Battery Degradation Model

Degradation is decomposed into two distinct temporal domains:

• Calendar Aging: Capacity fade occurring during storage at a specific State of Charge (SoC) and temperature, independent of usage. Driven by solid electrolyte interphase (SEI) growth.
• Cycling Aging: Capacity loss directly proportional to charge-throughput. Driven by mechanical stress from lithium intercalation and deintercalation.

Models must superimpose both mechanisms to predict total State of Health (SoH) accurately.

The dominant degradation mechanism in graphite-anode cells. A passivating film grows at the electrode-electrolyte interface, consuming cyclable lithium.

• Kinetic Model: SEI thickness grows with the square root of time (√t).
• Temperature Dependence: Follows an Arrhenius relationship; higher temperatures exponentially accelerate growth.
• SoC Impact: Higher anode potential at elevated SoC increases the rate of solvent reduction, thickening the SEI layer.

Capacity fade is attributed to two distinct stoichiometric losses:

• LLI: Cyclable lithium is trapped in the SEI or plated as dead lithium. This shifts the electrode balancing, reducing total capacity.
• LAM: Cathode or anode particles crack and electrically isolate due to volume strain, reducing the active mass available for intercalation.

Differential voltage analysis (DVA) is used to deconvolve these modes non-destructively.

Two primary modeling paradigms exist for predicting degradation:

• Empirical Models: Fit experimental data to mathematical functions like power-law (Ah-throughput) or exponential (calendar time). Computationally cheap but lack extrapolation capability.
• Physics-Based Models (P2D): Solve coupled partial differential equations for lithium concentration and potential in the electrode particles. The Single Particle Model with Degradation (SPMe) is a reduced-order variant suitable for real-time Battery Management System (BMS) integration.

Hybrid models combine physics with neural networks for residual learning.

A critical failure mode during fast charging at low temperatures. Instead of intercalating into the anode, lithium metal deposits on the surface.

• Trigger Conditions: High C-Rate combined with low temperature and high SoC.
• Consequences: Irreversible LLI and potential internal short circuits from dendrite growth.
• Detection: Voltage relaxation profiles exhibit a characteristic plateau during the stripping of plated lithium. Models enforce anode potential constraints (>0V vs Li/Li+) to prevent plating.

Power fade is quantified by the increase in DC internal resistance (DCIR), limiting the battery's ability to deliver peak power.

• Primary Cause: SEI thickening impedes lithium-ion migration, increasing ionic resistance.
• Secondary Cause: Cathode electrolyte interphase (CEI) formation and contact loss at the current collector interface.
• Modeling: Often modeled as a linear function of SEI thickness or an exponential function of calendar time. Directly impacts Depth of Discharge (DoD) limitations in vehicle-to-grid applications.

The primary output metric of a degradation model, representing the battery's current condition relative to its Beginning of Life (BoL) specifications. SoH is typically defined by two key indicators:

• Capacity Fade: The decrease in usable ampere-hours, calculated as (Current Capacity / Nominal Capacity) * 100%.
• Internal Resistance Growth: The increase in impedance, often measured via DC Internal Resistance (DCIR) or Electrochemical Impedance Spectroscopy (EIS), which reduces power capability. An accurate SoH estimation is critical for triggering warranty claims and planning second-life applications.

A primary stress factor input for empirical degradation models. DoD quantifies the percentage of capacity removed during a discharge cycle. The relationship between DoD and cycle life is non-linear:

• Shallow cycling (e.g., 10% DoD) can yield orders of magnitude more equivalent full cycles than deep cycling (e.g., 90% DoD).
• Degradation models use DoD as a key variable in cycle-life stress functions, often fitting experimental data to an inverse power-law or Wöhler curve to predict capacity loss per cycle.

A measure of the current magnitude relative to the battery's nominal capacity, expressed as 1/h. A 1C rate fully charges or discharges a cell in one hour; 2C does so in 30 minutes. High C-rates accelerate degradation through several mechanisms:

• Lithium Plating: At high charge rates, lithium ions deposit as metallic lithium on the anode instead of intercalating, causing irreversible capacity loss.
• Mechanical Stress: Rapid intercalation induces particle cracking in electrode materials, increasing internal resistance. Degradation models incorporate C-rate as a stress factor, often using an Arrhenius-type relationship to model accelerated aging.

The time-dependent degradation that occurs even when a battery is at rest, distinct from cyclic aging caused by usage. Calendar aging is driven by the growth of the Solid Electrolyte Interphase (SEI) layer on the anode, which consumes cyclable lithium. Key accelerating factors are:

• Temperature: Higher storage temperatures exponentially increase SEI growth, following an Arrhenius law.
• State of Charge (SoC): Higher storage voltages increase the thermodynamic driving force for electrolyte oxidation. A complete degradation model superimposes calendar aging losses onto cyclic aging losses to predict total capacity fade over a real-world mission profile.

The embedded electronic system that executes degradation model algorithms in real-time. The BMS performs critical estimation functions:

• SoC Estimation: Uses Coulomb Counting corrected by voltage-based look-up tables or Kalman Filters to track charge state.
• SoH Estimation: Runs the degradation model using accumulated cycle count, temperature history, and impedance measurements to update the battery's aging status.
• State of Power (SoP) Estimation: Predicts the maximum charge/discharge power available at the current SoC and SoH without violating voltage limits. The BMS uses these states to enforce safe operating limits and balance cells.

A laboratory and increasingly online diagnostic technique used to parameterize physics-based degradation models. EIS applies a small sinusoidal current across a range of frequencies and measures the impedance response. The resulting Nyquist plot can be fitted to an equivalent circuit model to separate degradation mechanisms:

• Ohmic Resistance (Rs): High-frequency intercept, indicating electrolyte and contact resistance.
• Charge Transfer Resistance (Rct): Mid-frequency semicircle diameter, reflecting kinetic barriers at the electrode interface.
• Diffusion Impedance (Warburg): Low-frequency tail, indicating solid-state lithium diffusion limitations. Tracking these parameters over life provides a mechanistic fingerprint of aging.