{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two formulations of DCOPF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As suggested in [1], the PTDF formulation is mainly used for ISO/RTO market clearing.\n",
    "Thus, `DCOPF2` is developed using PTDF formulation for market clearing analysis.\n",
    "\n",
    "In this demo, we will compare it with the `DCOPF` using B-theta formulation.\n",
    "\n",
    "References:\n",
    "\n",
    "1. Y. Chen et al., \"Security-Constrained Unit Commitment for Electricity Market: Modeling, Solution Methods, and Future Challenges,\" in IEEE Transactions on Power Systems, vol. 38, no. 5, pp. 4668-4681, Sept. 2023, doi: 10.1109/TPWRS.2022.3213001."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "import ams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ams.config_logger(stream_level=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A small-size PJM 5-bus case with ESD1 is used in this example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing input file \"/Users/jinningwang/work/ams/ams/cases/5bus/pjm5bus_demo.xlsx\"...\n",
      "Input file parsed in 0.0720 seconds.\n",
      "Zero Line parameters detected, adjusted to default values: rate_b, rate_c.\n",
      "All bus type are PQ, adjusted given load and generator connection status.\n",
      "System set up in 0.0026 seconds.\n"
     ]
    }
   ],
   "source": [
    "sp = ams.load(ams.get_case('5bus/pjm5bus_demo.xlsx'),\n",
    "              setup=True,\n",
    "              no_output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "  Whether the dual values are available depends on the solver/method. If you find the dual values are not fully computed, please try other solvers/methods.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can solve the two routines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For `DCOPF2`, it is a good practice to build the PTDF matrix first.\n",
    "\n",
    "You can also load a calculated PTDF matrix from a file, but AMS\n",
    "do not check the consistency between the PTDF matrix and the network data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Building system matrices\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<7x5 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 28 stored elements in List of Lists format>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.mats.build_ptdf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing OModel for <DCOPF2>\n",
      "Evaluating OModel for <DCOPF2>\n",
      "Finalizing OModel for <DCOPF2>\n",
      "<DCOPF2> initialized in 0.0392 seconds.\n",
      "<DCOPF2> solved as optimal in 0.0192 seconds, converged in 7 iterations with CLARABEL.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF2.run(solver='CLARABEL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system energy price is calculated after solving the optimization, using `pie`, an ``ExpressionCalc`` object defined in the routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15705242184924276"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF2.pie.v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The congestion price is also calculated, using `pic`, another ``ExpressionCalc`` object defined in the routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.07942907, -0.14705242,  0.14294758,  0.        , -0.06534746])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF2.pic.v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we can also run the `DCOPF`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing OModel for <DCOPF>\n",
      "Evaluating OModel for <DCOPF>\n",
      "Finalizing OModel for <DCOPF>\n",
      "<DCOPF> initialized in 0.0123 seconds.\n",
      "<DCOPF> solved as optimal in 0.0206 seconds, converged in 8 iterations with CLARABEL.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.run(solver='CLARABEL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the Bus results and Line results as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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>idx</th>\n",
       "      <th>pi-2 [$/MW]</th>\n",
       "      <th>pi [$/MW]</th>\n",
       "      <th>aBus-2 [rad]</th>\n",
       "      <th>aBus [rad]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000776</td>\n",
       "      <td>0.000776</td>\n",
       "      <td>0.023989</td>\n",
       "      <td>0.023989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.034668</td>\n",
       "      <td>0.034668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.003000</td>\n",
       "      <td>0.003000</td>\n",
       "      <td>0.013068</td>\n",
       "      <td>0.013068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.001571</td>\n",
       "      <td>0.001571</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.000917</td>\n",
       "      <td>0.000917</td>\n",
       "      <td>0.022896</td>\n",
       "      <td>0.022896</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   idx  pi-2 [$/MW]  pi [$/MW]  aBus-2 [rad]  aBus [rad]\n",
       "0    0     0.000776   0.000776      0.023989    0.023989\n",
       "1    1     0.000100   0.000100      0.034668    0.034668\n",
       "2    2     0.003000   0.003000      0.013068    0.013068\n",
       "3    3     0.001571   0.001571      0.000000   -0.000000\n",
       "4    4     0.000917   0.000917      0.022896    0.022896"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resBus = pd.DataFrame()\n",
    "resBus['idx'] = sp.Bus.idx.v\n",
    "resBus['pi-2 [$/MW]'] = sp.DCOPF2.get(src='pi', idx=resBus['idx']) / sp.config.mva\n",
    "resBus['pi [$/MW]'] = sp.DCOPF.get(src='pi', idx=resBus['idx']) / sp.config.mva\n",
    "resBus['aBus-2 [rad]'] = sp.DCOPF2.get(src='aBus', idx=resBus['idx'])\n",
    "resBus['aBus [rad]'] = sp.DCOPF.get(src='aBus', idx=resBus['idx'])\n",
    "resBus.round(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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>idx</th>\n",
       "      <th>ul</th>\n",
       "      <th>rate_a [MW]</th>\n",
       "      <th>plf-2 [MW]</th>\n",
       "      <th>plf [MW]</th>\n",
       "      <th>mu1-2 [$/MW]</th>\n",
       "      <th>mu1 [$/MW]</th>\n",
       "      <th>mu2-2 [$/MW]</th>\n",
       "      <th>mu2 [$/MW]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Line_1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>-38.000806</td>\n",
       "      <td>-38.000806</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Line_2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>78.912154</td>\n",
       "      <td>78.912153</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Line_3</td>\n",
       "      <td>1.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>17.089459</td>\n",
       "      <td>17.089459</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Line_4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00342</td>\n",
       "      <td>0.00342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Line_5</td>\n",
       "      <td>1.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>43.998388</td>\n",
       "      <td>43.998388</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Line_6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>-77.089459</td>\n",
       "      <td>-77.089459</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Line_7</td>\n",
       "      <td>1.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>-38.000806</td>\n",
       "      <td>-38.000806</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      idx   ul  rate_a [MW]  plf-2 [MW]    plf [MW]  mu1-2 [$/MW]  mu1 [$/MW]  \\\n",
       "0  Line_1  1.0        400.0  -38.000806  -38.000806           0.0         0.0   \n",
       "1  Line_2  1.0        200.0   78.912154   78.912153           0.0         0.0   \n",
       "2  Line_3  1.0        200.0   17.089459   17.089459           0.0         0.0   \n",
       "3  Line_4  1.0        200.0  200.000000  200.000000           0.0         0.0   \n",
       "4  Line_5  1.0        200.0   43.998388   43.998388           0.0         0.0   \n",
       "5  Line_6  1.0        240.0  -77.089459  -77.089459           0.0         0.0   \n",
       "6  Line_7  1.0        400.0  -38.000806  -38.000806           0.0         0.0   \n",
       "\n",
       "   mu2-2 [$/MW]  mu2 [$/MW]  \n",
       "0       0.00000     0.00000  \n",
       "1       0.00000     0.00000  \n",
       "2       0.00000     0.00000  \n",
       "3       0.00342     0.00342  \n",
       "4       0.00000     0.00000  \n",
       "5       0.00000     0.00000  \n",
       "6       0.00000     0.00000  "
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resLine = pd.DataFrame()\n",
    "resLine['idx'] = sp.Line.idx.v\n",
    "resLine['ul'] = sp.DCOPF2.get(src='ul', idx=resLine['idx'])\n",
    "resLine['rate_a [MW]'] = sp.DCOPF2.get(src='rate_a', idx=resLine['idx']) * sp.config.mva\n",
    "resLine['plf-2 [MW]'] = sp.DCOPF2.get(src='plf', idx=resLine['idx']) * sp.config.mva\n",
    "resLine['plf [MW]'] = sp.DCOPF.get(src='plf', idx=resLine['idx']) * sp.config.mva\n",
    "resLine['mu1-2 [$/MW]'] = sp.DCOPF2.get(src='mu1', idx=resLine['idx']) / sp.config.mva\n",
    "resLine['mu1 [$/MW]'] = sp.DCOPF.get(src='mu1', idx=resLine['idx']) / sp.config.mva\n",
    "resLine['mu2-2 [$/MW]'] = sp.DCOPF2.get(src='mu2', idx=resLine['idx']) / sp.config.mva\n",
    "resLine['mu2 [$/MW]'] = sp.DCOPF.get(src='mu2', idx=resLine['idx']) / sp.config.mva\n",
    "resLine.round(8)"
   ]
  }
 ],
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