Assessment of Round-Trip and Coulombic Efficiency in Lithium-Ion Batteries Using a Mathematical Modeling Approach under Variable Operating Conditions
This study develops and experimentally validates an analytical framework that quantifies the coupled evolution of Coulombic efficiency, capacity retention, and round-trip performance in lithium-ion batteries under varying aging and thermal conditions, revealing significant efficiency degradation alongside capacity loss over 1500 cycles.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Every day, billions of people rely on small, invisible power sources to keep their phones alive, their cars moving, and their homes lit. These are lithium-ion batteries, the rechargeable workhorses of the modern world. Inside them, tiny charged particles called ions shuttle back and forth between two ends of the battery, storing energy when plugged in and releasing it when needed. For these batteries to be useful, they must be efficient: they need to give back almost as much energy as they take in, and they must hold that energy for a long time before wearing out. However, like any machine, these batteries do not last forever. As they age and are used repeatedly, they slowly lose their ability to store power, and the process of charging and discharging becomes less perfect. Understanding exactly how and why this happens is critical, especially as the world shifts toward electric vehicles and large-scale energy storage, where a battery's failure can mean a car stopping on the highway or a city losing power.
A team of researchers set out to map this slow decline with precision. They wanted to move beyond simply counting how many times a battery could be charged before it died. Instead, they built a mathematical model to track two specific measures of health: how much energy is lost during the charging and discharging process, and how much total capacity remains after thousands of cycles. They tested their ideas using a standard 3.6-volt lithium-ion cell, the kind often found in portable electronics, subjecting it to a rigorous regimen of charging and draining. They ran this cycle 1,500 times, a number chosen to simulate years of heavy use, while also testing how the battery behaved in temperatures ranging from freezing cold to scorching heat.
The results painted a clear picture of aging. As the battery cycled through its life, its ability to hold a full charge shrank significantly. At the start of the test, the battery could deliver about 2.7 ampere-hours of power, a measure of its total energy capacity. After 1,500 cycles, that number dropped to roughly 1.8 ampere-hours. This represents a loss of about 34 percent of its original storage power. More importantly, the researchers found that the battery became increasingly inefficient at moving that energy. In the beginning, the battery was very good at keeping what it was given, returning about 90 percent of the charge it received. By the end of the 1,500 cycles, that efficiency had plummeted to just under 60 percent. This means that as the battery aged, a growing portion of the electricity put into it was simply lost as heat or trapped inside, never making it back out to power a device.
The study also revealed that temperature plays a major role in this degradation. When the researchers tested the battery in warmer conditions, the amount of energy it could deliver dropped noticeably. Even without counting the cycles, simply raising the temperature from a cool 0 degrees Celsius to a hot 75 degrees Celsius caused the battery's discharge capacity to fall by more than 17 percent. This suggests that keeping batteries cool is just as important as how often they are used. The researchers also tracked the time it took to complete a full charge and discharge cycle. Surprisingly, this time got shorter as the battery aged. While a shorter cycle might sound like an improvement, it was actually a sign of weakness. Because the battery could no longer hold as much charge, it filled up and emptied out much faster, completing the round trip in less time simply because there was less energy to move.
To ensure their mathematical model was accurate, the team built a physical prototype that mimicked the battery's behavior in a real-world setting. They used a microcontroller to manage the charging and discharging, measuring the current flowing in and out with high precision. When they compared the numbers from their computer simulations to the data from their physical hardware, the two matched closely. This confirmed that their model could reliably predict how a battery would perform under different conditions without needing to run thousands of hours of physical tests. The work provides a practical tool for engineers and battery managers. By monitoring how efficiently a battery moves energy and how much capacity it retains, systems can be designed to better predict when a battery is nearing the end of its useful life. This is vital for the future of electric transport and renewable energy, where knowing the true health of a battery ensures safety and reliability long after the initial purchase.
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