{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "f4rXez8ioy3l"
   },
   "source": [
    "<!--NOTEBOOK_HEADER-->\n",
    "*This notebook contains course material from [CBE40455](https://jckantor.github.io/CBE40455) by\n",
    "Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE40455.git).\n",
    "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n",
    "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XpVq9yGPoy3m"
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Jesuit Volunteer Corps](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/04.04-Jesuit-Volunteer-Corps.ipynb) | [Contents](toc.ipynb) | [Scheduling Multipurpose Batch Processes using State-Task Networks](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/04.06-Scheduling-Multipurpose-Batch-Processes-using-State-Task-Networks.ipynb) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455/blob/master/notebooks/04.05-Unit-Commitment.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://raw.githubusercontent.com/jckantor/CBE40455/master/notebooks/04.05-Unit-Commitment.ipynb\"><img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "eh0-fke71Hno"
   },
   "source": [
    "# Unit Commitment\n",
    "\n",
    "The production of electrical power to meet the demands of a regional power grid is among the most complex and important applications of mathematical optimization. A full treatment of the problem would consider the dispatch of mulitiple generating units and storage systems and the allocation of transportation resources to meet the projected demands of users.\n",
    "\n",
    "The scope of this notebook is an elementary introduction to the models used for unit commitment and closely follows [Unit Commitment](https://yalmip.github.io/example/unitcommitment/).  A more comprehensive discussion and implemenation can be found in the open source [Dispa-Set](http://www.dispaset.eu/en/latest/) package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SULnfFaYpXIQ"
   },
   "source": [
    "## Install Pyomo and Solvers for Google Colaboratory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4AAkdrrjrfdC"
   },
   "source": [
    "### Install and Import Pyomo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "owz_lt6S-uAH"
   },
   "outputs": [],
   "source": [
    "!pip install -q pyomo\n",
    "import pyomo.environ as pyo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "j7ABANpRpktv"
   },
   "source": [
    "### Install COIN-OR BONMIN and Create Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Vs8V6FbgdyK2"
   },
   "outputs": [],
   "source": [
    "!wget -N -q \"https://ampl.com/dl/open/bonmin/bonmin-linux64.zip\"\n",
    "!unzip -o -q bonmin-linux64\n",
    "bonmin = pyo.SolverFactory('bonmin', executable='/content/bonmin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "axFsSMlQp1qS"
   },
   "source": [
    "## Unit Specifications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 6631,
     "status": "ok",
     "timestamp": 1557426367466,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "b6Ur0rQC0_1q",
    "outputId": "51854313-74eb-490f-d7cf-932c9d90e6cd"
   },
   "outputs": [
    {
     "data": {
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guIwxdShetMgpsbJ+PTFn/oXE//7XSqyYkNLQfSoTgR7Av8U5SHsisBZIBOJF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\njPEbSyrGGGP8xpKKMcYYv/l/TszLMcoLwpgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "units = {\n",
    "    'A': {'Pmin': 20, 'Pmax': 100, 'Q': 0.04, 'C': 10, 'min_up':  6, 'min_down': 3},\n",
    "    'B': {'Pmin': 40, 'Pmax':  50, 'Q': 0.01, 'C': 20, 'min_up': 30, 'min_down': 6},\n",
    "    'C': {'Pmin':  1, 'Pmax':  25, 'Q': 0.02, 'C': 20, 'min_up':  1, 'min_down': 3},\n",
    "    'U': {'Pmin':  1, 'Pmax': 200, 'Q': 0.00, 'C': 60, 'min_up':  0, 'min_down': 0}\n",
    "}\n",
    "\n",
    "for key,unit in units.items():\n",
    "    P = np.linspace(unit['Pmin'], unit['Pmax'])\n",
    "    C = unit['Q']*P**2 + unit['C']*P\n",
    "    plt.plot(P, C, label=key)\n",
    "\n",
    "plt.title('individual unit characteristics')\n",
    "plt.xlabel('power / mw')\n",
    "plt.ylabel('cost / $/hr')\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 6857,
     "status": "ok",
     "timestamp": 1557426367702,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "v1CtCrb0xq1E",
    "outputId": "7d479c97-233d-4f46-c2b0-b25735c1be68"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7eff9ff2f630>"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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686G57bnI22zfMLdo+zNqxXxu5kNo/ZntLJdBM1soSanfx6MrCQCQjWwDfbukzanHmyU9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\nvf8yyqA6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(units).T\n",
    "df[['min_up','min_down']].plot(kind='bar', grid=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wDbFg8hy4O70"
   },
   "source": [
    "## Unit Commitment Model 1.  Constant Demand without Uptime or Downtime Constraints\n",
    "\n",
    "The model is created with a mutable parameter so that the model can be solved for multiple parameters without having to reconstruct the model from scratch for every value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "PUaZ7kYWGnDv"
   },
   "outputs": [],
   "source": [
    "def unit_commitment(units, Pforecast):\n",
    "    m = pyo.ConcreteModel()\n",
    "    \n",
    "    m.units = pyo.Set(initialize = units.keys())\n",
    "    m.P = pyo.Var(m.units, domain=pyo.NonNegativeReals)\n",
    "    m.x = pyo.Var(m.units, domain=pyo.Binary)\n",
    "\n",
    "    m.cost = pyo.Objective(expr=sum(units[k]['Q']*m.P[k]**2 + units[k]['C']*m.P[k] for k in m.units), sense=pyo.minimize)\n",
    "\n",
    "    m.a = pyo.Constraint(m.units, rule=lambda m, k: m.x[k]*units[k]['Pmin'] <= m.P[k])\n",
    "    m.b = pyo.Constraint(m.units, rule=lambda m, k: m.x[k]*units[k]['Pmax'] >= m.P[k])\n",
    "    m.c = pyo.Constraint(expr=sum([m.P[k] for k in m.units]) >= Pforecast)\n",
    "    \n",
    "    results = bonmin.solve(m)\n",
    "    return m\n",
    "  \n",
    "c = []\n",
    "P = []\n",
    "\n",
    "Pforecast = np.linspace(0, 175, 176)\n",
    "for p in Pforecast:\n",
    "  m = unit_commitment(units, p)\n",
    "  c.append(m.cost())\n",
    "  P.append([m.P[k]() for k in units.keys()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PoqKM3o6pgmE"
   },
   "source": [
    "### Cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 18112,
     "status": "ok",
     "timestamp": 1557426378978,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "bww8J5Qs8e9o",
    "outputId": "cc2c85e4-f8f1-4e72-d33c-6f974d3aa9ac"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V9W8AInKhqj4epozGmALk5Cr/nreFF7/eRK3K8PGoM+neok6kY5kyrqhDVfcD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\nHfeMMWFghcMncnOVWetTeWv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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Pforecast, c)\n",
    "plt.title('cost as function of total power')\n",
    "plt.xlabel('total power / mw')\n",
    "plt.ylabel('cost / $ per hr')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RhCKiKKZpkSj"
   },
   "source": [
    "### Unit Commitment Strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 18586,
     "status": "ok",
     "timestamp": 1557426379464,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "jdjLAcg-Ran3",
    "outputId": "d3f3efed-e2e1-47f7-9983-fab7e3cae58d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lJta3cmb2MlBnZh1m9n+B8cmW5dLioeTKUZwTLNeFC25nS/opsAQ/zaAqeCi5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\n51zZ+f8xmu27o+tOAQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "P = np.array(P)\n",
    "base = 0\n",
    "for k in range(len(P[0,:])):\n",
    "    ax.fill_between(Pforecast, base, base + P[:,k])\n",
    "    base += P[:,k]\n",
    "ax.set_title('unit commitment as function of total power')\n",
    "ax.set_xlabel('total power / mw')\n",
    "ax.set_ylabel('total power / mw')\n",
    "ax.legend(units.keys(), loc='upper left')\n",
    "ax.axis('equal')\n",
    "ax.axis('square')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LIBtve-6BqAC"
   },
   "source": [
    "## Unit Commitment Model 2. Variable Demand without Uptime or Downtime Constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 18851,
     "status": "ok",
     "timestamp": 1557426379742,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "VUYhhdwB1NiG",
    "outputId": "062e3b6e-853f-41f5-b2d7-98e91780e0c5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BEfFDSdVtu+qqLpF0CDAfOAJ4iezE97xa54+IJcASgN7e3qhUKo2UwbU3L+eqwfJ+kHzx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\nIMzMLNf/A5sjdUcaWZ1LAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "horizon = 48\n",
    "t = np.linspace(1, horizon, horizon)\n",
    "Pforecast = {t:100.0 + 50*np.sin(t*2*np.pi/24) for t in t}\n",
    "\n",
    "def poststep(x, y):\n",
    "  xstep = np.array([x[0]-(x[1]-x[0]), x[0]])\n",
    "  ystep = np.array([y[0], y[0]])\n",
    "  for k in range(1, len(x)):\n",
    "      xstep = np.append(xstep, [x[k-1], x[k]])\n",
    "      ystep = np.append(ystep, [y[k], y[k]])\n",
    "  return xstep, ystep\n",
    "\n",
    "fig, ax = plt.subplots(1,1)\n",
    "ts, ps = poststep(t, np.array([Pforecast[t] for t in t]))\n",
    "ax.fill_between(ts, 0, ps)\n",
    "ax.set_title('power forecast')\n",
    "ax.set_xlabel('hour')\n",
    "ax.set_ylabel('power')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-Yl1PKso2rwN"
   },
   "outputs": [],
   "source": [
    "def unit_commitment(units, horizon, Pforecast):\n",
    "    m = pyo.ConcreteModel()\n",
    "    m.t = pyo.RangeSet(1, horizon)\n",
    "    \n",
    "    m.units = pyo.Set(initialize = units.keys())\n",
    "    m.P = pyo.Var(m.units, m.t, domain=pyo.NonNegativeReals)\n",
    "    m.x = pyo.Var(m.units, m.t, domain=pyo.Binary)\n",
    "\n",
    "    m.cost = pyo.Objective(expr=sum(units[k]['Q']*m.P[k,t]**2 + units[k]['C']*m.P[k,t] for k in m.units for t in m.t), sense=pyo.minimize)\n",
    "\n",
    "    m.a = pyo.Constraint(m.units, m.t, rule=lambda m, k, t: m.x[k,t]*units[k]['Pmin'] <= m.P[k,t])\n",
    "    m.b = pyo.Constraint(m.units, m.t, rule=lambda m, k, t: m.x[k,t]*units[k]['Pmax'] >= m.P[k,t])\n",
    "    m.c = pyo.Constraint(m.t, rule=lambda m, t: sum([m.P[k,t] for k in m.units]) >= Pforecast[t])\n",
    "    \n",
    "    results = bonmin.solve(m)\n",
    "    return m\n",
    "\n",
    "m = unit_commitment(units, horizon, Pforecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WKwHYDrVyfLw"
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 26537,
     "status": "ok",
     "timestamp": 1557426387444,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "-XvJPS8N4qdp",
    "outputId": "8a6c84de-b9d7-4857-bce5-d7c0e486f5ca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GxPMR8QbQCUzPOKaKiogHgc19mqcD85LhecDpVQ2qSiJiXUQ8kQz/kdw/iwnU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\npXKBMDOzVP8f6i7O3JC9hlAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.array([t for t in m.t])\n",
    "P = {k:np.array([m.P[k,t]() for t in m.t]) for k in units.keys()}\n",
    "\n",
    "base = 0\n",
    "fig, ax = plt.subplots(1,1)\n",
    "for k in P.keys():\n",
    "  ts, ps = poststep(t, P[k])\n",
    "  ax.fill_between(ts, base, base + ps, label=k)\n",
    "  base += ps\n",
    "ax.legend()\n",
    "ax.set_title('power generation')\n",
    "ax.set_xlabel('hour')\n",
    "ax.set_ylabel('power')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LL8SzA6T77QV"
   },
   "source": [
    "## Unit Commitment Model 3. Variable Demand with Uptime and Downtime Constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "C5zaG28dt14e"
   },
   "outputs": [],
   "source": [
    "def unit_commitment(units, horizon, Pforecast):\n",
    "    m = pyo.ConcreteModel()\n",
    "    m.t = pyo.RangeSet(1, horizon)\n",
    "    \n",
    "    m.units = pyo.Set(initialize = units.keys())\n",
    "    m.P = pyo.Var(m.units, m.t, domain=pyo.NonNegativeReals)\n",
    "    m.x = pyo.Var(m.units, m.t, domain=pyo.Binary)\n",
    "    m.y = pyo.Var(m.units, m.t, domain=pyo.Binary)\n",
    "    m.z = pyo.Var(m.units, m.t, domain=pyo.Binary)\n",
    "\n",
    "    m.cost = pyo.Objective(expr=sum(units[k]['Q']*m.P[k,t]**2 + units[k]['C']*m.P[k,t] for k in m.units for t in m.t), sense=pyo.minimize)\n",
    "\n",
    "    m.a = pyo.Constraint(m.units, m.t, rule=lambda m, k, t: m.x[k,t]*units[k]['Pmin'] <= m.P[k,t])\n",
    "    m.b = pyo.Constraint(m.units, m.t, rule=lambda m, k, t: m.x[k,t]*units[k]['Pmax'] >= m.P[k,t])\n",
    "    m.c = pyo.Constraint(m.t, rule=lambda m, t: sum([m.P[k,t] for k in m.units]) >= Pforecast[t])\n",
    "    \n",
    "    def _d(m, k, t):\n",
    "        if t <= 1:\n",
    "            return pyo.Constraint.Skip\n",
    "        else:\n",
    "            return m.x[k,t] == m.x[k,t-1] + m.y[k,t] - m.z[k,t]\n",
    "    m.d = pyo.Constraint(m.units, m.t, rule=_d)\n",
    "    \n",
    "    def _e(m, k, t):\n",
    "        if units[k]['min_up'] == 0:\n",
    "            return pyo.Constraint.Skip\n",
    "        else:\n",
    "            return units[k]['min_up']*m.y[k,t] <= sum(m.x[k,s] for s in range(t, min(t+units[k]['min_up'], horizon)))\n",
    "    m.e = pyo.Constraint(m.units, m.t, rule=_e)\n",
    "    \n",
    "    def _f(m, k, t):\n",
    "        if units[k]['min_down'] == 0:\n",
    "            return pyo.Constraint.Skip\n",
    "        else:\n",
    "            return units[k]['min_down']*(1-m.z[k,t]) >= sum(m.x[k,s] for s in range(t, min(t+units[k]['min_down'], horizon)))\n",
    "    m.f = pyo.Constraint(m.units, m.t, rule=_f)\n",
    "    \n",
    "    results = bonmin.solve(m)\n",
    "    return m\n",
    "\n",
    "m = unit_commitment(units, horizon, Pforecast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 465140,
     "status": "ok",
     "timestamp": 1557426826062,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "522ur2fd7aaY",
    "outputId": "b22c9921-fcf1-4966-fb05-e4465ba24ac5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4QZiZWaqGTBCSpkl6RtJKSZdWOp5Sk3SzpPWSlmWV7S/pXknPJr/3q2SMpSJp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\nygnCzMxS/X+ZjOEBd9q9AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.array([t for t in m.t])\n",
    "P = {k:np.array([m.P[k,t]() for t in m.t]) for k in units.keys()}\n",
    "\n",
    "base = 0\n",
    "fig, ax = plt.subplots(1,1)\n",
    "for k in P.keys():\n",
    "    ts, ps = poststep(t, P[k])\n",
    "    ax.fill_between(ts, base, base + ps, label=k)\n",
    "    base += ps\n",
    "ax.legend()\n",
    "ax.set_title('power generation')\n",
    "ax.set_xlabel('hour')\n",
    "ax.set_ylabel('power')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 441
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 465879,
     "status": "ok",
     "timestamp": 1557426826809,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg",
      "userId": "09038942003589296665"
     },
     "user_tz": 240
    },
    "id": "wA7tCijD74bO",
    "outputId": "3571da02-7caa-443a-9963-eaae858d41ac"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oDs5D/pyD/DkH+as1Bz5FZWZmZoXjAsfMzMwKxwXOq83LOwBzDpqE85A/5yB/zkH+asqB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\nERGdkwInIiIiOicFTkRERHTO/0K7NpT94RLfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(len(P), 1, figsize=(8, 1.5*len(P)))\n",
    "keys = [k for k in P.keys()]\n",
    "\n",
    "for k in range(0, len(P)):\n",
    "    ts, ps = poststep(t, P[keys[k]])\n",
    "    ax[k].plot(ts, ps)\n",
    "    ax[k].set_title('power generation unit ' + str(keys[k]))\n",
    "    ax[k].grid()\n",
    "    \n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3iDYtaWvGJte"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jVl_koMgoy4X"
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Jesuit Volunteer Corps](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/04.04-Jesuit-Volunteer-Corps.ipynb) | [Contents](toc.ipynb) | [Scheduling Multipurpose Batch Processes using State-Task Networks](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/04.06-Scheduling-Multipurpose-Batch-Processes-using-State-Task-Networks.ipynb) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455/blob/master/notebooks/04.05-Unit-Commitment.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://raw.githubusercontent.com/jckantor/CBE40455/master/notebooks/04.05-Unit-Commitment.ipynb\"><img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "04.05-Unit-Commitment.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}