{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "\n",
    "\n",
    "# Simulation models with Python\n",
    "\n",
    "*Written by Marc Budinger (INSA Toulouse) and Scott Delbecq (ISAE-SUPAERO), Toulouse, France*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [],
    "user_expressions": []
   },
   "source": [
    "### Thermal model of an electric motor\n",
    "\n",
    "The thermal model of a motor, **Figure n° 1**, distinguish temperature between\n",
    "winding and yoke with a 2 bodies model. One can distinguish:\n",
    "\n",
    "-   heat capacity of the winding: *Cth1*\n",
    "\n",
    "-   heat capacity of the yoke: *Cth2*\n",
    "\n",
    "-   the thermal resistance between the winding and the yoke (corresponding to\n",
    "    the electrical insulator): *Rth1*\n",
    "\n",
    "-   the thermal resistance between the yoke and the ambient air: *Rth2*\n",
    "\n",
    "**Figure n° 1 –** *2 bodies thermal model of the motor*\n",
    "\n",
    "![ThermalModel](./assets/images/thermalmodel.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "### Modelica or state space model\n",
    "\n",
    "A Modelica model such as **Figure 2** could be simulated in Dymola or OpenModelica.\n",
    "**Figure n° 2** – *Modelica model*\n",
    "![Modelica Model](./assets/images/modelicathermalmodel.png)\n",
    "\n",
    "To simulate it in Python it is possible to use Functional Mock-up Units ([FMU](https://github.com/modelon-community/PyFMI)) which can be exported by system simulation softwares. \n",
    "\n",
    "Here, we propose to use a simple state-space approach using the [scipy](https://scipy.org) package.\n",
    "\n",
    "\n",
    "Recall: the transfert function of the problem can be expressed as  \n",
    "\n",
    "$Z_{th}=\\frac{\\theta(p)}{P(p)}=R_{th,eq}\\frac{1+T_0p}{1+(T_1+T_2)p+T_1T_2p}$  \n",
    "with:  \n",
    "- $R_{th,eq}=R_1+R_2$\n",
    "- $T_0=\\frac{R_1R_2}{R_1+R_2}C_2$\n",
    "- $T_1+T_2=(R_1+R_2)C_1 + R_2C_2$\n",
    "- $T_1T_2=R_1C_1R_2C_2$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import step\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "def motor_temperature(P, R1, C1, R2, C2, time=np.linspace(0, 200, 100)):\n",
    "    Rtheq = R1 + R2\n",
    "    T0 = R1 * R2 / (R1 + R2) * C2\n",
    "    T1pT2 = (R1 + R2) * C1 + R2 * C2\n",
    "    T1T2 = R1 * C1 * R2 * C2\n",
    "    t, y = step(system=([Rtheq * T0, Rtheq], [T1T2, T1pT2, 1]), T=time)\n",
    "    theta_winding = y * P\n",
    "    d = {\"t\": t, \"theta_winding\": theta_winding}\n",
    "    df = pd.DataFrame(data=d)\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "# Losses [W]\n",
    "P = 100.0\n",
    "# R1 [K/W]\n",
    "R1 = 0.3\n",
    "# C1 [J/K]\n",
    "C1 = 150.0\n",
    "# R2 [K/W]\n",
    "R2 = 0.3\n",
    "# C2 [J/K]\n",
    "C2 = 150.0\n",
    "# Simulation time [s]\n",
    "t_final = 150.0\n",
    "\n",
    "time = np.linspace(0, t_final, 100)\n",
    "\n",
    "df = motor_temperature(P, R1, C1, R2, C2, time=time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "We can now access to the simulation results and plot them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>t</th>\n",
       "      <th>theta_winding</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.515152</td>\n",
       "      <td>0.993470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.030303</td>\n",
       "      <td>1.955111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.545455</td>\n",
       "      <td>2.886946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.060606</td>\n",
       "      <td>3.790832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>143.939394</td>\n",
       "      <td>43.250294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>145.454545</td>\n",
       "      <td>43.464381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>146.969697</td>\n",
       "      <td>43.675729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>148.484848</td>\n",
       "      <td>43.884372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>44.090345</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             t  theta_winding\n",
       "0     0.000000       0.000000\n",
       "1     1.515152       0.993470\n",
       "2     3.030303       1.955111\n",
       "3     4.545455       2.886946\n",
       "4     6.060606       3.790832\n",
       "..         ...            ...\n",
       "95  143.939394      43.250294\n",
       "96  145.454545      43.464381\n",
       "97  146.969697      43.675729\n",
       "98  148.484848      43.884372\n",
       "99  150.000000      44.090345\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df[\"t\"], df[\"theta_winding\"])\n",
    "plt.xlabel(\"Time [s]\")\n",
    "plt.ylabel(\"Temperature [°C]\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "We can access the motor final temperature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final temperature = 44.09 °C\n"
     ]
    }
   ],
   "source": [
    "print(\"Final temperature = %.2f °C\" % df[\"theta_winding\"].iloc[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "We can use interpolation to estimate intermediate temperatures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The temperature at t = 100.00 s is 35.67 °C\n"
     ]
    }
   ],
   "source": [
    "from scipy import interpolate\n",
    "\n",
    "theta_mot_f = interpolate.interp1d(df[\"t\"], df[\"theta_winding\"])\n",
    "\n",
    "t = 100.0\n",
    "theta_mot = theta_mot_f(t)\n",
    "\n",
    "print(\"The temperature at t = %.2f s is %.2f °C\" % (t, theta_mot))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "## Exercise\n",
    "Simulate the winding temperature for 500 s and 200 W losses:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.linspace(0, 500, 1000)\n",
    "P = 200\n",
    "df = motor_temperature(P, R1, C1, R2, C2, time=time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x14304cb80>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df[\"t\"], df[\"theta_winding\"])\n",
    "plt.xlabel(\"Time [s]\")\n",
    "plt.ylabel(\"Temperature [°C]\")\n",
    "plt.grid()\n",
    "plt.legend([\"theta_winding\", \"theta_core\"], loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}