Global sensitivity analysis of the single particle lithium-ion battery model with electrolyte

The importance of global sensitivity analysis (GSA) has been well established in many scientific areas. However, despite its critical role in evaluating a model’s plausibility and relevance, most lithium ion battery models are published without any sensitivity analysis. In order to improve the lifetime performance of battery packs, researchers are investigating the application of physics based electrochemical models, such as the single particle model with electrolyte (SPMe). This is a challenging research area from both the parameter estimation and modelling perspective. One key challenge is the number of unknown parameters: the SPMe contains 31 parameters, many of which are themselves non-linear functions of other parameters. As such, relatively few authors have tackled this parameter estimation problem. This is exacerbated because there are no GSAs of the SPMe which have been published previously. This article addresses this gap in the literature and identifies the most sensitive parameter, preventing time being wasted on refining parameters which the output is insensitive to

Physical modeling of lithium-ion aging for automotive applications

This thesis extends the full-scale electrochemical model for a Lithium-ion battery based on the porous electrode theory to incorporate aging mechanisms of solid electrolyte interface formation, cyclic electrode degradation, and lithium plating during overcharge, automotive vibrations, mechanical stress, and cell temperature, as reported in the existing literature. Further, the thesis presents the scope of the parameters used in the model to enable designers to extend the equations for new mechanisms and variability of other parameters. An increased set of equations makes the complexity of the model even higher, and it would be very computationally complex to simulate this model. This makes this model unsuitable for inexpensive processors of mobile applications like an automotive battery management system while increasing the uncertainty faced by PDE solvers. However, as the physical models get close to an actual lithium-ion battery behavior, they could accelerate its development, shortening the design life of batteries

Control-Oriented Modeling of All-Solid-State Batteries Using Physics-Based Equivalent Circuits

Considered as one of the ultimate energy storage technologies for electrified transportation, the emerging all-solid-state batteries (ASSBs) have attracted immense attention due to their superior thermal stability, increased power and energy densities, and prolonged cycle life. To achieve the expected high performance, practical applications of ASSBs require accurate and computationally efficient models for the design and implementation of many onboard management algorithms, so that the ASSB safety, health, and cycling performance can be optimized under a wide range of operating conditions. A control-oriented modeling framework is thus established in this work by systematically simplifying a rigorous partial differential equation (PDE) based model of the ASSBs developed from underlying electrochemical principles. Specifically, partial fraction expansion and moment matching are used to obtain ordinary differential equation based reduced-order models (ROMs). By expressing the models in a canonical circuit form, excellent properties for control design such as structural simplicity and full observability are revealed. Compared to the original PDE model, the developed ROMs have demonstrated high fidelity at significantly improved computational efficiency. Extensive comparisons have also been conducted to verify its superiority to the prevailing models due to the consideration of concentration-dependent diffusion and migration. Such ROMs can thus be used for advanced control design in future intelligent management systems of ASSBs

A New Multiscale Modeling Framework for Lithium-Ion Battery Dynamics: Theory, Experiments, and Comparative Study with the Doyle-Fuller-Newman Model

Technological advancements and globalization in recent decades have largely been responsible for the ever-increasing energy and power demands across different industrial sectors. This has led to an extensive use of fossil fuel based resources such as gasoline and diesel, especially in the transportation industry [1]. The consequences of this utilization are excessive emission of greenhouse gases and degradation of air quality, which have raised significant environmental concerns. Added to this, concerns over the eventual depletion of fossil fuels has accelerated the exploration and development of new energy sources. At the same time, increasingly stringent regulations have been imposed to enhance the fuel efficiency and minimize emissions in automobiles. Efforts to meet current and future regulation targets have led to the development of new technologies, some of which are: a) vehicle electrification [2], b) gasoline direct injection technology [3], c) variable valve timing [4], d) advanced exhaust gas recirculation [5], and e) selective catalytic reduction for NOx [6]. On the energy front, wind and solar technologies have been vastly explored [7], but these technologies are time-dependent and intermittent in nature and must be supplemented by energy storage devices. Lithium-ion batteries have been considered the most preferred technology for grid energy storage and electrified transportation because of their higher energy and power densities, better efficiency, and longer lifespan in comparison with other energy storage devices such as lead acid, nickel metal hydride, and nickel cadmium [8]. Lithium-ion batteries are the most dominant technology today in small scale applications such as portable phones and computers [9]. However, their wide-scale adoption in automotive and grid energy storage applications has been hampered by concerns associated with battery life, safety, and reliability. A lack of comprehensive understanding of battery behavior across different environments and operating conditions make it challenging to extract their best performance. Currently, significant trade-offs are being made to optimize battery performance, such as over-sizing and under-utilization in automotive applications. While sensors are used to evaluate battery performance and regulate their operation, their fundamental limitation lies in the inability to measure battery internal states such as state-of-charge (SoC) or state-of-health (SoH). The aforementioned issues with lithium-ion batteries can addressed to a large extent with the help of mathematical modeling. They play an important role in the design and utilization of batteries in an efficient manner with existing technologies, because of their ability to predict battery behavior with minimal expenditure of time and materials [10]. While empirical mathematical models are computationally efficient, they rely on a significant amount of experimental data and calibration effort to predict future battery behavior. In addition, such models do not consider the underlying physicochemical transport processes and hence cannot predict battery degradation. Moreover, the knowledge acquired from such models cannot be generalized across different battery chemistry and geometry. This elucidates the need for fundamental physics-based mathematical models to aid in the development of advanced control strategies through model-based control and virtual sensor deployment. Such models can capture the underlying transport phenomena across various length and time scales, and enhance performance and longevity of batteries while ensuring safe operation. The overarching aim of this dissertation is to present a multiscale modeling approach that captures the behavior of such devices with high fidelity, starting from fundamental principles. The application of this modeling approach is focused on porous lithium-ion batteries. The major outcome of this work is to facilitate the development of advanced and comprehensive battery management systems by: a) developing a high fidelity multiscale electrochemical modeling framework for lithium-ion batteries, b) investigating the temperature-influenced and aging-influenced multiscale dynamics for different battery chemistry and operating conditions, c) formulating a methodology to analytically determine effective ionic transport properties using the electrode microstructure, and d) numerical simulation of the developed physics-based model and comparison analysis with the conventionally used Doyle-Fuller-Newman (DFN) electrochemical model. The new multiscale model presented in this dissertation has been derived using a rigorous homogenization approach which uses asymptotic expansions of variables to determine the macroscopic formulation of pore-scale governing transport equations. The conditions that allow successful upscaling from pore-to-macro scales are schematically represented using 2-D electrode and electrolyte phase diagrams. These phase diagrams are used to assess the predictability of macroscale models for different electrode chemistry and battery operating conditions. The effective transport coefficients of the homogenized model are determined by resolving a unit cell closure variable problem in the electrode microstructure, instead of conventionally employed empirical formulations. The equations of the developed full order homogenized multiscale (FHM) model are implemented and resolved using the finite element software COMSOL Multiphysics®. Numerical simulations are presented to demonstrate the enhanced predictability of the FHM against the traditionally used DFN model, particularly at higher temperatures of battery operation. Model parameter identification is performed by co-simulation studies involving COMSOL Multiphysics® and MATLAB® software using the Particle Swarm Optimization (PSO) technique. The parameter identification studies are performed using data from laboratory experiments conducted on 18650 cylindrical lithium-ion cells of nickel-manganese-cobalt oxide (NMC) cathode chemistry

A review on electric vehicle battery modelling: from lithium-ion toward lithium–sulphur

Accurate prediction of range of an electric vehicle (EV) is a significant issue and a key market qualifier. EV range forecasting can be made practicable through the application of advanced modelling and estimation techniques. Battery modelling and state-of-charge estimation methods play a vital role in this area. In addition, battery modelling is essential for safe charging/discharging and optimal usage of batteries. Much existing work has been carried out on incumbent Lithium-ion (Li-ion) technologies, but these are reaching their theoretical limits and modern research is also exploring promising next-generation technologies such as Lithium–Sulphur (Li–S). This study reviews and discusses various battery modelling approaches including mathematical models, electrochemical models and electrical equivalent circuit models. After a general survey, the study explores the specific application of battery models in EV battery management systems, where models may have low fidelity to be fast enough to run in real-time applications. Two main categories are considered: reduced-order electrochemical models and equivalent circuit models. The particular challenges associated with Li–S batteries are explored, and it is concluded that the state-of-the-art in battery modelling is not sufficient for this chemistry, and new modelling approaches are needed

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15–30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced b attery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted

Electrochemical Model and Sigma Point Kalman Filter Based Online Oriented Battery Model

This paper presents a reduced-order electrochemical battery model designed for online implementation of battery control systems. This model is based on porous-electrode and concentratedsolution theory frameworks and is able to predict voltage as well as the internal electrochemical variables of a battery. The reduction of the model leads to a physics-based one-dimensional discrete-time state-space reduced-order model (ROM) especially beneficial for online systems. Models optimized around different operational setpoints are combined in order to predict the cell variables over a wide range of temperature and state of charge (SOC) using the output-blending method. A sigma-point Kalman filter is further used in order to cope with inaccuracies generated by the reduction process and experimental-related issues such as measurement error (noise) on the current and voltage sensors. The state-estimation accuracies are measured against a full-order model (FOM) developed in COMSOL. The whole system is able to track the internal variables of the cell as well as the cell voltage and SOC with very high accuracy, demonstrating its suitability for an online battery control system

An Extended Differential Flatness Approach for the Health-Conscious Nonlinear Model Predictive Control of Lithium-Ion Batteries

This brief paper examines the problem of optimizing lithium-ion battery management online, in a health-conscious manner. This is a computationally intensive problem. Previous work by the authors addresses this challenge by exploiting the differential flatness of Fick's law of diffusion to improve computational efficiency, but is limited by the fact that the dynamics of a full battery cell are not differentially flat, even when the individual battery electrode dynamics are. The brief paper addresses this challenge by extending the application of differential flatness to a full single particle model. In particular, we use the conservation of charge to express the flat output trajectory of one electrode as an affine function of the other electrode's flat output trajectory. In this way, we enforce differential flatness for the full battery model. This makes it possible to express the battery charge/discharge trajectory in terms of one flat output trajectory. We optimize this trajectory using a pseudospectral method. This reduces the computational cost of the optimization by about a factor of 5 compared with pseudospectral optimization alone. In addition, the robustness of the nonlinear model predictive control strategy is demonstrated in simulation by adding state-of-health parameter uncertainties

Supervisory Control Optimization for a Series Hybrid Electric Vehicle with Consideration of Battery Thermal Management and Aging

This dissertation integrates battery thermal management and aging into the supervisory control optimization for a heavy-duty series hybrid electric vehicle (HEV). The framework for multi-objective optimization relies on novel implementation of the Dynamic Programing algorithm, and predictive models of critical phenomena. Electrochemistry based battery aging model is integrated into the framework to assesses the battery aging rate by considering instantaneous lithium ion (Li+) surface concentration rather than average concentration. This creates a large state-action space. Therefore, the computational effort required to solve a Deterministic or Stochastic Dynamic Programming becomes prohibitively intense, and a neuro-dynamic programming approach is proposed to remove the ‘curse of dimensionality’ in classical dynamic programming. First, unified simulation framework is developed for in-depth studies of series HEV system. The integration of a refrigerant system model enables prediction of energy use for cooling the battery pack. Side reaction, electrolyte decomposition, is considered as the main aging mechanism of LiFePO4/Graphite battery, and an electrochemical model is integrated to predict side reaction rate and the resulting fading of capacity and power. An approximate analytical solution is used to solve the partial difference equations (PDEs) for Li+ diffusion. Comparing with finite difference method, it largely reduces the number of states with only a slight penalty on prediction accuracy. This improves computational efficiency, and enables inclusion of the electrochemistry based aging model in the power management optimization framework. Next, a stochastic dynamic programming (SDP) approach is applied to the optimization of supervisory control. Auxiliary cooling power is included in addition to vehicle propulsion. Two objectives, fuel economy and battery life, are optimized by weighted sum method. To reduce the computation load, a simplified battery aging model coupled with equivalent circuit model is used in SDP optimization; Li+ diffusion dynamics are disregarded, and surface concentration is represented by the average concentration. This reduces the system state number to four with two control inputs. A real-time implementable strategy is generated and embedded into the supervisory controller. The result shows that SDP strategy can improve fuel economy and battery life simultaneously, comparing with Thermostatic SOC strategy. Further, the tradeoff between fuel consumption and active Li+ loss is studied under different battery temperature. Finally, the accuracy of battery aging model for optimization is improved by adding Li+ diffusion dynamics. This increases the number of states and brings challenges to classical dynamic programming algorithms. Hence, a neuro-dynamic programming (NDP) approach is proposed for the problem with large state-action space. It combines the idea of functional approximation and temporal difference learning with dynamic programming; in that case the computation load increases linearly with the number of parameters in the approximate function, rather than exponentially with state space. The result shows that ability of NDP to solve the complex control optimization problem reliably and efficiently. The battery-aging conscientious strategy generated by NDP optimization framework further improves battery life by 3.8% without penalty on fuel economy, compared to SDP strategy. Improvements of battery life compared to the heuristic strategy are much larger, on the order of 65%. This leads to progressively larger fuel economy gains over time