examples/fast_charging_CC-CT-CV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup\n",
    "\n",
    "Start by loading the PETLION package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PETLION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading the parameters for an LCO cell with 1D temperature enabled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 82.066481 seconds (202.10 M allocations: 12.424 GiB, 3.71% gc time, 96.55% compilation time)\n"
     ]
    }
   ],
   "source": [
    "@time p = petlion(LCO;\n",
    "    N_p = 10, # discretizations in the cathode\n",
    "    N_s = 10, # discretizations in the separator\n",
    "    N_n = 10, # discretizations in the anode\n",
    "    N_r_p = 10, # discretizations in the solid cathode particles\n",
    "    N_r_n = 10, # discretizations in the solid anode particles\n",
    "    temperature = true, # temperature enabled or disabled\n",
    "    jacobian = :AD, # :AD (automatic-differenation) for convenience or :symbolic for speed\n",
    "    );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, start by setting the initial SOC and bounds for the states and outputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.opts.SOC = 0 # fraction ∈ [0, 1]\n",
    "p.opts.outputs = :all # save all the states and outputs from the simulation\n",
    "\n",
    "p.bounds.T_max = 40 + 273.15 # K\n",
    "p.bounds.V_max = 4.1 # V\n",
    "p.bounds.I_max = 4 # C-rate\n",
    "p.bounds.I_min = 1/20 # C-rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation\n",
    "\n",
    "Now, we can begin to run the simulation. Start by fast charging at the maximum C-rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PETLION simulation\n",
       " --------\n",
       " Run:     I\n",
       " Time:    357.56 s\n",
       " Current: 4C\n",
       " Voltage: 4.0312 V\n",
       " Power:   471.33 W/m²\n",
       " SOC:     0.3973\n",
       " Temp.:   40.0 °C\n",
       " Exit:    Above max. temperature"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = simulate(p, I=p.bounds.I_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final exit reason can be accessed using the command"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Above max. temperature\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_exit_reason(sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We hit the temperature constraint, so let's hold the temperature constant using a constant temperature (CT) operating mode. The CT operating mode sets the *spatially averaged temperature*,\n",
    "\n",
    "$$\n",
    "\\overline{T}(t) = \\frac{1}{L}\\int_0^L T(x,t) \\, \\mathrm{d}x,\n",
    "$$\n",
    "\n",
    "to $T_{\\max}$. In the P2D model, the temperature does not have significant spatial variation. Numerically, the CT operating mode is achieved by setting\n",
    "\n",
    "$$\n",
    "\\frac{\\mathrm{d}\\overline{T}}{\\mathrm{d}t} = 0\n",
    "$$\n",
    "\n",
    "by solving for $I(t)$.\n",
    "\n",
    "`simulate!` continues the previous simulation, where the `!` operator indicates it is modifying `sol`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PETLION simulation\n",
       " --------\n",
       " Runs:    I → dT\n",
       " Time:    686.41 s\n",
       " Current: 2.7892C\n",
       " Voltage: 4.1 V\n",
       " Power:   334.26 W/m²\n",
       " SOC:     0.6714\n",
       " Temp.:   40.0 °C\n",
       " Exit:    Above max. voltage"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulate!(sol, p, dT=:hold) # equivalent to `simulate!(sol, p, dT=0)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we hit the voltage cap, so let's run a CV hold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PETLION simulation\n",
       " --------\n",
       " Runs:    I → dT → V\n",
       " Time:    1865.61 s\n",
       " Current: 0.1959C\n",
       " Voltage: 4.1 V\n",
       " Power:   23.47 W/m²\n",
       " SOC:     1.0\n",
       " Temp.:   25.6963 °C\n",
       " Exit:    Above max. SOC"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulate!(sol, p, V=:hold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation terminates upon hitting the maximum SOC of `1`.\n",
    "\n",
    "The list of exit reasons can be accessed using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{String}:\n",
       " \"Above max. temperature\"\n",
       " \"Above max. voltage\"\n",
       " \"Above max. SOC\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exit_reasons(sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting\n",
    "\n",
    "Let's load the plotting package and show the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "plot(sol, :V) # Voltage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sol, :I) # Current"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sol, :T) # 1D temperature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Upon hitting $T_{\\max}$ and entering the CT operating mode, the current drops precipitously to enforce the temperature constraint. At the CT-CV transition, the current drop is less dramatic."
   ]
  }
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