Linking Calendar and Cycle Ageing in Lithium-Ion Batteries through Consistent Parameterisation of an Electrochemical-Thermal-Degradation Model

This paper presents a consistently parameterized electrochemical-thermal-degradation model using PyBaMM to predict the capacity fade, state-of-health, and remaining useful life of NMC lithium-ion cells under 81 distinct calendar and cyclic ageing conditions, thereby providing mechanistic insights into the competing effects of solid-electrolyte interphase growth, lithium plating, and active material loss.

The Gist

Imagine you have a very expensive, high-tech lunchbox (a lithium-ion battery) that powers your electric scooter or phone. You want to know two things: How long will it last before it stops working? and What exactly is "eating" the food inside it over time?

This paper is like a sophisticated food critic and a weather forecaster rolled into one. The author, Ganesh Madabattula, built a digital "virtual twin" of a battery to simulate how it ages under different conditions, without needing to destroy thousands of real batteries in a lab.

Here is the breakdown of the paper using simple analogies:

1. The "Monkey" Problem

The author starts with a funny analogy: Imagine a bunch of hungry monkeys (degradation mechanisms) and a pile of bananas (the battery's capacity).

• The Question: If you leave the bananas out for a year, how many are left? Which monkey ate the most? Did the hot weather make them eat faster?
• The Reality: In a battery, the "monkeys" are chemical reactions that slowly eat away the battery's ability to hold a charge. Some monkeys are lazy, some are aggressive, and they all behave differently depending on the "mood" of the battery (temperature, how full it is, and how hard you push it).

2. The Three "Monkeys" (Degradation Mechanisms)

The paper focuses on three main ways a battery gets tired:

1. The SEI Layer (The Rusty Shield): Imagine the battery has a protective skin (like a layer of rust forming on a car). Over time, this skin gets thicker and eats up some of the battery's "fuel" just to exist. This happens mostly when the battery sits hot and fully charged.
2. Lithium Plating (The Ice on the Road): When it's cold and you try to charge the battery fast, the "fuel" (lithium) can't move fast enough. It gets stuck on the surface like ice on a road, forming a hard layer that blocks future fuel from getting in. This is dangerous and wastes capacity.
3. Active Material Loss (The Crumbling Bricks): Inside the battery, there are tiny bricks that store energy. Every time you charge and discharge, these bricks expand and shrink. Eventually, they crack and crumble (like old bricks in a wall), so they can't hold any energy anymore.

3. The "Virtual Lab" (The Model)

Instead of testing one battery for 10 years, the author used a computer program called PyBaMM to run a simulation.

• The Setup: They created a digital version of a specific battery (the LG M50).
• The Test: They ran 81 different scenarios. Think of this as testing the battery in 81 different "weather and driving conditions" at once:
  • Temperatures: Cold (10°C), Mild (25°C), Hot (40°C).
  • Charging Speed: Slow (0.1C), Medium (0.3C), Fast (1.0C).
  • How Full: Sitting at 10%, 60%, or 100% charge.
  • How Deep: Draining the battery by 50%, 70%, or 90% before recharging.

4. The Surprising Discoveries

The simulation revealed some counter-intuitive truths that you wouldn't guess just by looking at a battery:

• The "Rest" Trap: Sometimes, sitting still is worse than driving.
  • Example: If you drive a little bit (50% drain) but then leave the battery sitting fully charged (100%) in a hot room, the "Rusty Shield" (SEI) eats the battery faster than if you drove a lot (90% drain) and then rested. The long rest time at high heat is the killer.
• The Cold vs. Hot Swap:
  • In hot weather, the "Rusty Shield" is the main villain.
  • In cold weather, the "Ice on the Road" (plating) and "Crumbling Bricks" (stress) take over.
  • The Twist: Sometimes, a battery lasts longer at 40°C than at 25°C if you change how you use it (like charging it very slowly). This proves you can't just say "heat is bad" or "cold is bad"; it depends on the whole picture.
• The "Knee" Effect: Batteries don't always die slowly. Sometimes they fade gently (linear), and sometimes they seem fine for years and then suddenly crash (sup-linear/knee-type). The model predicts exactly when that "sudden death" happens based on your habits.

5. Why This Matters

Before this, scientists had to guess how batteries would age in new situations. If they tested a battery in summer, they couldn't be sure how it would act in winter or if you drove it aggressively.

This paper provides a universal rulebook. It shows that to predict how long a battery lasts, you have to look at the entire story: the temperature, how fast you charge, how deep you drain it, and how long you let it sit.

The Bottom Line:
The author built a crystal ball for batteries. By understanding which "monkey" is eating the bananas in which situation, we can design better batteries, tell electric car owners exactly how to charge them to make them last longer, and predict when a battery needs to be replaced before it fails.

The paper even made all the data from these 81 simulations available for free, so other scientists can use it to train AI and build even better battery systems in the future.

Technical Summary

1. Problem Statement

Predicting the State-of-Health (SoH) and Remaining Useful Life (RUL) of Lithium-Ion Batteries (LIBs) is a critical challenge for applications like electric vehicles (EVs) and energy storage. The core difficulty lies in the complex, coupled interactions between multiple degradation mechanisms (Solid-Electrolyte Interphase (SEI) growth, Lithium plating, and Active Material Loss (LAM)) which vary non-linearly with usage conditions:

• Usage Variables: C-rate, Depth-of-Discharge (DoD), Rest State-of-Charge (SoC), and Temperature.
• The Gap: Existing models often fail to consistently parameterize these mechanisms across different operating modes (calendar vs. cyclic). Furthermore, experimental validation for all possible combinations of these variables is impractical due to time and cost constraints. There is a lack of comprehensive physics-based models that can elucidate the competing effects of calendar and cyclic ageing under diverse conditions.

2. Methodology

The study employs a physics-based modeling framework using the PyBaMM (Python Battery Mathematical Modelling) open-source library.

• Model Architecture:
  • Base Model: Doyle-Fuller-Newman (DFN) electrochemical model (P2D).
  • Thermal Model: A lumped thermal model accounting for resistive heating, entropic heat, and convective cooling.
  • Degradation Mechanisms: The model integrates three primary degradation modes:
    1. SEI Growth: Modeled as a mixed diffusion-reaction limited process at the anode.
    2. Lithium Plating: Modeled as an irreversible reaction at the anode, driven by over-potential.
    3. Loss of Active Material (LAM): Modeled as stress-driven fracture in both positive and negative electrodes due to concentration gradients.
• Cell Chemistry: The model simulates an LG M50 (INR21700) cell with an NMC811 cathode and a composite Graphite/Si anode.
• Parameterisation Strategy:
  • The authors did not rely on a single dataset. Instead, they tuned degradation parameters to match Degradation Mode Analysis (DMA) data from experimental literature (Kirkaldy et al.).
  • Temperature Dependence: Parameters were tuned to reflect specific dominant mechanisms at different temperatures:
    • High Temp (40°C): Dominated by SEI growth.
    • Moderate Temp (25°C): Balanced SEI and mild LAM.
    • Low Temp (10°C): Dominated by Lithium plating and LAM (due to slow diffusion and high stress).
• Simulation Scope:
  • Calendar Ageing: 9 combinations of Temperature (10, 25, 40°C) and Rest SoC (30, 60, 100%).
  • Combined Ageing: 81 unique combinations of Temperature, C-rate (0.1, 0.3, 1.0C), Rest SoC (10, 60, 100%), and DoD (50, 70, 90%).
  • Protocol: Simulated a daily cycle (charge/discharge) followed by a rest period at a specific SoC to capture both cyclic and calendar effects.

3. Key Contributions

1. Consistent Parameterisation Framework: The paper presents a robust strategy to parameterize coupled degradation mechanisms using DMA insights, ensuring the model behaves physically correctly across a wide range of temperatures and conditions.
2. Comprehensive Simulation Dataset: The study generates and makes available a massive dataset covering 81 combined ageing scenarios and 9 calendar ageing scenarios, providing a benchmark for future model validation and data-driven research.
3. Mechanistic Insight into Competing Effects: The work explicitly demonstrates how calendar and cyclic ageing compete. For instance, it reveals that under certain conditions (high temp, low DoD), the rest time (calendar ageing) contributes more to capacity loss than the cycling time itself, a counter-intuitive finding for some operating profiles.
4. Prediction of Non-Linear Trajectories: The model successfully predicts sub-linear, linear, and super-linear (knee-point/accelerated) capacity fade trajectories based solely on usage conditions, without needing empirical curve fitting for each specific case.

4. Key Results

• Cycle Life Variability: The predicted cycle life to reach 75% SoH varies drastically from 0.8 to 14 years, depending on the specific combination of usage variables.
• Temperature and Mechanism Dominance:
  • 40°C: Capacity fade is dominated by SEI growth. Higher temperatures accelerate SEI kinetics.
  • 10°C: Capacity fade is dominated by Lithium plating and LAM. Low temperatures slow Li diffusion, increasing over-potential (promoting plating) and concentration gradients (promoting stress/LAM).
• The "DoD Paradox" (Competing Effects):
  • At 25°C and 40°C, a 50% DoD cycle resulted in faster capacity fade than a 90% DoD cycle.
  • Reasoning: The 50% DoD cycle takes less time to complete, leaving more time for the battery to rest at high SoC (100%). At high temperatures, this extended rest period accelerates calendar ageing (SEI growth), which outweighs the reduced cyclic stress of the lower DoD.
  • At 10°C, the trend reversed: 90% DoD caused faster fade because cyclic ageing (LAM) dominated over the minimal calendar ageing effects at low temperatures.
• Rest SoC Influence: High rest SoC (100%) significantly accelerates calendar ageing, particularly at elevated temperatures. Reducing rest SoC to 10% or 60% can extend cycle life by over an order of magnitude in some scenarios.
• Trajectory Types: The model showed that the same cell chemistry can exhibit:
  • Sub-linear fade: Gentle operation.
  • Linear fade: Moderate operation.
  • Super-linear (Knee) fade: Aggressive operation (high C-rate, high temp, high SoC).

5. Significance

• Battery Management Systems (BMS): The findings highlight that SoH and RUL cannot be estimated based on a single metric (like total cycles or average temperature). BMS algorithms must account for the history of usage (e.g., how much time was spent resting at high SoC vs. cycling) to accurately predict remaining life.
• Design and Operation: The study provides guidelines for extending battery life, such as avoiding high rest SoC at high temperatures or managing DoD based on ambient temperature.
• Data-Driven Modeling: By providing a validated, physics-based dataset for 81 complex scenarios, this work enables the training of "physics-informed" machine learning models, bridging the gap between expensive experimental testing and rapid data-driven prediction.
• Validation of Physics-Based Models: The work demonstrates that a single, consistently parameterized physics-based model can extrapolate to unseen conditions better than empirical models, which often fail when usage patterns change.

In conclusion, this paper establishes a rigorous methodology for linking electrochemical degradation mechanisms to macroscopic battery life, proving that the interplay between calendar and cyclic ageing is highly non-linear and condition-dependent.