{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 12.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fundamentals of Solar Cells and Photovoltaic Systems Engineering**\n",
    "\n",
    "**Solutions Manual - Chapter 12**\n",
    "\n",
    "**Problem 12.1**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In this problem, we will review the method to extract the main parameters in the I-V curve presented in Chapter 4. Let us assume that we have measured the dark I-V curve of a 10 cm$^2$ solar cell at 25 $^{\\circ}$C. The tabulated data is provided in this book’s online repository. The series resistance $R_s$ can be assumed to be zero so the dark I-V curve equation is:**\n",
    "\n",
    "$I = I_0(e^{(qV/nkT)}-1)+ \\frac{V}{R_p}$\n",
    "\n",
    "**Estimate the reverse saturation current $I_0$, the diode ideality factor $n$, and discuss the potential effect of the parallel resistance $R_p$**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the package [pandas](https://pandas.pydata.org/) to handle the data and [matplotlib.pyplot](https://matplotlib.org/stable/index.html) to plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by importing the data from the dark I-V curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>V (V)</th>\n",
       "      <th>I (A)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.1598</td>\n",
       "      <td>0.000003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2239</td>\n",
       "      <td>0.000004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2657</td>\n",
       "      <td>0.000006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3099</td>\n",
       "      <td>0.000008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.3568</td>\n",
       "      <td>0.000011</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    V (V)     I (A)\n",
       "0  0.1598  0.000003\n",
       "1  0.2239  0.000004\n",
       "2  0.2657  0.000006\n",
       "3  0.3099  0.000008\n",
       "4  0.3568  0.000011"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dark_IV = pd.read_csv('data/Dark_I_V_curve.csv',  header=0) \n",
    "dark_IV.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following the strategy described in the Advanced Materials of Chapter 4 (Dark I-V curve of solar cells), we plot the curve using a log y-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2158f242188>"
      ]
     },
     "execution_count": 3,
     "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(dark_IV['V (V)'], dark_IV['I (A)'],\n",
    "         linewidth=2, marker='o', markerfacecolor=\"None\",\n",
    "         label='dark')\n",
    "plt.yscale('log')\n",
    "plt.ylabel('Current (A)')\n",
    "plt.xlabel('Voltage (V)')\n",
    "plt.xlim([0,1])\n",
    "\n",
    "\n",
    "#fit the dark IV curve plotted with a log y-axis\n",
    "value_at_0V=5*10**-9\n",
    "slope=18.5\n",
    "plt.plot(np.append(0, dark_IV['V (V)'].values), \n",
    "         [math.exp(math.log(value_at_0V)+slope*V) for V in np.append(0, dark_IV['V (V)'].values)],\n",
    "         linewidth=2, linestyle='--',color='firebrick',\n",
    "         label='fitting')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have also plotted the linear fit to the dark IV curve ploted using a log y axis. \n",
    "The slope of the curve allow us the calculate the ideality coefficient.\n",
    "\n",
    "$ln(I)=ln(I_0)+ \\frac{V}{nKT/q}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 2.16\n"
     ]
    }
   ],
   "source": [
    "#assuming that the measuremen was taking at 25C\n",
    "KT_q=0.025\n",
    "\n",
    "n=1/(slope*KT_q)\n",
    "print(\"n = \" + str(round(n,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value of the fit at 0V indicates the reverse saturation current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I_0 = 5e-09\n"
     ]
    }
   ],
   "source": [
    "I_0=value_at_0V\n",
    "print(\"I_0 = \" + str(I_0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deviation of the IV curve from the linear fitting (in log-y representation) for high voltage values represents the effect of series resistance $R_s$. In this case, the fitting is almost perfect, indicating that there is no significant $R_s$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deviation of the IV curve from the linear fitting (in log-y representation) for low volage values represents the effect of parallel resistance $R_p$. In this case, the curve deviates from the linear fitting but only at current values below $10^{-4}$. As discussed in the Advanced Materials of Chapter 4, this should not create any significant reduction in the cell FF or efficiency. "
   ]
  }
 ],
 "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": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}