Data-driven model identification and state estimation of batteries: A sparse ageing-aware linear parameter-varying approach

The global push towards the electrification of everything has brought batteries—particularly lithium-ion batteries—to the forefront of modern research for the development of adequate battery-powered energy storage systems. Such energy storage systems employ battery management systems that act as the brain to ensure safe, efficient, and reliable battery usage via suitable control-oriented algorithms. A crucial building block of such algorithms is the underlying battery model, which should (i) exhibit sufficient accuracy for the intended model application, (ii) possess suitable analytical properties, such as admitting a direct state-space representation, and (iii) remain computationally efficient. Often, battery models derived from first principles do not admit a direct state-space representation and are computationally inefficient, thereby limiting their applicability in battery management systems. Alternatively, battery models can be obtained using system identification principles that satisfy the aforementioned requirements, through carefully chosen model structures along with informative experimental data and efficient optimisation (fitting) procedures. Furthermore, an important application of battery models in battery management systems is exemplified by state estimation algorithms, whose performance heavily depends on (i) the battery model used, (ii) the choice of algorithm, and (iii) the design of the algorithm (hyperparameter values). Accordingly, state estimation algorithms employing suitable data-driven battery models need to be systematically designed to achieve accurate and robust estimation results. Notably, a systematic approach to designing battery model identification and state estimation algorithms that carefully considers the link between various attributes of the corresponding building blocks and the desired algorithmic properties is currently lacking in the literature. This thesis provides a comprehensive linear parameter-varying (LPV)-based framework for battery model identification and state estimation. First, the thesis focuses on the identification of battery models using an LPV input–output model structure with an emphasis on informative identification datasets and efficient optimisation methods. Essentially, the model identification procedure follows the principle of parsimony, that is, only relevant model terms are selected from a pool of candidates to explain the dependence of the model output on suitable variables, such as state of charge (SOC), current magnitude, current direction, and temperature. Such an approach is also extended to enable model identification for batteries exhibiting the hysteresis phenomenon. Furthermore, the experimental design problem is addressed by proposing suitable current and temperature profile designs, which can be applied as input experimental conditions to the investigated batteries for obtaining informative identification datasets. In this thesis, the informativity of the identification datasets is also discussed in the context of a data selection problem, where the user needs to select the most informative data segment from a list of available segments. Correspondingly, an informativity measure is proposed to evaluate the goodness of an identification dataset for a given model application by quantifying how well the dataset fills the region of interest defined by the model application. The battery models thus identified are shown to exhibit adequate generalisability over a wide range of operating conditions, namely varying SOC, current magnitude, current direction, and temperature. Remarkably, the identified models exhibit adequate simulation performance under a wide temperature range (0–40°C) and voltage cutoff limit of 2.5 V, with the root-mean-squared-error value reaching as low as 7 mV. Subsequently, the thesis addresses two concerns commonly encountered in battery management systems, namely SOC estimation and ageing-aware model estimation. First, a systematic approach to SOC estimation is presented that utilises battery models identified using the proposed LPV-based framework. In this regard, estimators such as the extended Kalman filter and the particle filter are designed systematically instead of performing ad hoc tuning of the covariance matrices. The SOC estimation algorithms thus designed exhibit adequate estimation accuracy under varying battery operating conditions while being robust to large biases in the current sensor. Notably, adequate SOC estimation performance is achieved for a lithium-nickel-manganese-cobalt-oxide (NMC) cell and a lithium-iron-phosphate (LFP) cell with bias in the current sensor of approximately −3 A. Moreover, an approach to keep the battery models accurate over the battery lifetime is presented that involves estimation of model parameters and battery capacity as the battery behaviour evolves due to various ageing mechanisms. Specifically, a model structure comprising suitable model terms can be identified using experimental data obtained from a set of training cells, which can then be fitted to an unseen test cell of the same kind at different stages across its lifetime. Such fitting can be performed either in real-time via recursive state estimation or offline via batch estimation, though the latter is preferred in this thesis owing to more reliable parameter and capacity estimates. Remarkably, the batch-wise estimation approach is demonstrated to achieve reliable capacity estimates even when the test dataset spans a partial SOC range between 100% and 50%.The contributions of this thesis have been consolidated into two open-source Python packages, namely (i) PyBatteryID, which enables data-driven battery model identification using the proposed LPV-based modelling framework, and (ii) PyBatterySE, which utilises the identified models to perform battery state estimation, including SOC estimation and ageing-aware model estimation. Both packages have been rigorously tested on a variety of experimental datasets obtained from multiple battery cells of various form factors and chemistries. The obtained results using these packages demonstrate that the proposed model identification and state estimation methods offer significant improvements in multiple aspects, including model generalisability and estimation accuracy, compared to approaches currently adopted in the literature. Finally, the development of such packages can enable the battery research community to adopt, critique, and improve on the proposed methods, while highlighting fairness and transparency in the conducted research.