Battery degradation during storage, often referred to as calendar aging, is a critical factor in determining the lifespan and performance of energy storage systems. Unlike cyclic aging, which results from repeated charge and discharge cycles, calendar aging occurs even when batteries are inactive. Understanding and modeling this phenomenon is essential for applications such as renewable energy storage, backup power systems, and electric vehicles, where batteries may spend extended periods at rest.

The dominant mechanisms of calendar aging include electrolyte oxidation, passive solid electrolyte interphase (SEI) growth, and lithium inventory loss. Electrolyte oxidation occurs when the electrolyte reacts with the electrodes, particularly at high states of charge (SOC) and elevated temperatures. This reaction generates gaseous byproducts and consumes active lithium, reducing capacity. Passive SEI growth, on the other hand, involves the gradual thickening of the SEI layer on the anode surface. While the SEI layer is essential for stabilizing the electrode-electrolyte interface, its continued growth consumes lithium ions and increases cell impedance. Lithium inventory loss further exacerbates capacity fade, as lithium ions become trapped in inactive compounds or form metallic lithium deposits.

Temperature, SOC, and time are the primary factors influencing calendar aging rates. Higher temperatures accelerate chemical reactions, including electrolyte decomposition and SEI growth. For example, a battery stored at 40°C may degrade twice as fast as one stored at 25°C. Elevated SOC levels also exacerbate degradation due to increased electrode potentials, which drive parasitic reactions. A battery stored at 100% SOC typically experiences faster capacity loss than one stored at 50% SOC. Time is a linear factor in calendar aging, as degradation accumulates steadily over storage periods.

Calendar aging models can be broadly categorized into empirical and physics-based approaches. Empirical models rely on experimental data to establish correlations between aging factors and degradation. These models often use Arrhenius-type equations to describe temperature dependence and power-law or exponential functions to capture SOC and time effects. For instance, a common empirical model might express capacity loss as a function of storage time, SOC, and temperature:

Capacity Loss = A * exp(-Ea/RT) * SOC^B * time^C

Here, A, B, and C are fitting parameters, Ea is the activation energy, R is the gas constant, and T is temperature. Empirical models are computationally efficient and widely used in industry for lifetime predictions. However, they lack mechanistic insight and may not generalize well beyond the conditions under which they were derived.

Physics-based models, in contrast, explicitly describe the underlying chemical and physical processes driving degradation. These models incorporate equations for SEI growth kinetics, electrolyte oxidation rates, and lithium ion diffusion. For example, a physics-based SEI growth model might simulate the diffusion of solvent molecules through the SEI layer and their subsequent reduction at the anode surface. Such models provide deeper understanding but require detailed material properties and are computationally intensive. Hybrid approaches, combining empirical and physics-based elements, are increasingly popular for balancing accuracy and practicality.

Applications of calendar aging models span renewable energy storage, backup power systems, and electric vehicles. In grid-scale energy storage, batteries may remain at high SOC for extended periods to ensure readiness for demand spikes. Accurate aging models help optimize SOC setpoints to balance performance and longevity. For backup power systems, where batteries are rarely cycled but must remain reliable over years, calendar aging predictions inform maintenance schedules and replacement timelines. In electric vehicles, calendar aging contributes significantly to overall degradation, especially during long parking periods. Models enable manufacturers to design thermal management and charging strategies that minimize storage-related fade.

Comparative studies of empirical and physics-based models reveal trade-offs in accuracy, complexity, and applicability. Empirical models excel in scenarios where rapid predictions are needed, and experimental data is abundant. Physics-based models are preferable for fundamental research or when extrapolating to untested conditions. For example, a physics-based model might predict aging under novel electrolyte formulations, while an empirical model would require extensive testing to update its parameters.

The choice of model also depends on the application's requirements. Renewable energy storage systems, which prioritize cost-effectiveness, often use empirical models for fleet-level predictions. Backup power systems, where reliability is critical, may invest in physics-based models to identify failure risks. Electric vehicle manufacturers increasingly adopt hybrid models to capture both cyclic and calendar aging effects across diverse usage patterns.

Advancements in modeling techniques, such as machine learning and digital twins, are enhancing calendar aging predictions. Machine learning algorithms can identify complex patterns in aging data, improving empirical model accuracy. Digital twins combine real-time sensor data with physics-based models to provide dynamic updates on battery health. These innovations are particularly valuable for applications like grid storage, where operating conditions vary widely.

Despite progress, challenges remain in modeling calendar aging. Variability in cell manufacturing, environmental conditions, and usage history complicates predictions. Accelerated aging tests, commonly used to gather data, may not fully replicate real-world degradation mechanisms. Future research aims to refine models by incorporating more detailed material properties, multi-scale simulations, and validation across diverse conditions.

In summary, calendar aging models are indispensable tools for predicting battery degradation during storage. Dominant mechanisms like electrolyte oxidation and SEI growth are influenced by temperature, SOC, and time. Empirical models offer simplicity and speed, while physics-based models provide mechanistic insights. The choice of model depends on the application, with hybrid approaches gaining traction for their balanced capabilities. As battery technologies evolve, so too will the models that ensure their reliable and long-lasting performance in storage applications.