MSMR model #3116
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| { | ||
| "cells": [ | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Multi-Species Multi-Reaction model" | ||
| ] | ||
| }, | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Model Equations" | ||
| ] | ||
| }, | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [] | ||
| }, | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Example solving MSMR using PyBaMM" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "#%pip install pybamm -q # install PyBaMM if it is not installed\n", | ||
| "import pybamm\n", | ||
| "import numpy as np" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "model = pybamm.lithium_ion.SPM(\n", | ||
| " {\n", | ||
| " \"open-circuit potential\": \"MSMR\",\n", | ||
| " \"particle\": \"MSMR\",\n", | ||
| " }\n", | ||
| ")\n", | ||
| "\n", | ||
| "parameter_values = pybamm.ParameterValues(\"MSMR_Example\")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# x_n\n", | ||
| "U_n = model.variables[\"Negative electrode open-circuit potential [V]\"]\n", | ||
| "T = model.variables[\"Negative electrode temperature [K]\"]\n", | ||
| "f = pybamm.constants.F / (pybamm.constants.R * T)\n", | ||
| "for i in range(6):\n", | ||
| " U0 = pybamm.Parameter(f\"U0_n_{i}\")\n", | ||
| " w = pybamm.Parameter(f\"w_n_{i}\")\n", | ||
| " Xj = pybamm.Parameter(f\"Xj_n_{i}\")\n", | ||
| "\n", | ||
| " x_n = Xj / (1 + pybamm.exp(f * (U_n - U0) / w))\n", | ||
| " model.variables[f\"x{i}_n\"] = x_n\n", | ||
| " model.variables[f\"X-averaged x{i}_n\"] = pybamm.x_average(x_n)\n", | ||
| " \n", | ||
| "\n", | ||
| "# x_p\n", | ||
| "U_p = model.variables[\"Positive electrode open-circuit potential [V]\"]\n", | ||
| "T = model.variables[\"Positive electrode temperature [K]\"]\n", | ||
| "f = pybamm.constants.F / (pybamm.constants.R * T)\n", | ||
| "for i in range(4):\n", | ||
| " U0 = pybamm.Parameter(f\"U0_p_{i}\")\n", | ||
| " w = pybamm.Parameter(f\"w_p_{i}\")\n", | ||
| " Xj = pybamm.Parameter(f\"Xj_p_{i}\")\n", | ||
| "\n", | ||
| " x_p = Xj / (1 + pybamm.exp(f * (U_p - U0) / w))\n", | ||
| " model.variables[f\"x{i}_p\"] = x_p\n", | ||
| " model.variables[f\"X-averaged x{i}_p\"] = pybamm.x_average(x_p)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "<pybamm.solvers.solution.Solution at 0x14be066a0>" | ||
| ] | ||
| }, | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "experiment = pybamm.Experiment(\n", | ||
| " [\n", | ||
| " (\n", | ||
| " \"Discharge at 1C for 1 hour or until 3 V\",\n", | ||
| " \"Rest for 1 hour\",\n", | ||
| " \"Charge at C/3 until 4 V\",\n", | ||
| " \"Hold at 4 V until 10 mA\",\n", | ||
| " \"Rest for 1 hour\",\n", | ||
| " ),\n", | ||
| " ]\n", | ||
| ")\n", | ||
| "sim = pybamm.Simulation(model, parameter_values=parameter_values, experiment=experiment)\n", | ||
| "sim.solve()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "application/vnd.jupyter.widget-view+json": { | ||
| "model_id": "a2be754ae444465a9b5c413582e703f1", | ||
| "version_major": 2, | ||
| "version_minor": 0 | ||
| }, | ||
| "text/plain": [ | ||
| "interactive(children=(FloatSlider(value=0.0, description='t', max=5.86646556905814, step=0.0586646556905814), …" | ||
| ] | ||
| }, | ||
| "metadata": {}, | ||
| "output_type": "display_data" | ||
| }, | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "<pybamm.plotting.quick_plot.QuickPlot at 0x14fb3bcd0>" | ||
| ] | ||
| }, | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "sim.plot(\n", | ||
| " [\n", | ||
| " \"X-averaged negative particle stoichiometry\",\n", | ||
| " \"X-averaged positive particle stoichiometry\",\n", | ||
| " \"X-averaged negative particle potential [V]\",\n", | ||
| " \"X-averaged positive particle potential [V]\",\n", | ||
| " [f\"X-averaged x{i}_n\" for i in range(6)],\n", | ||
| " [f\"X-averaged x{i}_p\" for i in range(4)],\n", | ||
| " \"X-averaged negative electrode open-circuit potential [V]\",\n", | ||
| " \"X-averaged positive electrode open-circuit potential [V]\",\n", | ||
| " \"Current [A]\",\n", | ||
| " \"Voltage [V]\",\n", | ||
| " ]\n", | ||
| ")" | ||
| ] | ||
| }, | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Comparison with ideal diffusion and \"standard\" OCV model" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 162, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def U_n(sto):\n", | ||
| " u_eq = (\n", | ||
| " 0.3635 * pybamm.exp(-439.3 * sto)\n", | ||
| " + 0.6908\n", | ||
| " + 0.5489 * pybamm.tanh(-30.07 * sto)\n", | ||
| " - 0.0344 * pybamm.tanh(25.46 * (sto - 0.1713))\n", | ||
| " - 0.0276 * pybamm.tanh(14.27 * (sto - 0.5270))\n", | ||
| "\n", | ||
| " )\n", | ||
| " return u_eq\n", | ||
| "\n", | ||
| "def U_p(sto):\n", | ||
| " u_eq = (\n", | ||
| " -0.3415 * sto\n", | ||
| " + 4.116\n", | ||
| " - 0.2835 * pybamm.tanh(4.181 * (sto - 0.2324))\n", | ||
| " - 0.1020 * pybamm.tanh(29.61 * (sto - 1))\n", | ||
| " )\n", | ||
| " return u_eq" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "parameter_values_2 = parameter_values.copy()\n", | ||
| "parameter_values_2.update({\n", | ||
| " \"Negative electrode OCP [V]\": U_n,\n", | ||
| " \"Positive electrode OCP [V]\": U_p,\n", | ||
| "})" | ||
| ] | ||
| }, | ||
| { | ||
| "attachments": {}, | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## References\n", | ||
| "\n", | ||
| "The relevant papers for this notebook are:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 12, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "[1] Joel A. E. Andersson, Joris Gillis, Greg Horn, James B. Rawlings, and Moritz Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019. doi:10.1007/s12532-018-0139-4.\n", | ||
| "[2] Daniel R Baker and Mark W Verbrugge. Multi-species, multi-reaction model for porous intercalation electrodes: part i. model formulation and a perturbation solution for low-scan-rate, linear-sweep voltammetry of a spinel lithium manganese oxide electrode. Journal of The Electrochemical Society, 165(16):A3952, 2018.\n", | ||
| "[3] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, and others. Array programming with NumPy. Nature, 585(7825):357–362, 2020. doi:10.1038/s41586-020-2649-2.\n", | ||
| "[4] Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, and S. Jon Chapman. An asymptotic derivation of a single particle model with electrolyte. Journal of The Electrochemical Society, 166(15):A3693–A3706, 2019. doi:10.1149/2.0341915jes.\n", | ||
| "[5] Peyman Mohtat, Suhak Lee, Jason B Siegel, and Anna G Stefanopoulou. Towards better estimability of electrode-specific state of health: decoding the cell expansion. Journal of Power Sources, 427:101–111, 2019.\n", | ||
| "[6] Valentin Sulzer, Scott G. Marquis, Robert Timms, Martin Robinson, and S. Jon Chapman. Python Battery Mathematical Modelling (PyBaMM). Journal of Open Research Software, 9(1):14, 2021. doi:10.5334/jors.309.\n", | ||
| "[7] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, and others. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods, 17(3):261–272, 2020. doi:10.1038/s41592-019-0686-2.\n", | ||
| "[8] Andrew Weng, Jason B Siegel, and Anna Stefanopoulou. Differential voltage analysis for battery manufacturing process control. arXiv preprint arXiv:2303.07088, 2023.\n", | ||
| "\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "pybamm.print_citations()" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "dev", | ||
| "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": "3.9.16" | ||
| }, | ||
| "vscode": { | ||
| "interpreter": { | ||
| "hash": "bca2b99bfac80e18288b793d52fa0653ab9b5fe5d22e7b211c44eb982a41c00c" | ||
| } | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,26 @@ | ||
| import pybamm | ||
|
|
||
| pybamm.set_logging_level("DEBUG") | ||
| model = pybamm.lithium_ion.SPM( | ||
| { | ||
| "open-circuit potential": "MSMR", | ||
| "particle": "MSMR", | ||
| } | ||
| ) | ||
|
|
||
|
|
||
| parameter_values = pybamm.ParameterValues("MSMR_Example") | ||
| experiment = pybamm.Experiment( | ||
| [ | ||
| ( | ||
| "Discharge at 1C for 1 hour or until 3 V", | ||
| "Rest for 1 hour", | ||
| "Charge at C/3 until 4 V", | ||
| "Hold at 4 V until 10 mA", | ||
| "Rest for 1 hour", | ||
| ), | ||
| ] | ||
| ) | ||
| sim = pybamm.Simulation(model, parameter_values=parameter_values, experiment=experiment) | ||
| sim.solve() | ||
| sim.plot() |
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Picky comment, can you delete the empty cells at the end of the notebook?