examples/variable_input_functions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PETLION, Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = petlion(LCO;\n",
    "    jacobian=:symbolic\n",
    "    );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variable current/power/voltage guide\n",
    "\n",
    "All operating modes to PETLION (`I`, `V`, and `P`) accept constants or functions as inputs. Say you have some custom current protocol `I_fun` that you want to run with\n",
    "```julia\n",
    "sol = simulate(p, 1000, I=I_fun)\n",
    "```\n",
    "You can set it up four different ways:\n",
    "1. A function of time\n",
    "```julia\n",
    "I_fun(t) = ...\n",
    "```\n",
    "2. A function of time and the parameters\n",
    "```julia\n",
    "I_fun(t,p) = ...\n",
    "```\n",
    "3. A function of time, parameters, and algebraic states\n",
    "```julia\n",
    "I_fun(t,Y,p) = ...\n",
    "```\n",
    "4. A function of time, parameters, algebraic states, and differential states\n",
    "```julia\n",
    "I_fun(t,Y,YP,p) = ...\n",
    "```\n",
    "\n",
    "The last two can be helpful for model predictive control purposes.\n",
    "\n",
    "\n",
    "\n",
    "**Important Info**\n",
    "<ul>\n",
    "<li>All times start at t = 0, even if the simulation follows another one</li>\n",
    "<li>Discontinuities are allowed (see examples)</li>\n",
    "<li>The functions may be discontinuous in time, but performance is best with continuous functions</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1: Discontinuous current function\n",
    "\n",
    "Let's run a multi-constant current segment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "I_fun1 (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function I_fun1(t)\n",
    "    if t < 100\n",
    "        return 1\n",
    "    else\n",
    "        return 0.5\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Right now, the model is unaware of the discontinuity at t = 100. Here's the compiled time for the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.005015 seconds (1.74 k allocations: 1.811 MiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PETLION simulation\n",
       "  --------\n",
       "  Run:     I func\n",
       "  Time:    200.0 s\n",
       "  Current: C/2\n",
       "  Voltage: 3.403 V\n",
       "  Power:   49.7344 W\n",
       "  SOC:     0.0417\n",
       "  Exit:    Final time reached"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sol = simulate(p,200,I=I_fun1,SOC=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can specify any number of discontinuities using the keyword argument `tdiscon`, which accepts a vector of numbers as an input. After specifying when the discontinuity occurs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.003363 seconds (1.25 k allocations: 893.570 KiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PETLION simulation\n",
       "  --------\n",
       "  Run:     I func\n",
       "  Time:    200.0 s\n",
       "  Current: C/2\n",
       "  Voltage: 3.4029 V\n",
       "  Power:   49.7341 W\n",
       "  SOC:     0.0417\n",
       "  Exit:    Final time reached"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sol = simulate(p,200,I=I_fun1,SOC=0,tdiscon=[100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much better!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2: Current Ramp\n",
    "\n",
    "We can add new parameters to our functions as well so we don't have to deal with compilation time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "I_ramp (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I_ramp(t,p) = p.θ[:ramp_val]*t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try a ramp of $$ I(t) = \\frac{t}{100} .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.001810 seconds (587 allocations: 859.664 KiB)\n",
      "PETLION simulation\n",
      "  --------\n",
      "  Run:     I func\n",
      "  Time:    100.0 s\n",
      "  Current: 1C\n",
      "  Voltage: 3.2398 V\n",
      "  Power:   94.6988 W\n",
      "  SOC:     0.0139\n",
      "  Exit:    Final time reached\n"
     ]
    },
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       "</svg>\n"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.θ[:ramp_val] = 1/100\n",
    "@time sol_ramp1 = simulate(p,100,I=I_ramp,SOC=0)\n",
    "println(sol_ramp1)\n",
    "plot(sol_ramp1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's try a ramp of $$ I(t) = \\frac{t}{10} .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.002809 seconds (876 allocations: 872.523 KiB)\n",
      "PETLION simulation\n",
      "  --------\n",
      "  Run:     I func\n",
      "  Time:    100.0 s\n",
      "  Current: 10C\n",
      "  Voltage: 4.1823 V\n",
      "  Power:   1222.4761 W\n",
      "  SOC:     0.1389\n",
      "  Exit:    Final time reached\n"
     ]
    },
    {
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       "  1847.92,244.249 1892.2,227.136 1936.47,210.459 1980.75,194.369 2069.3,162.959 2157.84,132.551 2246.39,102.264 2293.25,86.1857 \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.θ[:ramp_val] = 1/10\n",
    "@time sol_ramp2 = simulate(p,100,I=I_ramp,SOC=0)\n",
    "println(sol_ramp2)\n",
    "plot(sol_ramp2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No extra compilation cost!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 3: Variable power and voltage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "V_fun (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_fun(t) = sin(t)\n",
    "V_fun(t) = 3.5 + 0.1cos(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.002149 seconds (978 allocations: 1.160 MiB)\n"
     ]
    },
    {
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      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sol_P_fun = simulate(p,10,P=P_fun,SOC=0.5,outputs=:all)\n",
    "plot(sol_P_fun, :P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.001839 seconds (1.17 k allocations: 1.209 MiB)\n"
     ]
    },
    {
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       "  2188.82,1383.61 2245.75,1348.09 2293.22,1279.91 \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time sol_V_fun = simulate(p,10,V=V_fun,SOC=0.5,outputs=:all)\n",
    "plot(sol_V_fun, :V)"
   ]
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
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