Lithium-ion Battery Model Research Articles

Use of life cycle assessment to evaluate circular economy business models in the case of Li-ion battery remanufacturing

PurposeThe purpose of this study is to advance and illustrate how life cycle assessment (LCA) can assess circular economy business models for lithium-ion batteries to verify potential environmental benefits compared to linear business models. Scenarios for battery repurpose are assessed to support future decision-makers regarding the choice of new versus second life batteries for stationary energy storage. A procedure to determine the substitution coefficient for repurpose and reuse of batteries is proposed.MethodsTwo different circular economy business models are assessed by applying primary data from two Norwegian companies for the development of a new life cycle inventory. With this new data, the authors compare second life battery (from first life in electric vehicle) scenarios and avoided production potential by performing a complete consequential LCA. Building on earlier work, a procedure to identify the substitution coefficient (i.e., potential for avoided production) for battery life cycle assessments is proposed. Interviews during factory visits were performed to identify a technical and a market factor affecting the substitution coefficient.Results and discussionThis study illustrates how life cycle assessment methodology can detect and thus enhance the potential environmental benefits and trade-offs of circular economy business models. Results show that the CBMs which use second life batteries correspond to 16% (for global warming potential) of manufacturing a new battery. This means that a second life battery must avoid > 16% production of a new battery to become the preferred alternative. Hence, circular economy business models with second life batteries can generate net environmental benefits while the remaining battery capacity and market price are identified factors that can alter the potential environmental benefits. The findings suggest that assumptions concerning the avoided production emissions are crucial for understanding the overall impacts of battery value chains.ConclusionsCircular economy business models which enable second life batteries show lower environmental impacts compared to a new battery when it can partly avoid production of a new battery. Based on the identified technical and market factor affecting this potential, a key message to industry and other organizations is that second life batteries should be chosen over new batteries. This depends on the remaining capacity being satisfactory for the new application, and the investment is not performed because of a low price compared to a new battery. Consequential LCA practitioners adopting a market approach while evaluating battery reuse and repurpose should model and account for the avoided production potential.

Electrical Modeling and Impedance Spectra of Lithium-Ion Batteries and Supercapacitors

In this study, electrical models for cylindrical/pouch-type lithium Li-ion batteries and supercapacitors were investigated, and the impedance spectra characteristics were studied. Cylindrical Li-ion batteries use Ni, Co, and Al as the main materials, while pouch-type Li-ion batteries use Ni, Co, and Mn as the main materials. Herein, 2600–3600 mAh 18650-type cylindrical Li-ion batteries, 5000 mAh 21700-type cylindrical Li-ion batteries, 37–50.5 Ah pouch-type Li-ion batteries, and a 2.7 V, 600 F supercapacitor are compared and analyzed. For a cylindrical Li-ion battery, the RS value of a battery with a protection device (circular thermal disc cap) is in the range of 14–38 mΩ. For the 18650-type cylindrical Li-ion battery with a protection device, the RS value of the battery is between 48 and 105 mΩ, and the protection device increases the RS value by at least 33 mΩ. A good Li-ion battery exhibits RS. Moreover, it has small overall RP and CP values. For the 21700-type cylindrical Li-ion battery with a protection device, the RS value of the battery is 25 mΩ. For the pouch-type Li-ion battery, the RS value of the battery is between 0.86 and 1.04 mΩ. For the supercapacitor, the RS value of the battery is between 0.4779 and 0.5737 mΩ. A cylindrical Li-ion battery exhibits a semicircular shape in the impedance spectrum, due to the oxidation and reduction reactions of Li ions, and the impedance increases with a slope of 45° in the complex plane, due to the ZW generated by Li ion diffusion. However, for a pouch-type Li-ion battery, the impedance spectrum exhibits a part of the semicircular shape, due to the oxidation and reduction reactions of Li ions, and the ZW generated by Li ion diffusion does not appear. In a supercapacitor, the oxidation and reduction reactions of ions do not appear at all, and the ZW generated by Li ion diffusion does not occur.

Fast self-preheating system and energy conversion model for lithium-ion batteries under low-temperature conditions

Low temperature is one of the major drawbacks of electric cars in high latitudes. This problem can be addressed using a battery self-preheating system. The existing self-heating systems have problems, such as slow heating rate, complex control system, single thermal management function and poor safety. Herein, we propose a conductive phase change material (cPCM)-based self-preheating system that generates heat simultaneously using the internal resistance of cells and external resistance of the cPCM. This self-preheating system shows a high heating rate of 17.14 °C/min and excellent temperature uniformity (temperature difference of 3.58 °C). The system can preheat the battery safely in the capacity range of 20%–100%. When the battery pack is set in −20 °C, the effective electric energy can be increased by 550% after preheating. An energy conversion model is also built to measure the relationship between the energy improvement of battery and the energy consumption by preheating. This energy conversion model can help the system to make the optimal preheating strategy and obtain the maximum discharge energy. Nevertheless, based on the outcome of this study, this self-preheating strategy can effectively solve the problem of battery in low temperatures and maximize the effective electric energy of the battery.

A Time-Adaptive Order Reduction Technique for the Doyle-Fuller-Newman Electrochemical Model of Lithium-Ion Batteries

A time-adaptive reduced order model (ROM) is developed for the electrochemical model for lithium-ion cells derived by Doyle, Fuller, and Newman (DFN) [M. Doyle, T. F. Fuller and J. Newman, J. Electrochem. Soc., 140 1526 (1993)]. The main advantage of a time-adaptive strategy is that it does not require a set of full order model simulations to be generated beforehand and, thus, it is the most cost-effective alternative when no databases are available. However, the reduction of this electrochemical problem exhibits special features that require ad hoc solutions, preventing the application of generic strategies. This complexity is carefully analysed, focusing on mode selection, treatment of non-linearities and error estimation. Despite of all this analysis being done for a pseudo-two-dimensional DFN model, we show that such complexity is intrinsic to the physics of the electrochemical problem, making the analysis applicable to a pseudo-four-dimensional DFN model, where results prove that the benefits of a reduction in the number of degrees of freedom are more self-evident. The efficiency, robustness and accuracy of our method are remarkable, as shown by the macroscopic (cell voltage) and internal (variable distributions) results obtained from the simulation of two different electrochemical cells under several charge/discharge C-rates.

Order reduction electrochemical mechanism model of lithium-ion battery based on variable parameters

Electrochemical model is of great significance for the research of state estimation and aging of lithium-ion batteries (LIBs). However, the mechanism model has some problems, such as difficult parameter acquisition, time-consuming online identification and poor adaptability, which limit the accuracy of the model in practical application. In this paper, a novel order reduction mechanism model of LIB based on variable parameters is proposed to overcome the above problems. First, a spectral method is used to reduce the partial differential equation (PDE) of solid-phase diffusion process, and a lithium-ion concentration model in the radial direction can be obtained. Next, a terminal voltage model of battery including liquid potential, electrochemical polarization potential and ohmic polarization potential is established. This modeling process considers the double electric layer (DEL) effect on liquid potential. Finally, a variable parameter model based on temperature and SOC is developed to improve the adaptability of the mechanism model, and a novel adaptive multi-innovation unscented Kalman filtering (AMUKF) is proposed to estimation the SOC of LIB. A various of experiments and verifications show that the presented model is effective, and has better modeling ability in the full SOC stage and changeable environment compared with other several common models.

Improved Parameter Identification for Lithium-Ion Batteries Based on Complex-Order Beetle Swarm Optimization Algorithm

With the aim of increasing the model accuracy of lithium-ion batteries (LIBs), this paper presents a complex-order beetle swarm optimization (CBSO) method, which employs complex-order (CO) operator concepts and mutation into the traditional beetle swarm optimization (BSO). Firstly, a fractional-order equivalent circuit model of LIBs is established based on electrochemical impedance spectroscopy (EIS). Secondly, the CBSO is used for model parameters' identification, and the model accuracy is verified by simulation experiments. The root-mean-square error (RMSE) and maximum absolute error (MAE) optimization metrics show that the model accuracy with CBSO is superior when compared with the fractional-order BSO.

A comparative study of fractional-order models for lithium-ion batteries using Runge Kutta optimizer and electrochemical impedance spectroscopy

With the popularity of new energy vehicles and various electronic products, lithium-ion batteries are widely used in daily life. For lithium-ion batteries, an accurate model is the basis of battery management. In the process of continuous pursuit for model accuracy, it often leads to an increase in model complexity. Fractional-order models can effectively balance model accuracy and complexity between electrochemical models and equivalent circuit models, thus having good application prospects. In this paper, four typical fractional-order models for lithium-ion batteries are compared, and the Runge Kutta optimizer (RUN) algorithm, which has fast convergence speed and high precision, is employed to identify the model parameters. The accuracy for predicting terminal voltage and the time required for parameter identification process are compared respectively under different dynamic conditions for each model. Finally, the model impedance spectrum fitted results and model parameter values are discussed through electrochemical impedance spectroscopy test. This paper provides guidance on the modeling and parameter identification for lithium-ion batteries through analyzing different fractional-order models and introducing impedance spectroscopy to help explore the battery characteristics.

Thermal Model and Experimental Verification of Lithium-Ion Battery Based on Heat Generation Rate

In order to study the temperature distribution in a lithium-ion battery (LIB), a series of experiments including open-circuit voltage (OCV) test, discharge rate test, hybrid pulse power characteristic (HPPC) test, and discharge temperature rise test based on the Bernardi heat generation model were conducted. The thermal model (TM) of the LIB under different discharge rates was established. The temperatures of the cell at different discharge rates calculated by the TM, which leverages the user-defined function (UDF) to import a variable heat generation rate, were compared with the experimental data. Moreover, this TM was used to simulate the LIB temperature at different ambient temperatures and different heat-transfer coefficients and analyze the temperature distribution of cell. The results showed that the TM can accurately simulate the temperature rise of the LIB at different discharge rates, which provides a reference value for LIB thermal management.

Equivalent Circuit Model for High-Power Lithium-Ion Batteries under High Current Rates, Wide Temperature Range, and Various State of Charges

The most employed technique to mimic the behavior of lithium-ion cells to monitor and control them is the equivalent circuit model (ECM). This modeling tool should be precise enough to ensure the system’s reliability. Two significant parameters that affect the accuracy of the ECM are the applied current rate and operating temperature. Without a thorough understating of the influence of these parameters on the ECM, parameter estimation should be carried out manually within the calibration, which is not favorable. In this work, an enhanced ECM was developed for high-power lithium-ion capacitors (LiC) for a wide temperature range from the freezing temperature of −30 °C to the hot temperature of +60 °C with the applied rates from 10 A to 500 A. In this context, experimental tests were carried out to mimic the behavior of the LiC by modeling an ECM with two RC branches. In these branches, two resistance and capacitance (RC) are required to maintain the precision of the model. The validation results proved that the semi-empirical second-order ECM can estimate the electrical and thermal parameters of the LiC with high accuracy. In this context, when the current rate was less than 150 A, the error of the developed ECM was lower than 3%. Additionally, when the demanded power was high, in current rates above 150 A, the simulation error was lower than 5%.

Iterative Nonlinear Fuzzy Modeling of Lithium-Ion Batteries

Electric vehicles (EVs), in their pure and hybrid variants, have become the main alternative to ensure the decarbonization of the current vehicle fleet. Due to its excellent performance, EV technology is closely linked to lithium-ion battery (LIB) technology. A LIB is a complex dynamic system with extraordinary nonlinear behavior defined by electrical, thermal and electrochemical dynamics. To ensure the proper management of a LIB in such demanding applications as EVs, it is crucial to have an accurate mathematical model that can adequately predict its dynamic behavior. Furthermore, this model must be able to iteratively adapt its parameters to accommodate system disturbances during its operation as well as performance loss in terms of efficiency and nominal capacity during its life cycle. To this end, a methodology that employs the extended Kalman filter to iteratively improve a fuzzy model applied to a real LIB is presented in this paper. This algorithm allows to improve the classical Takagi–Sugeno fuzzy model (TSFM) with each new set of data obtained, adapting the model to the variations of the battery characteristics throughout its operating cycle. Data for modeling and subsequent validation were collected during experimental tests on a real LIB under EVs driving cycle conditions according to the “worldwide harmonised light vehicle test procedure” (WLTP) standard. The TSFM results allow the creation of an accurate nonlinear dynamic model of the LIB, even under fluctuating operating conditions, demonstrating its suitability for modeling and design of model-based control systems for LIBs used in EVs applications.

Efficient Electrochemical State of Health Model for Lithium Ion Batteries under Storage Conditions

Capacity degradation of batteries negatively impacts the lifetime of battery packs as well as the residual value of electric vehicles. Developing a degradation model for the prognosis of the state of health (SOH) under storage conditions is a critical aspect of developing algorithms to maximize the remaining useful lifetime of these systems. It is known that electrochemical degradation models have superior predictive ability compared to more empirical or data-driven models, but these still require improvement in terms of computational efficiency. In this work, we thus introduce a simple, reduced-order electrochemical degradation model for lithium-ion batteries. This model considers three key aging mechanisms with the ability to predict the SOH under various calendar aging conditions. Lumped model results are validated against a single particle-based degradation model and show close agreement, even as the simulation time is reduced by 2 orders of magnitude. This indicates significant potential in real-world applications to account and correct for the effects of storage on cell performance and lifetime.

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model (ECM). The traditional recursive least squares (RLS) method is easily biased with the noise disturbances from sensors, which degrades the modeling accuracy in practice. Meanwhile, the recursive total least squares (RTLS) method can deal with the noise interferences, but the parameter slowly converges to the reference with initial value uncertainty. To alleviate the above issues, this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM. RLS converges quickly by updating the parameters along the gradient of the cost function. RTLS is applied to attenuate the noise effect once the parameters have converged. Both simulation and experimental results prove that the proposed method has good accuracy, a fast convergence rate, and also robustness against noise corruption.

Extreme learning machine–radial basis function neural network–based state-of-charge estimation of lithium-ion batteries assisted with fiber Bragg grating sensor measurements

Lithium-ion batteries have been widely used in power systems for accepting large-scale renewable energy generations and in the transport sector to facilitate vehicle decarbonization, the accuracy of state-of-charge (SOC) estimation is extremely crucial for the battery systems to operate safely and reliably. Many approaches have been developed for battery SOC estimation based on the measurable electrical signals. However, the electrical measurements are usually corrupted by sensor noise and are also limited by insulation, corrosion, and electromagnetic compatibility. To address these problems, fiber Bragg grating (FBG) sensors are used to replace thermocouple sensors, the battery SOC therefore can be estimated based on the measurement of the strain information. In order to train the SOC estimation model for lithium-ion batteries, an FBG sensor–based battery SOC estimator, namely, ELM-RBFNN, is developed using the radial basis function neural network (RBFNN) identified by extreme learning machine (ELM). According to the ELM principle, the ELM-RBFNN model randomly selects the radial basis function (RBF) centers and determines the parameters of the hidden-layer nodes without any manual adjustment. The ELM-RBFNN estimation model has the advantages of fast learning speed, global optimization, and excellent generalization. Experimental results confirm that compared to the linear estimator and the polynomial estimator, the developed SOC estimator is able to produce more accurate results.

An investigation on thermal runaway behaviour of a cylindrical lithium-ion battery under different states of charge based on thermal tests and a three-dimensional thermal runaway model

A significant risk for lithium-ion batteries (LIBs) is fire and explosions caused by thermal runaway (TR). A TR model for LIBs with various states of charge (SOCs) can help design safer battery modules. In this work, the TR mechanism of a commercial Li[Ni5Co2Mn3]O2/graphite 18650 type cylindrical battery with various SOCs has been investigated through differential scanning calorimetry (DSC) tests on the single and mixed components. Then, a three-dimensional (3D) TR model is developed to predict the battery TR behaviours under different SOCs. This model fits well with the accelerating rate calorimetry (ARC) test results of the batteries with various SOCs. Furthermore, the validated model and ARC experiment results are employed to investigate the TR mechanism of different SOC batteries. The results show that the reaction onset temperature for cathode-anode and anode-electrolyte roughly advances as the SOC increases and the reaction enthalpy of the cathode-anode, anode-electrolyte and cathode increases with the increase of SOC. Cathode-anode, anode-electrolyte are the main heat generation in the process of battery TR, and their proportion of heat generation will decrease with the decrease of SOC.

Aging diagnosis-oriented three-scale impedance model of lithium-ion battery inspired by and reflecting morphological evolution

Numerous mutually coupled factors contribute to the aging of lithium-ion battery (LIB). Inspired by the observation of microscopic morphological changes and their mechanistic analysis, this paper considers the evolving agglomerate fracture and growing SEI film as the main driving forces, and the aging of LIB and consequential impedance changes are represented with the fracture expansion of secondary particle and thickness growth of SEI layer, leading to a full-cell impedance model suitable for describing aging behavior of LIB, which is capable of effectively approximating the electrochemical impedance spectrum (EIS) throughout the usable life. By analyzing the identified parameters with regard to the state of health (SOH), the fracture depth of cathode agglomerate and the thickness of anode SEI film exhibit trends consistent with the morphological development on electrode materials and the deduction of multi-physical mechanisms, and such strong correlation is conveniently used to estimate the SOH of LIB. A large number of qualitative studies are emerging regarding the aging of LIB, and this paper aims to supplement research on the aging modeling and diagnosis of SOH in the frequency-domain by unifying the cause and effect from a quantitative perspective.

Remaining useful life prognostics of lithium-ion batteries based on a coordinate reconfiguration of degradation trajectory and multiple linear regression

Lithium battery has been widely applied as new energy to cope with pressures in both form environment and energy. The remaining useful life (RUL) prognostics of lithium-ion batteries have become more critical. Convenient battery life prediction allows early detection of performance deficiencies to help maintain the battery system promptly. This paper proposes a RUL prognostics model of lithium-ion batteries based on a coordinate reconfiguration of degradation trajectory and multiple linear regression. First, a new sampling rule is used to reconfigure the coordinates of degradation data of new batteries and truncated similar batteries. Then, the relationship between similar and new lithium-ion batteries is established by using the reconfiguration data. Moreover, a new RUL prognostics model based on a coordinate reconfiguration of degradation trajectory and multiple linear regression is established by considering the influence of time-varying factors, which can improve prediction accuracy with small sample data and significantly reduce product development time and cost.

Mechanical characterization and modelling of lithium-ion batteries

Mechanical phenomena in lithium-ion batteries are one of the main sources of damage, as well as an indicator of battery health and charge. Then, a deep study of these phenomena may improve battery life, management and safety. Mechanical phenomena are caused by the insertion of lithium ions in the microstructure of the electrodes and can be divided into two main categories: stress and degradation of the electrode microstructure, and battery volume change. The stress and fracture behaviour of the electrode microstructure due to lithium intercalation are studied with an electrochemical-mechanical model. Stress intensity factor is computed to assess how current rate and the geometry of the electrode microstructure affect fracture and may reduce the battery life. In addition to stress in the microstructure, lithium insertion causes the swelling of the entire battery. Then, the thickness change of batteries with different chemistries is measured. These measurements carry important information on the battery states and represent an alternative to voltage to extrapolate charge and health states.

Remaining useful life prediction of the lithium-ion battery based on CNN-LSTM fusion model and grey relational analysis

<abstract> <p>The performance of lithium-ion batteries will decline dramatically with the increase in usage time, which will cause anxiety in using lithium-ion batteries. Some data-driven models have been employed to predict the remaining useful life (RUL) model of lithium-ion batteries. However, there are limitations to the accuracy and applicability of traditional machine learning models or just a single deep learning model. This paper presents a fusion model based on convolutional neural network (CNN) and long short-term memory network (LSTM), named CNN-LSTM, to measure the RUL of lithium-ion batteries. Firstly, this model uses the grey relational analysis to extract the main features affecting the RUL as the health index (HI) of the battery. In addition, the fusion model can capture the non-linear characteristics and time-space relationships well, which helps find the capacity decay and failure threshold of lithium-ion batteries. The experimental results show that: 1) Traditional machine learning is less effective than LSTM. 2) The CNN-LSTM fusion model is superior to the single LSTM model in predicting performance. 3) The proposed model is superior to other comparable models in error indexes, which could reach 0.36% and 0.38e-4 in mean absolute percentage error (MAPE) and mean square error (MSE), respectively. 4) The proposed model can accurately find the failure threshold and the decay fluctuation for the lithium-ion battery.</p> </abstract>

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r-dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

Bayesian Model Selection of Lithium-Ion Battery Models via Bayesian Quadrature

A wide variety of battery models are available, and it is not always obvious which model ‘best’ describes a dataset. This paper presents a Bayesian model selection approach using Bayesian quadrature. The model evidence is adopted as the selection metric, choosing the simplest model that describes the data, in the spirit of Occam's razor. However, estimating this requires integral computations over parameter space, which is usually prohibitively expensive. Bayesian quadrature offers sample-efficient integration via model-based inference that minimises the number of battery model evaluations. The posterior distribution of model parameters can also be inferred as a byproduct without further computation. Here, the simplest lithium-ion battery models, equivalent circuit models, were used to analyse the sensitivity of the selection criterion to given different datasets and model configurations. We show that popular model selection criteria, such as root-mean-square error and Bayesian information criterion, can fail to select a parsimonious model in the case of a multimodal posterior. The model evidence can spot the optimal model in such cases, simultaneously providing the variance of the evidence inference itself as an indication of confidence. We also show that Bayesian quadrature can compute the evidence faster than popular Monte Carlo based solvers.