Accelerated aging models for state-of-health prediction are critical for evaluating battery performance under realistic operating conditions. These models account for combined stresses such as temperature, voltage, and current, which collectively influence degradation mechanisms. The interaction effects between these factors complicate prediction accuracy, necessitating physics-based approaches combined with empirical validation.
Temperature is a primary driver of degradation, with Arrhenius relationships describing its exponential impact on reaction rates. The Arrhenius equation quantifies the temperature dependence of chemical degradation processes, where the rate constant increases with temperature. Voltage stress follows Eyring relationships, particularly for side reactions like solid electrolyte interphase growth or cathode oxidation. Current stress affects cycle aging through mechanisms like lithium plating or particle cracking, often modeled using power-law relationships.
Combined stress acceleration requires multiplicative models that account for interactions. The general form combines Arrhenius for temperature, Eyring for voltage, and power-law for current:
Degradation Rate = A * exp(-Ea/RT) * (V/V0)^n * (I/I0)^m
Here, A is a pre-exponential factor, Ea is activation energy, R is the gas constant, T is temperature, V and I are stress levels, and n, m are exponents.
Calendar aging models focus on time-dependent degradation under storage conditions. The dominant factors are temperature and state-of-charge (voltage). Acceleration factors for calendar aging are derived by comparing degradation rates at reference and elevated stress conditions. For example, a cell stored at 45°C may degrade twice as fast as one at 25°C, yielding an acceleration factor of 2.
Cycle aging models incorporate current-related stresses, including charge/discharge rates and depth-of-discharge. The Rainflow counting method is often used to quantify cycle stress profiles. Cycle acceleration factors depend on the degradation mode; high currents may accelerate lithium plating, while deep discharges may accelerate cathode cracking.
Non-linear superposition of calendar and cycle aging presents challenges. Degradation mechanisms may interact synergistically or antagonistically. For instance, high temperature may exacerbate cycle-induced lithium plating but mitigate mechanical particle cracking. Empirical data is required to calibrate interaction terms in combined models.
Standardized test protocols provide frameworks for accelerated aging studies. IEC 62660-1 outlines cycle life testing for electric vehicle batteries, specifying temperature, current, and voltage ranges. SAE J1798 defines calendar life testing protocols, including storage conditions and measurement intervals. These standards ensure reproducibility but may not capture all real-world stress combinations.
Model calibration requires partial degradation data from accelerated tests. The process involves:
1. Conducting tests at multiple stress levels to isolate individual factor effects.
2. Fitting degradation curves to extract rate constants for each mechanism.
3. Validating models with independent data sets.
Machine learning techniques supplement physics-based models by identifying hidden patterns in degradation data. Neural networks can approximate complex interactions between stress factors when analytical models are insufficient. However, they require large datasets and lack interpretability.
Practical implementation involves tradeoffs between model complexity and predictive accuracy. Simplified models with fewer parameters are easier to calibrate but may miss critical interactions. High-fidelity models capture more mechanisms but demand extensive experimental data.
Future advancements will focus on multi-stress accelerated testing protocols and improved interaction models. Standardization efforts are needed to unify testing methodologies across industries. Additionally, real-world validation using field data will enhance model reliability for diverse applications.
In summary, accelerated aging models for SOH prediction under combined stresses rely on Arrhenius-Eyring frameworks with empirical calibration. Deriving acceleration factors requires isolating individual stress contributions while accounting for non-linear interactions. Standardized protocols provide baselines, but model accuracy ultimately depends on comprehensive experimental validation.