V_oc-vs-SoC-Determination/EKF_plotting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "085e5ca7-b297-426e-a7b3-b26d34cb3362",
   "metadata": {},
   "source": [
    "# 🔋 **Extended Kalman Filter for Generating Open Circuit Voltage vs SoC Relationship**\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a33459d-e9d3-4d40-a80f-fa58de3110eb",
   "metadata": {},
   "source": [
    "### The notebook being divided into phases 📖\n",
    "🧪 **Data Proceesing** \n",
    "\n",
    "📊 **Data Visualization** \n",
    "\n",
    "📉 **Data Fitting** \n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3bc6cb7-e550-4c82-a939-7b7fa447d7f3",
   "metadata": {},
   "source": [
    "#### 📚Library Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e030dd77-2eaa-42e7-8e57-b081ef4712a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import serial\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17963e06-8c0c-46ea-af16-1be0e28e9d3e",
   "metadata": {
    "tags": []
   },
   "source": [
    "***\n",
    "## 🧪Phase 1 - Data Processing\n",
    ">   - Recieves open circuit voltage and current through bleeder resistor data from Measurement-to-Serial.ino\n",
    ">   - Extended Kalman Filter is applied to the data to process SoC\n",
    ">   - Open Circuit Voltage and SoC is stored in a CSV"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597f0fa6-2277-4d85-bd03-a9d58b062106",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### 💾 Ardunio NANO connected to COM5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1d363fbd-b64e-4358-914e-d1f28e111bfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "arduino_port = \"COM5\"\n",
    "baud = 9600 \n",
    "fileName=\"V_oc&SoC.csv\"\n",
    "ser = serial.Serial(arduino_port, baud)\n",
    "file = open(fileName, \"a\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a92f9eab-f2eb-4447-a1af-1be38cc4ddbe",
   "metadata": {},
   "source": [
    "#### 📲 Dual Polarization Model and EKF Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1fd3b79f-7a64-40f3-8874-53fe6bea8199",
   "metadata": {},
   "outputs": [],
   "source": [
    "del_t = 100       #in milliseconds(ms)\n",
    "SoC = 1;\n",
    "V_ct = 0.007;\n",
    "V_df = 0.004;\n",
    "tau_ct = 4;\n",
    "tau_df = 100;\n",
    "R_ct = 0.001;\n",
    "R_df = 0.01;\n",
    "R_0 = 0.2;\n",
    "R_l = 2.2;\n",
    "Charge = 1.082*3600;\n",
    "\n",
    "\n",
    "x = np.array([[SoC],\n",
    "              [V_ct],\n",
    "              [V_df]]);\n",
    "\n",
    "A = np.array([[1, 0, 0],\n",
    "              [0, np.exp(-(del_t/1000)/tau_ct), 0],\n",
    "              [0, 0, np.exp(-(del_t/1000)/tau_df)]]);\n",
    "              \n",
    "B = np.array([[-(del_t/1000)/Charge],\n",
    "              [R_ct*(1-np.exp(-(del_t/1000)/tau_ct))],\n",
    "              [R_df*(1-np.exp(-(del_t/1000)/tau_df))]]);\n",
    "\n",
    "P = np.array([[1e-25, 0, 0],\n",
    "              [0, 1e-23, 0],         \n",
    "              [0, 0, 1e-23]]);\n",
    "\n",
    "R = np.array([1e-7]);\n",
    "\n",
    "Q = np.array([[1e-25, 0, 0],\n",
    "              [0, 1e-23, 0],         \n",
    "              [0, 0, 1e-23]]);\n",
    "\n",
    "C = np.array([1, -1, -1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37597052-b6de-464e-b131-ae858b10b006",
   "metadata": {},
   "source": [
    "#### 🧮 **Extended Kalman Filter**\n",
    "> - Data Estimation\n",
    "> - Data Storage\n",
    "\n",
    "[1] Algorithm based on Carlo Taborelli, Simona Onori. (2014).\"[State of Charge Estimation\n",
    " Using Extended Kalman Filters for Battery Management System](https://ieeexplore.ieee.org/document/7056126)\". \n",
    " \n",
    " \n",
    "[2] Parameter Update based on \n",
    "    yu, Zhihao & Huai, Ruituo & Xiao, Linjing. (2015). \n",
    "    \"[State-of-Charge Estimation for Lithium-Ion Batteries \n",
    "    Using a Kalman Filter Based on Local Linearization](https://www.researchgate.net/publication/282462924_State-of-Charge_Estimation_for_Lithium-Ion_Batteries_Using_a_Kalman_Filter_Based_on_Local_Linearization)\".\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8b752dee-8c75-4bfc-9eb3-992e3e098ea5",
   "metadata": {},
   "outputs": [],
   "source": [
    "SoC = 1\n",
    "I = 0\n",
    "x[0][0] = 1\n",
    "\n",
    "while SoC > 0:\n",
    "    getData=str(ser.readline())[2:][:-5]\n",
    "    I = getData[5:][:]\n",
    "    I = float(I)\n",
    "    \n",
    "    #Extended Kalman Estimator\n",
    "    \n",
    "    #19a\n",
    "    x_pred = np.dot(A, x)+(B*I)\n",
    "    \n",
    "    #19b\n",
    "    P_pred = np.dot(np.dot(A, P), np.transpose(A)) + Q\n",
    "    \n",
    "    #Parameter Update\n",
    "    C[0] = (float(getData[0:][:-5]))/x_pred[0][0]\n",
    "                                \n",
    "    #20a\n",
    "    L = np.dot(P_pred, np.transpose(C))/(np.dot(C, np.dot(P_pred, np.transpose(C)))+R)\n",
    "    \n",
    "    #20b\n",
    "    x = x_pred + (L*(I*R_l - np.dot(C, x_pred) + I*R_0))\n",
    "    \n",
    "    #20c\n",
    "    P = np.dot((np.identity(3, dtype = float) - np.dot(L, C)), P_pred)\n",
    "    \n",
    "    SoC = x[0][0]\n",
    "    \n",
    "    #Write to CSV\n",
    "    file = open(fileName, \"a\")\n",
    "    file.write(getData[0:][:-5]+\",\")\n",
    "    file.write(str(SoC))\n",
    "    file.write(\"\\n\")\n",
    "    \n",
    "file.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caf3f2f3-ab3a-46b9-bc2f-03fad76cf77d",
   "metadata": {},
   "source": [
    "***\n",
    "## 📊 Phase 2 - Data Visualization\n",
    ">   - Reads data from CSV\n",
    ">   - Performs a Matplolib mapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "d0829897-d538-4ad4-9668-a8fcc8bc1fb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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Lq+6G9cTXYc63ur58763g1JU+pmHWw+W9RXI98GPgV+30PwscGRHLJR0PTAQOL+ofHRGvVLfExjRo9SNww+hsKxn5X3DoDytSj5k1jlyDJCKmS9q9g/6HiyYfBXauelGNbOkD8McjADigq+s45iEYUoE775pZw1JEvlcJp0FyW1u7tlrN92Vgn4g4O51+FlgOBHBtREzsYNkJwASAIUOGHHrjjTdWqPr6pljD/q/+N4PWzMq8rr8MuZ43+wwj1FiH0ZqbmxkwYECty6gLHouExyFRPA6jR4+eVc7hg7oMEkmjgZ8AH4iIV9O2YRGxRNJQ4B7g3IiY3tnrjRw5MubPn1+Z4uvRmhVw7zGwbEa29fTfNbkIcPgnYL//rkxtdahQKNDU1FTrMuqCxyLhcUgUj4OksoKk7v7clHQA8HPg+A0hAhARS9LHpZJ+D4wCOg2ShrRmBbxwJ7x0Hyy4Nvv6PvISbDk0+3rMrEeqqyCRtCvwO+ATEfF0UfvWQK+IeCN9fixwaY3KrJ1ogaXT4U8ZD5r/6+9glw9XpiYz6/HyPv13MtAEDJa0GLgY6AsQEdcAFwHvAH6i5JTSDaf57gD8Pm3rA9wQEXfmWXvN3To80zcFTt/pTo4YfVzl6jEzS+V91tb4TvrPBs5uo30hcGC16qpLfzoaXvpT15cfdS3sNeHtyZZCIXtNZmZtqKtdWz3aMz+FGZ/Nvp7xLb5A0Mxy5SCppSW3wf0nZV/PuHW+l5WZ1YyDJE/RAnMvT75BMIsBe8KRt8FWO0Df7b0FYmY15SCptpa1sOwxWPBTWHh9tnUN2ANG/Qx2PKoipZmZVYKDpFrWrYJFv4dHTs++rq12guP+Av19xxgzqz8OkkqKAAJWzIVp+3d9PYf/HPY8q2JlmZlVk4OkUuZ8B57IcGuRsc/CgN0rVo6ZWV4cJFlEC0zOcLbUuLXQy/8EZta9+bdYuSJgcq+uL/+xfG+SaWZWbQ6SUs29Ah7/WteW7d0fTm32abpm1pAcJG2JgEfPhGfb+yLHErz3l7D1brD9/rDFoIqVZmZWbxwkxSLgqUtgdoYbC/cZAGMXwpZDKlaWmVk9c5BAEiAvP/j219J2SdM0eOfxlavJzKybcJBkOXi+9XA4fhb0G1jZmszMupGeGyRrlsPNZR67OOHJ5JiHmZm9recFybqVcOOA8pY59s8weFR16jEz6+Z6VpDcUMbptyfOh233rl4tZmYNouGDpF/LsvICxF8MZWZWlrKCRNLuwPqIWFSdcipvi/WvdD7TiM/CrqfCDkdWvyAzswZT7ulK1wDbFjdI2lfSfqWuQNIkSUslzW6nX5KukrRA0pOSDinqO0PSM+nPGWXW3rbjH4P3XO0QMTPronKDZJuImNOq7SXgqjLWcT0wpoP+44ER6c8E4KcAkgYBFwOHA6OAiyVlO+/2tLdg4EGZVmFm1tNluPtgIiJeBfqWMf90YFkHs5wM/CoSjwLbS9oJOA64JyKWRcRy4B46DqS2bbM3fPS15OaJvfuVvbiZmW2q3IPt90u6ICK+06q95CApwTCg+BjM4rStvfbNSJpAsjXDocM3tv956P/yZp9h8PBjFSy3e2hubqZQKNS6jJrzOGzksUh4HBJZxqHcILkYuFbSQ8DNwFLgBOC+Lr16lUTERGAiwCF79gsOuQL2+QKH17iuWioUCjQ1NdW6jJrzOGzksUh4HBJZxqGsXVsRsTYi/gM4FxgIvAe4LSIyfDXgZpYAuxRN75y2tdfeoZV9hsM+X6hgeWZmVqxL15FExF+Bv1a4lg2mAudImkJyYH1FRLwg6S7g20UH2I8FLqhSDWZmVqJyryPZGrgIeB/QDPwWmBQRJX/tn6TJQBMwWNJikt1lfQEi4hpgGsnusgXAKuCTad8ySZcBM9JVXRoRHR20NzOzHJS7RXIN8DTwOWAQcCpwlqQPpWdSdSoixnfSH+n62+qbBEwqq2IzM6uqcoNkl4j4RNH0/ZJOBK4EzqxYVWZm1m2Uex3JZsETEbcBe1SmHDMz627KDZKCpK+00d67EsWYmVn302GQSBrXqukbwLslTZf0eUkfl3QD8HDVKjQzs7rW2RbJtZLuljQC3r6O5AzgSyTXcXwAuAP4anXLNDOzetXZwfZ9gO8BT0r6HvCtiFgdETPYeBqumZn1YB1ukUTECxHxcZKL/04C5kj6UC6VmZlZt1DSwfaIeAA4BPgh8GtJt0jatZqFmZlZ91DyWVsR0RIRPwL2Bl4BZkv6WtUqMzOzbqGs03/TL5d6N/AkMB/4djWKMjOz7qPDg+2STgcOAPZPH3ckuf/VU8BM4OfVLtDMzOpbZ2dtfQd4AphFco+rx4EF5dyk0czMGluHQRIRu3TUb2Zmlvk7283MrGdzkJiZWSYOEjMzy8RBYmZmmThIzMwsEweJmZll4iAxM7NMcg8SSWMkzZe0QNL5bfRfKenx9OdpSa8V9a0v6puaa+FmZtamzq5sryhJvYGrgWOAxcAMSVMjYu6GeSLivKL5zwUOLlrFmxFxUE7lmplZCfLeIhlFcouVhRGxBpgCnNzB/OOByblUZmZmXZLrFgkwDFhUNL0YOLytGSXtBgwH7i1q3lLSTGAdcHlE3NLOshOACQBDhgyhUChkLry7a25u9jjgcSjmsUh4HBJZxiHvICnHOODmiFhf1LZbRCyRtAdwr6SnIuLvrReMiInARICRI0dGU1NTLgXXs0KhgMfB41DMY5HwOCSyjEPeu7aWAMU3gtw5bWvLOFrt1oqIJenjQqDApsdPzMysBvIOkhnACEnDJfUjCYvNzr6StA8wEHikqG2gpC3S54OB9wNzWy9rZmb5ynXXVkSsk3QOcBfQG5gUEXMkXQrMjIgNoTIOmNLqe0/eBVwrqYUkAC8vPtvLzMxqI/djJBExDZjWqu2iVtOXtLHcwyTf1GhmZnXEV7abmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpnkHiSSxkiaL2mBpPPb6D9T0suSHk9/zi7qO0PSM+nPGflWbmZmbemT54tJ6g1cDRwDLAZmSJoaEXNbzfqbiDin1bKDgIuBw4AAZqXLLs+hdDMza0feWySjgAURsTAi1gBTgJNLXPY44J6IWJaGxz3AmCrVaWZmJco7SIYBi4qmF6dtrZ0i6UlJN0vapcxlzcwsR7nu2irRH4DJEfGWpP8EfgkcVc4KJE0AJgAMGTKEQqFQ8SK7m+bmZo8DHodiHouExyGRZRzyDpIlwC5F0zunbW+LiFeLJn8OXFG0bFOrZQttvUhETAQmAowcOTKampramq1HKRQKeBw8DsU8FgmPQyLLOOS9a2sGMELScEn9gHHA1OIZJO1UNDkWmJc+vws4VtJASQOBY9M2MzOroVy3SCJinaRzSAKgNzApIuZIuhSYGRFTgc9LGgusA5YBZ6bLLpN0GUkYAVwaEcvyrN/MzDaX+zGSiJgGTGvVdlHR8wuAC9pZdhIwqaoFmplZWXxlu5mZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwyyT1IJI2RNF/SAknnt9H/RUlzJT0p6U+SdivqWy/p8fRnar6Vm5lZW/rk+WKSegNXA8cAi4EZkqZGxNyi2R4DDouIVZI+A1wBnJb2vRkRB+VZs5mZdSzvLZJRwIKIWBgRa4ApwMnFM0TEfRGxKp18FNg55xrNzKwMuW6RAMOARUXTi4HDO5j/LOCOouktJc0E1gGXR8QtbS0kaQIwAWDIkCEUCoUMJTeG5uZmjwMeh2Iei4THIZFlHPIOkpJJOh04DDiyqHm3iFgiaQ/gXklPRcTfWy8bEROBiQAjR46MpqamPEqua4VCAY+Dx6GYxyLhcUhkGYe8d20tAXYpmt45bduEpKOBC4GxEfHWhvaIWJI+LgQKwMHVLNbMzDqXd5DMAEZIGi6pHzAO2OTsK0kHA9eShMjSovaBkrZInw8G3g8UH6Q3M7MayHXXVkSsk3QOcBfQG5gUEXMkXQrMjIipwHeBAcBNkgCej4ixwLuAayW1kATg5a3O9jIzsxrI/RhJREwDprVqu6jo+dHtLPcwsH91qzMzs3L5ynYzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZeIgMTOzTBwkZmaWiYPEzMwycZCYmVkmDhIzM8vEQWJmZpk4SMzMLBMHiZmZZZJ7kEgaI2m+pAWSzm+jfwtJv0n7/yxp96K+C9L2+ZKOy7VwMzNrU65BIqk3cDVwPLAvMF7Svq1mOwtYHhF7AVcC/zdddl9gHLAfMAb4Sbo+MzOroby3SEYBCyJiYUSsAaYAJ7ea52Tgl+nzm4EPSlLaPiUi3oqIZ4EF6frMzKyG+uT8esOARUXTi4HD25snItZJWgG8I21/tNWyw9p6EUkTgAnp5FuSZmcvvdsbDLxS6yLqgMdhI49FwuOQKB6H3cpZMO8gyUVETAQmAkiaGRGH1bikmvM4JDwOG3ksEh6HRJZxyHvX1hJgl6LpndO2NueR1AfYDni1xGXNzCxneQfJDGCEpOGS+pEcPJ/aap6pwBnp848C90ZEpO3j0rO6hgMjgL/kVLeZmbUj111b6TGPc4C7gN7ApIiYI+lSYGZETAV+Afxa0gJgGUnYkM53IzAXWAd8LiLWl/CyE6vxXrohj0PC47CRxyLhcUh0eRyU/LFvZmbWNb6y3czMMnGQmJlZJg0TJFluvdJIShiHL0qaK+lJSX+SVNb54t1FZ+NQNN8pkkJSQ57+Wco4SDo1/T8xR9INedeYlxI+G7tKuk/SY+nn44Ra1FlNkiZJWtretXVKXJWO0ZOSDilpxRHR7X9IDtz/HdgD6Ac8Aezbap7PAtekz8cBv6l13TUah9FA//T5Z3rqOKTzbQNMJ7nQ9bBa112j/w8jgMeAgen00FrXXcOxmAh8Jn2+L/BcreuuwjgcARwCzG6n/wTgDkDAe4E/l7LeRtkiyXLrlUbS6ThExH0RsSqdfJTkepxGU8r/B4DLSO7ltjrP4nJUyjh8Crg6IpYDRMTSnGvMSyljEcC26fPtgH/mWF8uImI6ydmw7TkZ+FUkHgW2l7RTZ+ttlCBp69YrrW+fssmtV4ANt15pJKWMQ7GzSP76aDSdjkO6yb5LRNyeZ2E5K+X/w97A3pIekvSopDG5VZevUsbiEuB0SYuBacC5+ZRWV8r9HQI06C1SrHOSTgcOA46sdS15k9QL+AFwZo1LqQd9SHZvNZFsnU6XtH9EvFbLompkPHB9RHxf0vtIrmd7d0S01LqwetcoWyRZbr3SSEq6jYyko4ELgbER8VZOteWps3HYBng3UJD0HMm+4KkNeMC9lP8Pi4GpEbE2krtqP00SLI2mlLE4C7gRICIeAbYkuZFhT9KlW1E1SpBkufVKI+l0HCQdDFxLEiKNuj+8w3GIiBURMTgido+I3UmOFY2NiJm1KbdqSvlc3EKyNYKkwSS7uhbmWGNeShmL54EPAkh6F0mQvJxrlbU3Ffg/6dlb7wVWRMQLnS3UELu2IsOtVxpJiePwXWAAcFN6rsHzETG2ZkVXQYnj0PBKHIe7gGMlzQXWA1+JiEbbUi91LL4E/EzSeSQH3s9stD82JU0m+cNhcHos6GKgL0BEXENybOgEku97WgV8sqT1Ntg4mZlZzhpl15aZmdWIg8TMzDJxkJiZWSYOEjMzy8RBYmZmmThIzMwsEweJWQVJer+kaZJekNQsaaGkb5axfC9JZ0t6RNJyScvSrz34dDXrNsvCQWJWIekND+8gucv0bsAg4FSS27SXsnxvklt0fIXkQrGh6c+FwElVKNmsInxBolmFSPoD0BwR4zuYZxxwPrAnyT2Mzo+IW9K+i4H/BA5q4NvXWAPyFolZ5bwMHCPpv9J7NW1C0gTgO8CnImIb4DxgcvrNfNuRbIl80yFi3Y23SMwqRNI2wBeAU4ADSL7X4ZKIuC7tew74aETcV7TM8+kyAL8l+abC1/Kr2iw7b5GYVUhEvBERl0XEQcCOwO3AzyXtDBwFrG8VIiK5Tfkyktt1v+4Qse7IQWJWBenuqZtJPmP9Sb7CdXmr2U4C3iS5jf0LwDaSBuVZp1klOEjMKkDSBZKOkTQgPYX3EOAK4K6IeBr4M7C7pCMk9ZZ0FHAN8KWIWE2y9fIccJ2kXdN1bivpFEkX1eZdmZWmIb6PxKwO9AeuBHYFWki+JOnXwI8AIuJpSWcD15Hs9noa+HxE3Jz2r5L0fuAbwP3pl0y9AcwCvp/zezEriw+2m5lZJt61ZWZmmThIzMwsEweJmZll4iAxM7NMHCRmZpaJg8TMzDJxkJiZWSYOEjMzy+T/A5kRSzlgtuuAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = pd.read_csv(\"V_oc&SoC.csv\")\n",
    "plt.plot((values[\"SoC\"]+0.8041270)/1.8041270, values[\"Voc\"], color='orange', linewidth=3)\n",
    "plt.xlabel(\"$SoC$\", fontsize=13)\n",
    "plt.ylabel(\"$V_{OC}$\", fontsize=13)\n",
    "plt.ylim(0, 1.9)\n",
    "plt.xlim(-0.001, 1.01)\n",
    "plt.grid(True)\n",
    "plt.title(\"$V_{OC}$ vs $SoC$\", fontsize=15)\n",
    "plt.savefig('V_oc-vs-SoC.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "376a900e-4105-4d18-9c3c-3f59e97bf9fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = pd.read_csv(\"V_oc&SoC.csv\")\n",
    "plt.plot(values[\"SoC\"], values[\"Voc\"], color='orange', linewidth=3)\n",
    "plt.xlabel(\"$SoC$\", fontsize=13)\n",
    "plt.ylabel(\"$V_{OC}$\", fontsize=13)\n",
    "plt.ylim(0, 1.9)\n",
    "plt.xlim(-0.9, 1.01)\n",
    "plt.grid(True)\n",
    "plt.title(\"$V_{OC}$ vs $SoC$\", fontsize=15)\n",
    "plt.arrow(-0.402, 0.75, 0.402, 0, head_width=0.05, head_length=0.07, linewidth=2.7, color='g', length_includes_head=True)\n",
    "plt.arrow(-0.402, 0.75, -0.402, 0, head_width=0.05, head_length=0.07, linewidth=2.7, color='g', length_includes_head=True)\n",
    "plt.text(-0.55, 0.6, 'Offset', size=14)\n",
    "plt.savefig('V_oc-vs-SoC_offeset.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e7f9370-f39f-41c3-b732-7efeb950ffa2",
   "metadata": {},
   "source": [
    "***\n",
    "## 📉 Phase 3 - Data Fitting\n",
    ">  Fits curve to the generated plot for further SoC estimation using open circuit voltage measurement\n",
    "\n",
    "##### Fitting equation based on \n",
    "##### $$V_{OC}(SoC) = K_0-K_{1}/SoC-K_{2}SoC+K_{3}ln(SoC)+K_{4}ln(1-SoC)$$\n",
    "pg. 7 of yu, Zhihao & Huai, Ruituo & Xiao, Linjing. (2015). \n",
    "    \"[State-of-Charge Estimation for Lithium-Ion Batteries \n",
    "    Using a Kalman Filter Based on Local Linearization](https://www.researchgate.net/publication/282462924_State-of-Charge_Estimation_for_Lithium-Ion_Batteries_Using_a_Kalman_Filter_Based_on_Local_Linearization)\".\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "a34f9d88-1fa1-4e24-aed6-44127626e431",
   "metadata": {},
   "outputs": [],
   "source": [
    "def guess_function(x, K0, K1, K2, K3, K4) :\n",
    "    return (K0-(K1/x)-(K2*x)+(K3*np.log(x))+(K4*np.log(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "89596b92-f98e-4930-865c-dd427de664cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "popt, pcov = curve_fit(guess_function, (values[\"SoC\"]+0.8141270)/1.8041270, values[\"Voc\"], p0=(2, 0.02, 5.2874, -2700.40315, 1400.91685), maxfev=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "9772a7f1-f7b7-4c82-a037-83cc895944d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "param_file = open(\"Relation_param.csv\", \"a\")\n",
    "param_file.write(str(popt[0])+\",\"+str(popt[1])+\",\"+str(popt[2])+\",\"+str(popt[3])+\",\"+str(popt[4]))\n",
    "param_file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "ad449a18-fb5b-4a75-8633-d38905569faa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t= np.linspace(0.01001, 1, 2000)\n",
    "plt.plot((values[\"SoC\"]+0.8141270)/1.8041270, values[\"Voc\"], 'co', markersize=2)\n",
    "plt.ylim(0, 1.9)\n",
    "plt.xlim(0, 1.1)\n",
    "plt.xlabel(\"$SoC$\", fontsize=13)\n",
    "plt.ylabel(\"$V_{OC}$\", fontsize=13)\n",
    "plt.title(\"$V_{OC}$ vs $SoC$\", fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(t, guess_function(t, popt[0], popt[1], popt[2], popt[3], popt[4]),'r-', linewidth = 4)\n",
    "plt.legend(['Measured', 'Fitted Curve'], borderpad=1.1)\n",
    "plt.savefig('V_oc-vs-SoC-fitted.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe55e36-4d0e-444b-9acb-364dbbe311f9",
   "metadata": {},
   "source": [
    "#### We get the curve fitting parameters as follows\n",
    "\n",
    "$$\\theta = \\begin{bmatrix} K_0 \\\\ K_1 \\\\ K_2 \\\\ K_3 \\\\ K_4 \\end{bmatrix}=\\begin{bmatrix}  2.22221763 \\\\ -0.0119085674 \\\\ 0.492858021 \\\\ 13186.4572 \\\\  -13185.9561 \\end{bmatrix}$$\n",
    "##### Covariance for the fitting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "e5a9831f-750f-451f-9819-4b5e3d5a7dd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcov\n",
    "plt.imshow(np.log(np.abs(pcov)))\n",
    "plt.colorbar()\n",
    "plt.title('Covariance ColourBar')\n",
    "plt.savefig('Relation-param-cov-cbar.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "228836d0-1630-446a-abaf-1c2914df3bb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.22221763e+00, -1.19085674e-02,  4.92858021e-01,  1.31864572e+04,\n",
       "       -1.31859561e+04])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffb488d7-64f0-470e-b59f-b3c5becdc729",
   "metadata": {},
   "source": [
    "***\n",
    "## <center> 🔋Notebook Concludes 📖"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0630536d-2c62-4135-b723-681d3bf30220",
   "metadata": {},
   "source": [
    "***\n",
    "## Prasanna Paithankar\n",
    "### Department of Electrical Engineering, Indian Institute of Technology, Kharagpur\n",
    "\n",
    "##### Submitted to Autonomous Ground Vehical Research Group, IIT Kharagpur\n",
    "\n",
    "<img src=\"AGVlogo.png\" class=\"bg-primary\" width=\"200px\">"
   ]
  }
 ],
 "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": "3.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}