{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 5.3  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Integrated Energy Grids**\n",
    "\n",
    "**Problem 5.3**\n",
    "\n",
    "_Note: This is equivalent to Problem 2.2 which we solved using linopy, but here we will use PyPSA._\n",
    "\n",
    "**Consider the following economic dispatch problem:**\n",
    "\n",
    "**• we have three generators: solar, wind and gas**\n",
    "\n",
    "**• solar and wind have no marginal costs, and gas has fuel costs of 60 EUR/MWh.**\n",
    "\n",
    "**• we need to cover a electricity demand of 13.2 MWh**\n",
    "\n",
    "**• the installed capacities are 15 MW, 20 MW and 20 MW for wind, solar, and gas, respectively**\n",
    "\n",
    "**• assume the capacity factor for solar is 0.17 and for wind 0.33.**\n",
    "\n",
    "**Use PYPSA to find the optimal solution as well and obtain the electricity price (Lagrange multiplier for the energy balance constraint)**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "If you have not yet set up Python on your computer, you can execute this tutorial in your browser via [Google Colab](https://colab.research.google.com/). Click on the rocket in the top right corner and launch \"Colab\". If that doesn't work download the `.ipynb` file and import it in [Google Colab](https://colab.research.google.com/).\n",
    "\n",
    "Then install the following packages by executing the following command in a Jupyter cell at the top of the notebook.\n",
    "\n",
    "```sh\n",
    "!pip install numpy pypsa\n",
    "```\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pypsa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by creating the network object and adding the bus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "network = pypsa.Network()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>v_nom</th>\n",
       "      <th>type</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>carrier</th>\n",
       "      <th>unit</th>\n",
       "      <th>v_mag_pu_set</th>\n",
       "      <th>v_mag_pu_min</th>\n",
       "      <th>v_mag_pu_max</th>\n",
       "      <th>control</th>\n",
       "      <th>generator</th>\n",
       "      <th>sub_network</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bus</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>my bus</th>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>AC</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>inf</td>\n",
       "      <td>PQ</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        v_nom type    x    y carrier unit  v_mag_pu_set  v_mag_pu_min  \\\n",
       "Bus                                                                     \n",
       "my bus    1.0       0.0  0.0      AC                1.0           0.0   \n",
       "\n",
       "        v_mag_pu_max control generator sub_network  \n",
       "Bus                                                 \n",
       "my bus           inf      PQ                        "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.add(\"Bus\", \"my bus\") \n",
    "network.buses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add the generators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bus</th>\n",
       "      <th>control</th>\n",
       "      <th>type</th>\n",
       "      <th>p_nom</th>\n",
       "      <th>p_nom_mod</th>\n",
       "      <th>p_nom_extendable</th>\n",
       "      <th>p_nom_min</th>\n",
       "      <th>p_nom_max</th>\n",
       "      <th>p_min_pu</th>\n",
       "      <th>p_max_pu</th>\n",
       "      <th>...</th>\n",
       "      <th>min_up_time</th>\n",
       "      <th>min_down_time</th>\n",
       "      <th>up_time_before</th>\n",
       "      <th>down_time_before</th>\n",
       "      <th>ramp_limit_up</th>\n",
       "      <th>ramp_limit_down</th>\n",
       "      <th>ramp_limit_start_up</th>\n",
       "      <th>ramp_limit_shut_down</th>\n",
       "      <th>weight</th>\n",
       "      <th>p_nom_opt</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Generator</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>solar</th>\n",
       "      <td>my bus</td>\n",
       "      <td>PQ</td>\n",
       "      <td></td>\n",
       "      <td>15.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>0.0</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.17</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wind</th>\n",
       "      <td>my bus</td>\n",
       "      <td>PQ</td>\n",
       "      <td></td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>0.0</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.33</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>my bus</td>\n",
       "      <td>PQ</td>\n",
       "      <td></td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>0.0</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 37 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              bus control type  p_nom  p_nom_mod  p_nom_extendable  p_nom_min  \\\n",
       "Generator                                                                       \n",
       "solar      my bus      PQ        15.0        0.0             False        0.0   \n",
       "wind       my bus      PQ        20.0        0.0             False        0.0   \n",
       "gas        my bus      PQ        20.0        0.0             False        0.0   \n",
       "\n",
       "           p_nom_max  p_min_pu  p_max_pu  ...  min_up_time  min_down_time  \\\n",
       "Generator                                 ...                               \n",
       "solar            inf       0.0      0.17  ...            0              0   \n",
       "wind             inf       0.0      0.33  ...            0              0   \n",
       "gas              inf       0.0      1.00  ...            0              0   \n",
       "\n",
       "           up_time_before  down_time_before  ramp_limit_up ramp_limit_down  \\\n",
       "Generator                                                                    \n",
       "solar                   1                 0            NaN             NaN   \n",
       "wind                    1                 0            NaN             NaN   \n",
       "gas                     1                 0            NaN             NaN   \n",
       "\n",
       "           ramp_limit_start_up  ramp_limit_shut_down  weight  p_nom_opt  \n",
       "Generator                                                                \n",
       "solar                      1.0                   1.0     1.0        0.0  \n",
       "wind                       1.0                   1.0     1.0        0.0  \n",
       "gas                        1.0                   1.0     1.0        0.0  \n",
       "\n",
       "[3 rows x 37 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.add(\"Generator\", \n",
    "            \"solar\", \n",
    "            bus=\"my bus\", \n",
    "            p_nom=15, \n",
    "            p_max_pu=0.17, #capacity factor\n",
    "            marginal_cost=0) \n",
    "    \n",
    "network.add(\"Generator\", \n",
    "            \"wind\", \n",
    "            bus=\"my bus\", \n",
    "            p_nom=20, \n",
    "            p_max_pu=0.33, #capacity factor\n",
    "            marginal_cost=0) \n",
    "\n",
    "network.add(\"Generator\", \n",
    "            \"gas\", \n",
    "            bus=\"my bus\", \n",
    "            p_nom=20, \n",
    "            marginal_cost=60) #EUR/MWh_elec\n",
    "network.generators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add the load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>bus</th>\n",
       "      <th>carrier</th>\n",
       "      <th>type</th>\n",
       "      <th>p_set</th>\n",
       "      <th>q_set</th>\n",
       "      <th>sign</th>\n",
       "      <th>active</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Load</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>electricity demand</th>\n",
       "      <td>my bus</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>13.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bus carrier type  p_set  q_set  sign  active\n",
       "Load                                                               \n",
       "electricity demand  my bus                13.2    0.0  -1.0    True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.add(\"Load\", \n",
    "            \"electricity demand\", \n",
    "            bus=\"my bus\", \n",
    "            p_set=13.2)\n",
    "network.loads"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the optimal economic dispatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pypsa.consistency:The following buses have carriers which are not defined:\n",
      "Index(['my bus'], dtype='object', name='Bus')\n",
      "WARNING:pypsa.consistency:The following buses have carriers which are not defined:\n",
      "Index(['my bus'], dtype='object', name='Bus')\n",
      "INFO:linopy.model: Solve problem using Highs solver\n",
      "INFO:linopy.io: Writing time: 0.02s\n",
      "INFO:linopy.constants: Optimization successful: \n",
      "Status: ok\n",
      "Termination condition: optimal\n",
      "Solution: 3 primals, 7 duals\n",
      "Objective: 2.43e+02\n",
      "Solver model: available\n",
      "Solver message: optimal\n",
      "\n",
      "INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper were not assigned to the network.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "('ok', 'optimal')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can show the optimal dispatch and the electricity price (marginal cost at the bus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Generator</th>\n",
       "      <th>solar</th>\n",
       "      <th>wind</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>snapshot</th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>now</th>\n",
       "      <td>2.55</td>\n",
       "      <td>6.6</td>\n",
       "      <td>4.05</td>\n",
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      ],
      "text/plain": [
       "Generator  solar  wind   gas\n",
       "snapshot                    \n",
       "now         2.55   6.6  4.05"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.generators_t.p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Bus</th>\n",
       "      <th>my bus</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>snapshot</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>now</th>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Bus       my bus\n",
       "snapshot        \n",
       "now         60.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.buses_t.marginal_price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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