Review—Dynamic Models of Li-Ion Batteries for Diagnosis and Operation: A Review and Perspective

Abstract

This article discusses the options and challenges of dynamic models for the diagnosis and operation of Li-ion batteries. It provides a concise yet understandable overview on models and dynamics, and it discusses future developments needed to progress the field. The diagnosis and operation of batteries require an understanding of the main processes and their dynamics, parameters, and time constants. Processes with large time constants, such as thermal transport are equally important for safe high-performance operation as are processes with shorter time constants such as diffusion. Depending on the specific problem or operating condition, taking all of the scales into account is often unavoidable. Three separate, yet closely connected model classes are reviewed in terms of physical insight and their capabilities and limits: mechanistic models, equivalent circuit models, and data-driven models. We provide guidance for the selection of a suitable model for the particular diagnosis and operation problem of interest. The optimization of battery diagnosis and operation require versatile and simple models that span multiple time scales and allow physical insight and ease of parameterization. Fusing the existing modeling approaches may help to fully exploit their potential while integrating first-principles physical insight and measurement data. Li-ion batteries power portable equipment and appliances, are essential components in electrical cars, and bear large potential as buffer and storage elements in electrical grids to overcome fluctuations caused by the intermittent nature of renewable energy sources. For many applications, such as in automotives or energy storage, Li-ion batteries need to operate at the upper performance limits to provide cost-effective solutions. Operating outside these limits causes fast deterioration and may lead to uncontrollable behavior. 1,2 As such, optimal design and diagnosis of cell state and optimal operation need to be addressed carefully at all levels, from cell to module and system. Dynamic mathematical models provide a means to address these challenges. Many different approaches for the dynamical modeling of batteries exist, see for example Refs. 3 and 4, which describe the dynamic behavior of the cells, battery modules, or complete battery systems. Battery cells consist of a separator sandwiched between two electrically conductive, porous electrodes, the positive and negative electrodes, cf. Figure 1. The components are soaked in electrolyte to allow for transport of Li ions between both electrodes. During charging and discharging, an electrochemical or charge transfer reaction occurs at the interfaces of electrode and electrolyte, where Li ions are either reduced and intercalated, i.e. stored in the electrode particles, or the stored Li is oxidized, releasing electrons. Besides internal variables such as concentrations and temperatures, two essential, performance-related variables of a battery are of general interest for its diagnosis and operation: the state of charge, SOC, and the state of health, SOH. SOC relates the available capacity at a given time to the maximum available capacity when fully discharging a battery: SOC = C Ah,max − C Ah (t) C Ah,max [1] SOH in contrast takes into account that the maximum capacity decreases with time due to degradation: SO H = C Ah,max C Ah,max (t = 0). [2] Too high charge or discharge rates or (dis)charging electrodes to extreme ratios of active material to lithium cause degradation and can trigger side reactions that lead to uncontrollable behavior. The stable z E-mail: u.krewer@tu-braunschweig.de operating range not only depends on electrode and electrolyte material and the structure of electrode and battery, but also on temperature, state of charge, and state of health. Further, slow relaxation processes in the cell, which may take up to hours, 5,6 mean that even the recent history of operation needs to be considered. The highly complex and nonlinear interplay of these factors and that only current, voltage, and external cell temperature with no internal state variables can be measured in commercial cells makes optimal design, state estimation, and optimal operation challenging. A battery management system is usually employed to actively determine and monitor the battery states, and to control the charging and discharging rate of the battery cells. Practically SOC is often estimated by charge counting, i.e. integrating the current withdrawn from or inserted into the cell, or by correlation of SOC to open-circuit voltage (OCV). 7 Charging of Li batteries, on the other side, is often performed by simple charging protocols, which often only take limited information of the battery state into account. 2,8,9 Due to the lack of insight into the battery processes and state, intuition or experimental trial-and-error design and operation of batteries do not fully exploit the potential of the battery and may even lead to failures of the battery system. Dynamic models provide insight into the battery states and allow the use of systems tools for identification of optimal battery configurations and trajectories. 2,3 These models should be dynamic to account for temporal changes of state variables in the cell, provide insight into slow and fast processes, and allow for better parameterization, and for assessing and adjusting dynamic operation. A detailed discussion on dynamic processes and time constants Figure 1. Schematic of a Li-ion battery.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see