The lithium-ion battery (LiB) has become increasingly popular in electric vehicles (EVs), laptops, phones and many other devices that people use every day. It is popular due to its high energy density, low cost, lack of memory effect (typical of older battery types), longer&nbsp;life cycle (more full cycles till battery dies), and more. Because of its common use in everyday applications, knowing the state of charge (SOC) of a lithium-ion battery becomes an important problem to solve. For EVs the SOC of the LiB is especially important because it relates directly to the number of miles the car can drive before the battery is dead. Laptops and mobile phones typically have an indicator in the shape of a battery that allows the user to know the percentage of power the battery has left out of its full capacity. An indicator with the time left until the battery can no longer provide power is also usually displayed. These indicators rely on some kind of battery model in order to tell the user how much charge the battery has left.&nbsp; 
The first goal of this work was to develop and present a new battery model derived from fundamental principles of electrochemistry, Fick's first law of diffusion, Ohm's law, and a mass balance of lithium-ions between the anode and cathode. This new model aims to accurately determine&nbsp;the battery SOC by tracking the movement of lithium ions without being too computationally demanding. A basic circuit analysis was performed using Ohm's voltage law to obtain an equation that calculated the battery voltage at any given time. The cell voltage depends on the amount of lithium in the anode and cathode, the current in the circuit and is reflected in the model. Due to the highly nonlinear nature of the voltage equation, a linearization technique was applied to reduce the computational effort required. The voltage equation helped relate the amount of lithium in the anode and cathode to a measurable parameter, the actual voltage of the battery. How well the model matched the measured voltage was an indication of the model's accuracy. 
The amount of lithium in both the anode and cathode were&nbsp;modeled by considering the fact that the lithium-ions diffuse from the anode to the cathode across the separator&nbsp;while discharging the battery, and assuming that mass is conserved. While it is assumed that mass is conserved, one consideration for the model is the percentage of lithium that is involved in the chemical reaction, where in this case it is assumed that 100% of the lithium ions take part in the reaction. This value can change to reflect the lowering state of health of the battery with time.&nbsp; Four control volumes were modeled in the cell (a bulk and surface volume for both the anode and cathode) and make up the four states in the equation, and&nbsp;were written in state-space form, where the output is the cell voltage.&nbsp; 
The second goal&nbsp;of this work was to optimize the parameters of the battery model to make it match experimental data.&nbsp; A cost function was defined as the sum of the square of the&nbsp;difference between the actual voltage and the predicted voltage.&nbsp; A&nbsp;genetic algorithm was implemented to minimize the cost function, and the probabilities of&nbsp;replacement and mutation were allowed to vary to find the best possible parameters.&nbsp; The cost function was reduced from&nbsp;3.5728 to&nbsp;3.3734 over 21,602 data points.&nbsp; The new battery model matched the experimental voltage very well and is ready to be&nbsp;used to determine the SOC of LiBs in use today.

Parameter Optimization of a New Battery Model

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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