{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DC Line dispatch with pandapower OPF\n",
    "This is an introduction into the usage of the pandapower optimal power flow with dc lines.\n",
    "\n",
    "## Example Network\n",
    "\n",
    "We use the following four bus example network for this tutorial:\n",
    "\n",
    "<img src=\"pics/example_opf_dcline.png\" width=\"100%\">\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",
    "from numpy import array\n",
    "net = pp.create_empty_network()\n",
    "\n",
    "b1 = pp.create_bus(net, 380)\n",
    "b2 = pp.create_bus(net, 380)\n",
    "b3 = pp.create_bus(net, 380)\n",
    "b4 = pp.create_bus(net, 380)\n",
    "b5 = pp.create_bus(net, 380)\n",
    "\n",
    "l1 = pp.create_line(net, b1, b2, 30, \"490-AL1/64-ST1A 380.0\")\n",
    "l2 = pp.create_line(net, b3, b4, 20, \"490-AL1/64-ST1A 380.0\")\n",
    "l3 = pp.create_line(net, b4, b5, 20, \"490-AL1/64-ST1A 380.0\")\n",
    "\n",
    "dcl1 = pp.create_dcline(net, name=\"dc line\", from_bus=b2, to_bus=b3, p_kw=0.2e6, loss_percent=1.0, \n",
    "                  loss_kw=500, vm_from_pu=1.01, vm_to_pu=1.012, max_p_kw=1e6,\n",
    "                  in_service=True)\n",
    "\n",
    "eg1 = pp.create_ext_grid(net, b1, 1.02, max_p_kw=0.)\n",
    "eg2 = pp.create_ext_grid(net, b5, 1.02, max_p_kw=0.)\n",
    "\n",
    "l1 = pp.create_load(net, bus=b4, p_kw=800e3, controllable = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We now run a regular load flow to check out the DC line model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pp.runpp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The transmission power of the DC line is defined in the loadflow as given by the p_kw parameter, which was set to 0.2 GW:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>200000.0</td>\n",
       "      <td>152443.185449</td>\n",
       "      <td>-197500.0</td>\n",
       "      <td>74491.758943</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>1.01</td>\n",
       "      <td>-0.48595</td>\n",
       "      <td>1.012</td>\n",
       "      <td>-0.725627</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  vm_from_pu  \\\n",
       "0   200000.0  152443.185449 -197500.0  74491.758943  2500.0        1.01   \n",
       "\n",
       "   va_from_degree  vm_to_pu  va_to_degree  \n",
       "0        -0.48595     1.012     -0.725627  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The losses amount to 2500 kW, which are made up of 500 kW conversion loss and 200 MW * 0.01 = 2 MW transmission losses. The voltage setpoints defined at from and to bus are complied with. \n",
    "\n",
    "Now lets define costs for the external grids to run an OPF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
   "costeg0 = pp.create_polynomial_cost(net, 0, 'ext_grid', array([.1, 0]))\n",
   "costeg1 = pp.create_polynomial_cost(net, 1, 'ext_grid', array([.08, 0]))\n",
   "net.bus['max_vm_pu'] = 1.5\n",
   "net.line['max_loading_percent'] = 1000\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we defined lower costs for Ext Grid 2, it fully services the load:"
   ]
  },
  {
   "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>p_kw</th>\n",
       "      <th>q_kvar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-500.078353</td>\n",
       "      <td>7787.557732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-805091.476316</td>\n",
       "      <td>-628.307279</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            p_kw       q_kvar\n",
       "0    -500.078353  7787.557732\n",
       "1 -805091.476316  -628.307279"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the DC line does not transmit any power:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>500.075407</td>\n",
       "      <td>7787.456005</td>\n",
       "      <td>-0.07466</td>\n",
       "      <td>-627.126367</td>\n",
       "      <td>500.000747</td>\n",
       "      <td>1.019994</td>\n",
       "      <td>-0.001448</td>\n",
       "      <td>1.013925</td>\n",
       "      <td>-1.563437</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  vm_from_pu  \\\n",
       "0  500.075407  7787.456005 -0.07466 -627.126367  500.000747    1.019994   \n",
       "\n",
       "   va_from_degree  vm_to_pu  va_to_degree  \n",
       "0       -0.001448  1.013925     -1.563437  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we set the costs of the left grid to a lower value than the right grid and run the loadflow again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net.polynomial_cost.c.at[costeg0]= array([[0.08, 0]])\n",
    "net.polynomial_cost.c.at[costeg1]= array([[0.1, 0]])\n",
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the power now comes from the left ext_grid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-821525.358281</td>\n",
       "      <td>7787.558529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.054350</td>\n",
       "      <td>21048.592139</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            p_kw        q_kvar\n",
       "0 -821525.358281   7787.558529\n",
       "1      -0.054350  21048.592139"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And is transmitted over the DC line:"
   ]
  },
  {
   "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>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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>813573.88367</td>\n",
       "      <td>-26446.047364</td>\n",
       "      <td>-805023.647198</td>\n",
       "      <td>-21736.311963</td>\n",
       "      <td>8550.236472</td>\n",
       "      <td>1.011014</td>\n",
       "      <td>-2.39987</td>\n",
       "      <td>1.027504</td>\n",
       "      <td>1.522333</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  813573.88367 -26446.047364 -805023.647198 -21736.311963  8550.236472   \n",
       "\n",
       "   vm_from_pu  va_from_degree  vm_to_pu  va_to_degree  \n",
       "0    1.011014        -2.39987  1.027504      1.522333  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can however see that the lines on the left hand side are now overloaded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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>821525.358281</td>\n",
       "      <td>-7787.558529</td>\n",
       "      <td>-813573.883670</td>\n",
       "      <td>26446.047364</td>\n",
       "      <td>7951.474611</td>\n",
       "      <td>18658.488835</td>\n",
       "      <td>1.223760</td>\n",
       "      <td>1.223277</td>\n",
       "      <td>1.223760</td>\n",
       "      <td>127.474952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>805023.647198</td>\n",
       "      <td>21736.311963</td>\n",
       "      <td>-800001.920574</td>\n",
       "      <td>-10668.101730</td>\n",
       "      <td>5021.726624</td>\n",
       "      <td>11068.210233</td>\n",
       "      <td>1.190800</td>\n",
       "      <td>1.191114</td>\n",
       "      <td>1.191114</td>\n",
       "      <td>124.074383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.920574</td>\n",
       "      <td>10668.101730</td>\n",
       "      <td>0.054350</td>\n",
       "      <td>-21048.592139</td>\n",
       "      <td>1.974924</td>\n",
       "      <td>-10380.490409</td>\n",
       "      <td>0.015882</td>\n",
       "      <td>0.031353</td>\n",
       "      <td>0.031353</td>\n",
       "      <td>3.265934</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  821525.358281  -7787.558529 -813573.883670  26446.047364  7951.474611   \n",
       "1  805023.647198  21736.311963 -800001.920574 -10668.101730  5021.726624   \n",
       "2       1.920574  10668.101730       0.054350 -21048.592139     1.974924   \n",
       "\n",
       "        ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0  18658.488835   1.223760  1.223277  1.223760       127.474952  \n",
       "1  11068.210233   1.190800  1.191114  1.191114       124.074383  \n",
       "2 -10380.490409   0.015882  0.031353  0.031353         3.265934  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we set the maximum line loading to 100% and run the OPF again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net.line[\"max_loading_percent\"] = 100\n",
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the lines are no longer overloaded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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>644488.858958</td>\n",
       "      <td>-642.506854</td>\n",
       "      <td>-639594.566319</td>\n",
       "      <td>6169.959158</td>\n",
       "      <td>4894.292639</td>\n",
       "      <td>5527.452303</td>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.959878</td>\n",
       "      <td>0.960000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>632766.897378</td>\n",
       "      <td>10098.568594</td>\n",
       "      <td>-629647.068718</td>\n",
       "      <td>-7138.702673</td>\n",
       "      <td>3119.828660</td>\n",
       "      <td>2959.865921</td>\n",
       "      <td>0.938624</td>\n",
       "      <td>0.938836</td>\n",
       "      <td>0.938836</td>\n",
       "      <td>97.795376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-170352.931282</td>\n",
       "      <td>7138.702673</td>\n",
       "      <td>170582.491792</td>\n",
       "      <td>-16527.962212</td>\n",
       "      <td>229.560511</td>\n",
       "      <td>-9389.259539</td>\n",
       "      <td>0.254211</td>\n",
       "      <td>0.255281</td>\n",
       "      <td>0.255281</td>\n",
       "      <td>26.591809</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  644488.858958   -642.506854 -639594.566319   6169.959158  4894.292639   \n",
       "1  632766.897378  10098.568594 -629647.068718  -7138.702673  3119.828660   \n",
       "2 -170352.931282   7138.702673  170582.491792 -16527.962212   229.560511   \n",
       "\n",
       "       ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0  5527.452303   0.960000  0.959878  0.960000       100.000000  \n",
       "1  2959.865921   0.938624  0.938836  0.938836        97.795376  \n",
       "2 -9389.259539   0.254211  0.255281  0.255281        26.591809  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the load is serviced from both grids:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-644488.858782</td>\n",
       "      <td>642.506837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-170582.491792</td>\n",
       "      <td>16527.962212</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "            p_kw        q_kvar\n",
       "0 -644488.858782    642.506837\n",
       "1 -170582.491792  16527.962212"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the DC line transmits only part of the power needed to service the load:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>639594.566352</td>\n",
       "      <td>-6169.958242</td>\n",
       "      <td>-632766.897378</td>\n",
       "      <td>-10098.568594</td>\n",
       "      <td>6827.668974</td>\n",
       "      <td>1.012429</td>\n",
       "      <td>-1.875</td>\n",
       "      <td>1.024385</td>\n",
       "      <td>0.875621</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  639594.566352 -6169.958242 -632766.897378 -10098.568594  6827.668974   \n",
       "\n",
       "   vm_from_pu  va_from_degree  vm_to_pu  va_to_degree  \n",
       "0    1.012429          -1.875  1.024385      0.875621  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can also define transmission costs for the DC line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "costeg1 = pp.create_polynomial_cost(net, 0, 'dcline', array([.03, 0]))\n",
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the sum of the costs for generating power on the left hand side (0.08) and transmitting it to the right side (0.03) is now larger than for generating on the right side (0.1), the OPF draws as much power from the right side as is possible without violating line loading constraints:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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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>161370.351241</td>\n",
       "      <td>-7787.557137</td>\n",
       "      <td>-161063.552750</td>\n",
       "      <td>-6442.901692</td>\n",
       "      <td>306.798490</td>\n",
       "      <td>-14230.458829</td>\n",
       "      <td>0.240649</td>\n",
       "      <td>0.240554</td>\n",
       "      <td>0.240649</td>\n",
       "      <td>25.067628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>158973.810254</td>\n",
       "      <td>-4896.498618</td>\n",
       "      <td>-158773.820749</td>\n",
       "      <td>-4539.248232</td>\n",
       "      <td>199.989505</td>\n",
       "      <td>-9435.746850</td>\n",
       "      <td>0.237798</td>\n",
       "      <td>0.237781</td>\n",
       "      <td>0.237798</td>\n",
       "      <td>24.770574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-641226.170349</td>\n",
       "      <td>4539.247144</td>\n",
       "      <td>644488.776263</td>\n",
       "      <td>-880.672692</td>\n",
       "      <td>3262.605914</td>\n",
       "      <td>3658.574451</td>\n",
       "      <td>0.959936</td>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.960000</td>\n",
       "      <td>100.000031</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  161370.351241 -7787.557137 -161063.552750 -6442.901692   306.798490   \n",
       "1  158973.810254 -4896.498618 -158773.820749 -4539.248232   199.989505   \n",
       "2 -641226.170349  4539.247144  644488.776263  -880.672692  3262.605914   \n",
       "\n",
       "        ql_kvar  i_from_ka   i_to_ka      i_ka  loading_percent  \n",
       "0 -14230.458829   0.240649  0.240554  0.240649        25.067628  \n",
       "1  -9435.746850   0.237798  0.237781  0.237798        24.770574  \n",
       "2   3658.574451   0.959936  0.960000  0.960000       100.000031  "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>161063.55275</td>\n",
       "      <td>6442.901692</td>\n",
       "      <td>-158973.814604</td>\n",
       "      <td>4896.534963</td>\n",
       "      <td>2089.738146</td>\n",
       "      <td>1.018095</td>\n",
       "      <td>-0.467991</td>\n",
       "      <td>1.016202</td>\n",
       "      <td>-0.938725</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  161063.55275  6442.901692 -158973.814604  4896.534963  2089.738146   \n",
       "\n",
       "   vm_from_pu  va_from_degree  vm_to_pu  va_to_degree  \n",
       "0    1.018095       -0.467991  1.016202     -0.938725  "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we broaden the line loading constraint and run the OPF again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "net.line[\"max_loading_percent\"] = 1000\n",
    "pp.runopp(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The load is once again fully serviced by the grid on the right hand side:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-500.300942</td>\n",
       "      <td>7787.555581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-805091.253109</td>\n",
       "      <td>-628.302293</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            p_kw       q_kvar\n",
       "0    -500.300942  7787.555581\n",
       "1 -805091.253109  -628.302293"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_ext_grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the DC line is in open loop operation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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>vm_from_pu</th>\n",
       "      <th>va_from_degree</th>\n",
       "      <th>vm_to_pu</th>\n",
       "      <th>va_to_degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>500.297993</td>\n",
       "      <td>7787.458105</td>\n",
       "      <td>-0.295043</td>\n",
       "      <td>-627.119172</td>\n",
       "      <td>500.00295</td>\n",
       "      <td>1.019994</td>\n",
       "      <td>-0.001448</td>\n",
       "      <td>1.013925</td>\n",
       "      <td>-1.563436</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  vm_from_pu  \\\n",
       "0  500.297993  7787.458105 -0.295043 -627.119172  500.00295    1.019994   \n",
       "\n",
       "   va_from_degree  vm_to_pu  va_to_degree  \n",
       "0       -0.001448  1.013925     -1.563436  "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.res_dcline"
   ]
  }
 ],
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