, 3, 6)] - 0_qg[3] = 0.0\n",
      " 0_p[(7, 8, 2)] + 0_p[(8, 8, 9)] + 0_p[(6, 8, 7)] = 0.0\n",
      " 0_q[(7, 8, 2)] + 0_q[(8, 8, 9)] + 0_q[(6, 8, 7)] = 0.0\n",
      " 0_p[(3, 5, 6)] + 0_p[(2, 5, 4)] = -0.9\n",
      " 0_q[(3, 5, 6)] + 0_q[(2, 5, 4)] = -0.3\n",
      " 0_p[(5, 6, 7)] + 0_p[(4, 6, 3)] + 0_p[(3, 6, 5)] = 0.0\n",
      " 0_q[(5, 6, 7)] + 0_q[(4, 6, 3)] + 0_q[(3, 6, 5)] = 0.0\n",
      " 0_p[(1, 1, 4)] - 0_pg[1] = 0.0\n",
      " 0_q[(1, 1, 4)] - 0_qg[1] = 0.0\n",
      " -16 0_vi[8]*0_vr[2] + 16 0_vi[2]*0_vr[8] + 0_p[(7, 8, 2)] = 0.0\n",
      " -16 0_vr[8]² - 16 0_vi[8]² + 16 0_vr[8]*0_vr[2] + 16 0_vi[8]*0_vi[2] + 0_q[(7, 8, 2)] = 0.0\n",
      " 16 0_vi[8]*0_vr[2] - 16 0_vr[8]*0_vi[2] + 0_p[(7, 2, 8)] = 0.0\n",
      " -16 0_vr[2]² - 16 0_vi[2]² + 16 0_vr[8]*0_vr[2] + 16 0_vi[8]*0_vi[2] + 0_q[(7, 2, 8)] = 0.0\n",
      " -17.064846416382252 0_vi[3]*0_vr[6] + 17.064846416382252 0_vi[6]*0_vr[3] + 0_p[(4, 3, 6)] = 0.0\n",
      " -17.064846416382252 0_vr[3]² - 17.064846416382252 0_vi[3]² + 17.064846416382252 0_vr[3]*0_vr[6] + 17.064846416382252 0_vi[3]*0_vi[6] + 0_q[(4, 3, 6)] = 0.0\n",
      " 17.064846416382252 0_vi[3]*0_vr[6] - 17.064846416382252 0_vr[3]*0_vi[6] + 0_p[(4, 6, 3)] = 0.0\n",
      " -17.064846416382252 0_vr[6]² - 17.064846416382252 0_vi[6]² + 17.064846416382252 0_vr[3]*0_vr[6] + 17.064846416382252 0_vi[3]*0_vi[6] + 0_q[(4, 6, 3)] = 0.0\n",
      " -1.36518771331058 0_vr[9]² - 1.36518771331058 0_vi[9]² + 1.36518771331058 0_vr[9]*0_vr[4] + 1.36518771331058 0_vi[9]*0_vi[4] - 11.60409556313993 0_vi[9]*0_vr[4] + 11.60409556313993 0_vi[4]*0_vr[9] + 0_p[(9, 9, 4)] = 0.0\n",
      " -11.516095563139931 0_vr[9]² - 11.516095563139931 0_vi[9]² + 11.60409556313993 0_vr[9]*0_vr[4] + 11.60409556313993 0_vi[9]*0_vi[4] + 1.36518771331058 0_vi[9]*0_vr[4] - 1.36518771331058 0_vi[4]*0_vr[9] + 0_q[(9, 9, 4)] = 0.0\n",
      " -1.36518771331058 0_vr[4]² - 1.36518771331058 0_vi[4]² + 1.36518771331058 0_vr[9]*0_vr[4] + 1.36518771331058 0_vi[9]*0_vi[4] + 11.60409556313993 0_vi[9]*0_vr[4] - 11.60409556313993 0_vr[9]*0_vi[4] + 0_p[(9, 4, 9)] = 0.0\n",
      " -11.516095563139931 0_vr[4]² - 11.516095563139931 0_vi[4]² + 11.60409556313993 0_vr[9]*0_vr[4] + 11.60409556313993 0_vi[9]*0_vi[4] - 1.36518771331058 0_vi[9]*0_vr[4] + 1.36518771331058 0_vr[9]*0_vi[4] + 0_q[(9, 4, 9)] = 0.0\n",
      " -1.9421912487147266 0_vr[4]² - 1.9421912487147266 0_vi[4]² + 1.9421912487147266 0_vr[4]*0_vr[5] + 1.9421912487147266 0_vi[4]*0_vi[5] - 10.510682051867931 0_vi[4]*0_vr[5] + 10.510682051867931 0_vi[5]*0_vr[4] + 0_p[(2, 4, 5)] = 0.0\n",
      " -10.43168205186793 0_vr[4]² - 10.43168205186793 0_vi[4]² + 10.510682051867931 0_vr[4]*0_vr[5] + 10.510682051867931 0_vi[4]*0_vi[5] + 1.9421912487147266 0_vi[4]*0_vr[5] - 1.9421912487147266 0_vi[5]*0_vr[4] + 0_q[(2, 4, 5)] = 0.0\n",
      " -1.9421912487147266 0_vr[5]² - 1.9421912487147266 0_vi[5]² + 1.9421912487147266 0_vr[4]*0_vr[5] + 1.9421912487147266 0_vi[4]*0_vi[5] + 10.510682051867931 0_vi[4]*0_vr[5] - 10.510682051867931 0_vr[4]*0_vi[5] + 0_p[(2, 5, 4)] = 0.0\n",
      " -10.43168205186793 0_vr[5]² - 10.43168205186793 0_vi[5]² + 10.510682051867931 0_vr[4]*0_vr[5] + 10.510682051867931 0_vi[4]*0_vi[5] - 1.9421912487147266 0_vi[4]*0_vr[5] + 1.9421912487147266 0_vr[4]*0_vi[5] + 0_q[(2, 5, 4)] = 0.0\n",
      " -1.2820091384241148 0_vr[5]² - 1.2820091384241148 0_vi[5]² + 1.2820091384241148 0_vr[5]*0_vr[6] + 1.2820091384241148 0_vi[5]*0_vi[6] - 5.588244962361526 0_vi[5]*0_vr[6] + 5.588244962361526 0_vi[6]*0_vr[5] + 0_p[(3, 5, 6)] = 0.0\n",
      " -5.409244962361526 0_vr[5]² - 5.409244962361526 0_vi[5]² + 5.588244962361526 0_vr[5]*0_vr[6] + 5.588244962361526 0_vi[5]*0_vi[6] + 1.2820091384241148 0_vi[5]*0_vr[6] - 1.2820091384241148 0_vi[6]*0_vr[5] + 0_q[(3, 5, 6)] = 0.0\n",
      " -1.2820091384241148 0_vr[6]² - 1.2820091384241148 0_vi[6]² + 1.2820091384241148 0_vr[5]*0_vr[6] + 1.2820091384241148 0_vi[5]*0_vi[6] + 5.588244962361526 0_vi[5]*0_vr[6] - 5.588244962361526 0_vr[5]*0_vi[6] + 0_p[(3, 6, 5)] = 0.0\n",
      " -5.409244962361526 0_vr[6]² - 5.409244962361526 0_vi[6]² + 5.588244962361526 0_vr[5]*0_vr[6] + 5.588244962361526 0_vi[5]*0_vi[6] - 1.2820091384241148 0_vi[5]*0_vr[6] + 1.2820091384241148 0_vr[5]*0_vi[6] + 0_q[(3, 6, 5)] = 0.0\n",
      " -1.1876043792911484 0_vr[8]² - 1.1876043792911484 0_vi[8]² + 1.1876043792911484 0_vr[8]*0_vr[9] + 1.1876043792911484 0_vi[8]*0_vi[9] - 5.975134533308591 0_vi[8]*0_vr[9] + 5.975134533308591 0_vi[9]*0_vr[8] + 0_p[(8, 8, 9)] = 0.0\n",
      " -5.822134533308591 0_vr[8]² - 5.822134533308591 0_vi[8]² + 5.975134533308591 0_vr[8]*0_vr[9] + 5.975134533308591 0_vi[8]*0_vi[9] + 1.1876043792911484 0_vi[8]*0_vr[9] - 1.1876043792911484 0_vi[9]*0_vr[8] + 0_q[(8, 8, 9)] = 0.0\n",
      " -1.1876043792911484 0_vr[9]² - 1.1876043792911484 0_vi[9]² + 1.1876043792911484 0_vr[8]*0_vr[9] + 1.1876043792911484 0_vi[8]*0_vi[9] + 5.975134533308591 0_vi[8]*0_vr[9] - 5.975134533308591 0_vr[8]*0_vi[9] + 0_p[(8, 9, 8)] = 0.0\n",
      " -5.822134533308591 0_vr[9]² - 5.822134533308591 0_vi[9]² + 5.975134533308591 0_vr[8]*0_vr[9] + 5.975134533308591 0_vi[8]*0_vi[9] - 1.1876043792911484 0_vi[8]*0_vr[9] + 1.1876043792911484 0_vr[8]*0_vi[9] + 0_q[(8, 9, 8)] = 0.0\n",
      " -1.155087480890097 0_vr[6]² - 1.155087480890097 0_vi[6]² + 1.155087480890097 0_vr[6]*0_vr[7] + 1.155087480890097 0_vi[6]*0_vi[7] - 9.784270426363173 0_vi[6]*0_vr[7] + 9.784270426363173 0_vi[7]*0_vr[6] + 0_p[(5, 6, 7)] = 0.0\n",
      " -9.679770426363174 0_vr[6]² - 9.679770426363174 0_vi[6]² + 9.784270426363173 0_vr[6]*0_vr[7] + 9.784270426363173 0_vi[6]*0_vi[7] + 1.155087480890097 0_vi[6]*0_vr[7] - 1.155087480890097 0_vi[7]*0_vr[6] + 0_q[(5, 6, 7)] = 0.0\n",
      " -1.155087480890097 0_vr[7]² - 1.155087480890097 0_vi[7]² + 1.155087480890097 0_vr[6]*0_vr[7] + 1.155087480890097 0_vi[6]*0_vi[7] + 9.784270426363173 0_vi[6]*0_vr[7] - 9.784270426363173 0_vr[6]*0_vi[7] + 0_p[(5, 7, 6)] = 0.0\n",
      " -9.679770426363174 0_vr[7]² - 9.679770426363174 0_vi[7]² + 9.784270426363173 0_vr[6]*0_vr[7] + 9.784270426363173 0_vi[6]*0_vi[7] - 1.155087480890097 0_vi[6]*0_vr[7] + 1.155087480890097 0_vr[6]*0_vi[7] + 0_q[(5, 7, 6)] = 0.0\n",
      " -1.6171224732461358 0_vr[7]² - 1.6171224732461358 0_vi[7]² + 1.6171224732461358 0_vr[7]*0_vr[8] + 1.6171224732461358 0_vi[7]*0_vi[8] - 13.697978596908444 0_vi[7]*0_vr[8] + 13.697978596908444 0_vi[8]*0_vr[7] + 0_p[(6, 7, 8)] = 0.0\n",
      " -13.623478596908443 0_vr[7]² - 13.623478596908443 0_vi[7]² + 13.697978596908444 0_vr[7]*0_vr[8] + 13.697978596908444 0_vi[7]*0_vi[8] + 1.6171224732461358 0_vi[7]*0_vr[8] - 1.6171224732461358 0_vi[8]*0_vr[7] + 0_q[(6, 7, 8)] = 0.0\n",
      " -1.6171224732461358 0_vr[8]² - 1.6171224732461358 0_vi[8]² + 1.6171224732461358 0_vr[7]*0_vr[8] + 1.6171224732461358 0_vi[7]*0_vi[8] + 13.697978596908444 0_vi[7]*0_vr[8] - 13.697978596908444 0_vr[7]*0_vi[8] + 0_p[(6, 8, 7)] = 0.0\n",
      " -13.623478596908443 0_vr[8]² - 13.623478596908443 0_vi[8]² + 13.697978596908444 0_vr[7]*0_vr[8] + 13.697978596908444 0_vi[7]*0_vi[8] - 1.6171224732461358 0_vi[7]*0_vr[8] + 1.6171224732461358 0_vr[7]*0_vi[8] + 0_q[(6, 8, 7)] = 0.0\n",
      " -17.36111111111111 0_vi[1]*0_vr[4] + 17.36111111111111 0_vi[4]*0_vr[1] + 0_p[(1, 1, 4)] = 0.0\n",
      " -17.36111111111111 0_vr[1]² - 17.36111111111111 0_vi[1]² + 17.36111111111111 0_vr[1]*0_vr[4] + 17.36111111111111 0_vi[1]*0_vi[4] + 0_q[(1, 1, 4)] = 0.0\n",
      " 17.36111111111111 0_vi[1]*0_vr[4] - 17.36111111111111 0_vr[1]*0_vi[4] + 0_p[(1, 4, 1)] = 0.0\n",
      " -17.36111111111111 0_vr[4]² - 17.36111111111111 0_vi[4]² + 17.36111111111111 0_vr[1]*0_vr[4] + 17.36111111111111 0_vi[1]*0_vi[4] + 0_q[(1, 4, 1)] = 0.0\n",
      " -0_vr[7]² - 0_vi[7]² ≥ -1.2100000000000002\n",
      " -0_vr[4]² - 0_vi[4]² ≥ -1.2100000000000002\n",
      " -0_vr[9]² - 0_vi[9]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[8]² - 0_vi[8]² ≥ -1.2100000000000002\n",
      " -0_vr[5]² - 0_vi[5]² ≥ -1.2100000000000002\n",
      " -0_vr[6]² - 0_vi[6]² ≥ -1.2100000000000002\n",
      " -0_vr[1]² - 0_vi[1]² ≥ -1.2100000000000002\n",
      " 0_vi[8]*0_vr[2] - 0_vi[2]*0_vr[8] + 1.732060602824032 0_vr[8]*0_vr[2] + 1.732060602824032 0_vi[8]*0_vi[2] ≥ 0.0\n",
      " 0_vi[3]*0_vr[6] - 0_vi[6]*0_vr[3] + 1.732060602824032 0_vr[3]*0_vr[6] + 1.732060602824032 0_vi[3]*0_vi[6] ≥ 0.0\n",
      " 0_vi[9]*0_vr[4] - 0_vi[4]*0_vr[9] + 1.732060602824032 0_vr[9]*0_vr[4] + 1.732060602824032 0_vi[9]*0_vi[4] ≥ 0.0\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] + 1.732060602824032 0_vr[4]*0_vr[5] + 1.732060602824032 0_vi[4]*0_vi[5] ≥ 0.0\n",
      " 0_vi[5]*0_vr[6] - 0_vi[6]*0_vr[5] + 1.732060602824032 0_vr[5]*0_vr[6] + 1.732060602824032 0_vi[5]*0_vi[6] ≥ 0.0\n",
      " 0_vi[8]*0_vr[9] - 0_vi[9]*0_vr[8] + 1.732060602824032 0_vr[8]*0_vr[9] + 1.732060602824032 0_vi[8]*0_vi[9] ≥ 0.0\n",
      " 0_vi[6]*0_vr[7] - 0_vi[7]*0_vr[6] + 1.732060602824032 0_vr[6]*0_vr[7] + 1.732060602824032 0_vi[6]*0_vi[7] ≥ 0.0\n",
      " 0_vi[7]*0_vr[8] - 0_vi[8]*0_vr[7] + 1.732060602824032 0_vr[7]*0_vr[8] + 1.732060602824032 0_vi[7]*0_vi[8] ≥ 0.0\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] + 1.732060602824032 0_vr[1]*0_vr[4] + 1.732060602824032 0_vi[1]*0_vi[4] ≥ 0.0\n",
      " -0_vr[7]² - 0_vi[7]² ≤ -0.81\n",
      " -0_vr[4]² - 0_vi[4]² ≤ -0.81\n",
      " -0_vr[9]² - 0_vi[9]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[8]² - 0_vi[8]² ≤ -0.81\n",
      " -0_vr[5]² - 0_vi[5]² ≤ -0.81\n",
      " -0_vr[6]² - 0_vi[6]² ≤ -0.81\n",
      " -0_vr[1]² - 0_vi[1]² ≤ -0.81\n",
      " 0_vi[8]*0_vr[2] - 0_vi[2]*0_vr[8] - 1.732060602824032 0_vr[8]*0_vr[2] - 1.732060602824032 0_vi[8]*0_vi[2] ≤ 0.0\n",
      " 0_p[(7, 8, 2)]² + 0_q[(7, 8, 2)]² ≤ 6.25\n",
      " 0_p[(7, 2, 8)]² + 0_q[(7, 2, 8)]² ≤ 6.25\n",
      " 0_vi[3]*0_vr[6] - 0_vi[6]*0_vr[3] - 1.732060602824032 0_vr[3]*0_vr[6] - 1.732060602824032 0_vi[3]*0_vi[6] ≤ 0.0\n",
      " 0_p[(4, 3, 6)]² + 0_q[(4, 3, 6)]² ≤ 9.0\n",
      " 0_p[(4, 6, 3)]² + 0_q[(4, 6, 3)]² ≤ 9.0\n",
      " 0_vi[9]*0_vr[4] - 0_vi[4]*0_vr[9] - 1.732060602824032 0_vr[9]*0_vr[4] - 1.732060602824032 0_vi[9]*0_vi[4] ≤ 0.0\n",
      " 0_p[(9, 9, 4)]² + 0_q[(9, 9, 4)]² ≤ 6.25\n",
      " 0_p[(9, 4, 9)]² + 0_q[(9, 4, 9)]² ≤ 6.25\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] - 1.732060602824032 0_vr[4]*0_vr[5] - 1.732060602824032 0_vi[4]*0_vi[5] ≤ 0.0\n",
      " 0_p[(2, 4, 5)]² + 0_q[(2, 4, 5)]² ≤ 6.25\n",
      " 0_p[(2, 5, 4)]² + 0_q[(2, 5, 4)]² ≤ 6.25\n",
      " 0_vi[5]*0_vr[6] - 0_vi[6]*0_vr[5] - 1.732060602824032 0_vr[5]*0_vr[6] - 1.732060602824032 0_vi[5]*0_vi[6] ≤ 0.0\n",
      " 0_p[(3, 5, 6)]² + 0_q[(3, 5, 6)]² ≤ 2.25\n",
      " 0_p[(3, 6, 5)]² + 0_q[(3, 6, 5)]² ≤ 2.25\n",
      " 0_vi[8]*0_vr[9] - 0_vi[9]*0_vr[8] - 1.732060602824032 0_vr[8]*0_vr[9] - 1.732060602824032 0_vi[8]*0_vi[9] ≤ 0.0\n",
      " 0_p[(8, 8, 9)]² + 0_q[(8, 8, 9)]² ≤ 6.25\n",
      " 0_p[(8, 9, 8)]² + 0_q[(8, 9, 8)]² ≤ 6.25\n",
      " 0_vi[6]*0_vr[7] - 0_vi[7]*0_vr[6] - 1.732060602824032 0_vr[6]*0_vr[7] - 1.732060602824032 0_vi[6]*0_vi[7] ≤ 0.0\n",
      " 0_p[(5, 6, 7)]² + 0_q[(5, 6, 7)]² ≤ 2.25\n",
      " 0_p[(5, 7, 6)]² + 0_q[(5, 7, 6)]² ≤ 2.25\n",
      " 0_vi[7]*0_vr[8] - 0_vi[8]*0_vr[7] - 1.732060602824032 0_vr[7]*0_vr[8] - 1.732060602824032 0_vi[7]*0_vi[8] ≤ 0.0\n",
      " 0_p[(6, 7, 8)]² + 0_q[(6, 7, 8)]² ≤ 6.25\n",
      " 0_p[(6, 8, 7)]² + 0_q[(6, 8, 7)]² ≤ 6.25\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] - 1.732060602824032 0_vr[1]*0_vr[4] - 1.732060602824032 0_vi[1]*0_vi[4] ≤ 0.0\n",
      " 0_p[(1, 1, 4)]² + 0_q[(1, 1, 4)]² ≤ 6.25\n",
      " 0_p[(1, 4, 1)]² + 0_q[(1, 4, 1)]² ≤ 6.25\n",
      " 0_vr[7] ≥ -1.1\n",
      " 0_vr[4] ≥ -1.1\n",
      " 0_vr[9] ≥ -1.1\n",
      " 0_vr[2] ≥ -1.1\n",
      " 0_vr[3] ≥ -1.1\n",
      " 0_vr[8] ≥ -1.1\n",
      " 0_vr[5] ≥ -1.1\n",
      " 0_vr[6] ≥ -1.1\n",
      " 0_vr[1] ≥ -1.1\n",
      " 0_vi[7] ≥ -1.1\n",
      " 0_vi[4] ≥ -1.1\n",
      " 0_vi[9] ≥ -1.1\n",
      " 0_vi[2] ≥ -1.1\n",
      " 0_vi[3] ≥ -1.1\n",
      " 0_vi[8] ≥ -1.1\n",
      " 0_vi[5] ≥ -1.1\n",
      " 0_vi[6] ≥ -1.1\n",
      " 0_vi[1] ≥ -1.1\n",
      " 0_pg[2] ≥ 0.1\n",
      " 0_pg[3] ≥ 0.1\n",
      " 0_pg[1] ≥ 0.1\n",
      " 0_qg[2] ≥ -3.0\n",
      " 0_qg[3] ≥ -3.0\n",
      " 0_qg[1] ≥ -3.0\n",
      " 0_p[(7, 8, 2)] ≥ -2.5\n",
      " 0_p[(4, 3, 6)] ≥ -3.0\n",
      " 0_p[(9, 9, 4)] ≥ -2.5\n",
      " 0_p[(2, 4, 5)] ≥ -2.5\n",
      " 0_p[(3, 5, 6)] ≥ -1.5\n",
      " 0_p[(8, 8, 9)] ≥ -2.5\n",
      " 0_p[(5, 6, 7)] ≥ -1.5\n",
      " 0_p[(6, 7, 8)] ≥ -2.5\n",
      " 0_p[(1, 1, 4)] ≥ -2.5\n",
      " 0_p[(7, 2, 8)] ≥ -2.5\n",
      " 0_p[(4, 6, 3)] ≥ -3.0\n",
      " 0_p[(9, 4, 9)] ≥ -2.5\n",
      " 0_p[(2, 5, 4)] ≥ -2.5\n",
      " 0_p[(3, 6, 5)] ≥ -1.5\n",
      " 0_p[(8, 9, 8)] ≥ -2.5\n",
      " 0_p[(5, 7, 6)] ≥ -1.5\n",
      " 0_p[(6, 8, 7)] ≥ -2.5\n",
      " 0_p[(1, 4, 1)] ≥ -2.5\n",
      " 0_q[(7, 8, 2)] ≥ -2.5\n",
      " 0_q[(4, 3, 6)] ≥ -3.0\n",
      " 0_q[(9, 9, 4)] ≥ -2.5\n",
      " 0_q[(2, 4, 5)] ≥ -2.5\n",
      " 0_q[(3, 5, 6)] ≥ -1.5\n",
      " 0_q[(8, 8, 9)] ≥ -2.5\n",
      " 0_q[(5, 6, 7)] ≥ -1.5\n",
      " 0_q[(6, 7, 8)] ≥ -2.5\n",
      " 0_q[(1, 1, 4)] ≥ -2.5\n",
      " 0_q[(7, 2, 8)] ≥ -2.5\n",
      " 0_q[(4, 6, 3)] ≥ -3.0\n",
      " 0_q[(9, 4, 9)] ≥ -2.5\n",
      " 0_q[(2, 5, 4)] ≥ -2.5\n",
      " 0_q[(3, 6, 5)] ≥ -1.5\n",
      " 0_q[(8, 9, 8)] ≥ -2.5\n",
      " 0_q[(5, 7, 6)] ≥ -1.5\n",
      " 0_q[(6, 8, 7)] ≥ -2.5\n",
      " 0_q[(1, 4, 1)] ≥ -2.5\n",
      " 0_vr[7] ≤ 1.1\n",
      " 0_vr[4] ≤ 1.1\n",
      " 0_vr[9] ≤ 1.1\n",
      " 0_vr[2] ≤ 1.1\n",
      " 0_vr[3] ≤ 1.1\n",
      " 0_vr[8] ≤ 1.1\n",
      " 0_vr[5] ≤ 1.1\n",
      " 0_vr[6] ≤ 1.1\n",
      " 0_vr[1] ≤ 1.1\n",
      " 0_vi[7] ≤ 1.1\n",
      " 0_vi[4] ≤ 1.1\n",
      " 0_vi[9] ≤ 1.1\n",
      " 0_vi[2] ≤ 1.1\n",
      " 0_vi[3] ≤ 1.1\n",
      " 0_vi[8] ≤ 1.1\n",
      " 0_vi[5] ≤ 1.1\n",
      " 0_vi[6] ≤ 1.1\n",
      " 0_vi[1] ≤ 1.1\n",
      " 0_pg[2] ≤ 3.0\n",
      " 0_pg[3] ≤ 2.7\n",
      " 0_pg[1] ≤ 2.5\n",
      " 0_qg[2] ≤ 3.0\n",
      " 0_qg[3] ≤ 3.0\n",
      " 0_qg[1] ≤ 3.0\n",
      " 0_p[(7, 8, 2)] ≤ 2.5\n",
      " 0_p[(4, 3, 6)] ≤ 3.0\n",
      " 0_p[(9, 9, 4)] ≤ 2.5\n",
      " 0_p[(2, 4, 5)] ≤ 2.5\n",
      " 0_p[(3, 5, 6)] ≤ 1.5\n",
      " 0_p[(8, 8, 9)] ≤ 2.5\n",
      " 0_p[(5, 6, 7)] ≤ 1.5\n",
      " 0_p[(6, 7, 8)] ≤ 2.5\n",
      " 0_p[(1, 1, 4)] ≤ 2.5\n",
      " 0_p[(7, 2, 8)] ≤ 2.5\n",
      " 0_p[(4, 6, 3)] ≤ 3.0\n",
      " 0_p[(9, 4, 9)] ≤ 2.5\n",
      " 0_p[(2, 5, 4)] ≤ 2.5\n",
      " 0_p[(3, 6, 5)] ≤ 1.5\n",
      " 0_p[(8, 9, 8)] ≤ 2.5\n",
      " 0_p[(5, 7, 6)] ≤ 1.5\n",
      " 0_p[(6, 8, 7)] ≤ 2.5\n",
      " 0_p[(1, 4, 1)] ≤ 2.5\n",
      " 0_q[(7, 8, 2)] ≤ 2.5\n",
      " 0_q[(4, 3, 6)] ≤ 3.0\n",
      " 0_q[(9, 9, 4)] ≤ 2.5\n",
      " 0_q[(2, 4, 5)] ≤ 2.5\n",
      " 0_q[(3, 5, 6)] ≤ 1.5\n",
      " 0_q[(8, 8, 9)] ≤ 2.5\n",
      " 0_q[(5, 6, 7)] ≤ 1.5\n",
      " 0_q[(6, 7, 8)] ≤ 2.5\n",
      " 0_q[(1, 1, 4)] ≤ 2.5\n",
      " 0_q[(7, 2, 8)] ≤ 2.5\n",
      " 0_q[(4, 6, 3)] ≤ 3.0\n",
      " 0_q[(9, 4, 9)] ≤ 2.5\n",
      " 0_q[(2, 5, 4)] ≤ 2.5\n",
      " 0_q[(3, 6, 5)] ≤ 1.5\n",
      " 0_q[(8, 9, 8)] ≤ 2.5\n",
      " 0_q[(5, 7, 6)] ≤ 1.5\n",
      " 0_q[(6, 8, 7)] ≤ 2.5\n",
      " 0_q[(1, 4, 1)] ≤ 2.5\n"
     ]
    }
   ],
   "source": [
    "pm = instantiate_model(file, ACRPowerModel, PowerModels.build_opf)\n",
    "print(pm.model)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\u001b[39m\n",
      "------------------------------------------------------------------\n",
      "          COSMO v0.7.2 - A Quadratic Objective Conic Solver\n",
      "                         Michael Garstka\n",
      "                University of Oxford, 2017 - 2020\n",
      "------------------------------------------------------------------\n",
      "\n",
      "Problem:  x ∈ R^{171},\n",
      "          constraints: A ∈ R^{549x171} (771 nnz),\n",
      "          matrix size to factor: 720x720 (2262 nnz)\n",
      "Sets:     Nonnegatives of dim: 180\n",
      "          DensePsdConeTriangle of dim: 171\n",
      "          ZeroSet of dim: 135\n",
      "          SecondOrderCone of dim: 3\n",
      "          SecondOrderCone of dim: 3\n",
      "          SecondOrderCone of dim: 3\n",
      "          ... and 19 more\n",
      "Settings: ϵ_abs = 1.0e-04, ϵ_rel = 1.0e-04,\n",
      "          ϵ_prim_inf = 1.0e-06, ϵ_dual_inf = 1.0e-04,\n",
      "          ρ = 0.1, σ = 1.0e-6, α = 1.6,\n",
      "          max_iter = 2500,\n",
      "          scaling iter = 10 (on),\n",
      "          check termination every 40 iter,\n",
      "          check infeasibility every 40 iter,\n",
      "          KKT system solver: CHOLMOD\n",
      "Setup Time: 1645.44ms\n",
      "\n",
      "Iter:\tObjective:\tPrimal Res:\tDual Res:\tRho:\n",
      "1\t-1.5401e+07\t5.3996e+03\t2.4610e+02\t1.0000e-01\n",
      "40\t6.2662e+03\t6.5165e+00\t6.0134e-02\t1.0000e-01\n",
      "80\t5.6534e+02\t1.7099e-01\t5.5398e+00\t1.8199e+01\n",
      "120\t7.2914e+02\t1.7580e-01\t2.6056e+00\t1.8199e+01\n",
      "160\t9.6956e+02\t1.3891e-01\t2.8917e+00\t1.8199e+01\n",
      "200\t1.2010e+03\t1.0672e-01\t1.4620e+00\t1.8199e+01\n",
      "240\t1.7140e+03\t5.3979e-02\t2.3316e+01\t1.0595e+02\n",
      "280\t1.9436e+03\t5.4622e-02\t1.1950e+01\t1.0595e+02\n",
      "320\t2.0265e+03\t5.0778e-02\t2.4823e+01\t1.0595e+02\n",
      "360\t2.4770e+03\t3.9905e-02\t2.2623e+01\t1.0595e+02\n",
      "400\t3.0492e+03\t2.3383e-02\t1.4938e+01\t1.0595e+02\n",
      "440\t3.3028e+03\t1.4060e-02\t1.1001e+01\t1.0595e+02\n",
      "480\t3.5341e+03\t1.0753e-02\t4.7881e+00\t1.0595e+02\n",
      "520\t3.6971e+03\t7.3953e-03\t2.5154e+00\t1.0595e+02\n",
      "560\t3.8030e+03\t5.2498e-03\t2.2209e+00\t1.0595e+02\n",
      "600\t3.8882e+03\t3.9887e-03\t2.0175e+00\t1.0595e+02\n",
      "640\t3.9484e+03\t2.8933e-03\t1.6512e+00\t1.0595e+02\n",
      "680\t3.9928e+03\t2.1455e-03\t1.7619e+00\t1.0595e+02\n",
      "720\t4.0264e+03\t1.6259e-03\t1.7806e+00\t1.0595e+02\n",
      "760\t4.0507e+03\t1.1993e-03\t1.7526e+00\t1.0595e+02\n",
      "800\t4.0685e+03\t8.8875e-04\t1.7089e+00\t1.0595e+02\n",
      "840\t4.0815e+03\t6.5814e-04\t1.6606e+00\t1.0595e+02\n",
      "880\t4.0909e+03\t4.8350e-04\t1.6149e+00\t1.0595e+02\n",
      "920\t4.0975e+03\t3.5432e-04\t1.5722e+00\t1.0595e+02\n",
      "960\t4.1022e+03\t2.5886e-04\t1.5333e+00\t1.0595e+02\n",
      "1000\t4.1054e+03\t1.8766e-04\t1.4608e+00\t1.0595e+02\n",
      "1040\t4.1169e+03\t7.4188e-04\t1.0936e+00\t1.0595e+02\n",
      "1080\t4.1189e+03\t8.8765e-04\t6.2394e-01\t1.0595e+02\n",
      "1120\t4.1159e+03\t5.4700e-04\t5.2321e-01\t1.0595e+02\n",
      "1160\t4.1139e+03\t3.6120e-04\t2.8349e-01\t1.0595e+02\n",
      "1200\t4.1124e+03\t2.0381e-04\t1.6195e-01\t1.0595e+02\n",
      "1240\t4.1105e+03\t1.2626e-04\t1.1038e-01\t1.0595e+02\n",
      "\n",
      "------------------------------------------------------------------\n",
      ">>> Results\n",
      "Status: Solved\n",
      "Iterations: 1240\n",
      "Optimal objective: 4110.5462\n",
      "Runtime: 3.403s (3402.8ms)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 3.4028\n",
       "  \"optimizer\"          => \"COSMO\"\n",
       "  \"termination_status\" => OPTIMAL\n",
       "  \"dual_status\"        => FEASIBLE_POINT\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5299.3\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\n",
       "  \"objective_lb\"       => -Inf"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# COSMO for SDP relaxation experiment\n",
    "cosmo_sdp = run_opf(file, SDPWRMPowerModel, COSMO.Optimizer) # does not support SOC constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\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            : 405             \n",
      "  Cones                  : 21              \n",
      "  Scalar variables       : 234             \n",
      "  Matrix variables       : 1               \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 : 51\n",
      "Eliminator terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 0\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 2                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - number                 : 36              \n",
      "Presolve terminated. Time: 0.00    \n",
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 405             \n",
      "  Cones                  : 21              \n",
      "  Scalar variables       : 234             \n",
      "  Matrix variables       : 1               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 4               \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 237\n",
      "Optimizer  - Cones                  : 22\n",
      "Optimizer  - Scalar variables       : 160               conic                  : 118             \n",
      "Optimizer  - Semi-definite variables: 1                 scalarized             : 171             \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 : 1.54e+04          after factor           : 1.62e+04        \n",
      "Factor     - dense dim.             : 0                 flops                  : 1.86e+06        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   7.3e+00  1.2e+03  2.3e+03  0.00e+00   3.330064030e+03   1.041939340e+03   1.0e+00  0.01  \n",
      "1   1.0e+00  1.7e+02  8.5e+02  -9.98e-01  2.003204116e+03   -2.619751097e+02  1.4e-01  0.01  \n",
      "2   5.9e-01  9.9e+01  6.1e+02  -9.49e-01  1.317841978e+03   -8.095951571e+02  8.1e-02  0.01  \n",
      "3   4.3e-01  7.2e+01  3.9e+02  -4.57e-01  2.011527269e+03   3.422074489e+02   5.9e-02  0.01  \n",
      "4   1.1e-01  1.9e+01  9.2e+01  -2.30e-01  1.805705485e+03   1.069012869e+03   1.5e-02  0.01  \n",
      "5   7.9e-02  1.3e+01  6.3e+01  3.58e-01   1.923749989e+03   1.296590235e+03   1.1e-02  0.01  \n",
      "6   2.5e-02  4.2e+00  1.7e+01  3.76e-01   2.268238342e+03   1.970821328e+03   3.4e-03  0.01  \n",
      "7   1.7e-02  2.8e+00  1.3e+01  5.02e-02   2.387631953e+03   2.103494964e+03   2.3e-03  0.01  \n",
      "8   6.6e-03  1.1e+00  5.1e+00  -5.04e-03  2.787455834e+03   2.601495854e+03   9.1e-04  0.02  \n",
      "9   4.1e-03  6.9e-01  3.9e+00  -2.77e-01  2.920875050e+03   2.735616639e+03   5.7e-04  0.02  \n",
      "10  2.3e-03  3.9e-01  2.1e+00  -2.56e-01  3.411908741e+03   3.275035646e+03   3.2e-04  0.02  \n",
      "11  4.3e-04  7.2e-02  2.5e-01  1.65e-01   4.656422866e+03   4.621795790e+03   5.9e-05  0.02  \n",
      "12  6.9e-05  1.2e-02  1.8e-02  7.70e-01   5.179212222e+03   5.173172238e+03   9.4e-06  0.02  \n",
      "13  1.1e-05  1.9e-03  1.2e-03  9.71e-01   5.278610778e+03   5.277587706e+03   1.6e-06  0.02  \n",
      "14  3.2e-06  5.4e-04  1.8e-04  9.97e-01   5.290919835e+03   5.290629916e+03   4.4e-07  0.02  \n",
      "15  1.7e-06  2.8e-04  7.1e-05  1.00e+00   5.293791116e+03   5.293641870e+03   2.3e-07  0.02  \n",
      "16  3.8e-07  6.4e-05  7.9e-06  1.00e+00   5.295994682e+03   5.295960714e+03   5.3e-08  0.02  \n",
      "17  3.4e-08  5.7e-06  2.2e-07  1.00e+00   5.296623873e+03   5.296620877e+03   4.7e-09  0.03  \n",
      "18  4.9e-09  1.2e-07  6.5e-10  1.00e+00   5.296684915e+03   5.296684852e+03   9.7e-11  0.03  \n",
      "19  4.5e-09  9.0e-08  4.2e-10  1.00e+00   5.296685232e+03   5.296685185e+03   7.3e-11  0.03  \n",
      "20  4.5e-09  9.0e-08  4.2e-10  1.00e+00   5.296685232e+03   5.296685185e+03   7.3e-11  0.04  \n",
      "21  4.5e-09  9.0e-08  4.2e-10  1.00e+00   5.296685232e+03   5.296685185e+03   7.3e-11  0.04  \n",
      "Optimizer terminated. Time: 0.05    \n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 0.047209\n",
       "  \"optimizer\"          => \"Mosek\"\n",
       "  \"termination_status\" => SLOW_PROGRESS\n",
       "  \"dual_status\"        => FEASIBLE_POINT\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5296.69\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\n",
       "  \"objective_lb\"       => 0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mosek_sdp = run_opf(file, SDPWRMPowerModel, Mosek.Optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\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] = -4.0\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)] = -3.0\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] = -3.0\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] + 1.732060602824032 0_vr[2]*0_vr[3] + 1.732060602824032 0_vi[2]*0_vi[3] ≥ 0.0\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] + 1.732060602824032 0_vr[1]*0_vr[4] + 1.732060602824032 0_vi[1]*0_vi[4] ≥ 0.0\n",
      " 0_vi[1]*0_vr[5] - 0_vi[5]*0_vr[1] + 1.732060602824032 0_vr[1]*0_vr[5] + 1.732060602824032 0_vi[1]*0_vi[5] ≥ 0.0\n",
      " 0_vi[3]*0_vr[4] - 0_vi[4]*0_vr[3] + 1.732060602824032 0_vr[3]*0_vr[4] + 1.732060602824032 0_vi[3]*0_vi[4] ≥ 0.0\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] + 1.732060602824032 0_vr[4]*0_vr[5] + 1.732060602824032 0_vi[4]*0_vi[5] ≥ 0.0\n",
      " 0_vi[1]*0_vr[2] - 0_vi[2]*0_vr[1] + 1.732060602824032 0_vr[1]*0_vr[2] + 1.732060602824032 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] - 1.732060602824032 0_vr[2]*0_vr[3] - 1.732060602824032 0_vi[2]*0_vi[3] ≤ 0.0\n",
      " 0_vi[1]*0_vr[4] - 0_vi[4]*0_vr[1] - 1.732060602824032 0_vr[1]*0_vr[4] - 1.732060602824032 0_vi[1]*0_vi[4] ≤ 0.0\n",
      " 0_vi[1]*0_vr[5] - 0_vi[5]*0_vr[1] - 1.732060602824032 0_vr[1]*0_vr[5] - 1.732060602824032 0_vi[1]*0_vi[5] ≤ 0.0\n",
      " 0_vi[3]*0_vr[4] - 0_vi[4]*0_vr[3] - 1.732060602824032 0_vr[3]*0_vr[4] - 1.732060602824032 0_vi[3]*0_vi[4] ≤ 0.0\n",
      " 0_vi[4]*0_vr[5] - 0_vi[5]*0_vr[4] - 1.732060602824032 0_vr[4]*0_vr[5] - 1.732060602824032 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] - 1.732060602824032 0_vr[1]*0_vr[2] - 1.732060602824032 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] ≥ -1.5\n",
      " 0_qg[2] ≥ -1.275\n",
      " 0_qg[3] ≥ -3.9\n",
      " 0_qg[5] ≥ -4.5\n",
      " 0_qg[1] ≥ -0.3\n",
      " 0_p[(6, 4, 5)] ≥ -2.4\n",
      " 0_p[(1, 1, 2)] ≥ -4.0\n",
      " 0_p[(6, 5, 4)] ≥ -2.4\n",
      " 0_p[(1, 2, 1)] ≥ -4.0\n",
      " 0_q[(6, 4, 5)] ≥ -2.4\n",
      " 0_q[(1, 1, 2)] ≥ -4.0\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] ≤ 2.0\n",
      " 0_pg[2] ≤ 1.7\n",
      " 0_pg[3] ≤ 5.2\n",
      " 0_pg[5] ≤ 6.0\n",
      " 0_pg[1] ≤ 0.4\n",
      " 0_qg[4] ≤ 1.5\n",
      " 0_qg[2] ≤ 1.275\n",
      " 0_qg[3] ≤ 3.9\n",
      " 0_qg[5] ≤ 4.5\n",
      " 0_qg[1] ≤ 0.3\n",
      " 0_p[(6, 4, 5)] ≤ 2.4\n",
      " 0_p[(1, 1, 2)] ≤ 4.0\n",
      " 0_p[(6, 5, 4)] ≤ 2.4\n",
      " 0_p[(1, 2, 1)] ≤ 4.0\n",
      " 0_q[(6, 4, 5)] ≤ 2.4\n",
      " 0_q[(1, 1, 2)] ≤ 4.0\n",
      " 0_q[(6, 5, 4)] ≤ 2.4\n",
      " 0_q[(1, 2, 1)] ≤ 4.0\n"
     ]
    }
   ],
   "source": [
    "pm = instantiate_model(file, SDPWRMPowerModel, PowerModels.build_opf)\n",
    "print(pm.model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 8 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 8 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 4 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 4 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 1 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 1 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 5 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 5 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 2 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 2 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 6 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 6 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 7 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 7 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 9 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 9 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmin values in -90 deg. to 90 deg., tightening the value on branch 3 from -360.0 to -60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: this code only supports angmax values in -90 deg. to 90 deg., tightening the value on branch 3 from 360.0 to 60.0 deg.\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 1 does not match the value at bus 1\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 2 does not match the value at bus 2\u001b[39m\n",
      "\u001b[35m[warn | PowerModels]: the voltage setpoint on generator 3 does not match the value at bus 3\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 90 rows, 69 columns and 258 nonzeros\n",
      "Model fingerprint: 0xdeb661c2\n",
      "Model has 3 quadratic objective terms\n",
      "Model has 27 quadratic constraints\n",
      "Coefficient statistics:\n",
      "  Matrix range     [9e-01, 2e+01]\n",
      "  QMatrix range    [1e+00, 1e+00]\n",
      "  Objective range  [1e+02, 5e+02]\n",
      "  QObjective range [2e+03, 2e+03]\n",
      "  Bounds range     [1e-01, 3e+00]\n",
      "  RHS range        [2e-01, 1e+00]\n",
      "  QRHS range       [2e+00, 9e+00]\n",
      "Presolve removed 3 rows and 3 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 238 rows, 104 columns, 440 nonzeros\n",
      "Presolved model has 28 second-order cone constraints\n",
      "Ordering time: 0.00s\n",
      "\n",
      "Barrier statistics:\n",
      " AA' NZ     : 1.857e+03\n",
      " Factor NZ  : 3.216e+03\n",
      " Factor Ops : 4.998e+04 (less than 1 second per iteration)\n",
      " Threads    : 1\n",
      "\n",
      "                  Objective                Residual\n",
      "Iter       Primal          Dual         Primal    Dual     Compl     Time\n",
      "   0   1.57005959e+03  1.52430276e+03  1.39e+02 1.34e+01  1.26e+03     0s\n",
      "   1   1.47726682e+03 -3.13997889e+03  4.73e+01 1.48e-05  2.40e+02     0s\n",
      "   2   1.44191034e+03 -1.29585502e+03  8.61e+00 1.62e-11  4.73e+01     0s\n",
      "   3   1.41063835e+03  2.62346771e+00  3.39e+00 1.59e-12  1.80e+01     0s\n",
      "   4   1.50897621e+03  6.38400767e+02  2.29e+00 8.97e-12  1.16e+01     0s\n",
      "   5   1.63156524e+03  1.02011381e+03  1.09e+00 1.22e-11  6.85e+00     0s\n",
      "   6   1.83692210e+03  1.87360749e+03  6.04e-01 4.38e-12  3.07e+00     0s\n",
      "   7   2.06308714e+03  2.17690077e+03  3.86e-01 1.46e-11  1.95e+00     0s\n",
      "   8   2.31364520e+03  2.50984416e+03  2.61e-01 5.31e-10  1.20e+00     0s\n",
      "   9   2.40949478e+03  2.89409292e+03  2.42e-01 1.14e-09  1.10e+00     0s\n",
      "  10   2.52071300e+03  3.04992201e+03  2.30e-01 1.00e-09  1.24e+00     0s\n",
      "  11   2.69347050e+03  3.16857699e+03  1.85e-01 1.10e-10  1.21e+00     0s\n",
      "  12   2.76989552e+03  3.36100795e+03  1.62e-01 4.27e-11  9.83e-01     0s\n",
      "  13   2.79128407e+03  3.48327280e+03  1.56e-01 2.13e-10  9.38e-01     0s\n",
      "  14   2.84765987e+03  3.54793984e+03  1.43e-01 3.34e-11  8.37e-01     0s\n",
      "  15   2.90241966e+03  3.60359271e+03  1.32e-01 8.44e-11  7.70e-01     0s\n",
      "  16   2.97613783e+03  3.69426412e+03  1.21e-01 6.62e-10  8.02e-01     0s\n",
      "  17   2.98702476e+03  3.98395179e+03  1.19e-01 5.67e-10  7.35e-01     0s\n",
      "  18   3.02323563e+03  4.32721526e+03  1.12e-01 6.49e-10  6.54e-01     0s\n",
      "  19   3.07539625e+03  4.48294193e+03  1.04e-01 5.50e-10  6.95e-01     0s\n",
      "  20   3.16683828e+03  4.59330241e+03  7.58e-02 6.85e-10  7.01e-01     0s\n",
      "  21   3.37109992e+03  4.66668800e+03  5.82e-02 6.01e-10  6.12e-01     0s\n",
      "  22   3.61757573e+03  4.76815433e+03  4.87e-02 1.53e-09  5.26e-01     0s\n",
      "  23   4.22279712e+03  5.03360173e+03  3.06e-02 3.22e-09  5.66e-01     0s\n",
      "  24   4.97437742e+03  5.18257412e+03  8.85e-03 5.07e-09  4.05e-01     0s\n",
      "  25   5.11652450e+03  5.28734201e+03  7.46e-03 6.11e-09  1.12e-01     0s\n",
      "  26   5.28654094e+03  5.29479413e+03  2.91e-04 1.06e-09  1.41e-02     0s\n",
      "  27   5.29422887e+03  5.29636716e+03  6.90e-05 1.55e-08  2.77e-03     0s\n",
      "  28   5.29611327e+03  5.29665110e+03  1.54e-05 9.86e-08  4.03e-04     0s\n",
      "  29   5.29656530e+03  5.29666183e+03  3.18e-06 4.93e-07  6.53e-05     0s\n",
      "  30   5.29664895e+03  5.29666456e+03  4.32e-07 2.30e-06  9.43e-06     0s\n",
      "  31   5.29666100e+03  5.29666574e+03  1.25e-07 1.71e-07  1.92e-06     0s\n",
      "  32   5.29666234e+03  5.29666607e+03  9.19e-08 5.35e-07  5.65e-07     0s\n",
      "\n",
      "Barrier solved model in 32 iterations and 0.01 seconds\n",
      "Optimal objective 5.29666234e+03\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String,Any} with 8 entries:\n",
       "  \"solve_time\"         => 0.00756884\n",
       "  \"optimizer\"          => \"Gurobi\"\n",
       "  \"termination_status\" => OPTIMAL\n",
       "  \"dual_status\"        => NO_SOLUTION\n",
       "  \"primal_status\"      => FEASIBLE_POINT\n",
       "  \"objective\"          => 5296.66\n",
       "  \"solution\"           => Dict{String,Any}(\"baseMVA\"=>100,\"branch\"=>Dict{String…\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": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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