Predictive battery life models are commonly utilized to extrapolate degradation trends observed during accelerated aging tests for simulation of degradation in real-world applications. Thus, fitting accelerated aging data as accurately as possible and with low uncertainty is crucial for making believable projections of battery lifetime, but it is challenging to identify algebraic expressions that accurately fit multivariate degradation trends. A review of models published in literature reveal some common expressions for fitting calendar aging data, which is only dependent on temperature and state-of-charge, but no consistency across many models for fitting cycle aging data, indicating the need for a statistically rigorous data driven approach for developing empirical models. This talk will describe a machine-learning assisted method for identification of predictive battery life models utilizing bilevel optimization and symbolic regression. Bilevel optimization with cross-validation is used to statistically determine cell- and stress-dependent model parameters, while symbolic regression identifies both linear and multiplicative candidate expressions to predict stress-dependent degradation rates by selecting low-order subsets of features from a generated feature library. Because model expressions are identified empirically, it is crucial to ensure resulting models behave according to physical expectations, so the stability of models for interpolation or extrapolation is interrogated qualitatively through simulation and quantitatively through cross-validation and uncertainty quantification via bootstrap resampling. This model identification approach substantially improves upon models identified purely using expert judgement in terms of both accuracy and uncertainty. Model simulation and validation is then conducted by deriving a state-equation form of the predictive model, enabling simulation of battery aging under dynamic stresses. This enables validation of the predictive battery model on lab-based tests with varying conditions or on drive-cycle or application-cycle testing protocols. Parameter uncertainty can be carried forward into model simulation, giving lifetime estimates and confidence windows for cell- or system-level lifetime. The financial impact of battery model uncertainty can be estimated by incorporating uncertainty into a technoeconomic model.
Battery energy storage systems (BESS) are used for a variety of applications, with their economic benefit often being the decisive factor for deployment. A multitude of physico-chemical aging mechanisms lead to capacity fade over a BESS life cycle. The models that are used to describe this capacity fade are prone to inherent model errors. Through a holistic techno-economic modelling approach, we investigate the impact of battery degradation modelling uncertainty on the economic benefit of representative BESS applications. Here, it is shown how improved parameter fit quality can reduce the resulting economic uncertainty. Furthermore, we highlight that the consideration of degradation modelling uncertainty is especially crucial when: (i) the cash flow highly depends on the available battery capacity, (ii) a fixed, e.g. warranty mandated, state of health limit acts as the threshold for battery end-of-life, (iii) long evaluation periods and low discount rates are the focus of economic evaluation.
Machine-Learning Assisted Identification of Accurate Battery Lifetime Models with Uncertainty
(2022)
Reduced-order battery lifetime models, which consist of algebraic expressions for various aging modes, are widely utilized for extrapolating degradation trends from accelerated aging tests to real-world aging scenarios. Identifying models with high accuracy and low uncertainty is crucial for ensuring that model extrapolations are believable, however, it is difficult to compose expressions that accurately predict multivariate data trends; a review of cycling degradation models from literature reveals a wide variety of functional relationships. Here, a machine-learning assisted model identification method is utilized to fit degradation in a stand-out LFP-Gr aging data set, with uncertainty quantified by bootstrap resampling. The model identified in this work results in approximately half the mean absolute error of a human expert model. Models are validated by converting to a state-equation form and comparing predictions against cells aging under varying loads. Parameter uncertainty is carried forward into an energy storage system simulation to estimate the impact of aging model uncertainty on system lifetime. The new model identification method used here reduces life-prediction uncertainty by more than a factor of three (86% ± 5% relative capacity at 10 years for human-expert model, 88.5% ± 1.5% for machine-learning assisted model), empowering more confident estimates of energy storage system lifetime.
For reliable lifetime predictions of lithium-ion batteries, models for cell degradation are required. A comprehensive semi-empirical model based on a reduced set of internal cell parameters and physically justified degradation functions for the capacity loss is developed and presented for a commercial lithium iron phosphate/graphite cell. One calendar and several cycle aging effects are modeled separately. Emphasis is placed on the varying degradation at different temperatures. Degradation mechanisms for cycle aging at high and low temperatures as well as the increased cycling degradation at high state of charge are calculated separately. For parameterization, a lifetime test study is conducted including storage and cycle tests. Additionally, the model is validated through a dynamic current profile based on real-world application in a stationary energy storage system revealing the accuracy. Tests for validation are continued for up to 114 days after the longest parametrization tests. The model error for the cell capacity loss in the application-based tests is at the end of testing below 1% of the original cell capacity and the maximum relative model error is below 21%.
For reliable lifetime predictions of lithium-ion batteries, models for cell degradation are required. A comprehensive semi-empirical model based on a reduced set of internal cell parameters and physically justified degradation functions for the capacity loss is developed and presented for a commercial lithium iron phosphate/graphite cell. One calendar and several cycle aging effects are modeled separately. Emphasis is placed on the varying degradation at different temperatures. Degradation mechanisms for cycle aging at high and low temperatures as well as the increased cycling degradation at high state of charge are calculated separately.For parameterization, a lifetime test study is conducted including storage and cycle tests. Additionally, the model is validated through a dynamic current profile based on real-world application in a stationary energy storage system revealing the accuracy. The model error for the cell capacity loss in the application-based tests is at the end of testing below 1 % of the original cell capacity.