{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pandapower Optimal Power Flow\n",
    "This is an introduction into the usage of the pandapower optimal power flow. It shows how to set the constraints and the cost factors into the pandapower element tables.\n",
    "\n",
    "## Example Network\n",
    "\n",
    "We use the following four bus example network for this tutorial:\n",
    "\n",
    "<img src=\"pics/example_opf.png\" width=\"50%\">\n",
    "\n",
    "We first create this network in pandapower:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandapower as pp\n",
    "import numpy as np\n",
    "net = pp.create_empty_network()\n",
    "\n",
    "#create buses\n",
    "bus1 = pp.create_bus(net, vn_kv=220.)\n",
    "bus2 = pp.create_bus(net, vn_kv=110.)\n",
    "bus3 = pp.create_bus(net, vn_kv=110.)\n",
    "bus4 = pp.create_bus(net, vn_kv=110.)\n",
    "\n",
    "#create 220/110 kV transformer\n",
    "pp.create_transformer(net, bus1, bus2, std_type=\"100 MVA 220/110 kV\")\n",
    "\n",
    "#create 110 kV lines\n",
    "pp.create_line(net, bus2, bus3, length_km=70., std_type='149-AL1/24-ST1A 110.0')\n",
    "pp.create_line(net, bus3, bus4, length_km=50., std_type='149-AL1/24-ST1A 110.0')\n",
    "pp.create_line(net, bus4, bus2, length_km=40., std_type='149-AL1/24-ST1A 110.0')\n",
    "\n",
    "#create loads\n",
    "pp.create_load(net, bus2, p_kw=60e3, controllable = False)\n",
    "pp.create_load(net, bus3, p_kw=70e3, controllable = False)\n",
    "pp.create_load(net, bus4, p_kw=10e3, controllable = False)\n",
    "\n",
    "#create generators\n",
    "eg = pp.create_ext_grid(net, bus1)\n",
    "g0 = pp.create_gen(net, bus3, p_kw=-80*1e3, min_p_kw=-80e3, max_p_kw=0,vm_pu=1.01, controllable=True)\n",
    "g1 = pp.create_gen(net, bus4, p_kw=-100*1e3, min_p_kw=-100e3, max_p_kw=0, vm_pu=1.01, controllable=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loss Minimization\n",
    "\n",
    "We specify the same costs for the power at the external grid and all generators to minimize the overall power feed in. This equals an overall loss minimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "costeg = pp.create_polynomial_cost(net, 0, 'ext_grid', np.array([1, 0]))\n",
    "costgen1 = pp.create_polynomial_cost(net, 0, 'gen', np.array([1, 0]))\n",
    "costgen2 = pp.create_polynomial_cost(net, 1, 'gen', np.array([1, 0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run an OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PYPOWER Version 5.0.0, 29-May-2015 -- AC Optimal Power Flow\n",
      "Python Interior Point Solver - PIPS, Version 1.0, 07-Feb-2011\n",
      "Numerically failed.\n",
      "Did not converge in 2 iterations.\n"
     ]
    },
    {
     "ename": "OPFNotConverged",
     "evalue": "Optimal Power Flow did not converge!",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOPFNotConverged\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-89e51745b9f9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrunopp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\run.py\u001b[0m in \u001b[0;36mrunopp\u001b[0;34m(net, verbose, calculate_voltage_angles, check_connectivity, suppress_warnings, r_switch, delta, **kwargs)\u001b[0m\n\u001b[1;32m    290\u001b[0m                      voltage_depend_loads=False, delta=delta)\n\u001b[1;32m    291\u001b[0m     \u001b[0m_add_opf_options\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrafo_loading\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrafo_loading\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mac\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mac\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m--> 292\u001b[0;31m     \u001b[0m_optimal_powerflow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msuppress_warnings\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    293\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\optimal_powerflow.py\u001b[0m in \u001b[0;36m_optimal_powerflow\u001b[0;34m(net, verbose, suppress_warnings, **kwargs)\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"success\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m---> 54\u001b[0;31m         \u001b[1;32mraise\u001b[0m \u001b[0mOPFNotConverged\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Optimal Power Flow did not converge!\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     55\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[1;31m# ppci doesn't contain out of service elements, but ppc does -> copy results accordingly\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mOPFNotConverged\u001b[0m: Optimal Power Flow did not converge!"
     ]
    }
   ],
   "source": [
    "pp.runopp(net, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apparently the OPF did not converge. Sometimes the constraints are too broad or too narrow for the OPF to converge. So let's try setting the voltage constraints first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.bus['max_vm_pu'] = 2\n",
    "pp.runopp(net, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's check the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since all costs were specified the same, the OPF minimizes overall power generation, which is equal to a loss minimization in the network. The loads at buses 3 and 4 are supplied by generators at the same bus, the load at Bus 2 is provided by a combination of the other generators so that the power transmission leads to minimal losses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Individual Generator Costs\n",
    "\n",
    "Let's now assign individual costs to each generator.\n",
    "\n",
    "We assign a cost of 10 ct/kW for the external grid, 15 ct/kw for the generator g0 and 12 ct/kw for generator g1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net.polynomial_cost.c.at[costeg] = np.array([[0.1, 0]])\n",
    "net.polynomial_cost.c.at[costgen1] = np.array([[0.15, 0]])\n",
    "net.polynomial_cost.c.at[costgen2] = np.array([[0.12, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now run an OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PYPOWER Version 5.0.0, 29-May-2015 -- AC Optimal Power Flow\n",
      "Python Interior Point Solver - PIPS, Version 1.0, 07-Feb-2011\n",
      "Numerically failed.\n",
      "Did not converge in 32 iterations.\n"
     ]
    },
    {
     "ename": "OPFNotConverged",
     "evalue": "Optimal Power Flow did not converge!",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOPFNotConverged\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-89e51745b9f9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrunopp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\run.py\u001b[0m in \u001b[0;36mrunopp\u001b[0;34m(net, verbose, calculate_voltage_angles, check_connectivity, suppress_warnings, r_switch, delta, **kwargs)\u001b[0m\n\u001b[1;32m    290\u001b[0m                      voltage_depend_loads=False, delta=delta)\n\u001b[1;32m    291\u001b[0m     \u001b[0m_add_opf_options\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrafo_loading\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrafo_loading\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mac\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mac\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m--> 292\u001b[0;31m     \u001b[0m_optimal_powerflow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msuppress_warnings\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    293\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\optimal_powerflow.py\u001b[0m in \u001b[0;36m_optimal_powerflow\u001b[0;34m(net, verbose, suppress_warnings, **kwargs)\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"success\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m---> 54\u001b[0;31m         \u001b[1;32mraise\u001b[0m \u001b[0mOPFNotConverged\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Optimal Power Flow did not converge!\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     55\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[1;31m# ppci doesn't contain out of service elements, but ppc does -> copy results accordingly\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mOPFNotConverged\u001b[0m: Optimal Power Flow did not converge!"
     ]
    }
   ],
   "source": [
    "pp.runopp(net, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that all active power is provided by the external grid. This makes sense, because the external grid has the lowest cost of all generators and we did not define any constraints.\n",
    "\n",
    "The dispatch costs are given in net.res_cost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformer Constraint\n",
    "\n",
    "Since all active power comes from the external grid and subsequently flows through the transformer, the transformer is overloaded with a loading of about 145%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.res_trafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now limit the transformer loading to 50%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.trafo[\"max_loading_percent\"] = 50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(the max_loading_percent parameter can also be specified directly when creating the transformer)\n",
    "and run the OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the transformer complies with the maximum loading:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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    "And power generation is now split between the external grid and generator 1 (which is the second cheapest generation unit):"
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       "      <td>-3453.342439</td>\n",
       "      <td>-1.237884</td>\n",
       "      <td>1.025709</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar  va_degree     vm_pu\n",
       "0     -0.009347 -2993.145553  -6.232828  0.985230\n",
       "1 -93304.076626 -3453.342439  -1.237884  1.025709"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "This comes of course with an increase in dispatch costs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16191.876760535753"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Line Loading Constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wen now look at the line loadings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_from_kw</th>\n",
       "      <th>q_from_kvar</th>\n",
       "      <th>p_to_kw</th>\n",
       "      <th>q_to_kvar</th>\n",
       "      <th>pl_kw</th>\n",
       "      <th>ql_kvar</th>\n",
       "      <th>i_from_ka</th>\n",
       "      <th>i_to_ka</th>\n",
       "      <th>i_ka</th>\n",
       "      <th>loading_percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19780.007620</td>\n",
       "      <td>-2479.435263</td>\n",
       "      <td>-19341.693479</td>\n",
       "      <td>1104.392907</td>\n",
       "      <td>438.314142</td>\n",
       "      <td>-1375.042356</td>\n",
       "      <td>0.104309</td>\n",
       "      <td>0.103207</td>\n",
       "      <td>0.104309</td>\n",
       "      <td>22.193318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-50658.297175</td>\n",
       "      <td>1888.752646</td>\n",
       "      <td>52783.695174</td>\n",
       "      <td>921.063740</td>\n",
       "      <td>2125.398000</td>\n",
       "      <td>2809.816386</td>\n",
       "      <td>0.270061</td>\n",
       "      <td>0.270140</td>\n",
       "      <td>0.270140</td>\n",
       "      <td>57.476546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>30520.381452</td>\n",
       "      <td>2532.278698</td>\n",
       "      <td>-29946.196656</td>\n",
       "      <td>-2688.017331</td>\n",
       "      <td>574.184796</td>\n",
       "      <td>-155.738633</td>\n",
       "      <td>0.156712</td>\n",
       "      <td>0.157323</td>\n",
       "      <td>0.157323</td>\n",
       "      <td>33.472995</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      p_from_kw  q_from_kvar       p_to_kw    q_to_kvar        pl_kw  \\\n",
       "0  19780.007620 -2479.435263 -19341.693479  1104.392907   438.314142   \n",
       "1 -50658.297175  1888.752646  52783.695174   921.063740  2125.398000   \n",
       "2  30520.381452  2532.278698 -29946.196656 -2688.017331   574.184796   \n",
       "\n",
       "       ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0 -1375.042356   0.104309  0.103207  0.104309        22.193318  \n",
       "1  2809.816386   0.270061  0.270140  0.270140        57.476546  \n",
       "2  -155.738633   0.156712  0.157323  0.157323        33.472995  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and run the OPF with a 50% loading constraint:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PYPOWER Version 5.0.0, 29-May-2015 -- AC Optimal Power Flow\n",
      "Python Interior Point Solver - PIPS, Version 1.0, 07-Feb-2011\n",
      "Converged!\n"
     ]
    }
   ],
   "source": [
    "net.line[\"max_loading_percent\"] = 50\n",
    "pp.runopp(net, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the line loading constraint is complied with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_from_kw</th>\n",
       "      <th>q_from_kvar</th>\n",
       "      <th>p_to_kw</th>\n",
       "      <th>q_to_kvar</th>\n",
       "      <th>pl_kw</th>\n",
       "      <th>ql_kvar</th>\n",
       "      <th>i_from_ka</th>\n",
       "      <th>i_to_ka</th>\n",
       "      <th>i_ka</th>\n",
       "      <th>loading_percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16727.532318</td>\n",
       "      <td>-3194.198556</td>\n",
       "      <td>-16412.740583</td>\n",
       "      <td>1533.356250</td>\n",
       "      <td>314.791735</td>\n",
       "      <td>-1660.842305</td>\n",
       "      <td>0.088848</td>\n",
       "      <td>0.087130</td>\n",
       "      <td>0.088848</td>\n",
       "      <td>18.903796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-44451.211099</td>\n",
       "      <td>867.137901</td>\n",
       "      <td>46059.955230</td>\n",
       "      <td>832.560223</td>\n",
       "      <td>1608.744131</td>\n",
       "      <td>1699.698124</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>49.999997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27533.096563</td>\n",
       "      <td>4051.891931</td>\n",
       "      <td>-27060.152701</td>\n",
       "      <td>-4429.882352</td>\n",
       "      <td>472.943862</td>\n",
       "      <td>-377.990422</td>\n",
       "      <td>0.141965</td>\n",
       "      <td>0.143058</td>\n",
       "      <td>0.143058</td>\n",
       "      <td>30.437792</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      p_from_kw  q_from_kvar       p_to_kw    q_to_kvar        pl_kw  \\\n",
       "0  16727.532318 -3194.198556 -16412.740583  1533.356250   314.791735   \n",
       "1 -44451.211099   867.137901  46059.955230   832.560223  1608.744131   \n",
       "2  27533.096563  4051.891931 -27060.152701 -4429.882352   472.943862   \n",
       "\n",
       "       ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0 -1660.842305   0.088848  0.087130  0.088848        18.903796  \n",
       "1  1699.698124   0.235000  0.235000  0.235000        49.999997  \n",
       "2  -377.990422   0.141965  0.143058  0.143058        30.437792  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all generators are involved in supplying the loads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-49787.594269</td>\n",
       "      <td>4603.789001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar\n",
       "0 -49787.594269  4603.789001"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>vm_pu</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-9136.048164</td>\n",
       "      <td>-2400.493544</td>\n",
       "      <td>-5.814910</td>\n",
       "      <td>0.992992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-83593.051621</td>\n",
       "      <td>-4884.451800</td>\n",
       "      <td>-1.511686</td>\n",
       "      <td>1.028900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar  va_degree     vm_pu\n",
       "0  -9136.048164 -2400.493544  -5.814910  0.992992\n",
       "1 -83593.051621 -4884.451800  -1.511686  1.028900"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This of course comes with a once again rising dispatch cost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16380.332845968122"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Voltage Constraints\n",
    "\n",
    "Finally, we have a look at the bus voltage:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>lam_p</th>\n",
       "      <th>lam_q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-49787.594269</td>\n",
       "      <td>4603.789001</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>-1.673841e-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.006025</td>\n",
       "      <td>-3.408832</td>\n",
       "      <td>60000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>130.952237</td>\n",
       "      <td>-5.410368e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.992992</td>\n",
       "      <td>-5.814910</td>\n",
       "      <td>60863.951836</td>\n",
       "      <td>-2400.493544</td>\n",
       "      <td>149.999983</td>\n",
       "      <td>7.893715e-22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.028900</td>\n",
       "      <td>-1.511686</td>\n",
       "      <td>-73593.051621</td>\n",
       "      <td>-4884.451800</td>\n",
       "      <td>120.000009</td>\n",
       "      <td>1.859168e-21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      vm_pu  va_degree          p_kw       q_kvar       lam_p         lam_q\n",
       "0  1.000000   0.000000 -49787.594269  4603.789001  100.000000 -1.673841e-21\n",
       "1  1.006025  -3.408832  60000.000000     0.000000  130.952237 -5.410368e-01\n",
       "2  0.992992  -5.814910  60863.951836 -2400.493544  149.999983  7.893715e-22\n",
       "3  1.028900  -1.511686 -73593.051621 -4884.451800  120.000009  1.859168e-21"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and constrain it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net.bus[\"min_vm_pu\"] = 1.0\n",
    "net.bus[\"max_vm_pu\"] = 1.02\n",
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that all voltages are within the voltage band:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>lam_p</th>\n",
       "      <th>lam_q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-49906.847832</td>\n",
       "      <td>3050.617583</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>-5.175965e-22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.004168</td>\n",
       "      <td>-3.421015</td>\n",
       "      <td>60000.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>131.268594</td>\n",
       "      <td>-2.133680e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-5.976094</td>\n",
       "      <td>59278.207273</td>\n",
       "      <td>-14858.927798</td>\n",
       "      <td>149.999993</td>\n",
       "      <td>2.520634e-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.020000</td>\n",
       "      <td>-1.366892</td>\n",
       "      <td>-71863.493411</td>\n",
       "      <td>9172.685486</td>\n",
       "      <td>120.000004</td>\n",
       "      <td>-1.555865e-21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      vm_pu  va_degree          p_kw        q_kvar       lam_p         lam_q\n",
       "0  1.000000   0.000000 -49906.847832   3050.617583  100.000000 -5.175965e-22\n",
       "1  1.004168  -3.421015  60000.000000      0.000000  131.268594 -2.133680e-01\n",
       "2  1.000000  -5.976094  59278.207273 -14858.927798  149.999993  2.520634e-21\n",
       "3  1.020000  -1.366892 -71863.493411   9172.685486  120.000004 -1.555865e-21"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all generators are once again involved in supplying the loads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-49906.847832</td>\n",
       "      <td>3050.617583</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar\n",
       "0 -49906.847832  3050.617583"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>vm_pu</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-10721.792727</td>\n",
       "      <td>-14858.927798</td>\n",
       "      <td>-5.976094</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-81863.493411</td>\n",
       "      <td>9172.685486</td>\n",
       "      <td>-1.366892</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw        q_kvar  va_degree  vm_pu\n",
       "0 -10721.792727 -14858.927798  -5.976094   1.00\n",
       "1 -81863.493411   9172.685486  -1.366892   1.02"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This of course comes once again with rising dispatch costs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16422.572901622079"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DC OPF\n",
    "\n",
    "pandapower also provides the possibility of running a DC Optimal Power Flow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pp.rundcopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since voltage magnitudes are not included in the DC power flow formulation, voltage constraints canot be considered in the DC OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>lam_p</th>\n",
       "      <th>lam_q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-49999.999962</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.436967</td>\n",
       "      <td>60000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>130.909091</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-5.708566</td>\n",
       "      <td>61488.746675</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.362340</td>\n",
       "      <td>-71488.746713</td>\n",
       "      <td>NaN</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   vm_pu  va_degree          p_kw  q_kvar       lam_p  lam_q\n",
       "0    NaN   0.000000 -49999.999962     NaN  100.000000    0.0\n",
       "1    NaN  -3.436967  60000.000000     NaN  130.909091    0.0\n",
       "2    NaN  -5.708566  61488.746675     NaN  150.000000    0.0\n",
       "3    NaN  -1.362340 -71488.746713     NaN  120.000000    0.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Line and transformer loading limits are however complied with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_from_kw</th>\n",
       "      <th>q_from_kvar</th>\n",
       "      <th>p_to_kw</th>\n",
       "      <th>q_to_kvar</th>\n",
       "      <th>pl_kw</th>\n",
       "      <th>ql_kvar</th>\n",
       "      <th>i_from_ka</th>\n",
       "      <th>i_to_ka</th>\n",
       "      <th>i_ka</th>\n",
       "      <th>loading_percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16715.233326</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-16715.233326</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.087732</td>\n",
       "      <td>0.087732</td>\n",
       "      <td>0.087732</td>\n",
       "      <td>18.666430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-44773.513348</td>\n",
       "      <td>NaN</td>\n",
       "      <td>44773.513348</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>26715.233365</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-26715.233365</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.140219</td>\n",
       "      <td>0.140219</td>\n",
       "      <td>0.140219</td>\n",
       "      <td>29.833747</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      p_from_kw  q_from_kvar       p_to_kw  q_to_kvar  pl_kw  ql_kvar  \\\n",
       "0  16715.233326          NaN -16715.233326        NaN    NaN      NaN   \n",
       "1 -44773.513348          NaN  44773.513348        NaN    NaN      NaN   \n",
       "2  26715.233365          NaN -26715.233365        NaN    NaN      NaN   \n",
       "\n",
       "   i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0   0.087732  0.087732  0.087732        18.666430  \n",
       "1   0.235000  0.235000  0.235000        50.000000  \n",
       "2   0.140219  0.140219  0.140219        29.833747  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_hv_kw</th>\n",
       "      <th>q_hv_kvar</th>\n",
       "      <th>p_lv_kw</th>\n",
       "      <th>q_lv_kvar</th>\n",
       "      <th>pl_kw</th>\n",
       "      <th>ql_kvar</th>\n",
       "      <th>i_hv_ka</th>\n",
       "      <th>i_lv_ka</th>\n",
       "      <th>loading_percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49999.999962</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-49999.999962</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.131216</td>\n",
       "      <td>0.262432</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        p_hv_kw  q_hv_kvar       p_lv_kw  q_lv_kvar  pl_kw  ql_kvar   i_hv_ka  \\\n",
       "0  49999.999962        NaN -49999.999962        NaN    NaN      NaN  0.131216   \n",
       "\n",
       "    i_lv_ka  loading_percent  \n",
       "0  0.262432             50.0  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_trafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As are generator limits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>bus</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>sn_kva</th>\n",
       "      <th>min_q_kvar</th>\n",
       "      <th>max_q_kvar</th>\n",
       "      <th>scaling</th>\n",
       "      <th>in_service</th>\n",
       "      <th>type</th>\n",
       "      <th>min_p_kw</th>\n",
       "      <th>max_p_kw</th>\n",
       "      <th>controllable</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>None</td>\n",
       "      <td>2</td>\n",
       "      <td>-80000.0</td>\n",
       "      <td>1.01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>True</td>\n",
       "      <td>None</td>\n",
       "      <td>-80000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>None</td>\n",
       "      <td>3</td>\n",
       "      <td>-100000.0</td>\n",
       "      <td>1.01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>True</td>\n",
       "      <td>None</td>\n",
       "      <td>-100000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   name  bus      p_kw  vm_pu  sn_kva  min_q_kvar  max_q_kvar  scaling  \\\n",
       "0  None    2  -80000.0   1.01     NaN         NaN         NaN      1.0   \n",
       "1  None    3 -100000.0   1.01     NaN         NaN         NaN      1.0   \n",
       "\n",
       "  in_service  type  min_p_kw  max_p_kw controllable  \n",
       "0       True  None  -80000.0       0.0         True  \n",
       "1       True  None -100000.0       0.0         True  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>vm_pu</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-8511.253325</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-5.708566</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-81488.746713</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.362340</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw  q_kvar  va_degree  vm_pu\n",
       "0  -8511.253325     NaN  -5.708566    1.0\n",
       "1 -81488.746713     NaN  -1.362340    1.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost function is the same for the linearized OPF as for the non-linear one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600528508"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Piecewise linear cost functions**\n",
    "The OPF also offers us piecewise linear cost functions. Let us first check the actual cost function setup:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>type</th>\n",
       "      <th>element</th>\n",
       "      <th>element_type</th>\n",
       "      <th>c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>p</td>\n",
       "      <td>0</td>\n",
       "      <td>ext_grid</td>\n",
       "      <td>[[0.1, 0.0]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>p</td>\n",
       "      <td>0</td>\n",
       "      <td>gen</td>\n",
       "      <td>[[0.15, 0.0]]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>p</td>\n",
       "      <td>1</td>\n",
       "      <td>gen</td>\n",
       "      <td>[[0.12, 0.0]]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  type element element_type              c\n",
       "0    p       0     ext_grid   [[0.1, 0.0]]\n",
       "1    p       0          gen  [[0.15, 0.0]]\n",
       "2    p       1          gen  [[0.12, 0.0]]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.polynomial_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An element can either have polynomial costs or piecewise linear costs at the same time. So let us first delete the polynomial costs in order to avoid confusion and errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.polynomial_cost= net.polynomial_cost.drop(net.polynomial_cost.index.values)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results above have been produced with polynomial cost functions, that were linear. Let's try to reproduce the results using piecewise linear cost functions. Note: The cost functions need to have the same gradient!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Cost function must be defined for whole power range of the generator",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-33-90f53fab73a0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcreate_piecewise_linear_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"gen\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m \u001b[1;33m,\u001b[0m \u001b[1;36m0.15\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcreate_piecewise_linear_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"gen\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.12\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcreate_piecewise_linear_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"ext_grid\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\create.py\u001b[0m in \u001b[0;36mcreate_piecewise_linear_cost\u001b[0;34m(net, element, element_type, data_points, type, index)\u001b[0m\n\u001b[1;32m   2127\u001b[0m             if not (net[element_type].max_p_kw.at[element] <= max(p) and\n\u001b[1;32m   2128\u001b[0m                     net[element_type].min_p_kw.at[element] >= min(p)):\n\u001b[0;32m-> 2129\u001b[0;31m                 raise ValueError(\"Cost function must be defined for whole power range of the \"\n\u001b[0m\u001b[1;32m   2130\u001b[0m                                  \"generator\")\n\u001b[1;32m   2131\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mtype\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m\"q\"\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Cost function must be defined for whole power range of the generator"
     ]
    }
   ],
   "source": [
    "pp.create_piecewise_linear_cost(net, 0, \"gen\", np.array([[0, 0], [1 , 0.15]]))\n",
    "pp.create_piecewise_linear_cost(net, 1, \"gen\", np.array([[0, 0], [1, 0.12]]))\n",
    "pp.create_piecewise_linear_cost(net, 0, \"ext_grid\", np.array([[0, 0], [1, 0.1]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we forgot is that the piecewise linear function should be defined for the whole range of the generator. The range is determined by p_max and p_min. Let's check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.0\n",
       "1    0.0\n",
       "Name: max_p_kw, dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen.max_p_kw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    -80000.0\n",
       "1   -100000.0\n",
       "Name: min_p_kw, dtype: float64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen.min_p_kw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.create_piecewise_linear_cost(net, 0, \"gen\", np.array([[-80000* 1 , -80000*0.15], [0, 0]]))\n",
    "pp.create_piecewise_linear_cost(net, 1, \"gen\", np.array([[-100000*1, -100000*0.12], [0, 0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An external grid usually has no operational limits, but this is a problem for the OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "No operational constraints defined for controllable element!",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-37-42b079913cbe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcreate_piecewise_linear_cost\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnet\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"ext_grid\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32mC:\\Users\\fmeier\\pandapower\\pandapower\\create.py\u001b[0m in \u001b[0;36mcreate_piecewise_linear_cost\u001b[0;34m(net, element, element_type, data_points, type, index)\u001b[0m\n\u001b[1;32m   2124\u001b[0m             if not (hasattr(net[element_type], \"max_p_kw\") and hasattr(net[element_type],\n\u001b[1;32m   2125\u001b[0m                                                                        \"min_p_kw\")):\n\u001b[0;32m-> 2126\u001b[0;31m                 \u001b[1;32mraise\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"No operational constraints defined for controllable element!\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2127\u001b[0m             if not (net[element_type].max_p_kw.at[element] <= max(p) and\n\u001b[1;32m   2128\u001b[0m                     net[element_type].min_p_kw.at[element] >= min(p)):\n",
      "\u001b[0;31mAttributeError\u001b[0m: No operational constraints defined for controllable element!"
     ]
    }
   ],
   "source": [
    "pp.create_piecewise_linear_cost(net, 0, \"ext_grid\", np.array([[0, 0], [1, 0.1]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we set imaginary constraints, that we can choose very broad:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net.ext_grid[\"max_p_kw\"] = 1e9\n",
    "net.ext_grid[\"min_p_kw\"] = -1e9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>bus</th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>in_service</th>\n",
       "      <th>max_p_kw</th>\n",
       "      <th>min_p_kw</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>None</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>True</td>\n",
       "      <td>1.000000e+09</td>\n",
       "      <td>-1.000000e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   name  bus  vm_pu  va_degree in_service      max_p_kw      min_p_kw\n",
       "0  None    0    1.0        0.0       True  1.000000e+09 -1.000000e+09"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.create_piecewise_linear_cost(net, 0, \"ext_grid\", np.array([[-1e9, -1e9*.1], [1e9, 1e9*0.1]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check the results from the previous OPF again!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>lam_p</th>\n",
       "      <th>lam_q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-49999.999962</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.436967</td>\n",
       "      <td>60000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>130.909091</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-5.708566</td>\n",
       "      <td>61488.746675</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.362340</td>\n",
       "      <td>-71488.746713</td>\n",
       "      <td>NaN</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   vm_pu  va_degree          p_kw  q_kvar       lam_p  lam_q\n",
       "0    NaN   0.000000 -49999.999962     NaN  100.000000    0.0\n",
       "1    NaN  -3.436967  60000.000000     NaN  130.909091    0.0\n",
       "2    NaN  -5.708566  61488.746675     NaN  150.000000    0.0\n",
       "3    NaN  -1.362340 -71488.746713     NaN  120.000000    0.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600528508"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run the same OPF now with different cost function setup. We should get the exact same results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pp.rundcopp(net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600298368"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vm_pu</th>\n",
       "      <th>va_degree</th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "      <th>lam_p</th>\n",
       "      <th>lam_q</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-6.163691e-25</td>\n",
       "      <td>-49999.999965</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-3.436967e+00</td>\n",
       "      <td>60000.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>130.909091</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-5.708566e+00</td>\n",
       "      <td>61488.746680</td>\n",
       "      <td>NaN</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.362340e+00</td>\n",
       "      <td>-71488.746715</td>\n",
       "      <td>NaN</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   vm_pu     va_degree          p_kw  q_kvar       lam_p  lam_q\n",
       "0    NaN -6.163691e-25 -49999.999965     NaN  100.000000    0.0\n",
       "1    NaN -3.436967e+00  60000.000000     NaN  130.909091    0.0\n",
       "2    NaN -5.708566e+00  61488.746680     NaN  150.000000    0.0\n",
       "3    NaN -1.362340e+00 -71488.746715     NaN  120.000000    0.0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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