Analysis of Lithium-Ion Battery Failure andPyBaMM’s Viability in Simulating Them

Alexander Cho Stephen Nahac229@outlook.com stephen02nah@gmail.com

Greyson Sapio Daniel Vail Patrick Wangsapio.greyson@hermits.org danielvail44@gmail.com 21wangp@mtps.us

Thomas Hodson*th627@rutgers.edu

New Jersey’s Governor’s School of Engineering and TechnologyJuly 18, 2020

*Corresponding Author

Abstract—Energy storage, especially in the form of lithium-ionbatteries in smartphones and electric vehicles, has become anessential part of today’s world. However, lithium-ion batterieshave some significant safety concerns after many instances ofthese batteries catching fire or exploding. As lithium ion batteriesare extremely useful, mainly due to their power density andprice, it is imperative to figure out the possible factors leadingto their catastrophic failure. In order to do this, a Pythonpackage (PyBaMM) was used to simulate these batteries inaction along with experimental data from Thomas Hodson’s labat Columbia university. By comparing these different types ofdata and exploring each individually, it was possible to work outthe different factors that lead to lithium-ion batteries exploding.It was determined that many factors, such as temperature anddegradation, could impact the explosion of the battery. However,in running these experiments, it was also determined thatPyBaMM, despite showing general trends of different factors thatled to combustion, was not the most useful program in replicatingthe attributes of lithium-ion batteries, due to its overall lackof advanced thermal simulation and nonexistent simulated heatexchange between cells and the surrounding environment. Theresults indicate that discharge rate and repeated cycling are theleading causes of thermal runaway in lithium ion batteries, butthere is room for further research on this topic, mainly in thefield of what occurs during a real world lithium ion batterycombustion.

I. INTRODUCTION

Today, large scale energy storage is becoming more im-portant than ever as renewable energies grow in popularity.Since most renewable energy sources experience significantvariation in power output due to the unpredictability of theEarth’s weather, energy storage is currently one of the bestways to make these methods practical [1].

Over the past 20 years, lithium-ion batteries have revolu-tionized the world of energy storage, allowing compact smart-

phones to last several days on a single charge, electric vehiclesto drive hundreds of miles, and even providing megawatts ofpower to the grid at a moment’s notice. Despite their versa-tility and large advantages over previous battery chemistries,lithium-ion batteries suffer from one fatal flaw—the possibilityof fires and explosions [2].

Incidents involving lithium-ion battery fires and explosionsmade recent headlines. Events such as the Samsung GalaxyNote 7 explosions, numerous electric vehicles catching fire,and Boeing 787 battery fires are all notable examples of theshortcomings of lithium-ion batteries. [2-4].

This study aims to develop a better understanding of themechanisms that cause lithium-ion battery explosions and howto prevent them. Both experimental data collected by Dr.Thomas Hodson at his lab at Columbia University and simu-lation data from PyBaMM, a Python-based battery simulationsoftware developed by the Oxford Battery Modelling group,were utilized to build an understanding of how lithium ionbatteries react to varying conditions. PyBaMM allows for themodification of several parameters that would normally bepresent during a battery experiment, such as charge and dis-charge current, cutoff voltages, battery chemistry, and ambienttemperature. Experiments were conducted on a remote servervia Jupyter Notebook, which allowed for the creation of docu-ments containing text, images, and executable code. PyBaMMis implemented as a Python library, giving a significant amountof flexibility in creating simulations and in the utilization ofPython to analyze battery data.

II. BACKGROUND

From a scientific standpoint, energy is the ability to dowork. Almost all of Earth’s usable energy is derived from the

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sun’s radiation, which has been converted into different forms.There are three main components of energy: kinetic, potential,and internal. Kinetic energy is derived from the movementof objects and particles. The faster an object is moving, themore kinetic energy it has. Potential energy is the energy of anobject as the result of its position or orientation. The furtherthe object is from equilibrium, the more potential energy isstored. Finally, internal energy is stored within an object. Thiscan be stored and released in many forms such as thermal,chemical, and nuclear energy [5]. The movement of energywithin a system is governed by the laws of thermodynamics.

Thermodynamics is a branch of science that pertains toheat and other forms of energy. The laws of thermodynamicsdictate that thermodynamic equilibrium is transitive, energy isconserved, entropy remains constant in reversible reactions andincreases otherwise, and that entropy approaches a constantvalue as temperature approaches absolute zero [6]. Because ofthermodynamics, it is understood that energy is never gainedwithout loss, and that any transfer of energy will cause anincrease in entropy. It is also understood that energy canbe converted from one form to another (e.g. electrical tomechanical, mechanical to chemical, etc.).

Energy storage devices have the ability to store energy(charging) and release it later (discharging). This concepthas been the backbone of revolutionary technologies such ascell phones and electric cars, and is becoming increasinglyimportant to the electric grid. Energy storage in the form ofbatteries has allowed for the production of electric vehicleswhich are 77% efficient, about 2.5-6.5 times the efficiency ofcommonly used Internal Combustion Engine cars [7]. Energystorage has also allowed for renewable energy to become morepractical, as solar and wind produce power inconsistently.It allows power produced at peak time to be spread outthroughout the day, smoothing the irregular power output andallowing excess power generated to be stored until it is needed.

Fig. 1. The basic layout and components of a lithium ion batterySource: [13]

There is no known way to have perfectly efficient energystorage, and energy is always lost. Furthermore, there is a cor-relation between high energy storage and low charge/dischargespeeds and vice versa, making the balance of these two thingsa concern during battery design. Round trip efficiency is theratio between energy in and energy out of storage. Because it

costs energy to store energy, having a high round trip efficiencymeans that the amount of energy stored is very similar to theamount of energy returned, which is a goal in energy storagedesign [5].

High energy density usually means that an object can store agreat deal of energy, but objects with high energy density oftendon’t have a very high power density, such as most batteries.High power density means an object can take and get rid ofenergy very quickly. However, objects with high power densityusually have a lower energy density or don’t store energy wellover long periods of time, such as a capacitor. The inverserelationship between energy and power density are shown inthe Ragone plot, which is a graph of power density vs energydensity (Fig. 1).

Batteries are able to convert chemical energy into electricalcharge by making use of different chemical reactions thatcause electron flow. One characteristic batteries have is theirlarge energy density, and this can be attributed to its utilizationof chemical energy storage, which is significantly more energydense than mechanical or electrical energy storage, while alsohaving a relatively high power density. Due to this advantage,lithium ion batteries are becoming an attractive option for largescale energy storage.

Fig. 2. A Ragone plot of various different battery chemistriesSource: [12]

During the operation of a battery, the anode (negativeelectrode) releases electrons into a connected wire, whilesimultaneously releasing positively charged ions into the elec-trolyte in an oxidation reaction. The electrons are accepted atthe cathode, completing the circuit, and subsequently becomeattracted to the positive ions in the electrolyte [6]. The majorbenefit of electrochemical energy storage is the energy density.For example, a single AA battery can hold nearly 15,000 J ofenergy [10]. Meanwhile, an entire kilogram of water whichis pumped 1 meter into the air only holds around 9.8 J ofgravitational potential energy. As such, the battery containsabout 1,500 times the energy of the water, at only a fortiethof the mass.

Recently, lithium-ion batteries have emerged as the promi-nent rechargeable battery technology. They output power at ahigher voltage than the average AA battery or NiCd/NiMH

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(3.7V vs. 1.5/1.4V) and also have higher energy and powerdensities. Additionally, lithium-ion batteries have significantlylower self-discharge rates than NiMH batteries, allowing themto store energy for long periods of time. Lithium-ion batteriesare considered “secondary batteries”, meaning that they arerechargeable (up to 3000+ full cycles in the Lithium-ionbattery’s case), whereas alkaline batteries are single-use. Theyare also incredibly modular and can be used in a plethoraof electronic devices, from tiny wearables to megawatt-scalepower stations. As a result of the increased worldwide manu-facturing capacity and demand for lithium-ion batteries, priceshave dropped significantly, and continue to fall [2].

Despite their benefits, lithium-ion batteries are not withoutdrawbacks. They are hermetically sealed to prevent foreignliquids and gases from getting in, but this also means thatheat and gases generated from within the battery cannot escapeeasily either. This can contribute to catastrophic failure in theform of rapid combustion. Lithium-ion batteries are also notvery power dense compared to other chemical methods ofenergy storage. In comparison to gasoline, lithium-ion batteriescontain only one hundredth the energy per kilogram [15].

During the operation of a battery, heat is generated insidedue to Joule heating, which occurs as current flows througha material. The amount of heat produced by this processare completely normal and will not lead to any kind offailure. However, short circuiting caused by abuse or otherfactors can cause a high current, resulting in dangerouslyhigh battery temperatures. As the battery heats up, it beginsto degrade, eventually reaching a thermal runaway. Uponreaching high enough temperatures, the electrolyte vaporizes,causing hydrogen gas and oxygen gas to accumulate at theanode and cathode respectively. When enough of the gasesare exposed to heat, a combustion reaction can spontaneouslyoccur, triggering a catastrophic failure in the form of a rapidlyburning fire [11].

III. EXPERIMENTAL PROCEDURE

A. PyBaMM Data Collection

Virtual PyBaMM battery tests were run to gather dataabout battery behavior under various conditions. To run thesimulations, a web server was configured to run JupyterNotebook, with PyBaMM and all of its dependencies installed.For all voltage simulations, the Chen2020 battery modelincluded with PyBaMM was used. A Python script was writtento simulate a lithium-ion battery discharging to 3.3v andexecuting the following cycle:

1) Charge to 4.2 V at constant current2) Rest for 30 minutes3) Discharge to 2.7 V at constant current

The full simulation code can be seen in Appendix A. Thisscript was run under ambient temperatures of 5°C, 10°C, 20°C,and 50°C, with charge and discharge rates of C/10, C/2, 1C,and 2C. For each run, data was collected for temperature overtime and voltage over time.

B. Experimental Data Collection

During experimental testing, a Neware BTS 3000 batterytester was utilized to accurately control the voltage and currentof a battery and log data for further analysis. It has 0.1% full-scale accuracy and a 1Hz data logging rate. Shown in Figure 1,the batteries tested were housed within a modified minifridge,which utilizes Peltier coolers to establish precise control ofambient temperature. The cells used in the experiment werelithium-ion polymer battery cells from AA Portable PowerCorp. They measure 29mm x 16.5 mm x 6.5 mm, have anominal capacity of 210 mAh, and have a rating of at least300 cycles. All cells used for testing were brand-new andordered from the same batch to ensure that their propertiesare as similar as possible.

Fig. 3. An image of the miniature refrigerator used to house the batteriesduring tests

The cells were tested under the same conditions as thePyBaMM simulations, and were put through the same cycleof charging to 4.2 V, resting for 30 minutes, and dischargingto 2.7 V. During testing, data was collected for the cell current[A], voltage [V], charged capacity [mAh], and dischargedcapacity [mAh]. All experimental data was stored in .p files,and imported into Python using a script that parsed the dataand stored it in a dictionary. Data from the simulation wasstored directly in a dictionary as it was run. Following all datacollection and importing, the data was graphed for analysisusing Pyplot.

C. Thermal Simulation

To test PyBaMM’s capability of simulating battery failuredue to temperature, a Python script was written to simulatebattery behavior that would lead to an explosion. The code(seen in Appendix B) was created in order to determinehow changing certain parameters would impact the number ofcycles needed to reach a temperature high enough to cause acatastrophic failure, around 140 degrees Celsius [14]. This wasaccomplished by establishing a temperature-intensive charge-discharge cycle, and running it one hundred times (seen inFig. 4).

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Fig. 4. The experiment designed to charge at 4C, rest for 10 min, dischargeat 1C, rest for 10 min, and repeat 100 times

For a set of stress tests, the Marquis2019 parameter setwas used, allowing for several parameters such as ambienttemperature, cell cooling surface area, charge-discharge rates,and electrolyte concentration to be modified. The code for eachof these modifications can be seen in Fig. 5.

Fig. 5. This line of code was modified for each parameter manipulated

After establishing a control value for the preset parametersthat come with the Marquis2019 set, the behavior of lithium-ion batteries with higher or lower values for each of the afore-mentioned parameters was observed. The specific experimentprotocol is very similar to the previous Python script, but withthree new sections of code:

Fig. 6. Code establishing explosion temperature, initializing counter variable,and importing the Marquis2019 set

The first section, shown in Fig 6, introduces several criticalvariables and imports new parameters for the experiment.A hard cap on the temperature is established to act as athreshold temperature for battery failure. The variable calledExplodey Temp is initialized at 140 degrees Celsius for thispurpose. A counter variable called cycles is also initialized,and this variable keeps track of how many cycles the batterygoes through before explosion. Here, the Marquis2019 datasetis also imported.

Fig. 7. Code allowing for the manipulation of parameters, and the cycle tobe repeated.

The second section, shown in Fig 7, allows for the manip-ulation of parameters, and details the experiment cycle run.The line allowing for the manipulation of parameters allowedfor the modification of the ambient temperature, cell coolingsurface area, and electrolyte concentration. The experimentalcycle run is as follows:

1) Charge at 1C until 4.1 V2) Discharge at 1C until 3.3 V3) Rest for 10 minutes

This code was run until the battery temperature exceeded 140degrees Celsius.

Fig. 8. Code formatting output, extracting data, and simulating battery failure

The third section, shown in Fig 8, formats the output ofthe program, extracts data, and controls when the batteryexplodes. The first line extracts all of the Volume-averaged celltemperature values from the dataset and stores it in a variablecalled temperature. The last value of this array is pulled andprinted, and its value is compared with Explodey Temp. Ifit is smaller than Explodey Temp, the whole program willloop through again, but with cycles being 1 larger. However,if the value is greater than Explodey Temp, the program prints“Boom! Battery exploded during cycle “Cycles” ” and end theprogram.

This same procedure was repeated for each set of parametersto evaluate PyBaMM’s response to conditions that wouldcause an explosion. The full simulation code can be seen inAppendix C.

The parameters tested were ambient temperature, cell cool-ing surface area, and electrolyte concentration. The ambienttemperature test was run nine times, with each test increasingthe ambient temperature by ten degrees Celsius [°C]. The cellcooling surface area test was run five times, with each testincreasing the cell cooling surface area by .001 meters squared[m2]. The electrolyte concentration test was run six times, witheach test increasing the electrolyte concentration by 100 molper cubic meter [mol·m-3].

IV. RESULTS

A. PyBaMM voltage data compared with experimental data

Data gathered from several PyBaMM simulations and ex-perimental data were compared for analysis. An examplecomparison between the experimental results and PyBaMMsimulations is shown below in Fig. 9. In this graph, the voltageis plotted against time for both the experiment and simulationfor one cycle. For the experimental data and the simulation,the protocol for this cycle was a 1C rate charge to 4.2 V,followed by a 30 minute rest, followed by a 1C rate dischargeto 2.7v.

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Fig. 9. Comparison between simulated and experimental voltage over timeat a 1C rate

Comparing the experimental and simulation data from Fig.9, there are a few key differences. First, the simulation cycletook about fifteen minutes longer than the experimental cycle,a difference of 14%. Looking closer, both the charge anddischarge steps took longer for the experimental data, con-tributing the approximately fifteen minute difference overall.Possible reasons for this discrepancy include slight differencesbetween the chemistry battery being tested and the batterybeing simulated. Additionally, the voltage versus time graphshape is similar, mainly during the charging phase. In theexperimental data, voltage increases roughly logarithmically.Alternatively, the simulated voltage increases linearly through-out the charging process. Graphs for simulated vs experimentaldata at rates 2C and C/2 can be found in Appendix D.

Fig. 10. Comparison between simulated and experimental voltage over timeat a C/10 rate

Comparing data from a significantly lower rate in Fig. 10,similar observations can be made. In this test, the simulationcompleted 12% faster than the experiment, compared with14% at 1C. Additionally, the difference in graph shape is also

similar, with the simulated voltage following a more linearpath, while the experimental data follows a curve.

B. Battery Explosion simulation results

After running the code detailed in Appendix B, the Py-BaMM simulated battery delivered extremely high temperaturevalues as shown in Fig. 11 that appeared to grow continuously.

Fig. 11. Graph of the PyBaMM battery’s Volume-averaged cell temperaturerelative to the ambient temperature, which was set to room temperature (25°C)

C. Li-ion battery explosion factor simulations

In the PyBaMM simulation data, it was discovered thatthe ambient temperature played absolutely no role in thetemperature of the PyBaMM-simulated battery. Every singletest had the battery explode after twenty-four cycles, regardlessof temperature. Such was also the case for the cell coolingsurface area. Again, every test exploded after twenty-fourcycles, regardless of the surface area given to the program.The concentration of electrolyte does not play a role in batterytemperature as well. Every test exploded after twenty-fourcycles. The results from the ambient temperature, cell coolingsurface area, and electrolyte concentration tests had identicalresults, regardless of what the values of these parameterswere. However, the value of the discharge current plays a rolein PyBaMM; by comparing the temperature increase of thesimulated cell under different charge/discharge rates, insightcan be gained about how discharge rate contributes to batteryfailure.

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Fig. 12. Comparison between different discharge rates and their impact onthe battery’s change in temperature

Fig. 12 shows cell temperature plotted over total testprogress and shows that a 2C discharge rate increases the cell’stemperature over ambient temperature by more than 5 timesas much as a C/10 discharge rate. Additionally, the 2C testcycle took less than one twentieth of the time of the C/10test cycle, meaning that the temperature increased much morerapidly. This increase makes sense because a higher currentrunning through a battery leads to a higher amount of jouleheating, significantly increasing the cell’s overall temperatureabove ambient. Extrapolating from this data, a short circuit,causing tens of amps to flow through a battery, definitely hasthe potential to heat the battery enough to cause vaporizationof electrolyte and ultimately explode.

V. DISCUSSION

Based on the data collected, it can be determined thatdespite its advanced battery models, PyBaMM does not accu-rately simulate battery explosions and temperature. The firstshortcoming that makes PyBaMM inaccurate is the software’sinability to track heat loss from the battery or heat gain fromexternal sources. This is best shown by the battery’s constanttemperature, even during rests, and the nonexistent effect ofambient temperature on the battery’s internal temperature. Thisis inaccurate because although most lithium-ion batteries arehermetically sealed, heat can still be transferred in and outthrough conduction, and during rest periods, the temperaturesshould move in the direction of equilibrium with the ambienttemperature. Another limitation lies in PyBaMM’s inabilityto simulate battery failure and general battery deterioration.The simulations do not take these behaviors into considerationwhatsoever. In the test in which the battery was cycled onehundred times, there were no notifications or warnings whenthe battery approached over 200 degrees Celsius [°C] aboveroom temperature, which is significantly more than enoughto cause any lithium ion battery to explode. This draws the

relative safety of any batteries simulated in PyBaMM forsafety into question.

Despite PyBaMM’s failure to properly simulate batteryfatigue and thermal behavior, it did closely match the voltageover time results that were obtained from experimental testing.This makes PyBaMM a useful source of information for theelectrical behavior of lithium ion batteries, but gives it limitedusefulness when attempting to understand and test the thermalproperties of batteries. As such, the data gathered from thePyBaMM simulations should only be used to make generalconclusions, like how a battery tends to act under certain con-ditions. More specific predictions of battery behavior shouldbe based on data collected from physical batteries instead.

Potential sources of error in the experimental data may liein the regulation of ambient temperature. The fridge used fortemperature regulation maintains its temperature by heatingand cooling consecutively, putting the temperature of the airinside the fridge in minute, but constant fluctuation. Thismeans that the ambient temperature surrounding the batterywill also fluctuate constantly. Furthermore, the temperature ofthe fridge is only measured at one location, so the temperaturemeasurements made by the instrument may not reflect theeffective temperature of the air around the battery. Anotherpotential source of error is that despite being from the samebatch, the batteries used for testing may not be completelyidentical due to tiny manufacturing variances.

VI. CONCLUSIONS

It is clear that despite its usefulness in simulating lithium-ion batteries, the PyBaMM modeling software is greatlyflawed in that it doesn’t account for most of the factorsleading to catastrophic battery failure. As for determiningthe relationships between ambient temperature, cell coolingsurface area, electrolyte concentration and battery temperature,PyBaMM did not give sufficient insight into their effects onactual lithium-ion batteries. These results also showed thetrue limitations of simulations, as well as simulation-basedresearch.

However, PyBaMM had plenty of benefits as well. Notonly did it enable tests to be run at a much higher ratethan in a physical lab, the simulations provided a lot of data,including thermal information, which would otherwise wouldnot have been available as a result of the limitations of theCOVID-19 lock down. The simulations showed general trendswhich may be useful in understanding the certain practiceswhich put lithium-ion batteries under stress. While the specificlimitations of this stress will be different in the real world, itcan be concluded that certain practices are not healthy forlithium-ion batteries, and can cause artificial degradation. Forexample, the act of charging and discharging a battery in rapidsuccession puts inherent stress on the battery and is detrimentalto the longevity of lithium-ion batteries.

Already, technology companies are building around thecharacteristic limitations of lithium-ion batteries by intro-ducing stop-gap measures which shut a device down onceunexpectedly high temperatures are detected in or near the

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battery itself. In the future, it will be important that the groupperforms further testing on physical batteries. Initial testscould include modifying the tests run in PyBaMM to work onphysical batteries instead. Through this testing, the aspects ofthe battery which have the greatest impact on heat generationcan be revealed. With this information, new types of batteriescan be developed which have slightly varied compositions, thatimprove on the current characteristics of lithium-ion batteries.For example, a battery may be configured so that it is able todissipate the heat generated by its charging and dischargingprocesses.

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APPENDIX A

1 import pybamm # importing pybamm2 import sys #allows access to files3 # the above script has functions named get_data(), get_charge(data,rate), and

↪→ get_discharge(data,rate)4 from matplotlib import pyplot as plt # this is for plotting5 sys.path.insert(0,"/home/thodson/data/") #allows importing data script6 from data_script import * # here is where we are pulling the data7

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9 def c_to_k(c):10 return c + 273.1511

12 def k_to_c(k):13 return k - 273.1514

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16 chemistry = pybamm.parameter_sets.Chen2020 #get battery chemistry17 parameter_values = pybamm.ParameterValues(chemistry=chemistry) #put battery chemistry

↪→ in a list18 model = pybamm.lithium_ion.SPMe() #set battery model19

20 parameter_values["Ambient temperature [K]"] = c_to_k(20) #modify ambient temperature21 parameter_values["Reference temperature [K]"] = c_to_k(20)22 parameter_values["Initial temperature [K]"] = c_to_k(20)23

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25 data = get_data()# import expermintal data26

27 rates = ["C/10", "C/2", "1C", "2C"] # define charge rates28

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30 simdata = {31

32 }33

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35 for i in rates:36 experiment = pybamm.Experiment(37 [38 f"Discharge at 1C until 2.7 V",39 "Hold at 3.4 V until 50 mA",40 "Rest for 30 minutes",41 f"Charge at {i} until 4.2 V",42 "Rest for 30 minutes",43 f"Discharge at {i} until 2.7 V"44 ] * 145 )46 sim = pybamm.Simulation(model,experiment=experiment, parameter_values =

↪→ parameter_values) # call on the pybamm package to run a simulation with our↪→ parameters

47 sim.solve()48 simdata[i] = sim

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APPENDIX B

1 import pybamm # we need to first import the pybamm package2

3 options = {"thermal": "x-full"} # we additionally need a thermal model (so we can get↪→ temperature info)

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5 model = pybamm.lithium_ion.SPMe(options=options) # loading in options6

7 experiment = pybamm.Experiment( # details of battery cycling experiment below8 [9 "Discharge at 4C for 15 minutes or until 3.3 V",

10 "Rest for 10 minutes",11 "Charge at 1C for 60 minutes or until 4.1 V",12 "Rest for 10 minutes",13 ] * 10014 )15

16 sim = pybamm.Simulation(model,experiment=experiment) # call on the pybamm package to↪→ run a simulation with our parameters

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18 sim.solve()19 # model.variables.search("temp") # this function can be used to search for variable to

↪→ names to plot20 # using the variables found from the search command above, we can choose what we want

↪→ to plot below21 quick_plot_vars = ["Battery voltage [V]",["Volume-averaged cell temperature","Ambient

↪→ temperature"],"Current [A]"]22

23 sim.plot(quick_plot_vars) # this command plots

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APPENDIX C

1 import pybamm # we need to first import the pybamm package2

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4 cycles = 0 #Counter for the number of cycles we will do5 temperature = 0 #literally just to declare the temperature integer. This number could

↪→ be anything6 Explodey_temp = 273.15+140 #temperature at which the electrolyte vaporizes and battery

↪→ gets ready to go boom7 Min_temp = 298.15 #Default8 print("Explosion temperature = " + str(Explodey_temp))9 while(1==1):

10 cycles+=111 print("Cycle #" + str(cycles))12 options = {"thermal": "x-full"} # we additionally need a thermal model (so we can

↪→ get temperature info)13 chemistry = pybamm.parameter_sets.Marquis201914

15 parameter_values = pybamm.ParameterValues(chemistry=chemistry)16

17 # change input temperatures to be 40 deg C using variable above (note that input↪→ temperatures need to be in K, so we need to convert)

18 parameter_values["Cell cooling surface area [m2]"] = 0.0093100000000000005, #.001↪→ m2 greater than normal

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20 model = pybamm.lithium_ion.SPMe(options=options) # loading in options21

22 experiment = pybamm.Experiment( # details of battery cycling experiment below23 [24 "Charge at 1C until 4.1 V", # initial charge step to 100%25 # start at 100%26 "Discharge at 1C until 3.3 V", # everything from this point on is our

↪→ simulation27 "Rest for 10 minutes"28 ] * cycles29 )30 sim = pybamm.Simulation(model,experiment=experiment) # call on the pybamm package

↪→ to run a simulation with our parameters31

32 sim.solve_fast()33 solution = sim.solution34 temperature = solution["Volume-averaged cell temperature [K]"]35

36 print("Min_temp = " + str(Min_temp))37 print("Temperature = " + str(temperature.entries[-1]))38 print("Temperature increase for cycle " + str(cycles) + " = " + str(int(temperature

↪→ .entries[-1])-Min_temp))39 Min_temp = temperature.entries[-1]40 if(int(temperature.entries[-1])>=Explodey_temp):41 print("BOOM! Battery exploded during cycle " + str(cycles))42 break

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APPENDIX D

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ACKNOWLEDGEMENTS

The authors of this paper would like to acknowledge andthank the project mentor, Thomas Hodson, for being a guideand providing the experimental data from his lab at ColumbiaUniversity; Residential Teaching Assistant and Project LiaisonNicholas Kravchenko for his invaluable insight; Dean JeanPatrick Antoine, the director of the Governor’s School of En-gineering and Technology, for creating a unique environmentfor so many students to come together especially during suchdifficult times; Dean Ilene Rosen, the Director Emeritus ofthe Governor’s School of Engineering and Technology, forher continued support in such a wonderful program; HeadCounselor Rajas Karajgikar for his leadership and guidance;Research Coordinator Benjamin Lee for giving us directionwith the project; and lastly, the sponsors—Rutgers University,Rutgers School of Engineering, Lockheed Martin, the Gover-nor’s School of Engineering and Technology Alumni, and theNew Jersey Space Grant Consortium—for providing the fundsand resources to make this research possible.

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