tutorials/opf_basic.ipynb

{
 "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": 216,
   "metadata": {},
   "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, min_p_kw = -1e9, max_p_kw = 1e9)\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": 217,
   "metadata": {},
   "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": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.run - INFO: These missing columns in ext_grid are considered in OPF as +- 1000 TW.: ['min_q_kvar' 'max_q_kvar']\n",
      "hp.pandapower.run - INFO: These elements have missing power constraint values, which are considered in OPF as +- 1000 TW: ['gen']\n",
      "hp.pandapower.run - INFO: min_vm_pu is missing in bus table. In OPF these limits are considered as 0.0 pu.\n",
      "hp.pandapower.run - INFO: max_vm_pu is missing in bus table. In OPF these limits are considered as 2.0 pu.\n"
     ]
    },
    {
     "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": [
    "pp.runopp(net, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's check the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <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>-56530.125753</td>\n",
       "      <td>-1974.470643</td>\n",
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      ],
      "text/plain": [
       "           p_kw       q_kvar\n",
       "0 -56530.125753 -1974.470643"
      ]
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     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
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       "    <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>-71313.391997</td>\n",
       "      <td>1969.654771</td>\n",
       "      <td>-3.712810</td>\n",
       "      <td>1.000009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-12299.771985</td>\n",
       "      <td>1451.159898</td>\n",
       "      <td>-3.712777</td>\n",
       "      <td>1.000010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "           p_kw       q_kvar  va_degree     vm_pu\n",
       "0 -71313.391997  1969.654771  -3.712810  1.000009\n",
       "1 -12299.771985  1451.159898  -3.712777  1.000010"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 221,
   "metadata": {},
   "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": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.run - INFO: These missing columns in ext_grid are considered in OPF as +- 1000 TW.: ['min_q_kvar' 'max_q_kvar']\n",
      "hp.pandapower.run - INFO: These elements have missing power constraint values, which are considered in OPF as +- 1000 TW: ['gen']\n",
      "hp.pandapower.run - INFO: min_vm_pu is missing in bus table. In OPF these limits are considered as 0.0 pu.\n",
      "hp.pandapower.run - INFO: max_vm_pu is missing in bus table. In OPF these limits are considered as 2.0 pu.\n"
     ]
    },
    {
     "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": [
    "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": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14455.950328285482"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <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",
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       "      <td>144559.444871</td>\n",
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       "      <td>15993.742384</td>\n",
       "      <td>599.928539</td>\n",
       "      <td>25186.808841</td>\n",
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       "      <td>0.759988</td>\n",
       "      <td>144.85146</td>\n",
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      ],
      "text/plain": [
       "         p_hv_kw    q_hv_kvar        p_lv_kw     q_lv_kvar       pl_kw  \\\n",
       "0  144559.444871  9193.066457 -143959.516332  15993.742384  599.928539   \n",
       "\n",
       "        ql_kvar   i_hv_ka   i_lv_ka  loading_percent  \n",
       "0  25186.808841  0.380136  0.759988        144.85146  "
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "net.res_trafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now limit the transformer loading to 50%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "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": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.run - INFO: These missing columns in ext_grid are considered in OPF as +- 1000 TW.: ['min_q_kvar' 'max_q_kvar']\n",
      "hp.pandapower.run - INFO: These elements have missing power constraint values, which are considered in OPF as +- 1000 TW: ['gen']\n",
      "hp.pandapower.run - INFO: min_vm_pu is missing in bus table. In OPF these limits are considered as 0.0 pu.\n",
      "hp.pandapower.run - INFO: max_vm_pu is missing in bus table. In OPF these limits are considered as 2.0 pu.\n"
     ]
    }
   ],
   "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": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <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",
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       "      <th>i_lv_ka</th>\n",
       "      <th>loading_percent</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49953.864488</td>\n",
       "      <td>-2147.313884</td>\n",
       "      <td>-49833.813812</td>\n",
       "      <td>5167.453489</td>\n",
       "      <td>120.050676</td>\n",
       "      <td>3020.139605</td>\n",
       "      <td>0.131216</td>\n",
       "      <td>0.262153</td>\n",
       "      <td>49.999995</td>\n",
       "    </tr>\n",
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       "</table>\n",
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      ],
      "text/plain": [
       "        p_hv_kw    q_hv_kvar       p_lv_kw    q_lv_kvar       pl_kw  \\\n",
       "0  49953.864488 -2147.313884 -49833.813812  5167.453489  120.050676   \n",
       "\n",
       "       ql_kvar   i_hv_ka   i_lv_ka  loading_percent  \n",
       "0  3020.139605  0.131216  0.262153        49.999995  "
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_trafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And power generation is now split between the external grid and generator 1 (which is the second cheapest generation unit):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<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>-49953.864488</td>\n",
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      "text/plain": [
       "           p_kw       q_kvar\n",
       "0 -49953.864488  2147.313884"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <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>-0.005754</td>\n",
       "      <td>-2993.145845</td>\n",
       "      <td>-6.232829</td>\n",
       "      <td>0.985230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-93304.077572</td>\n",
       "      <td>-3453.343461</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     -0.005754 -2993.145845  -6.232829  0.985230\n",
       "1 -93304.077572 -3453.343461  -1.237884  1.025709"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_gen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This comes of course with an increase in dispatch costs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16191.876620556382"
      ]
     },
     "execution_count": 230,
     "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": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <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>19780.009515</td>\n",
       "      <td>-2479.435419</td>\n",
       "      <td>-19341.695290</td>\n",
       "      <td>1104.393239</td>\n",
       "      <td>438.314225</td>\n",
       "      <td>-1375.042180</td>\n",
       "      <td>0.104309</td>\n",
       "      <td>0.103207</td>\n",
       "      <td>0.104309</td>\n",
       "      <td>22.193320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-50658.298957</td>\n",
       "      <td>1888.752606</td>\n",
       "      <td>52783.697109</td>\n",
       "      <td>921.064101</td>\n",
       "      <td>2125.398152</td>\n",
       "      <td>2809.816707</td>\n",
       "      <td>0.270061</td>\n",
       "      <td>0.270140</td>\n",
       "      <td>0.270140</td>\n",
       "      <td>57.476548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>30520.380464</td>\n",
       "      <td>2532.279360</td>\n",
       "      <td>-29946.195703</td>\n",
       "      <td>-2688.018070</td>\n",
       "      <td>574.184761</td>\n",
       "      <td>-155.738710</td>\n",
       "      <td>0.156712</td>\n",
       "      <td>0.157323</td>\n",
       "      <td>0.157323</td>\n",
       "      <td>33.472994</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  19780.009515 -2479.435419 -19341.695290  1104.393239   438.314225   \n",
       "1 -50658.298957  1888.752606  52783.697109   921.064101  2125.398152   \n",
       "2  30520.380464  2532.279360 -29946.195703 -2688.018070   574.184761   \n",
       "\n",
       "       ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0 -1375.042180   0.104309  0.103207  0.104309        22.193320  \n",
       "1  2809.816707   0.270061  0.270140  0.270140        57.476548  \n",
       "2  -155.738710   0.156712  0.157323  0.157323        33.472994  "
      ]
     },
     "execution_count": 231,
     "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": 232,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.run - INFO: These missing columns in ext_grid are considered in OPF as +- 1000 TW.: ['min_q_kvar' 'max_q_kvar']\n",
      "hp.pandapower.run - INFO: These elements have missing power constraint values, which are considered in OPF as +- 1000 TW: ['gen']\n",
      "hp.pandapower.run - INFO: min_vm_pu is missing in bus table. In OPF these limits are considered as 0.0 pu.\n",
      "hp.pandapower.run - INFO: max_vm_pu is missing in bus table. In OPF these limits are considered as 2.0 pu.\n"
     ]
    },
    {
     "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": 233,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "  <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",
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       "      <th>0</th>\n",
       "      <td>16727.519781</td>\n",
       "      <td>-3194.974086</td>\n",
       "      <td>-16412.725022</td>\n",
       "      <td>1534.133994</td>\n",
       "      <td>314.794759</td>\n",
       "      <td>-1660.840092</td>\n",
       "      <td>0.088849</td>\n",
       "      <td>0.087130</td>\n",
       "      <td>0.088849</td>\n",
       "      <td>18.903945</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-44451.195382</td>\n",
       "      <td>868.876229</td>\n",
       "      <td>46059.937188</td>\n",
       "      <td>830.815836</td>\n",
       "      <td>1608.741806</td>\n",
       "      <td>1699.692065</td>\n",
       "      <td>0.234999</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>0.235000</td>\n",
       "      <td>49.999998</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27533.080431</td>\n",
       "      <td>4051.080417</td>\n",
       "      <td>-27060.140775</td>\n",
       "      <td>-4429.078165</td>\n",
       "      <td>472.939657</td>\n",
       "      <td>-377.997748</td>\n",
       "      <td>0.141964</td>\n",
       "      <td>0.143057</td>\n",
       "      <td>0.143057</td>\n",
       "      <td>30.437636</td>\n",
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       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "      p_from_kw  q_from_kvar       p_to_kw    q_to_kvar        pl_kw  \\\n",
       "0  16727.519781 -3194.974086 -16412.725022  1534.133994   314.794759   \n",
       "1 -44451.195382   868.876229  46059.937188   830.815836  1608.741806   \n",
       "2  27533.080431  4051.080417 -27060.140775 -4429.078165   472.939657   \n",
       "\n",
       "       ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0 -1660.840092   0.088849  0.087130  0.088849        18.903945  \n",
       "1  1699.692065   0.234999  0.235000  0.235000        49.999998  \n",
       "2  -377.997748   0.141964  0.143057  0.143057        30.437636  "
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "net.res_line"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all generators are involved in supplying the loads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
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       "          p_kw       q_kvar\n",
       "0 -49787.59354  4603.760721"
      ]
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     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "net.res_ext_grid"
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  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "      <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>-9136.079301</td>\n",
       "      <td>-2403.009062</td>\n",
       "      <td>-5.814954</td>\n",
       "      <td>0.992994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-83593.017290</td>\n",
       "      <td>-4881.895570</td>\n",
       "      <td>-1.511656</td>\n",
       "      <td>1.028899</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar  va_degree     vm_pu\n",
       "0  -9136.079301 -2403.009062  -5.814954  0.992994\n",
       "1 -83593.017290 -4881.895570  -1.511656  1.028899"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "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": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16380.333324014744"
      ]
     },
     "execution_count": 236,
     "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": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\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",
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       "      <td>-49787.593540</td>\n",
       "      <td>4603.760721</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>-2.642153e-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>130.952263</td>\n",
       "      <td>-5.410268e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.992994</td>\n",
       "      <td>-5.814954</td>\n",
       "      <td>60863.920699</td>\n",
       "      <td>-2403.009062</td>\n",
       "      <td>149.999973</td>\n",
       "      <td>1.192009e-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.028899</td>\n",
       "      <td>-1.511656</td>\n",
       "      <td>-73593.017290</td>\n",
       "      <td>-4881.895570</td>\n",
       "      <td>120.000014</td>\n",
       "      <td>2.988531e-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 -49787.593540  4603.760721  100.000000 -2.642153e-21\n",
       "1  1.006025  -3.408832  60000.000000     0.000000  130.952263 -5.410268e-01\n",
       "2  0.992994  -5.814954  60863.920699 -2403.009062  149.999973  1.192009e-21\n",
       "3  1.028899  -1.511656 -73593.017290 -4881.895570  120.000014  2.988531e-21"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and constrain it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "hp.pandapower.run - INFO: These missing columns in ext_grid are considered in OPF as +- 1000 TW.: ['min_q_kvar' 'max_q_kvar']\n",
      "hp.pandapower.run - INFO: These elements have missing power constraint values, which are considered in OPF as +- 1000 TW: ['gen']\n"
     ]
    }
   ],
   "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": 239,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\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>-49906.847219</td>\n",
       "      <td>3050.617054</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>-6.408104e-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>131.268596</td>\n",
       "      <td>-2.133663e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-5.976094</td>\n",
       "      <td>59278.204655</td>\n",
       "      <td>-14858.933373</td>\n",
       "      <td>149.999992</td>\n",
       "      <td>3.120534e-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.020000</td>\n",
       "      <td>-1.366892</td>\n",
       "      <td>-71863.491321</td>\n",
       "      <td>9172.691847</td>\n",
       "      <td>120.000005</td>\n",
       "      <td>-1.926105e-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 -49906.847219   3050.617054  100.000000 -6.408104e-22\n",
       "1  1.004168  -3.421015  60000.000000      0.000000  131.268596 -2.133663e-01\n",
       "2  1.000000  -5.976094  59278.204655 -14858.933373  149.999992  3.120534e-21\n",
       "3  1.020000  -1.366892 -71863.491321   9172.691847  120.000005 -1.926105e-21"
      ]
     },
     "execution_count": 239,
     "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": 240,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
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       "</style>\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>-49906.847219</td>\n",
       "      <td>3050.617054</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p_kw       q_kvar\n",
       "0 -49906.847219  3050.617054"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "  <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>-10721.795345</td>\n",
       "      <td>-14858.933373</td>\n",
       "      <td>-5.976094</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-81863.491321</td>\n",
       "      <td>9172.691847</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 -10721.795345 -14858.933373  -5.976094   1.00\n",
       "1 -81863.491321   9172.691847  -1.366892   1.02"
      ]
     },
     "execution_count": 241,
     "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": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16422.57298217286"
      ]
     },
     "execution_count": 242,
     "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": 243,
   "metadata": {},
   "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": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "<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",
       "    </tr>\n",
       "    <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": 244,
     "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": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\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>16715.233329</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-16715.233329</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</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>-44773.513351</td>\n",
       "      <td>0.0</td>\n",
       "      <td>44773.513351</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</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>26715.233363</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-26715.233363</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</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  16715.233329          0.0 -16715.233329        0.0    0.0      0.0   \n",
       "1 -44773.513351          0.0  44773.513351        0.0    0.0      0.0   \n",
       "2  26715.233363          0.0 -26715.233363        0.0    0.0      0.0   \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": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<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",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49999.999965</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</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  49999.999965        0.0 -49999.999965        0.0    0.0      0.0  0.131216   \n",
       "\n",
       "    i_lv_ka  loading_percent  \n",
       "0  0.262432             50.0  "
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_trafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As are generator limits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>None</td>\n",
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       "      <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",
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       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
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       "    <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",
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       "</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": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\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>-8511.253320</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>-81488.746715</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  -8511.253320     NaN  -5.708566    1.0\n",
       "1 -81488.746715     NaN  -1.362340    1.0"
      ]
     },
     "execution_count": 248,
     "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": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600298368"
      ]
     },
     "execution_count": 249,
     "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": 250,
   "metadata": {},
   "outputs": [
    {
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       "  <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": 250,
     "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": 251,
   "metadata": {},
   "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": 252,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Cost function must be defined for whole power range of the generator",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-252-5d2a2efd8ee4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \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;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;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;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;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;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;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;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;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;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;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;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\pandapower\\pandapower\\create.py\u001b[0m in \u001b[0;36mcreate_piecewise_linear_cost\u001b[1;34m(net, element, element_type, data_points, type, index)\u001b[0m\n\u001b[0;32m   2498\u001b[0m             if not (net[element_type].max_p_kw.at[element] <= max(p) and\n\u001b[0;32m   2499\u001b[0m                     net[element_type].min_p_kw.at[element] >= min(p)):\n\u001b[1;32m-> 2500\u001b[1;33m                 raise ValueError(\"Cost function must be defined for whole power range of the \"\n\u001b[0m\u001b[0;32m   2501\u001b[0m                                  \"generator\")\n\u001b[0;32m   2502\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[1;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([[-1 , 0.15] ,[0, 0]]))\n",
    "pp.create_piecewise_linear_cost(net, 1, \"gen\", np.array([[-1, 0.12], [0, 0]]))\n",
    "pp.create_piecewise_linear_cost(net, 0, \"ext_grid\", np.array([[-1, 0.1], [0, 0]]))"
   ]
  },
  {
   "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": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.0\n",
       "1    0.0\n",
       "Name: max_p_kw, dtype: float64"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen.max_p_kw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    -80000.0\n",
       "1   -100000.0\n",
       "Name: min_p_kw, dtype: float64"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.gen.min_p_kw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 255,
     "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": 256,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Cost function must be defined for whole power range of the generator",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-256-e06a56395857>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \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[1;32m~\\pandapower\\pandapower\\create.py\u001b[0m in \u001b[0;36mcreate_piecewise_linear_cost\u001b[1;34m(net, element, element_type, data_points, type, index)\u001b[0m\n\u001b[0;32m   2498\u001b[0m             if not (net[element_type].max_p_kw.at[element] <= max(p) and\n\u001b[0;32m   2499\u001b[0m                     net[element_type].min_p_kw.at[element] >= min(p)):\n\u001b[1;32m-> 2500\u001b[1;33m                 raise ValueError(\"Cost function must be defined for whole power range of the \"\n\u001b[0m\u001b[0;32m   2501\u001b[0m                                  \"generator\")\n\u001b[0;32m   2502\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[1;31mValueError\u001b[0m: Cost function must be defined for whole power range of the generator"
     ]
    }
   ],
   "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": 257,
   "metadata": {},
   "outputs": [],
   "source": [
    "net.ext_grid[\"max_p_kw\"] = 1e9\n",
    "net.ext_grid[\"min_p_kw\"] = -1e9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<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>min_p_kw</th>\n",
       "      <th>max_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",
       "      <td>0.0</td>\n",
       "      <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      min_p_kw      max_p_kw\n",
       "0  None    0    1.0        0.0        True -1.000000e+09  1.000000e+09"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.ext_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 259,
     "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": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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",
       "    </tr>\n",
       "    <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": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600298368"
      ]
     },
     "execution_count": 261,
     "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": 262,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp.rundcopp(net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16055.337600298368"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <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",
       "    </tr>\n",
       "    <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": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_bus"
   ]
  }
 ],
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