Final project for APC524 Fall 2021, Princeton University. Single-particle modelling (SPM) for lithium-ion batteries (LIBs).
By Alex Caldwell, Alex Preston, Antti Valkonen, Jerry Xiang, Jose Yanez.
The third-party packages required are: python3, numpy, scipy.interpolate, math, and matplotlib. These packages can all be installed via pip3.
The repo can be cloned from https://github.com/jerryzxiang/libsim.git or installed via pip3 install git+ssh://[email protected]:jerryzxiang/libsim.git
This program is run through the driver code file, main.py, which takes 8 command line arguments. As of now, there is no GUI. The inputs are the cathode, anode, input current, capacity of the cell in amp hours, the number of radial segments, the simulation time in seconds, and the time steps. An example is shown here for an LIB with an LFP cathode and graphite anode:
python3 main.py 'LFP' 'graphite' 0.5 2.3 1.5 10 10 0.001
To get help, use
python3 main.py -h
All documentation is generated using Sphinx. In order to generate the documentation you must have Sphinx installed into your computer.
Install Sphinx by running the following command in your terminal window:
python -m pip3 install sphinx
Once Sphinx is installed, navigate to the sphinx_doc folder and run the following command:
sphinx-apidoc -o . ..
If you created changes to the documentation, you must add the -h option after .. in order to
overwrite the .rst files generated by Sphinx with the new updates.
The .rst files are what Sphinx uses to generate the final output documentation. There are many
output file options for the documentation including html and pdf. You can go over the various
output file options by typing make help.
To generate a pdf you can run the command make latexpdf. It will generate the documentation
under __build.
(You must have the basic latex packages installed in your machine to generate the pdf.)
One of the research challenges in the development of lithium-ion batteries (LIBs) is to predict their behavior under different operating modes, which is useful for estimating state of charge and state of health of batteries in electric vehicles (EVs). There exist empirical models, mostly equivalent circuit-based, widely used in the Battery Management Systems (BMS) of electronics and EVs. These types of models use past experimental data of a battery to anticipate its future states. Most of the experimental data used to find charge/discharge characteristics rely on the current or cell potential. On one hand, these empirical models are relatively fast and simple computationally, but they have drawbacks. For example, the physics-based parameters are not able to be predetermined. The battery characteristics are not updated as the battery ages and a battery’s model is unique to itself - it does not apply to all batteries but only a specific type.
Electrochemical models are, on the other hand, more sophisticated. These models are based on chemical/electrochemical kinetics and transport equations. They may be used to simulate the LIB's characteristics and reactions. Popular electrochemical models are the Pseudo-two-Dimensional (P2D) Model and Single Particle Model (SPM). The P2D model is commonly used in lithium-ion battery studies, and the predicted behavior of this model matches experimental data quite accurately. A significant drawback with this model is the difficulty to use in real-time due to its computationally expensive nature. The SPM model simplifies anode/cathode interactions and reduces the dimensionality down to one dimension, which greatly enhances its computational capabilities. However, it places greater importance on the parameters of the anodes and cathodes.
This project focuses on modelling lithium-ion batteries (LIBs) using a Single Particle Model (SPM). It accounts for the impact of complex parameters such as ion diffusivity, ion particle radius, and maximum ion concentration at the ion’s surface on the performance of the battery. Modelling these parameters is useful to compare to experimental results. Eventually, this project can be expanded to estimate and predict the state of charge (SOC) and state of health (SOH) of LIBs, in order to reduce the computational cost and allow for the model to be implemented in real-time EV LIBs modeling.
Background research and inspiration for this project derived from the below references.
[1] Hake, A. (2015). SINGLE-PARTICLE MODELING AND EXPERIMENTAL PARAMETER IDENTIFICATION FOR A LITHIUM-COBALT-OXIDE BATTERY CELL. THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE. https://honors.libraries.psu.edu/files/final_submissions/3057
[2] Meng, J., Luo, G., Ricco, M., Swierczynski, M., Stroe, D.-I., & Teodorescu, R. (2018). Overview of lithium-ion battery modeling methods for state-of-charge estimation in electrical vehicles. Applied Sciences, 8(5), 659. https://doi.org/10.3390/app8050659
[3] Jokar, A., Rajabloo, B., Désilets, M., & Lacroix, M. (2016). Review of simplified pseudo-two-dimensional models of lithium-ion batteries. Journal of Power Sources, 327, 44–55. https://doi.org/10.1016/j.jpowsour.2016.07.036