├── LICENSE
├── README.md
├── digitalTwin_Li_ION.ipynb
└── discharge.csv
/LICENSE:
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1 | MIT License
2 |
3 | Copyright (c) 2024 JAVIER MARIN
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
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/README.md:
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1 | 
2 |
3 | # Digital-Twin-in-python
4 | In this repo we will show how to build a simple but useful Digital Twin using python. Our asset will be a Li-ion battery. This Digital Twin will allow us to model and predict batteries behavior and can be included in any virtual asset management process.
5 | https://medium.com/towards-data-science/how-to-build-a-digital-twin-b31058fd5d3e
6 |
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/digitalTwin_Li_ION.ipynb:
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1 | {
2 | "nbformat": 4,
3 | "nbformat_minor": 0,
4 | "metadata": {
5 | "kernelspec": {
6 | "display_name": "Python 3",
7 | "language": "python",
8 | "name": "python3"
9 | },
10 | "language_info": {
11 | "codemirror_mode": {
12 | "name": "ipython",
13 | "version": 3
14 | },
15 | "file_extension": ".py",
16 | "mimetype": "text/x-python",
17 | "name": "python",
18 | "nbconvert_exporter": "python",
19 | "pygments_lexer": "ipython3",
20 | "version": "3.7.1"
21 | },
22 | "colab": {
23 | "name": "digitalTwin_Li_ION_.ipynb",
24 | "provenance": [],
25 | "collapsed_sections": []
26 | }
27 | },
28 | "cells": [
29 | {
30 | "cell_type": "markdown",
31 | "metadata": {
32 | "id": "AEil20eqS2So"
33 | },
34 | "source": [
35 | "# Hybrid digital twin of a Li-ion battery\n"
36 | ]
37 | },
38 | {
39 | "cell_type": "code",
40 | "metadata": {
41 | "id": "ZYaB7HSTS2Ss"
42 | },
43 | "source": [
44 | "import pandas as pd\n",
45 | "import numpy as np\n",
46 | "from sklearn.model_selection import train_test_split\n",
47 | "import keras\n",
48 | "import tensorflow as tf\n",
49 | "from keras.models import Sequential\n",
50 | "from keras.layers import LSTM, Dense\n",
51 | "from keras.optimizers import SGD\n",
52 | "from tensorflow.keras.layers import Dropout\n",
53 | "from matplotlib import pyplot as plt\n",
54 | "import plotly.express as px\n",
55 | "from plotly.subplots import make_subplots\n",
56 | "import plotly.graph_objects as go\n",
57 | "import plotly.figure_factory as ff"
58 | ],
59 | "execution_count": null,
60 | "outputs": []
61 | },
62 | {
63 | "cell_type": "markdown",
64 | "metadata": {
65 | "id": "NIhtsIQHS2St"
66 | },
67 | "source": [
68 | "### 1. Load experimental data"
69 | ]
70 | },
71 | {
72 | "cell_type": "code",
73 | "metadata": {
74 | "id": "UrmwSwuMS_iY"
75 | },
76 | "source": [
77 | "df = pd.read_csv('discharge.csv')"
78 | ],
79 | "execution_count": null,
80 | "outputs": []
81 | },
82 | {
83 | "cell_type": "code",
84 | "metadata": {
85 | "id": "rWmpbfS7W9zV"
86 | },
87 | "source": [
88 | "df = df[df['Battery'] == 'B0005']\n",
89 | "df = df[df['Temperature_measured'] > 36] #choose battery B0005\n",
90 | "#df['Time'] =pd.to_datetime(df['Time'], unit='s')\n",
91 | "dfb = df.groupby(['id_cycle']).max()\n",
92 | "dfb['Cumulated_T'] = dfb['Time'].cumsum()"
93 | ],
94 | "execution_count": null,
95 | "outputs": []
96 | },
97 | {
98 | "cell_type": "code",
99 | "metadata": {
100 | "colab": {
101 | "base_uri": "https://localhost:8080/",
102 | "height": 1000
103 | },
104 | "id": "CcBEYPoQC9SE",
105 | "outputId": "7e16313e-8ccf-4422-a787-a8dba8e29a22"
106 | },
107 | "source": [
108 | "import plotly.express as px\n",
109 | "fig = px.scatter_matrix(dfb.drop(columns=['Time','type', 'ambient_temperature', \n",
110 | " 'time', 'Battery']), \n",
111 | " )\n",
112 | "fig.update_traces(marker=dict(size=2,\n",
113 | " color='crimson',\n",
114 | " symbol='square')),\n",
115 | "fig.update_traces(diagonal_visible=False)\n",
116 | "fig.update_layout(\n",
117 | " title='Battery dataset',\n",
118 | " width=900,\n",
119 | " height=1200,\n",
120 | ")\n",
121 | "fig.update_layout({'plot_bgcolor': '#f2f8fd',\n",
122 | " 'paper_bgcolor': 'white',}, \n",
123 | " template='plotly_white',\n",
124 | " font=dict(size=7)\n",
125 | " )\n",
126 | "\n",
127 | "fig.show()"
128 | ],
129 | "execution_count": null,
130 | "outputs": [
131 | {
132 | "output_type": "display_data",
133 | "data": {
134 | "text/html": [
135 | "\n",
136 | "\n",
137 | "\n",
138 | " \n",
139 | " \n",
140 | " \n",
141 | " \n",
142 | "
\n",
143 | " \n",
181 | "
\n",
231 | " \n",
232 | " \n",
233 | " \n",
234 | "
\n",
235 | " \n",
273 | "
\n",
300 | " $L = 1 − (1 − L' )e^{-f_d}$
\n",
301 | "\n",
302 | "Where $L$ is the battery lifetime and $L'$ the initial battery lifetime. $f_d$ is a Linearized degradation rate per unit time and per cycle. It can be described as:
\n",
303 | " $f_d = f_d(t, δ, σ, T_c)$
\n",
304 | "\n",
305 | "where $t$ is charging time, δ is the cycle depth of discharge, σ is the cycle average state of charge, and $T_c$ is cell temperature. The equation for baatery capacity could be written as follows:
\n",
306 | " $C = C_0e^{f_d}$
\n",
307 | "\n",
308 | "We have empirically found that $f_d$ aproximates to:\n",
309 | " $f_d = \\frac{kT_Ci}{t}$
\n",
310 | "\n",
311 | "where $k= $ 0.13, $i$ the cycle number and $t$ the charge time for every cycle.\n",
312 | "\n",
313 | "- [1] *Xu, Bolun & Oudalov, Alexandre & Ulbig, Andreas & Andersson, Göran & Kirschen, D.s. (2016). Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment. IEEE Transactions on Smart Grid. 99. 1-1. 10.1109/TSG.2016.2578950.* "
314 | ]
315 | },
316 | {
317 | "cell_type": "code",
318 | "metadata": {
319 | "id": "rTU_ImZ1rPLf"
320 | },
321 | "source": [
322 | "from math import e\n",
323 | "L = (dfb['Capacity']-dfb['Capacity'].iloc[0:1].values[0])/-dfb['Capacity'].iloc[0:1].values[0]\n",
324 | "K = 0.13\n",
325 | "L_1 = 1-e**(-K*dfb.index*dfb['Temperature_measured']/(dfb['Time']))\n",
326 | "dfb['C. Capacity'] = -(L_1*dfb['Capacity'].iloc[0:1].values[0]) + dfb['Capacity'].iloc[0:1].values[0]"
327 | ],
328 | "execution_count": null,
329 | "outputs": []
330 | },
331 | {
332 | "cell_type": "code",
333 | "metadata": {
334 | "colab": {
335 | "base_uri": "https://localhost:8080/",
336 | "height": 542
337 | },
338 | "id": "l8bmHjJQCBEe",
339 | "outputId": "0030b53e-9dde-449a-9f29-ba6606820c2e"
340 | },
341 | "source": [
342 | "fig = go.Figure()\n",
343 | "\n",
344 | "fig.add_trace(go.Scatter(x=dfb.index, \n",
345 | " y=dfb['C. Capacity'],\n",
346 | " mode='lines',\n",
347 | " name='Physical model',\n",
348 | " line=dict(color='navy', \n",
349 | " width=2.5,\n",
350 | " )))\n",
351 | "\n",
352 | "fig.add_trace(go.Scatter(x=dfb.index, \n",
353 | " y=dfb['Capacity'],\n",
354 | " mode='markers',\n",
355 | " marker=dict(\n",
356 | " size=4,\n",
357 | " color='grey',\n",
358 | " symbol='cross'\n",
359 | " ),\n",
360 | " name='NASA dataset',\n",
361 | " line_color='navy'))\n",
362 | "fig.update_layout(\n",
363 | " title=\"Physical model comparison \",\n",
364 | " xaxis_title=\"Cycles\",\n",
365 | " yaxis_title=\"𝐶, Capacity [Ahr]\")\n",
366 | "\n",
367 | "fig.update_layout(legend=dict(\n",
368 | " yanchor=\"top\",\n",
369 | " y=0.9,\n",
370 | " xanchor=\"left\",\n",
371 | " x=0.8\n",
372 | "))\n",
373 | "\n",
374 | "fig.update_layout({'plot_bgcolor': '#f2f8fd',\n",
375 | " 'paper_bgcolor': 'white',}, \n",
376 | " template='plotly_white')"
377 | ],
378 | "execution_count": null,
379 | "outputs": [
380 | {
381 | "output_type": "display_data",
382 | "data": {
383 | "text/html": [
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