Continuum Representation for Simulating Discrete Events of Battery Operation

A mathematical approach for representing the discrete events in the cycling studies of lithium-ion batteries as a continuum event has been proposed to generate charge/discharge curves for N number of battery cycles. Simulations of up to 5000 cycles have been performed using this technique using the solid-phase diffusion model. A nonlinear electrochemical engineering model, which describes the galvanostatic charge/open-circuit/discharge processes of a thin-film nickel electrode, has also been investigated to test and validate the computational performance of the continuum representation technique. Finally, the tested technique is implemented for an existing full-order pseudo-two-dimensional lithium-ion battery model that has several coupled and nonlinear partial differential equations in multiple domains. The continuum representation, which is expressed as a function of a dependent variable in time t, works efficiently for several cycles with very minimal model initialization efforts and computation cost. However, it is not ideal for state detection. The mathematical simulation approaches that are currently followed for the modeling of charge/discharge cycles of lithium-ion batteries involve different computational schemes. 1-10 The complexity arises because of steep variations in the dependent variables ͑concentrations and potentials͒ between charge and discharge processes, difficulty in obtaining consistent initial values for the model equations, solver failure after a certain number of cycles due to high charge/discharge cutoff voltages, thermal effects, etc. We came up with a shooting method in a spatial direction 11 based on the steadystate model equations that work well for providing consistent initialization during a charge or discharge process. Wu and White 12 devised an initialization subroutine called differential algebraic equation initialization subroutine ͑DAEIS͒ to overcome numerical inconsistency and discussed in detail the initialization problems of battery models. Consistent initial values of the dependent variables for index-1 differential algebraic equation ͑DAE͒ systems can be obtained using DAEIS. DAEIS is effective in handling a DAE system with combined continuous processes and discrete events that are frequently encountered in battery operations. Before the advancement of computation capability, Tafel approximation of the electrokinetic expression and Ohm's law in electrolyte were used to calculate initial guesses for algebraic variables. 13 In this work, the complete protocol that includes many discrete events to constitute one cycle of lithium-ion battery was reformulated as a single continuous process. Then, this continuous process was repeatedly simulated up to the desired number of cycles. This was achieved by carefully changing the model variables that directly influence the cycling parameters, for example, changing the independent variable ͑in time͒ or the dependent variable ͑in solid-phase concentration at the surface of the intercalating particles͒ and expressing the same as an additional algebraic equation in terms of the number of battery cycles. This approach was attempted to overcome the difficulties mentioned during the conventional cycle studies, and it was an efficient method for many situations. Adding an additional nonlinear algebraic equation does not contribute to the significant computation cost for the model simulation; rather, it helps in effectively handling large cycle numbers and in generating the cycle data for further analysis. The proposed mathematical representation has been demonstrated for models with different degrees of complexity and in comparison with the results from those using the conventional approach. 14-16 The combination of this continuum representation and this efficient reformulated model helps in the use of meaningful models of batteries for emerging applications such as satellites, military, hybrid electric vehicles, etc. The combination of the continuum representation and the reformulated model is helpful in a way that solving the full-order physicsbased lithium-ion battery model with less computation cost was facilitated by the reformulated version of the full-order model that does not require a large system of differential and algebraic equations to be solved for each parameter in a cycle, for example, charge or discharge. Though the objective of this investigation is to devise a continuum representation for generating cycle data using a fullorder physics-based lithium-ion battery model, two other simple electrochemical models ͑mentioned above͒ are also discussed with the intention to provide more details and insight into the proposed continuum approach that can help readers to easily adopt the approach for other interesting cases

Extending explicit and linearly implicit ODE solvers for index-1 DAEs

Nonlinear differential-algebraic equations (DAE) are typically solved using implicit stiff solvers based on backward difference formula or RADAU formula, requiring a Newton-Raphson approach for the nonlinear equations or using Rosenbrock methods specifically designed for DAEs. Consistent initial conditions are essential for determining numeric solutions for systems of DAEs. Very few systems of DAEs can be solved using explicit ODE solvers. This paper applies a single-step approach to system initialization and simulation allowing for systems of DAEs to be solved using explicit (and linearly implicit) ODE solvers without a priori knowledge of the exact initial conditions for the algebraic variables. Along with using a combined process for initialization and simulation, many physical systems represented through large systems of DAEs can be solved in a more robust and efficient manner without the need for nonlinear solvers. The proposed approach extends the usability of explicit and linearly implicit ODE solvers and removes the requirement of Newton-Raphson type iteration. Published by Elsevier Ltd

Optimal charging profiles for mechanically constrained lithium-ion batteries

The cost and safety related issues of lithium-ion batteries require intelligent charging profiles that can efficiently utilize the battery. This paper illustrates the application of dynamic optimization in obtaining the optimal current profile for charging a lithium-ion battery using a single-particle model while incorporating intercalation-induced stress generation. In this paper, we focus on the problem of maximizing the charge stored in a given time while restricting the development of stresses inside the particle. Conventional charging profiles for lithium-ion batteries (e.g., constant current followed by constant voltage) were not derived by considering capacity fade mechanisms. These charging profiles are not only inefficient in terms of lifetime usage of the batteries but are also slower since they do not exploit the changing dynamics of the system. Dynamic optimization based approaches have been used to derive optimal charging and discharging profiles with different objective functions. The progress made in understanding the capacity fade mechanisms has paved the way for inclusion of that knowledge in deriving optimal controls. While past efforts included thermal constraints, this paper for the first time presents strategies for optimally charging batteries by guaranteeing minimal mechanical damage to the electrode particles during intercalation. In addition, an executable form of the code has been developed and provided. This code can be used to identify optimal charging profiles for any material and design parameters

Direct, Efficient, and Real-Time Simulation of Physics-Based Battery Models for Stand-Alone PV-Battery Microgrids

With renewable energy based electrical systems becoming more prevalent in homes across the globe, microgrids are becoming widespread and could pave the way for future energy distribution. Accurate and economical sizing of stand-alone power system components, including batteries, has been an active area of research, but current control methods do not make them economically feasible. Typically, batteries are treated as a black box that does not account for their internal states in current microgrid simulation and control algorithms. This might lead to under-utilization and over-stacking of batteries. In contrast, detailed physics-based battery models, accounting for internal states, can save a significant amount of energy and cost, utilizing batteries with maximized life and usability. It is important to identify how efficient physics-based models of batteries can be included and addressed in current grid control strategies. In this paper, we present simple examples for microgrids and the direct simulation of the same including physics-based battery models. A representative microgrid example, which integrates stand-alone PV arrays, a Maximum Power Point Tracking (MPPT) controller, batteries, and power electronics, is illustrated. Implementation of the MPPT controller algorithm and physics-based battery model along with other microgrid components as differential algebraic equations is presented. The results of the proposed approach are compared with the conventional control strategies and improvements in performance and speed are reported. (C) The Author(s) 2017. Published by ECS. All rights reserved

Efficient Simulation and Reformulation of Lithium-Ion Battery Models for Enabling Electric Transportation

Improving the efficiency and utilization of battery systems can increase the viability and cost-effectiveness of existing technologies for electric vehicles (EVs). Developing smarter battery management systems and advanced sensing technologies can circumvent problems arising due to capacity fade and safety concerns. This paper describes how efficient simulation techniques and improved algorithms can alleviate some of these problems to help electrify the transportation industry by improving the range of variables that are predictable and controllable in a battery in real-time within an electric vehicle. The use of battery models in a battery management system (BMS) is reviewed. The effect of different simulation techniques on computational cost and accuracy are also compared, and the validity of implementation in a microcontroller environment for model predictive control (MPC) is addressed. Using mathematical techniques to add more physics without losing efficiency is also discussed. (C) The Author(s) 2014. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved

A temperature-aware battery cycle life model for different battery chemistries

With the remarkable recent rise in the production of battery-powered devices, their reliability analysis cannot disregard the assessment of battery life. In the literature, there are several battery cycle life models that exhibit a generic trade-off between generality and accuracy. In this work we propose a compact cycle life model for batteries of different chemistries. Model parameters are obtained by fitting the curve based on information reported in datasheets, and can be adapted to the quantity and type of available data. Furthermore, we extend the basic model by including some derating factors when considering temperature and current rate as stress factors in cycle life. Applying the model to various commercial batteries yields an average estimation error, in terms of the number of cycles, generally smaller than 10%. This is consistent with the typical tolerance provided in the datasheets

State-of-the-art and Future Research Needs for Multiscale Analysis of Li-ion Cells

The performance, safety and reliability of Li-ion batteries are determined by a complex set of multiphysics, multiscale phenomena that must be holistically studied and optimized. This paper provides a summary of the state-of-the-art in a variety of research fields related to Li-ion battery materials, processes and systems. The material presented here is based on a series of discussions at a recently concluded bilateral workshop in which researchers and students from India and USA participated. It is expected that this summary will help understand the complex nature of Li-ion batteries, and help highlight critical directions for future research

State of the art and future research needs for multiscale analysis of li-ion cells

The performance, safety, and reliability of Li-ion batteries are determined by a complex set of multiphysics, multiscale phenomena that must be holistically studied and optimized. This paper provides a summary of the state of the art in a variety of research fields related to Li-ion battery materials, processes, and systems. The material presented here is based on a series of discussions at a recently concluded bilateral workshop in which researchers and students from India and the U.S. participated. It is expected that this summary will help understand the complex nature of Li-ion batteries and help highlight the critical directions for future research

State-of-the-art and Future Research Needs for Multiscale Analysis of Li-ion Cells

The performance, safety and reliability of Li-ion batteries are determined by a complex set of multiphysics, multiscale phenomena that must be holistically studied and optimized. This paper provides a summary of the state-of-the-art in a variety of research fields related to Li-ion battery materials, processes and systems. The material presented here is based on a series of discussions at a recently concluded bilateral workshop in which researchers and students from India and USA participated. It is expected that this summary will help understand the complex nature of Li-ion batteries, and help highlight critical directions for future research