04_mpc_cvx.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!/usr/bin/env python3\n",
    "# coding: utf-8\n",
    "\n",
    "# Load dependencies\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import pandas as pd\n",
    "\n",
    "# Optimization\n",
    "import cvxpy as cp\n",
    "\n",
    "# For more information about cvxpy: https://www.cvxpy.org/examples/\n",
    "# Model fitting example: https://colab.research.google.com/github/cvxgrp/cvx_short_course/blob/master/applications/model_fitting.ipynb\n",
    "# Book on convex optimization: https://web.stanford.edu/~boyd/cvxbook/\n",
    "# Course on optimization: https://web.stanford.edu/class/ee364a/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load the data from the Varennes NetZEB Library\n",
    "Column descriptions:\n",
    "\n",
    "    # Temperatures\n",
    "    'T_ext': exterior temp, C\n",
    "    'T_int': average interior temp, C\n",
    "    'T_slab: slab temperature, 2 inch from surface, C\n",
    "    'T_room_air_over_slab': average room temperature over the slab where there is a radiant system, C\n",
    "    'T_room_air_no_slab': same but where there isn't, C\n",
    "\n",
    "    # BIPV/T System\n",
    "    'BIPVT_outletT': temperature at BIPV/T outlet, C\n",
    "    'BIPVT_dT': ^ minus T_ext, K\n",
    "    'BIPVT_heat: m*cp*dT = fanstate*rated_flow*density*cp*dT, kW\n",
    "\n",
    "    # Heating/Cooling\n",
    "    'geo_heat': m*cp*dT at the geothermal well inlet: how much heat are we rejecting/extracting into the ground, kW\n",
    "    'heating_total': m*cp*dT at the heat pump condensor/hot side, kW\n",
    "    'cooling_total': evaporator/cold side, kW\n",
    "    'Q_slab': heat going into the radiant slab, kW\n",
    "    'Q_rest_heating': heat going into the air, kW\n",
    "    'Q_rest': heat - cooling going into the air, kW\n",
    "    'heating_slab_ratio': heating going into slab over total, rest goes into the air\n",
    "    'cooling_slab_ratio': cooling going into slab over total, rest goes into the air\n",
    "\n",
    "    # Windows\n",
    "    'window_state: 0: closed, 1: open\n",
    "\n",
    "    # Solar\n",
    "    'DNI': direct normal irradiance, kW/m^2\n",
    "    'GHI': global horizontal irradiance, kW/m^2\n",
    "    'DHI': diffuse horizontal irradiance, kW/m^2\n",
    "    'solar_projected_PV': unitized solar radiation incident on PV system, kW/m^2\n",
    "\n",
    "    # Electrical\n",
    "    'cons': total electrical consumption power, kW\n",
    "    'prod: total electrical production power, kW\n",
    "    'cons_noHVAC': approximate electrical consumption without the HVAC (cons - heating_total/4 - cooling_total/3.5), kW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                       T_ext    T_int  BIPVT_outletT  BIPVT_dT  BIPVT_heat  \\\n",
      "Datetime                                                                     \n",
      "2018-01-01 00:00:00 -21.8566  18.4578       -18.6184    3.2382         0.0   \n",
      "2018-01-01 00:15:00 -21.8434  18.4086       -18.6614    3.1820         0.0   \n",
      "2018-01-01 00:30:00 -21.9561  18.3142       -18.6459    3.3102         0.0   \n",
      "2018-01-01 00:45:00 -22.0408  18.2528       -18.7473    3.2935         0.0   \n",
      "2018-01-01 01:00:00 -22.1299  18.1697       -18.6353    3.4946         0.0   \n",
      "\n",
      "                      geo_heat  heating_total  cooling_total  window_state  \\\n",
      "Datetime                                                                     \n",
      "2018-01-01 00:00:00 -54.118034      38.025668            0.0      0.335996   \n",
      "2018-01-01 00:15:00 -50.619191      26.322083            0.0      0.336057   \n",
      "2018-01-01 00:30:00  -9.066210      13.017722            0.0      0.336118   \n",
      "2018-01-01 00:45:00 -37.896533      10.618306            0.0      0.336180   \n",
      "2018-01-01 01:00:00 -34.623417      10.781639            0.0      0.336241   \n",
      "\n",
      "                     heating_slab_ratio  ...  prod  cons_noHVAC  \\\n",
      "Datetime                                 ...                      \n",
      "2018-01-01 00:00:00            0.199966  ...   0.0     1.740303   \n",
      "2018-01-01 00:15:00            0.282259  ...   0.0     6.494799   \n",
      "2018-01-01 00:30:00            0.293446  ...   0.0    13.072209   \n",
      "2018-01-01 00:45:00            0.281554  ...   0.0    13.261424   \n",
      "2018-01-01 01:00:00            0.268706  ...   0.0    14.546990   \n",
      "\n",
      "                     Q_slab_heating    Q_slab  Q_rest_heating     Q_rest  DNI  \\\n",
      "Datetime                                                                        \n",
      "2018-01-01 00:00:00     7603.853490  7.603853       30.421814  30.421814  0.0   \n",
      "2018-01-01 00:15:00     7429.656592  7.429657       18.892426  18.892426  0.0   \n",
      "2018-01-01 00:30:00     3819.993391  3.819993        9.197729   9.197729  0.0   \n",
      "2018-01-01 00:45:00     2989.624193  2.989624        7.628682   7.628682  0.0   \n",
      "2018-01-01 01:00:00     2897.089583  2.897090        7.884549   7.884549  0.0   \n",
      "\n",
      "                     GHI  DHI  solar_projected_PV  \n",
      "Datetime                                           \n",
      "2018-01-01 00:00:00  0.0  0.0                 0.0  \n",
      "2018-01-01 00:15:00  0.0  0.0                 0.0  \n",
      "2018-01-01 00:30:00  0.0  0.0                 0.0  \n",
      "2018-01-01 00:45:00  0.0  0.0                 0.0  \n",
      "2018-01-01 01:00:00  0.0  0.0                 0.0  \n",
      "\n",
      "[5 rows x 25 columns]\n"
     ]
    }
   ],
   "source": [
    "# Load data from csv file, assign index and assure it's a datetime object\n",
    "df_full = pd.read_csv(\"data_varennes_subset.csv.zip\", index_col=[0], parse_dates=[0])\n",
    "print(df_full.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approach\n",
    "This is an example for 1 iteration. In application, you would optimize for a window of time (called the prediction horizon), only apply the controls within a much smaller window of time (called the control horizon and it could be as small as a single timestep), and redo the optimization all over again. It's not particularly difficult to do that and CVXPY documentation does provide more thorough examples.\n",
    "\n",
    "I'm also assuming electricity is billed at a unit rate. If you want to use the actual $\\$/kWh$ amounts, you have to consider the step size.\n",
    "\n",
    "I demo two cases: (1) minimize the energy, and (2) minimize the power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2018-01-16: Tuesday\n",
    "df = df_full[\"2018-01-17 0:00\":\"2018-01-17 12:00\"].copy()\n",
    "\n",
    "# Define our dependent/independent variables\n",
    "X_cols = [\"T_int\"]  # state_columns\n",
    "U_cols = [\"heating_total\"]  # control_columns\n",
    "W_cols = [\"T_ext\", \"GHI\"]  # exogenous_columns\n",
    "\n",
    "# TEST\n",
    "X = df[X_cols].values\n",
    "U = df[U_cols].iloc[:-1].values\n",
    "W = df[W_cols].iloc[:-1].values\n",
    "\n",
    "X_initial = X[0, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Business hours\n",
    "df[\"is_occupied\"] = (9. <= df.index.hour) & (df.index.hour < 18)\n",
    "\n",
    "# Setpoints when occupied/unoccupied\n",
    "heating_SP_unoccupied = 18.\n",
    "heating_SP_occupied = 21.\n",
    "df[\"heating_SP\"] = heating_SP_unoccupied\n",
    "# Update for occupied setpoint\n",
    "df.loc[df[\"is_occupied\"], \"heating_SP\"] = heating_SP_occupied\n",
    "\n",
    "# Equipment size, puting it in the dataframe since this is more flexible \n",
    "# if you want to have a different capacity depending on the time of day\n",
    "df[\"heating_power_min\"] = 0.  # kW\n",
    "df[\"heating_power_max\"] = 100.  # kW\n",
    "\n",
    "\n",
    "# df -> numpy\n",
    "heating_SP = df[\"heating_SP\"].values[:,np.newaxis]  # add new axis otherwise pandas is lazy and drops the extra dimension\n",
    "heating_power_min = df[\"heating_power_min\"].values[:-1,np.newaxis]\n",
    "heating_power_max = df[\"heating_power_max\"].values[:-1,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_ABC_model_5(params):\n",
    "    # Place parameters in A, B, C matrices\n",
    "    A = np.array([[1 - params[\"alpha\"]]])\n",
    "    B = np.array([[params[\"beta\"]]])\n",
    "    C = np.array([[params[\"alpha\"], params[\"gamma\"]]])\n",
    "    return A, B, C\n",
    "\n",
    "\n",
    "def run_mpc_step(\n",
    "    params, \n",
    "    X_initial, \n",
    "    U, \n",
    "    W,\n",
    "    build_ABC, \n",
    "    heating_SP, \n",
    "    heating_power_min, \n",
    "    heating_power_max,\n",
    "    objective_fn = 'energy'\n",
    "):\n",
    "    \"\"\" Run an MPC step. \"\"\"\n",
    "    # Build A, B, C matrices and get their dimensions\n",
    "    A, B, C = build_ABC(params)\n",
    "    nN, nM, nL = A.shape[1], B.shape[1], C.shape[1]\n",
    "\n",
    "    # Prediction horizon, assume same length as U\n",
    "    ph = len(U)\n",
    "\n",
    "    # Declare Variables\n",
    "    x = cp.Variable((ph+1, nN))\n",
    "    u = cp.Variable((ph, nM))\n",
    "    # we have no control over W, for the MPC run, it's a constant\n",
    "\n",
    "\n",
    "    # Constraints to be accumulated\n",
    "    constraints = []\n",
    "\n",
    "    # Initial Condition\n",
    "    constraints.append(x[0,] == X_initial)\n",
    "\n",
    "    # Dynamics\n",
    "    for t in range(ph): \n",
    "        constraints.append(x[t+1,] == A @ x[t,].T + B @ u[t,].T + C @ W[t,].T,)\n",
    "\n",
    "    # Comfort\n",
    "    constraints.append(x >= heating_SP)  # NOTE: these are vectors\n",
    "\n",
    "    # Constraint size of equipment\n",
    "    constraints.append(u >= heating_power_min)  # NOTE: these are vectors\n",
    "    constraints.append(u <= heating_power_max)  # NOTE: these are vectors\n",
    "\n",
    "\n",
    "    # Objective function\n",
    "    if objective_fn == 'energy':\n",
    "        # Option 1: minimize sum of energy (didn't put the timestep since it has no effect on the optimal solution)\n",
    "        objective = cp.Minimize(cp.sum(u))\n",
    "    elif objective_fn == 'power':\n",
    "        # Option 2: minimize peak use of energy using a norm-2 loss\n",
    "        objective = cp.Minimize(cp.norm2(u))\n",
    "    else:\n",
    "        # Unknown objective!\n",
    "        raise NotImplementedError(\"Either select `energy` or `power` for the objective function!\")\n",
    "\n",
    "    # Solve\n",
    "    problem = cp.Problem(objective, constraints)\n",
    "    problem.solve(solver=cp.ECOS, verbose=True)\n",
    "\n",
    "    return problem, x, u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters from previous notebook\n",
    "params = {\n",
    "    \"alpha\": 0.00053596,\n",
    "    \"beta\": 0.0012117,  # had to modify beta a bit :S\n",
    "    # \"beta\": 0.00012117,\n",
    "    \"gamma\": 0.30312252\n",
    "}\n",
    "\n",
    "# Additional information needed to describe the problem\n",
    "mpc_kwargs = {\n",
    "    \"X_initial\": X_initial,\n",
    "    \"U\": U,\n",
    "    \"W\": W,\n",
    "    \"build_ABC\": build_ABC_model_5,  # pass the ABC generator\n",
    "    \"heating_SP\": heating_SP,\n",
    "    \"heating_power_min\": heating_power_min,\n",
    "    \"heating_power_max\": heating_power_max,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Minimize Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ECOS 2.0.7 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS\n",
      "\n",
      "It     pcost       dcost      gap   pres   dres    k/t    mu     step   sigma     IR    |   BT\n",
      " 0  +2.399e+03  -3.420e+03  +7e+03  8e-05  4e-01  1e+00  5e+01    ---    ---    1  1  - |  -  - \n",
      " 1  +1.881e+03  -1.940e+03  +5e+03  5e-05  3e-02  1e+00  3e+01  0.3557  4e-02   1  0  0 |  0  0\n",
      " 2  +1.990e+03  -1.835e+03  +5e+03  5e-05  6e-03  2e+00  3e+01  0.0067  1e+00   1  0  1 |  0  0\n",
      " 3  +1.784e+03  +2.998e+02  +2e+03  2e-05  4e-04  9e+00  1e+01  0.8889  3e-01   1  0  0 |  0  0\n",
      " 4  +1.429e+03  +1.360e+03  +9e+01  9e-07  2e-05  4e-01  6e-01  0.9564  3e-03   1  0  0 |  0  0\n",
      " 5  +1.422e+03  +1.377e+03  +6e+01  6e-07  1e-05  3e-01  4e-01  0.4007  1e-01   1  0  0 |  0  0\n",
      " 6  +1.413e+03  +1.398e+03  +2e+01  2e-07  5e-06  1e-01  1e-01  0.7005  7e-02   1  0  0 |  0  0\n",
      " 7  +1.410e+03  +1.406e+03  +5e+00  5e-08  1e-06  3e-02  4e-02  0.7543  2e-02   1  0  0 |  0  0\n",
      " 8  +1.409e+03  +1.407e+03  +2e+00  2e-08  4e-07  1e-02  1e-02  0.6719  5e-02   1  0  0 |  0  0\n",
      " 9  +1.409e+03  +1.408e+03  +6e-01  5e-09  1e-07  3e-03  4e-03  0.7214  4e-02   1  0  0 |  0  0\n",
      "10  +1.408e+03  +1.408e+03  +4e-02  4e-10  9e-09  2e-04  2e-04  0.9474  1e-02   1  0  0 |  0  0\n",
      "11  +1.408e+03  +1.408e+03  +8e-04  2e-11  2e-10  5e-06  6e-06  0.9780  1e-03   1  0  0 |  0  0\n",
      "12  +1.408e+03  +1.408e+03  +9e-06  5e-13  2e-12  5e-08  6e-08  0.9890  1e-04   1  0  0 |  0  0\n",
      "\n",
      "OPTIMAL (within feastol=2.3e-12, reltol=6.6e-09, abstol=9.2e-06).\n",
      "Runtime: 0.002261 seconds.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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3VWX//v0kJyfnfW3ZsoXk5GS2bt3K8ePHATj33HO55JJL6N27N71796ZFixb2dKGMBCxhqOoeYI/z/piIbAISVHUJFD0y2dEV2KqqPzn7vgdcAZQ4YRhjKpakpCQ+fP99Er79L8eOHfN+pR0j7Vga36SlkZSRTvWwMK6Oq03z2nF0q1OX+P79adyoMS1HjKDZwAHkHDrE4Q8+gOXLObB8ed65Y3r3JrpNG7L37uXI3LmFrl1jwACimjcnKyWFowsXFiqPHTqUyMaNyfz5Z44tXVqovObllxNxzjlkbNlC2sqVhcprjRhBlfh40n/4geNffFGoPG7UKMJjY0lPSuL4mjWFymv/4Q+EVa3KiTVrOJGUdOq8V11Flbi4or+pZaRc2jBEpBlwAVD0QhAFJQC78n1OAXxO1CIi44HxQKWe9MuYUPDdd9/Ru3dvwtPT+aJFy1MFkVEQH8XWYcMIHz2KljVrcfKGG7xlBw96v7YkE9vd+2viZGoq+//+YqHzV6ldm+g2bcjZs8dneWTjxt6EsWOHz/Lotm29CWPrVp/l1bp08SaMjRt9lsdcfLE3YSQl+SyPHTqU8NhYjn+zhv0vFi6v9bvfEVa1Kmn/+ZwDr516SFNjwIBySRgBH7gnIjHASuBpVZ2Tb/sK4D5fbRhOO8cQVb3R+Xwt3vaOO4q7lq+Be8aYimHnzp306NGDxuHhvP/BbBp16lhoHwkPRyIiUI8H9bGujFSpglSpUvryiAgkPBw9eRLNzi59eU4O6mPuNomMRMLCzlyenY2ePFm4PCoKESlUnntcaQTNwD0RiQBmA9PzJws/pACN831uBJR+GTpjTFA7dOgQw4YN4/jx40zp3Qcm/YuwKVOK3F/CwpBievOddXl4OFLMOIwzljuJqdTlERFIRESpywMlYJMPireR4g1gk6oWrlsVbw3QSkTOFZFIYDRQ+IGjMabCy8zM5MorryQ5OZkPP/yQ6PBwJMq6dgejQM5W2wu4FugvIknO1yUicqWIpAA9gE9EZBGAiDQUkQUAqpoD3A4sAjYB76vqDwGM1RjjAo/Hw7hx41i5ciVTp06lX79+aHo6YVUtYQSjQPaS+g9QVFeoD33svxu4JN/nBcCCwERnjAkGDzzwAO+99x7PPvssV199NQCejAwk2gbTBSNbD8MY44pXXnmF559/nttuu437778/b7tmZBBmsw0EpUo/NYgxJvjMmDGDu+66iyuuuIKJEycWGJd1zmMTiLDR2EHJEoYxplzNmzePa6+9lt69ezNjxoxCs8LGDhvmUmTmTOyRlDGm3CxfvpyRI0dy4YUXMnfu3EIT/2lODse//obsvftcitAUxxKGMaZcfP311wwfPpyWLVuycOFCYmNjC+1z8tgxdo4dy7HFi12I0JyJJQxjTMBt2LCBYcOGUa9ePZYsWUJ8fLzP/TQjA8C61QYpSxjGmIDaunUrgwYNolq1aixdupQGDRoUua8n3ZswrFttcLJGb2NMwKSkpDBw4ECys7NZtmzZGZca0EynhhEdVR7hmRKyhGGMCYg9e/bQv39/Dh06xLJly2jXrt0Zj7EaRnCzhGGMKXN79+6lf//+7Nmzh8WLF9OlSxe/jos8txmN/vkq0e3PnFxM+bOEYYwpU6mpqQwcOJCdO3eycOFCevTo4fexVeLiqDFgQACjM2fDGr2NMWXm4MGDDBo0iK1btzJv3jx69+5douOz9+zh2IoVeE6cCFCE5mxYwjDGlIkjR44wZMgQNm7cyEcffUT//v1LfI7jX3xBys23cPLQoQBEaM6WPZIyxpy1Y8eOMXToUL777jvmzJnDkCFDSnUejzMOQ6pao3cwsoRhjDkrR48e5ZJLLmHNmjXMmjWLyy67rNTnyhu4F2XdaoORJQxjTKkdPnyYYcOGsWbNGmbMmMGVV155Vuc71a3WRnoHI0sYxphSOXjwIEOGDOG7775j1qxZZ50sADQjHYmMLHa9bOMeSxjGmBJLTU1l0KBBbNy4kTlz5pzVY6j8ao0aRfWLS9azypQfSxjGmBLZt28fAwYMYOvWrcydO7fUDdy+RDZuTGTjxmV2PlO2AtatVkQai8hyEdkkIj+IyF3O9toiskREkp3XuCKOPykiSc7X3EDFaYzx3549e+jbty/btm1j/vz5ZZosAE6sWUPaypVlek5TdgJZw8gB7lXVb0WkBrBORJYA44DPVPUZEXkAeAD4i4/j01W1cwDjM8aUwK5duxg4cCC//PILCxcupE+fPmV+jQPTppG9cxcxATi3OXsBq2Go6h5V/dZ5fwzYBCQAVwDTnN2mAb8NVAzGmLKxdetWLr74Yn799VcWLVoUkGQBoOkZiK2FEbTKZaS3iDQDLgC+Buqr6h7wJhWgXhGHRYvIWhH5SkSKTCoiMt7Zb+3+/fvLOHJjzIYNG7j44otJS0tj2bJl9OrVK2DX8mRkEGYz1QatgCcMEYkBZgN3q+rREhzaRFUTgauBf4hIC187qepkVU1U1cS6deuWQcTGmFxr166lT58+iAgrV670e9bZ0tKMDMJsDEbQCmjCEJEIvMliuqrOcTbvFZEGTnkDwOdq76q623n9CViBt4ZijCknq1evpn///sTGxrJ69WrOO++8gF/Tk5Fhg/aCWCB7SQnwBrBJVV/MVzQXGOu8Hwt87OPYOBGJct7XAXoBGwMVqzGmoEWLFjFkyBAaNmzI6tWradHCZwW/zDV6eSL17vlTuVzLlFwgaxi9gGuB/vm6x14CPAMMEpFkYJDzGRFJFJF/O8e2A9aKyHfAcuAZVbWEYUw5mD17NpdffjmtW7dm1apVNGrUqNyuHdWiBZFNm5bb9UzJBKxbrar+B5AiigutkKKqa4EbnfdfAB0DFZsxxrfXX3+dm2++mW7duvHJJ58QF+dzmFTAHHpvJtHt21G1U6dyva7xj62HYYxBVXnmmWcYP348gwcPZsmSJeWeLFSVX594gmPLl5frdY3/LGEYE+I8Hg/33XcfDz74IGPGjOHjjz+mevXq5R6HZmeDx2PdaoOYzSVlTAjLycnhxhtvZNq0adx+++1MnDiRsDB3/o7U9HQAwqJtLYxgZTUMY0JUeno6v/vd75g2bRqPP/44L7/8smvJAvKttmc1jKDlVw1DRJoCrVR1qYhUBao4030YYyqgw4cPc8UVV7B69Wr++c9/cuutt7od0qnV9mxqkKB1xoQhIjcB44HaQAugETAJHz2djDHB79dff2Xo0KFs3LiR6dOnM2bMGLdDAiCiYUNaLF5EeO3abodiiuBPDeM2oCveeaBQ1WQRKWr+J2NMENu2bRuDBw9m7969zJ8/n8GDB7sdUh6JiCCySRO3wzDF8OeBZaaqZuV+EJEqgAYuJGNMICQlJdGrVy+OHDnCZ599FlTJAiArJYXU118ne+9et0MxRfAnYawUkYeAqiIyCJgFzAtsWMaYsrRy5Ur69OlDZGQkq1evplu3bm6HVEjm1q3s//uL5FjCCFr+JIy/APuB9cAfgQXAI4EMyhhTdj766COGDBlCQkICn3/+Oe3atXM7JJ80r5eUNXoHq2LbMEQkDPheVTsAr5dPSMaYsvLGG28wfvx4LrroIj755BPi4+PdDqlInvTcXlLWrTZYFVvDUFUP8J2IWEuUMRVI7lQfN954I4MGDeKzzz4L6mQBoJlOwrAaRtDyp5dUA+AHEfkGOJ67UVWHBywqY0yp5U718dJLL3H11Vfz5ptvEhkZ6XZYZ5Rbw7BHUsHLn4Tx14BHYYwpE9nZ2Vx//fW888473Hnnnbz00kuujt4uibirx1Dz8ssIc2EeK+OfMyYMVV1ZHoEYY87OiRMnGDlyJAsWLODpp5/mwQcfxLuOWcUQFhVFWJTNIxXM/BnpfYxT4y4igQjguKrGBjIwY4z/Dh48yOWXX85XX33F5MmTuemmm9wOqcSOLVtG5pZk6tz8R7dDMUXwp4ZRI/9nEfkt3pHfxpgg8MsvvzBkyBCSk5OZNWsWI0aMcDukUklbsZJjy5dZwghiJX64qaofAf0DEIsxpoQ2b95Mz5492blzJ59++mmFTRYAnox0WwsjyPnzSCr/T2AYkIhNDWKM69auXcuwYcMQEVasWMGFF17odkhnRTMybS2MIOdPDePyfF9DgGPAFWc6SEQai8hyEdkkIj+IyF3O9toiskREkp1Xn+tAishYZ59kERnr/y0ZU/ktXbqUfv36ERMTw+eff17hkwV4axi2FkZw86db7b9V9fP8G0SkF7DvDMflAPeq6rciUgNYJyJLgHHAZ6r6jIg8ADyAd/qR/OevDTzGqdrMOhGZq6qH/LkpYyqzWbNm8Yc//IE2bdrw6aef0rBhQ7dDKhOanmGD9oKcPzWMV/zcVoCq7lHVb533x4BNQALe2sk0Z7dpwG99HD4EWKKqB50ksQQY6kesxlRqkyZNYtSoUXTt2pVVq1ZVmmQB0GTqmzR+fbLbYZhiFFnDEJEeQE+grojck68oFggvyUVEpBlwAd41Neqr6h7wJpUi1tZIAHbl+5zibPN17vF4F3iiic2lbyopVeXJJ5/kscce47LLLmPmzJlUq1bN7bDKlISHI+El+tViyllxNYxIIAZvUqmR7+socJW/FxCRGGA2cLeqHvX3MB/bfDa0q+pkVU1U1cS6dev6G5YxFYbH4+GOO+7gscceY+zYscyZM6fSJQuAfRMncmTefLfDMMUosobhjPBeKSJTVXVHaU4uIhF4k8V0VZ3jbN4rIg2c2kUDfLeFpAB9831uBKwoTQzGVGRZWVlcd911zJw5k/vuu4/nnnuuQo3eLonDH3xAjX79qXn5ZW6HYorgT6P3CRF5HjgPyGuRUtVix2KI96f6DWCTqr6Yr2guMBZ4xnn92Mfhi4D/zdeDajDwoB+xGlNppKWlMWLECJYsWcJzzz3H/fff73ZIAaXpGYh1qw1q/jR6Twd+BM7FOxHhdmCNH8f1Aq4F+otIkvN1Cd5EMUhEkoFBzmdEJFFE/g2gqgeBJ53rrAGecLYZExJSU1Pp378/y5YtY8qUKZU+WQB4MjJs4F6Q86eGEa+qb4jIXfkeU51xQkJV/Q++2yIABvjYfy1wY77PU4ApfsRnTKWyc+dOBg8ezI4dO5gzZw7Dh1f+lQQ0Oxtycgirat1qg5k/CSPbed0jIpcCu/G2KRhjytjGjRsZPHgwaWlpLFq0iN69e7sdUrnwZGYhUVE2cC/I+ZMwnhKRmsC9eMdfxAJ/CmhUxoSgL7/8kksvvZSoqChWrlzJ+eef73ZI5SY8pjptv0tyOwxzBmda0zscaKWq84EjQL9yiaqcPfjgg9SpU4c2bdrQtm1bmjVrRpUq/uRSY8rGwoULueqqq2jYsCGLFi2iefPmbodkTCHF/lZU1ZMiMhx4qZziKXc5OTm8+eab7N27N29bREQELVu2pG3btrRp06bAV+3atV2M1lRG06dPZ9y4cXTs2JGFCxdSv359t0Mqd9m7d7PvH/+g9rXXUbVjB7fDMUXw58/oL0TkVWAmBdf0/jZgUZWjKlWq8Ouvv3LgwAE2b97M5s2b+fHHH9m8eTObNm1i3rx55OTk5O2fWxNp06YNrVu3zntt0aIFUbZamCmhiRMncvfdd9OvXz8++ugjYmNDc12ynAMHODp3HrHDhrkdiimGPwmjp/P6RL5tSiVbEyM+Pp6ePXvSs2fPAtuzs7PZvn17XjLZvHkzW7ZsYcGCBUyZcqoTV1hYGM2aNctLIPm/GjVqVGHWVTblQ1V59NFHefrppxkxYgTTp08nOoQn3vOkpwMQVtUavYOZPyvuVcp2C39FRETQqlUrWrVqxWWXFRyBeuTIEZKTkwskks2bN7Ny5UpOnDiRt190dDStWrUqlEhat25NfHx8pR25a3w7efIkt9xyC6+//jo33XQT//rXvwgP8TmUNDMTwGarDXL+LKBUH/hfoKGqDhOR9kAPVX0j4NEFuZo1a5KYmEhiYmKB7arK7t272bJlS4Gv77//no8//rjAI664uDifyaRVq1bExMSU9y2ZAMvIyOCaa65hzpw5PPLIIzzxxBP2BwOnahhiCSOo+fNIairwJvCw83kL3vaMkE8YRREREhISSEhIoF+/ghW03EdcycnJeYkktxKdIi8AABlDSURBVFbyzjvvFNi3QYMGBRJI7qu1l1RMR48e5YorrmDFihVMnDiRO++80+2Qgkp4rVr2SCrIiWrxq62KyBpVvUhE/quqFzjbklS1c7lEWAKJiYm6du1at8MotRMnTrBt2za2bNmS96grOTmZ5ORk9u07NUdjWFgYTZo0KZRMWrduTdOmTUP+8UYw2rt3L8OGDWP9+vVMmzaNq6++2u2QjAFARNapauKZ9/SvhnFcROJxphcXke54x2SYMlatWjU6duxIx44dC5UdPnw4L3nk1kqSk5OZNm0ax44dy9svMjKS5s2b+2wvOeecc+zxhwt+/vlnBg8ezO7du5k3bx5Dh9paYKZi8qeGcSHeEd4dgA1AXeAqVf0+8OGVTEWvYZSGqrJv375CtZItW7awdetWMp3GRICYmJgi20vi4nwurW7O0vfff8/QoUPJzMzkk08+oXv37m6HFJSOLlzI0QULSHjpJcQGzZarMq1hOGty9wHa4J1McLOqZp/hMFNORIT69etTv359Lr744gJlJ0+eZNeuXYUSyZo1a5g1axYejydv3zp16hRIJrnvW7ZsSfXq1cv7tiqF1atXc/nllxMTE8Pq1atp37692yEFrczkZI59tgzscWpQ86eXVDRwK/AbvI+lVovIJFXNCHRw5uyEh4fTrFkzmjVrxqBBgwqUZWZm8vPPPxd4vJWcnMySJUuYNm1agX0TEhIKNLrnvjZv3twa34swb948fv/739O0aVMWL15sywefgSc9A4mOtkemQc6fut9bwDG8j6UAxgBvAyMDFZQJvKioKNq2bUvbtm0LlaWlpbF169a8x1y5NZM5c+aQmpqat19YWBhNmzYtUCvJTSih3Pg+bdo0brjhBi688EIWLFhAnTp13A4p6Hky0m0MRgXgT8Joo6r5p81cLiLfBSog476YmBg6d+5M586FO8IdPHiwQBLJff3iiy8KNL5HRETQokWLAkkk931CQkKlHfn+wgsvcP/99zNw4EDmzJlDjRo13A6pQtD0DEsYFYA/CeO/ItJdVb8CEJFuwOeBDcsEq9q1a9OtWze6detWYLuqsnfv3gK1ktxksmTJEjIyTj3BrFq1Ki1btiyQRHKTSr169SrkYwlV5YEHHuC5557j97//PW+99ZY9riuB8Jo1iWhqj+2CnT+9pDbhbfDe6WxqAmwCPICqaqeARlgCodhLqiLweDykpKQUqpkkJyezbdu2AiPfa9So4bNW0qpVK+Lj4128i6Ll5OQwfvx43nzzTW655RZeeeWVkH0cZyqekvSS8idhNC2uXFV3FHHcFOAyYJ+qdnC2nQ9MAmLwrg1+jaoe9XHsdrztJieBHH9vxhJGxZOTk8OOHTt8JpPt27cX6MkVFxdXKInkftWsWdOV+NPT0xk9ejRz587l8ccfZ8KECRWyhmRCV5kmDOeEcUBj8j3COtP05iLSG0gD3sqXMNYA96nqShG5HjhXVR/1cex2IFFVU08vK44ljMolKyuLn376qcAjrtyksmvXrgL71q1b12ciCeScXIcPH2b48OH85z//4ZVXXuG2224LyHVCwZ7HHic8NpZ6997jdighp0zHYYjIk8A4YBvOaG/8mN5cVVeJSLPTNrcBVjnvlwCLgEIJwxjwjlovqidXeno627ZtK5RMfHULPuecc3zWTFq2bEnVUs5d9OuvvzJ06FA2btzIu+++y+jRo0t1HuOVnpRERKNGbodhzsCfRu/fAy1UNasMrrcBGA58jLdbbuMi9lNgsYgo8JqqTi6Da5tKpGrVqnTo0IEOHQqvznb8+HG2bt1aKJnMnz+/wMqKAI0aNfJZKylugsdt27YxePBg9u7dy/z58xk8eHBA7jGUWLfaisGfhLEBqAXsO9OOfrgeeFlEJgBzgaKSUC9V3S0i9YAlIvKjqq7ytaOIjAfGAzY4ygBQvXp1zj//fM4///xCZUePHi2USJKTk5k9ezYHDhzI209EqFOnDjVr1iQ2NrbA66JFi8jJyeGzzz4r1FvMlI5mZCJVLWEEO38Sxt/wdq3dAORNTKSqw0t6MVX9ERgMICKtgUuL2G+387pPRD4EunLqUdbp+04GJoO3DaOkMZnQEhsbS5cuXejSpUuhskOHDhVIInv37uXo0aMcOXKEI0eO8PPPP3PkyBEaNGjAu+++S7t27Vy4g8rJk5FBWJQljGDnT8KYBjwLrMfblbbURKSekwTCgEfw9pg6fZ/qQJiqHnPeD6bg8rDGBERcXBxdu3ala9eubocScqKaN7c2jArAn4SRqqovl/TEIjID6AvUEZEU4DEgRkRyu5LMwbswEyLSEPi3ql4C1Ac+dLomVgHeVdVPS3p9Y0zF0WzGu26HYPzgzziMF/E+ippLwUdSxXardYN1qzXGmJIp6wWULnBe80/kf8ZutcYY44+Thw+z4/rrqTP+j8QOHeJ2OKYY/qyH0e9M+xhjTGl5jh8nc+MmPMfT3A7FnMEZpwwVkfoi8oaILHQ+txeRGwIfmjEmFHicVSHFxmEEPX/mmJ6Kd0R2Q+fzFuDuQAVkjAktnvR0AMJKOerelJ8iE4aI5D6uqqOq7+N0qVXVHLyTAhpjzFlTZ+p7G+kd/IqrYXzjvB4XkXiceaREpDtwJNCBGWNCg0RHU+2iiwgP0unrzSnFNXrnztF8D94utS1E5HOgLnBVoAMzxoSGquedR9O333I7DOOH4hJGXRHJnWv4Q2AB3iSSCQwEvg9wbMYYY4JIcY+kwvEudFQDqI43uYQD1Zxtxhhz1o4uWMC2IUPJ2b/f7VDMGRRXw9ijqjaHkzEmoHIOHCRrxw6o4s84YuOm4moYts6kMSbgPBlOt1rrJRX0iksYA8otCmNMyNJ0b7daKWLBKhM8ikwYqnqwPAMxxoQmT2YGEhWFhPkzjti4yf6FjDGuijr3XGL625R1FYG1MhljXFXrqquodZUN7aoIrIZhjDHGL5YwjDGu+uX+P7Pz+uvdDsP4wRKGMcZVJw+k4jmR7nYYxg+WMIwxrvJkZCJVbQxGRRCwhCEiU0Rkn4hsyLftfBH5UkTWi8g8EYkt4tihIrJZRLaKyAOBitEY4z5PRjphUZYwKoJA1jCmAkNP2/Zv4AFV7Yh3QsP7Tz9IRMKBfwLDgPbAGBFpH8A4jTEu0vQMq2FUEAFLGKq6Cjh98F8bYJXzfgnwOx+HdgW2qupPqpoFvAdcEag4jTHuiunbl2oXXeR2GMYP5T0OYwMwHPgYGAk09rFPArAr3+cUoFtRJxSR8cB4gCZNmpRZoMaY8lH/L392OwTjp/Ju9L4euE1E1uGdIj3Lxz6+Jj3Uok6oqpNVNVFVE+vWrVtGYRpjjDlduSYMVf1RVQerahdgBrDNx24pFKx5NAJ2l0d8xpjypar82Ol8UidNcjsU44dyTRgiUs95DQMeAXz9lKwBWonIuSISCYzGu0SsMaaS0awsNCsLwsLdDsX4IZDdamcAXwJtRCRFRG7A2+NpC/Aj3lrDm86+DUVkAYCq5gC3A4uATcD7qvpDoOI0xrhH020tjIokYI3eqjqmiKKJPvbdDVyS7/MCvGuIG2MqMU+GsxaGdautEGyktzHGNeokjLDoqi5HYvxhCcMY4xqpVo24q68msvm5bodi/GDrYRhjXBNRrx7nTHjU7TCMn6yGYYxxjebkoNnZbodh/GQJwxjjmrRVq/mxYyfS1284887GdZYwjDGu0QynW631kqoQLGEYY1zjycgEQKyXVIVgCcMY4xpPbg0jOsrlSIw/LGEYY1yj6c7APathVAiWMIwxronu2IH4G2+wGkYFYeMwjDGuqd61K9W7dnU7DOMnq2EYY1xzMi2Nk0ePuh2G8ZMlDGOMa/Y9+xw/XXqZ22EYP1nCMMa4xpORgdjU5hWGJQxjjGs0I93WwqhALGEYY1zjSc9AqlqX2orCEoYxxjWakWE1jArEutUaY1xT6/cjQezv1orCEoYxxjU1hw93OwRTAgFL7SIyRUT2iciGfNs6i8hXIpIkImtFxOeIHRE56eyTJCJzAxWjMcZdWSkp5Bw65HYYxk+BrAtOBYaetu054K+q2hmY4Hz2JV1VOztf9ieIMZXU9lGj2f+PiW6HYfwUsIShqquAg6dvBmKd9zWB3YG6vjEm+Gm6dautSMq7DeNuYJGIvIA3WfUsYr9oEVkL5ADPqOpHRZ1QRMYD4wGaNGlSxuEaYwJFVb0D92zxpAqjvLsn3AL8SVUbA38C3ihivyaqmghcDfxDRFoUdUJVnayqiaqaWLdu3bKP2BgTGNnZ4PFYDaMCKe+EMRaY47yfBfhs9FbV3c7rT8AK4ILyCM4YU348GblrYVjCqCjKO2HsBvo47/sDyafvICJxIhLlvK8D9AI2lluExphyIZGRnPP4Y1Tv3t3tUIyfAtaGISIzgL5AHRFJAR4DbgImikgVIAOn7UFEEoGbVfVGoB3wmoh48Ca0Z1TVEoYxlUxYdDRxo0e7HYYpgYAlDFUdU0RRFx/7rgVudN5/AXQMVFzGmODgOXGCrO3biWjShPCYGLfDMX6wMfnGGFdkJifz84jfkb5unduhGD9ZwjDGuMKTkQmARFmjd0VhCcMY4wrNSAcgzMZhVBiWMIwxrvCk53artfUwKgpLGMYYV3ishlHhWMIwxriiWpcuNHz2GarEx7sdivGTrYdhjHFFZOPGRDZu7HYYpgSshmGMcUVWSgon1q5FVd0OxfjJEoYxxhWHP/iAHWPHISJuh2L8ZAnDGOMKTc+wmWorGEsYxhhXeNfCsC61FYklDGOMKzTDahgVjSUMY4wrPBkZSHSU22GYErButcYYV8TfeCOe42luh2FKwBKGMcYVVTt2cDsEU0L2SMoY44rjX39D+voNbodhSsAShjHGFXufeooDk19zOwxTApYwjDGu8GRm2ky1FYwlDGOMKzQ9nTDrJVWhBDRhiMgUEdknIhvybessIl+JSJKIrBWRrkUcO1ZEkp2vsYGM0xhT/rzdaq2GUZEEuoYxFRh62rbngL+qamdggvO5ABGpDTwGdAO6Ao+JSFxgQzXGlCePDdyrcALarVZVV4lIs9M3A7HO+5rAbh+HDgGWqOpBABFZgjfxzAhEnBmbt/DLvfcU2l7//vuJ6dOH9O++Y/fDDxcqP2fCBKp37crxr77i16eeKlTe8G/PULVjB44tX86+v/+9UHmjiROJatGCowsWsP///q9QeZPXXiMiIYHDs2dz4M03C5U3ffttqsTFcfDtdzg0871C5efOmkVY1aqkvv46Rz7+uECZiNB83jwA9r/8CkcXLypQHlatOue+PxOAvc8+R9rqVQXKq9SOp+lb0wDY8/jjnFi7tkB5ZEIjGr82CYDdf/kL6T/8UKA8qlUrGr30EgApd9xJ5s8/FSiv2rETDf/2vwDsvGk82XsK/phU79qNcyY8CsD2P/yBk4cPFyiP6dOH+vffD8DPv7sKT2ZGgfLYocOoe/ttqMfDT8OHc7paV44g/obrOZl2nO2jRxUqr33NNcSNGUNOaio7xo0rVB5/w43UuvK3ZO3axa5bbilUXvf224kdOjSkf/aavjmFKvXqFTrWBC83xmHcDSwSkRfw1nB6+tgnAdiV73OKs60QERkPjAdo0qRJqQIKi44iqkXLwttr1PBeI7qq7/Jq1b2v1av7LndWEguvUcNnuUR5n9+Gxdb0WU5EhPf4WrV8Hx/mrSBWia/t+/i88jqFy/PNEFqlXt1C5fn/8qtSv16h8vCaNU+F2aBhofL8vwgiEhLwZGQWKI9s1OhUeePGebHmPyZv3yZNCKtWreD5G5yT9z7q3HM5efRYwePr1z91fPPmaFZWwePr1j11vI/vXZU63kV9JEx8lofHORXe8HDf5bW83x+JjPRdHuv9mymUf/aqJSYWPs4ENQn0XPRODWO+qnZwPr8MrFTV2SLye2C8qg487Zj7gShVfcr5/ChwQlUL/6mUT2Jioq497S9dY4wxRRORdarqV/Z2o5fUWGCO834W3jaK06UA+ZfiaoTvR1fGGGPKiRsJYzfQx3nfH0j2sc8iYLCIxDmN3YOdbcYYY1wS0DYMEZkB9AXqiEgK3p5PNwETRaQKkIHT/iAiicDNqnqjqh4UkSeBNc6pnshtADfGGOOOgLdhlCdrwzDGmJIJ9jYMY4wxFZAlDGOMMX6xhGGMMcYvljCMMcb4pVI1eovIfmBHKQ+vA6SWYTgVSSjfO4T2/du9h67c+2+qqnXPtDNUsoRxNkRkrb89BSqbUL53CO37t3sPzXuH0t2/PZIyxhjjF0sYxhhj/GIJ45TJbgfgolC+dwjt+7d7D10lvn9rwzDGGOMXq2EYY4zxiyUMY4wxfgn5hCEiQ0Vks4hsFZEH3I4n0ERkiojsE5EN+bbVFpElIpLsvFbK9dNFpLGILBeRTSLyg4jc5WwPlfuPFpFvROQ75/7/6mw/V0S+du5/pohEuh1roIhIuIj8V0TmO59D4t5FZLuIrBeRJBFZ62wr8c99SCcMEQkH/gkMA9oDY0SkvbtRBdxUvOuj5/cA8JmqtgI+cz5XRjnAvaraDugO3Ob8e4fK/WcC/VX1fKAzMFREugPPAi85938IuMHFGAPtLmBTvs+hdO/9VLVzvrEXJf65D+mEgXe1v62q+pOqZgHvAVe4HFNAqeoq4PS1Ra4ApjnvpwG/Ldegyomq7lHVb533x/D+4kggdO5fVTXN+RjhfCnehcw+cLZX2vsXkUbApcC/nc9CiNx7EUr8cx/qCSMB2JXvc4qzLdTUV9U94P2lCtRzOZ6Ac9aavwD4mhC6f+eRTBKwD1gCbAMOq2qOs0tl/j/wD+DPgMf5HE/o3LsCi0VknYiMd7aV+Oc+oCvuVQDiY5v1M67kRCQGmA3crapHvX9ohgZVPQl0FpFawIdAO1+7lW9UgScilwH7VHWdiPTN3exj10p3745eqrpbROoBS0Tkx9KcJNRrGClA43yfG+FdczzU7BWRBgDO6z6X4wkYEYnAmyymq+ocZ3PI3H8uVT0MrMDbllPLWTIZKu//gV7AcBHZjvfRc3+8NY5QuHdUdbfzug/vHwpdKcXPfagnjDVAK6enRCQwGpjrckxumAuMdd6PBT52MZaAcZ5ZvwFsUtUX8xWFyv3XdWoWiEhVYCDedpzlwFXObpXy/lX1QVVtpKrN8P4/X6aq1xAC9y4i1UWkRu57YDCwgVL83If8SG8RuQTvXxrhwBRVfdrlkAJKRGYAffFObbwXeAz4CHgfaALsBEaq6ukN4xWeiPwGWA2s59Rz7IfwtmOEwv13wtu4GY73j8X3VfUJEWmO96/u2sB/gT+oaqZ7kQaW80jqPlW9LBTu3bnHD52PVYB3VfVpEYmnhD/3IZ8wjDHG+CfUH0kZY4zxkyUMY4wxfrGEYYwxxi+WMIwxxvjFEoYxxhi/WMIwFYqIxDszbiaJyK8i8ovzPk1E/i+A1+0rIj0DdX4f1xvpzCjrEZHEfNubiUh6vu/BpLO8zhMiMvDsIzahINSnBjEVjKoewDvTKiLyOJCmqi+Uw6X7AmnAF+VwLfAOrBoBvOajbJuqdi6Li6jqhLI4jwkNVsMwlYJTA8hd4+BxEZkmIouddQBGiMhzznoAnzrTgyAiXURkpTMh26J80yTcKSIbReR7EXnPmajwZuBPzl/1FzujpmeLyBrnq1e+a78tIsucdQZucrY3EJFVzvEbROTi4u5HVTep6uaz+H6ME5GPRGSeiPwsIreLyD3iXQviKxGp7ew3VUSuct5vF5G/isi3zveqbWmvbyonSximsmqBdyrrK4B3gOWq2hFIBy51ksYrwFWq2gWYAuSO8n8AuEBVOwE3q+p2YBLedRM6q+pqYKLz+SLgdzhTZjs6OdfuAUwQkYbA1cAip2ZwPpB0Fvd2rvOLf+UZEk8H57pdnXs7oaoXAF8C1xVxTKqqXgj8C7jvLGI0lZA9kjKV1UJVzRaR9XinwvjU2b4eaAa0wfsLdYkzW204sMfZ53tguoh8hHfaFF8GAu3zzXQbmztfD/CxqqYD6SKyHO8v7DXAFCdRfaSqpU0Ye4AmqnpARLoAH4nIeap61Me+y511P46JyBFgnrN9Pd6k5kvuhIzr8D4SMyaPJQxTWWUCqKpHRLL11Bw4Hrw/9wL8oKo9fBx7KdAbGA48KiLn+dgnDOjhJIY8TgI5fb4dVdVVItLbOffbIvK8qr5V0pty5jnKvbd1IrINaC0ijfHOCwZwo/Oaf04kT77Pud8DX3L3OVnMPiZE2SMpE6o2A3VFpAd4pz0XkfNEJAxorKrL8S62UwuIAY4BNfIdvxi4PfeDiORvhL5CvOtnx+NtLF8jIk3xrsfwOt4Zcy90jntLRLr6G7TTdhLuvG8OtAJ+UtUPncdlnVV1bcm+Fcb4xxKGCUnOkrxXAc+KyHd42xR64n009Y7zKOu/eNspDuN9nHNlbqM3cCeQ6DSMb8TbKJ7rG+AT4CvgSWctgr5Akoj8F2+bx0Rn306cehSWR0SuFJEUvO0gn4jIIqeoN/C9E/MHeNtYKt3MuiY42Wy1xpShknT1FZFY4A1VHRnwwIwpA/aM0hiXOA3VlixMhWE1DGOMMX6xNgxjjDF+sYRhjDHGL5YwjDHG+MUShjHGGL9YwjDGGOOX/wcAHFClGN0p1wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the optimization to minimize ENERGY\n",
    "opti_problem, opti_x, opti_u = run_mpc_step(params, **mpc_kwargs, objective_fn='energy')  # the double ** unrolls the dictionary\n",
    "\n",
    "# Plot results\n",
    "# X: State\n",
    "x_val = np.arange(len(opti_x.value))\n",
    "plt.plot(x_val, opti_x.value, c=\"black\", label=\"Space\")\n",
    "plt.plot(x_val, heating_SP, c=\"tab:red\", linestyle=\"--\", label=\"Setpoint\")\n",
    "plt.xlabel(\"Timesteps, 15-min\")\n",
    "plt.ylabel(\"Temperature\")\n",
    "plt.title(\"State\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# U: Controls\n",
    "plt.plot(x_val[:-1], opti_u.value, c=\"black\", label=\"Heater\")\n",
    "plt.plot(x_val[:-1], heating_power_min, c=\"tab:grey\", linestyle=\"--\", label=\"Min\")\n",
    "plt.plot(x_val[:-1], heating_power_max, c=\"tab:red\", linestyle=\"--\", label=\"Max\")\n",
    "plt.xlabel(\"Timesteps, 15-min\")\n",
    "plt.ylabel(\"Heating Power\")\n",
    "plt.title(\"Controls\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# W: Exogenous inputs, measurable disturbances\n",
    "fig, ax1 = plt.subplots()\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('Timesteps, 15-min')\n",
    "ax1.set_ylabel('Temp Exterior', color=color)\n",
    "ax1.plot(x_val[:-1], W[:,0], color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('GHI', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(x_val[:-1], W[:,1], color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "plt.title(\"Exogenous Disturbances\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Minimize Power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ECOS 2.0.7 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS\n",
      "\n",
      "It     pcost       dcost      gap   pres   dres    k/t    mu     step   sigma     IR    |   BT\n",
      " 0  +0.000e+00  -3.879e+03  +7e+03  9e-02  2e-01  1e+00  5e+01    ---    ---    1  1  - |  -  - \n",
      " 1  +2.899e+02  -4.244e+02  +2e+03  2e-02  5e-03  9e+00  1e+01  0.9890  2e-01   1  1  1 |  0  0\n",
      " 2  +1.510e+02  -8.408e+01  +5e+02  6e-03  2e-03  3e+00  4e+00  0.6661  2e-02   1  1  1 |  0  0\n",
      " 3  +1.862e+02  -6.103e+01  +5e+02  6e-03  1e-03  3e+00  4e+00  0.0509  9e-01   1  1  1 |  0  0\n",
      " 4  +2.402e+02  +1.344e+02  +2e+02  3e-03  2e-04  2e+00  1e+00  0.7893  2e-01   1  1  1 |  0  0\n",
      " 5  +2.386e+02  +1.405e+02  +2e+02  3e-03  2e-04  1e+00  1e+00  0.3257  8e-01   1  1  1 |  0  0\n",
      " 6  +2.332e+02  +2.196e+02  +3e+01  3e-04  3e-05  2e-01  2e-01  0.9147  6e-02   1  1  1 |  0  0\n",
      " 7  +2.349e+02  +2.310e+02  +7e+00  1e-04  7e-06  5e-02  5e-02  0.8639  2e-01   1  1  1 |  0  0\n",
      " 8  +2.356e+02  +2.338e+02  +3e+00  5e-05  3e-06  2e-02  2e-02  0.6766  2e-01   1  1  1 |  0  0\n",
      " 9  +2.357e+02  +2.348e+02  +2e+00  2e-05  2e-06  1e-02  1e-02  0.7850  4e-01   1  1  1 |  0  0\n",
      "10  +2.360e+02  +2.357e+02  +6e-01  8e-06  6e-07  4e-03  4e-03  0.7341  1e-01   1  1  1 |  0  0\n",
      "11  +2.360e+02  +2.359e+02  +2e-01  3e-06  2e-07  1e-03  1e-03  0.8440  2e-01   2  1  1 |  0  0\n",
      "12  +2.361e+02  +2.361e+02  +6e-02  8e-07  6e-08  4e-04  4e-04  0.8099  1e-01   1  1  1 |  0  0\n",
      "13  +2.361e+02  +2.361e+02  +2e-02  2e-07  2e-08  1e-04  1e-04  0.8789  2e-01   2  1  1 |  0  0\n",
      "14  +2.361e+02  +2.361e+02  +5e-03  7e-08  5e-09  3e-05  4e-05  0.8647  2e-01   1  1  1 |  0  0\n",
      "15  +2.361e+02  +2.361e+02  +1e-03  2e-08  1e-09  9e-06  1e-05  0.8980  2e-01   2  1  1 |  0  0\n",
      "16  +2.361e+02  +2.361e+02  +4e-04  5e-09  4e-10  3e-06  3e-06  0.8902  2e-01   1  1  1 |  0  0\n",
      "17  +2.361e+02  +2.361e+02  +1e-04  1e-09  1e-10  7e-07  7e-07  0.9057  2e-01   2  1  1 |  0  0\n",
      "18  +2.361e+02  +2.361e+02  +3e-05  4e-10  3e-11  2e-07  2e-07  0.8999  2e-01   2  1  1 |  0  0\n",
      "19  +2.361e+02  +2.361e+02  +7e-06  1e-10  7e-12  5e-08  5e-08  0.9082  2e-01   2  1  1 |  0  0\n",
      "20  +2.361e+02  +2.361e+02  +2e-06  3e-11  2e-12  1e-08  1e-08  0.9047  2e-01   2  1  1 |  0  0\n",
      "\n",
      "OPTIMAL (within feastol=2.6e-11, reltol=8.1e-09, abstol=1.9e-06).\n",
      "Runtime: 0.002578 seconds.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the optimization to minimize POWER\n",
    "opti_problem, opti_x, opti_u = run_mpc_step(params, **mpc_kwargs, objective_fn='power')  # the double ** unrolls the dictionary\n",
    "\n",
    "# Plot results\n",
    "# X: State\n",
    "x_val = np.arange(len(opti_x.value))\n",
    "plt.plot(x_val, opti_x.value, c=\"black\", label=\"Space\")\n",
    "plt.plot(x_val, heating_SP, c=\"tab:red\", linestyle=\"--\", label=\"Setpoint\")\n",
    "plt.xlabel(\"Timesteps, 15-min\")\n",
    "plt.ylabel(\"Temperature\")\n",
    "plt.title(\"State\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# U: Controls\n",
    "plt.plot(x_val[:-1], opti_u.value, c=\"black\", label=\"Heater\")\n",
    "plt.plot(x_val[:-1], heating_power_min, c=\"tab:grey\", linestyle=\"--\", label=\"Min\")\n",
    "plt.plot(x_val[:-1], heating_power_max, c=\"tab:red\", linestyle=\"--\", label=\"Max\")\n",
    "plt.xlabel(\"Timesteps, 15-min\")\n",
    "plt.ylabel(\"Heating Power\")\n",
    "plt.title(\"Controls\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# W: Exogenous inputs, measurable disturbances\n",
    "fig, ax1 = plt.subplots()\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('Timesteps, 15-min')\n",
    "ax1.set_ylabel('Temp Exterior', color=color)\n",
    "ax1.plot(x_val[:-1], W[:,0], color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('GHI', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(x_val[:-1], W[:,1], color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "plt.title(\"Exogenous Disturbances\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "+ Notice the difference between running it to minimize energy vs power? How did the controls change? And the temperature?\n",
    "+ Change the start time and see what happens by modifying the range in this `df = df_full[\"2018-01-17 0:00\":\"2018-01-17 12:00\"].copy()` above.\n",
    "+ Override the initial temperature.\n",
    "+ Change the maximum value for the heater.\n",
    "+ Change the values for $\\alpha$, $\\beta$ and $\\gamma$. How does it change the behaviour?\n",
    "+ Try blending both cases to minimize a combination of energy and power."
   ]
  }
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