Fuel-Gauging: Part 4 – Aging and peak load effects on usable capacity
Fuel-Gauging: Part 4 – Aging and peak load effects on usable capacity
In the last of this quartet (Part 1, Part 2, Part 3) of articles, I consider the effects of aging and peak demand on usable capacity.
In Part 1, I had defined the problem in predicting TTE (time-to-empty) when a fuel gauge sees a dynamic load. In Part 2, the characteristics of a dynamic load and some of the methods fuel gauges use to handle them were discussed. Part 3 discussed how remaining capacity and TTE (time-to-empty) is affected by loads, temperature, and how a reasonably accurate estimate can be made when they are modeled.
FCC and Aging
Anecdotally, users may have observed that as the batteries in their devices undergo multiple charge/discharge cycles, the average per charge runtime would reduce. This is because of material degradation inside the batteries and factors like loss of charge carriers, increased internal impedance due to irreversible chemical and physical reactions. Since a multitude of factors are involved in modeling this, a combination of approaches needs to be adopted.
Some of them are
Cycle Life Degradation Model
This is one of the simplest models and attempts to create a single factor k that accounts for the effects of physical and chemical degradation. It associates the initial capacity C0 of the battery and models the current capacity after x number of cycles CN over N cycles.
The fitted Arrhenius model
Temperature is one the very influential factors affecting battery aging. At high temperatures chemical reactions that degrade the battery are sped up, at low temperatures lithium plating or reduced ion mobility cause the battery to lose charge carriers or have reduced conductivity. The Arrhenius equation can be used to model this. The equation is stated here,
Using experimental data and curve fitting techniques to fit the Arrhenius equation, the activation energy for battery degradation processes can be estimated. This is then used to predict the rate of aging at different temperatures, which is crucial for battery management systems and lifetime predictions.
State of Charge (SOC) and Depth of Discharge (DOD)
Depth of discharge is defined as the amount by which a battery is discharged in relation to its full charge. It is a ratio and can also be expressed in percentage. When a battery is cycled repeatedly, its depth of discharge (DOD) significantly impacts battery aging.
Simply put, a battery that is frequently discharged to very low states of charge (near 0%) and charged to high states (near 100%) tends to degrade faster than one that stays within a moderate range (e.g., 20%–80% SOC).
A lot of manufacturers use coulombic efficiency (CE) as one of the parameters to market the quality of cells and to measure the degradation due to cycling. Many Li-ion cells today come with efficiencies of greater than 90%. While this may seem to be great on the surface, the graph below shows how this can be equally misleading.
The above plot taken from Nature(1) shows that even with a 99% retention and coulombic efficiency, there is an extremely sharp reduction in capacity even within the first few tens of cycles. Cells in mass production typically feature 99.9% CE and even this is seen to cause a 20% drop in capacity after about 200 cycles.
If we take Coulombic efficiency (CE) to be the ratio of charge out to charge in, then
A simple empirical model to represent this could be:
The function f(DOD) can take various forms, but a common approach is to use a power law:
Where α is the sensitivity of capacity loss to DOD. Typically higher values of α indicate a greater sensitivity to DOD.
Electrochemical Model
Electrochemical models can simulate the physical processes occurring inside the battery, such as ion transport, SEI growth, and material degradation. These models are more detailed and complex than empirical models and are typically based on the P2D (Pseudo 2-Dimensional) model or SPM (Single Particle Model). They use partial differential equations to describe the movement of ions and electrons within the battery. When applied to aging, these models consider:
1.?????? Ion transport resistance: The increase in internal resistance over time due to changes in the SEI layer or material degradation.
2.?????? Lithium-ion diffusion: The difficulty of lithium ions moving within the electrodes as the battery ages.
3.?????? Reaction kinetics: The rate of the electrochemical reactions at the electrodes, which can slow down over time due to degradation of the active material.
These models typically require extensive computational resources but can give more precise predictions about capacity degradation. I have briefly touched on these models in previous articles posted here,? https://eepower.com/industry-articles/examining-alternative-battery-modelspart-ii/. The entire series of articles can be found here, https://eepower.com/author/vivek-chandrasekharan-qorvo/.
Since this series deals with coulomb counting and lookup tables as the primary method, I will not be expanding on them here.
Combined Degradation Model
A more comprehensive approach often combines several of the models mentioned above. This could involve:
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1. Using an empirical cycle life model to describe degradation based on cycling behavior.
2. Integrating temperature effects with the Arrhenius equation to adjust degradation rates based on operational temperature.
3. Accounting for the SOC and DOD effects on the aging process by modifying the degradation rate based on the charge/discharge profile.
An example of a more complex model might look like:
Data-driven Approaches
In recent years, data-driven approaches such as machine learning and artificial intelligence are also being used to model battery degradation. By training models on real-world data from thousands of charge/discharge cycles, these approaches can identify complex patterns of aging and make accurate predictions about remaining useful life (RUL) and capacity fade.
The degradation of capacity in lithium-ion batteries is a complex, multifaceted process that involves several factors including cycling behavior, temperature, state of charge, and internal physical/chemical changes. Different models—ranging from simple empirical formulas to complex electrochemical simulations and data-driven approaches—are used to model and predict battery aging. The choice of model depends on the desired level of accuracy, computational resources, and available data.
Peak Load Effect
This finally brings us to the effect of peak load. Peak loading refers to conditions where a battery is subjected to high current draws or discharge rates for short durations, such as in high-power applications. This type of usage is frequently seen in applications which use electric motors where a high inrush current is needed to overcome the inertia of rest. This can significantly impact FCC due to both immediate and long-term effects.
Effects of Peak Loading on FCC
Immediate Effects:
Long-Term Effects on FCC:
1. Accelerated SEI Growth:
High current densities on the anode surface lead to increased heat generation and stress, accelerating the growth of the Solid Electrolyte Interphase (SEI) layer.
This consumes active lithium ions and reduces FCC permanently.
2. Lithium Plating:
High peak loads during charging (or at low temperatures) can lead to lithium plating, where metallic lithium deposits on the anode. This results in permanent capacity loss as plated lithium becomes inactive.
3. Mechanical Stress and Electrode Degradation:
High currents induce rapid ion movement, causing mechanical stress and potential cracking of electrode materials, which reduces the active surface area and permanently decreases FCC.
4. Electrolyte Decomposition:
High current rates increase localized heat, which can degrade the electrolyte and form additional resistive layers on electrodes, further reducing FCC.
5. Thermal Effects:
Peak loads generate significant heat, leading to potential thermal runaway or increased aging rates if not properly managed.
6. Depth of Discharge (DoD) Interaction:
Peak loading often occurs alongside high DoD usage, exacerbating stress on the battery. Deeper discharges during peak loads amplify degradation mechanisms, further reducing FCC.
To qualitatively model this, we can develop equations along the following lines
The FCC degradation rate due to peak loading (DPEAK) can be modeled as a function of:
The degradation per cycle can be expressed as:
Such detailed modeling helps to better approximate the capacity towards what can be obtained in real usage.
To conclude we can see that extracting and predicting battery capacity and time-to-empty are not trivial problems. There are several approaches to address the factors that affect FCC, cycle life, and battery degradation. Lookup tables along with accurate coulomb counting and mathematical digital twin modeling offer a good cost benefit ratio for most applications. However, they are not the only approaches, and neither are they the best for all intents and purposes.
Other methods like physical models, electrochemical models and EIS can under correctly used situations also provide comparable or even better accuracy. The trade-off with them is in the increased computational cost and energy usage (the same battery that is monitored, also powers the systems monitoring it).
In future posts I will be discussing other hardware and firmware factors that can influence the selection of gauging or monitoring techniques.
For any questions, comments, or opportunities, please contact me on LinkedIn.
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