Battery Internal State Research Articles

A Comparative Study of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling

Lithium-ion battery (LIB) with high specific energy density and long cycle life is one widely used energy storage technology. In order to ensure longevity and safety of the battery system, a battery management system (BMS) that relies on battery model is required. With the development of BMS technique, more attention has been given to electrochemical models that provide insights into the battery internal states. In general, battery electrochemical models consist of partial differential equations (PDEs) describing the thermodynamic and electrochemical process inside the cell, and those PDEs can only be solved numerically due to their complexity.Existing battery simulation software utilize numerical methods such as finite difference method (FDM), finite volume method (FVM), and finite element method (FEM) to solve PDEs in battery models. However, there are little discussions for the selection of a specific numerical methods. In our recent study [1], we compare two spatial discretization methods commonly used to numerically solve the governing PDEs of LIB electrochemical models, namely FDM and FVM, in terms of model accuracy and mass conservation guarantee. First, we provide the mathematical details of the spatial discretization process for both FDM and FVM to solve the battery single particle model (SPM), this result has not been shown in any publication before. Second, we propose a new Hermite extrapolation based FVM scheme leading to higher accuracy when compared to the normally used linear extrapolation based FVM scheme. Then, SPM parameters are identified using experimental data, and a comprehensive parameter sensitivity analysis is conducted under different current input profiles to study parameter identifiability. Finally, model accuracy and mass conservation analysis of the FDM and FVM schemes are presented. Our study shows that the FVM scheme with Hermite extrapolation leads to accurate and robust control-oriented battery model while guaranteeing mass conservation and high accuracy. Also, the proposed new FVM scheme can be extended to solve other battery models, such as SPM model with electrolyte and Doyle-Fuller-Newman model. Moreover, we provide findings of mass conservation analysis for FDM and FVM schemes, which we hope can facilitate BMS model selection.

Rapid Inverse Parameter Inference Using Physics-Informed Neural Networks

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration.However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model.Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs. Figure~\\ref{fig:spm_2d} illustrates the absolute relative errors of trained PINN networks using several different training losses and neural network architectures.After determining a consistent training strategy for both the SPM and P2D PINN surrogate models, the PINNs are extended to determine additional internal state-of-health parameters. As more and more parameters were introduced, the PINN training suffered from ``the curse of dimensionality", which was mitigated by using a hierarchical training approach (where a PINN trained with fewer variable model parameters was used to train a PINN with more variable model parameters).Next, the high-dimensionality PINN surrogates are then integrated into Bayesian calibration schemes to identify internal Li-ion battery properties from experimentally measured voltages. Interpreting the high-dimensional parameter posteriors is discussed with respect to model error, parameter prior choices, and experimental errors. Figure 1

PINN surrogate of Li-ion battery models for parameter inference, Part I: Implementation and multi-fidelity hierarchies for the single-particle model

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery’s internal states by replacing physics-based Li-ion battery models – such as the single-particle model (SPM) and the pseudo-2D (P2D) model – with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/PINNSTRIPES). The techniques used to develop a PINN surrogate of the SPM are extended in Part II (Hassanaly et al., 2024) for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

A hybrid data-driven method optimized by physical rules for online state collaborative estimation of lithium-ion batteries

Accurate online estimation of state of charge (SOC) and state of health (SOH) is crucial for safe operation and reasonable planning of battery management system (BMS). However, battery internal states are unmeasurable directly and coupled with each other, which results in serious difficulties on multi-states accurate estimation. Considering SOC estimation is deeply influenced by SOH, this paper proposes a collaborative estimation method combined machine learning algorithm with simple physical rule. Integrated the merits of the above methods, it can not only improve the estimating accuracy but also low computational burden to a large extent. Firstly, SOH acts as input of SOC in collaboration, which means SOH should have been already known before SOC estimation operation. Thus, SOH is creatively predicted based on gate recurrent unit network in ahead of SOC estimation. Subsequently, the well-trained SOC data-driven model is combined with the ampere hour (Ah) integration, which act as observation and state equation respectively in the particle filtering algorithm to realize the final estimation of SOC. This way, the sole data-driven model is well improved under physics restriction without any other computational procedure, such as online parameter identification. Simultaneously, the predicted SOH is used to fill the Ah integration expression to realize the collaboration between SOC and SOH. What's more, the SOH is further corrected by the incremental capacity peak at the checkpoint, thereby further reducing the estimation deviation. The experimental result on battery shows that the SOH estimated error is below 0.3Ah (the rated capacity is 32.5Ah) and SOC error is less than 1.5 %. What's more, the generalization capacity of the proposed method is verified on different battery types based on public datasets. Obviously, the proposed method has fairly satisfactory property and performance and can totally support its promotion into state online evaluation of battery energy storage.

Implanted potential sensing separator enables smart battery internal state monitor and safety alert

The current battery management system is limited to testing external characteristics, leaving the battery's internal status as a “black box”. Advanced characterization techniques and battery sensing technologies are needed to assess the battery's internal state. However, due to their short lifespan, low sensitivity, invasive nature, and high cost, these technologies face challenges in practical applications and commercialization. Here, we propose a smart battery implanted with a potential sensor for in-situ measurement of anode potential, enabling the recognition of severe side reactions and abnormal Li plating behavior. Specifically, the potential sensing material is directly integrated into the battery separator, which provides a reliable potential reference and serves as a sensing terminal. The porous structure of the separator facilitates lithium-ion transport while simultaneously enabling high-accuracy monitoring with non-destructive implantation. Additionally, the potential sensing separator can detect pre-existing or latent defects in the battery at an early stage, which are difficult to discern from the battery's external characteristics in a timely manner. Furthermore, we have developed a multi-point potential sensor monitoring system that can not only monitor the distribution of anode potential but also pinpoint the location of battery defects.

A Review of Capacity Decay Studies of All-vanadium Redox Flow Batteries: Mechanism and State Estimation.

As a promising large-scale energy storage technology, all-vanadium redox flow battery has garnered considerable attention. However, the issue of capacity decay significantly hinders its further development, and thus the problem remains to be systematically sorted out and further explored. This review provides comprehensive insights into the multiple factors contributing to capacity decay, encompassing vanadium cross-over, self-discharge reactions, water molecules migration, gas evolution reactions, and vanadium precipitation. Subsequently, it analyzes the impact of various battery parameters on capacity. Based on this foundation, the article expounds upon the significance of battery internal state estimation technology. Additionally, the review also summarizes domestic and international mathematical models utilized for simulating capacity decay, serving as a valuable reference for future research endeavors. Finally, through the comparison of traditional experimental methods and mathematical modeling methods, this article offers effective guidance for the future development direction of battery state monitoring. This review generally overview the problems related to the capacity attenuation of all-vanadium flow batteries, which is of great significance for understanding the mechanism behind capacity decay and state monitoring technology of all-vanadium redox flow battery.

Bayesian Approach to Estimate Distribution of Relaxation Times for Lithium-Ion Batteries

Electrochemical impedance spectroscopy (EIS) has emerged as a powerful tool for analyzing the state of lithium-ion batteries due to its ability to provide rich electrochemical information. Traditionally, equivalent circuit and physical models have been utilized for interpreting EIS data. However, these methods possess inherent drawbacks: equivalent circuit models are non-unique, while physical models can be challenging to implement. As an alternative, the distribution of relaxation times (DRT) has garnered increasing attention in recent years. The DRT method enables the analysis of EIS data without predefining a model's shape, allowing for the decomposition of internal characteristics in complex systems, such as lithium-ion batteries. Despite its advantages, DRT estimation is an ill-posed inverse problem that often requires regularization or fine-tuning based on empirical choices, which can lead to the misinterpretation of EIS data.To address these challenges, we propose a Bayesian approach that enables the estimation of DRT while considering uncertainties, even in the presence of observational errors in EIS data. Moreover, the proposed method can assist in estimating the state of health (SOH) of the battery, which provides valuable insights into the battery's overall performance, longevity, and safety. To validate the efficacy of our proposed method, we apply it to synthetic EIS data and compare its performance with existing DRT estimation methods. The results show that the proposed Bayesian approach offers a more robust and accurate estimation of DRT. We also demonstrate the practical applicability of the proposed method by applying it to real lithium-ion battery EIS experimental data, where it successfully extracts meaningful information about the battery's internal state and SOH. In summary, the proposed DRT-based Bayesian method has the potential to enable a robust diagnosis of the internal state and SOH of lithium-ion batteries through EIS measurements. By incorporating this approach, researchers and industry practitioners can gain a deeper understanding of battery performance, facilitating the development of improved diagnostic techniques and battery management strategies to enhance the performance and reliability of lithium-ion batteries. This, in turn, could contribute to the broader adoption of sustainable energy solutions, such as electric vehicles and renewable energy storage systems.This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grants funded by the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20214910100070). Figure 1

Optimizing Extreme Fast Charging Strategy for Lithium-Ion Batteries: A Model Predictive Control Approach

With the increasing demand for extreme fast charging (XFC) in electric vehicles (EVs), there is an urgent need to develop health-conscious fast charging strategies for lithium-ion batteries. However, simply increasing the charging current can disproportionately accelerate battery aging, resulting in severe capacity and performance loss, while posing unacceptable safety risks during operation. In addition, the battery management system (BMS) needs to know the state of each cell for reliable and accurate management, but this involves significant computational burden. In other words, new fast charging strategies need to be developed to solve the dilemma between charging rate, battery aging, and computational complexity.In this work, we propose a novel framework for modelling, estimating, and balancing different types of state heterogeneities in a multi-cell battery module. This framework facilitates the development of optimal fast charging strategies based on battery electrochemical models and model predictive control (MPC). First, an electrochemical and thermal coupling model is formulated at the unit cell level, and a module model is formulated at the system level, taking into account various factors such as connection resistances and system terminals. Then, a non-linear MPC is used to achieve fast charging while considering the health of the battery module. Battery performance is tracked by accurately estimating the battery's internal state, which can support the balancing of all state heterogeneity types represented in the model by controlling the charging current according to the internal state. The proposed framework has three main advantages: (1) The modelling strategy has a flexible and configurable structure that can be applied to battery modules of any size. Using this, (2) the internal state of the battery can be estimated with reduced computational complexity. (3) MPC can be applied to cell-to-cell balancing and XFC strategy. The results of the proposed method provide important insights for achieving XFC and show promise for real-time online estimation and control. Figure 1

Dual Digital Twin: Cloud–edge collaboration with Lyapunov-based incremental learning in EV batteries

The soaring potential of edge computing leads to the emergence of cloud–edge collaboration. This hierarchy enables the deployment of artificial intelligence models in the cyber–physical venue. This paper presents Dual Digital Twin, the next level of digital twin, in the presence of two levels of communication availability, for battery system real-time monitoring and control in electric vehicles. To implement the dual digital twin concept, an online adaptive model reduction problem is formulated with time scale differences induced by the time sensitivity property of industrial applications and limitations of infrastructure. To minimize the model reduction error and battery system control penalty, the online adaptive battery reduced order model framework is proposed, consisting of the gated recurrent unit neural network to construct battery internal states given Internet of things sensor measurements, and incremental learning techniques to facilitate the update of the reduced-order model given data stream. Moreover, we design the physics-informed update of the neural network using the Lyapunov stability theorem to enhance the synchronization with the physical battery behavior. A Li-ion battery and single particle digital twin model with electrolyte and thermal dynamics are utilized in the simulation to justify the effectiveness of the proposed framework. Numerical results demonstrate 1.70% average reduced-order model prediction error and 43.3% accuracy improvement with the novel physics-informed online adaptive framework. The method is also robust concerning varying environmental factors and noise.

Physics-informed deep learning for lithium-ion battery diagnostics using electrochemical impedance spectroscopy

Lithium-ion batteries (LIBs) are prevalent energy storage devices in industrial fields and modern life, but are subjected to capacity degradation during operation due to the varying internal states. To ensure the efficiency, safety and reliability of LIBs, LIBs diagnostics by analyzing the internal states and estimating the capacity is crucial. However, model-based methods and deep learning models for LIBs diagnostics are mainly based on charging and discharging curves that contain limited information on battery internal states, and suffer from either model inaccuracy or limited interpretability. To achieve accurate and interpretable LIBs diagnostics, a novel physics-informed deep learning (PIDL) framework is proposed in this study using the electrochemical impedance spectroscopy (EIS), which is a powerful, non-invasive and information-rich technique. The EIS together with three physically informative parameters, which are extracted using model-based methods to investigate the varying internal states, are taken as inputs for capacity estimation, and two data fusion manners are proposed and investigated. Besides, to extract physically interpretable and conducive latent features, physical regularization and multi-task learning are incorporated, which make effective use of three information sources: physical knowledge, measurements and domain knowledge. Moreover, to evaluate the predictive uncertainty of capacity estimation, the deep ensemble strategy is adopted. The effectiveness and superiority of the PIDL framework are demonstrated using EIS datasets of eight commercially LIBs collected from the University of Cambridge.

Diffusion-aware voltage source: An equivalent circuit network to resolve lithium concentration gradients in active particles

Traditional equivalent circuit models (ECMs) have difficulties in estimating battery internal states due to the lack of relevant physics, such as the lithium diffusion in active particles. Here we configure a circuit network to describe the lithium diffusion and define it as a new high-level circuit element called diffusion-aware voltage source. The circuit representation is proven equivalent to the discretized diffusion equation. The new voltage source gives the electrode potential as a function of the surface concentration and thus automatically incorporates the diffusion overpotential. We show that an ECM with the proposed diffusion-aware voltage sources (called “shell ECM”) can reproduce the single particle model simulation results, making it a trustworthy easy-to-implement substitute. Furthermore, the simplest shell ECM consisting of a single diffusion-aware voltage source and a resistor is validated against experimental constant-current discharges at various rates. The diffusion-aware voltage source can be used to measure diffusivity by fitting the diffusion resistance against experimental data. The viability of the shell ECM for onboard usage is confirmed by implementation into a battery management system of WAE Technologies. By tracking the internal concentration states, the shell ECM demonstrates robustness to dynamic applied-current profiles.

A novel Co-estimation framework of state-of-charge, state-of-power and capacity for lithium-ion batteries using multi-parameters fusion method

A battery management system can intelligently manage and maintain battery systems by effectively estimating and predicting battery internal states. Owing to battery nonlinear characteristics related to various influence factors, the estimation of battery internal states should consider the available capacity and ohmic internal resistance. This paper proposes a co-estimation framework for state of charge (SOC), state of power (SOP) and battery available capacity. Firstly, the first-order equivalent model method is used to identify the battery parameters by recursive least squares algorithm with variable forgetting factor, and the SOC-OCV curve of the battery is obtained by combining the ampere-time integration method. Secondly, three Kalman filters are utilized to estimate battery SOCs and the maximum available capacity and internal resistance are estimated by a forgetting factor recursive least square algorithm. Then peak current and power are estimated under the composite constraints of the estimated capacity and internal resistance. Finally, the experimental data are collected at temperatures 25 °C and 40 °C to verify and analyze the proposed method. The results of battery state estimation indicate that the proposed framework can accurate estimation battery internal states and also provide an effective reference for the driving of powered vehicles.

In-situ temperature monitoring of a lithium-ion battery using an embedded thermocouple for smart battery applications

Uncertainty in the measurement of key battery internal states, such as temperature, impacts our understanding of battery performance, degradation and safety and underpins considerable complexity and cost when scaling-up battery components into complete systems. Our research presents a systematic methodology for the engineering of a commercially available cylindrical cell format to accept in-cell instrumentation. We have developed bespoke cell opening methods and unique fixtures that facilitate a reliable instrumentation process. Extensive experimental results are presented that highlight the performance of both the sensor and the lithium-ion battery are not adversely affected by instrumentation. Our modified test cells were evaluated the energy capacity and impedance for a range of different electrical loading conditions and compared to a set of reference or unmodified batteries. The longer-term implications of embedding instrumentation within a battery are also evaluated with cell performance evaluated after a period of calendar and cyclic ageing. Our study demonstrates the importance of internal temperature monitoring during cell operation by comparing internal and surface temperatures measurements. We found that the internal temperature is consistently and notably higher than surface temperature during cell characterisation and when the cell was electrically loaded with a dynamic real-world profile derived from an electric vehicle. No significant effect on the electrochemical performance of the instrumented cells was observed. Measurement data demonstrates that there is a negligible reduction in energy capacity and only a marginal increase in internal resistance.

Real-time estimation of negative electrode potential and state of charge of lithium-ion battery based on a half-cell-level equivalent circuit model

Equivalent circuit models (ECMs) have been widely used for capturing the electrical behaviour of lithium-ion batteries (LIBs). However, one limitation of the conventional full-cell level ECM is that it cannot capture the battery's internal states at half-cell level, e.g., the negative electrode (NE) potential. Real-time monitoring of NE potential is highly desirable for improving battery performance and safety, as it can prevent lithium plating which occurs when the NE potential drops below a threshold value. This paper proposes an easy-to-implement framework for real-time estimation of the NE potential of LIBs. An ECM at half-cell level is developed and parametrised by a bespoke experimental method, exemplified on a commercial 21700 LIB cell. The cell is instrumented with a lithium reference electrode that enables direct measurement of the per-electrode potential. Based on the developed model, an extended Kalman filter is implemented to estimate the battery's NE potential and SoC in real-time using only onboard available signals including the terminal current and voltage. Experimental results show that the proposed method achieves high modelling and estimation accuracy. The root mean square error of the real-time NE potential estimation is below 8 mV. The low computational complexity of the developed algorithm can facilitate practical implementation in commercial BMS.

Enabling high-fidelity electrochemical P2D modeling of lithium-ion batteries via fast and non-destructive parameter identification

Physics-based electrochemical models provide insight into the battery internal states and have shown great potential in battery design optimization and automotive and aerospace applications. However, the complexity of the electrochemical model makes it difficult to obtain parameter values accurately. In this study, a novel non-destructive parameter identification method is proposed to parameterize the most commonly used electrochemical pseudo-two-dimensional model. The whole identification process consists of three key steps. First, in order to find the optimal identification conditions, the sensitivity of model parameters is analyzed, and parameters are classified into three types according to their most sensitive conditions. Second, feasible initial guess values of these unknown parameters are obtained using a deep learning algorithm, which can not only help avoid the divergence problem of the identification algorithm but also speed up the subsequent identification process. Finally, two different approaches are combined and used for parameter identification, and parameters that have high sensitivity are estimated in a step-wise manner. We show that 14 electrochemical parameters can be estimated accurately within 1 h using simulation and experimental data. After estimating the model parameters, the root-mean-square error of the predicted voltage from the model is less than 14 mV.

A decomposed electrode model for real-time anode potential observation of lithium-ion batteries

The anode potential inside the lithium-ion battery is crucial for battery internal state observation in electric vehicles since it indicates the states of lithium deposition at the anode surface. Conventional equivalent circuit models (ECMs) used in the battery management system (BMS) can only predict limited battery external characteristics. Electrochemical models which can simulate the battery internal behaviors are too complex for onboard applications. In this paper, a novel decomposed electrode model (DEM) is proposed for real-time anode potential observation in real BMSs. The cathode and anode parameters can be calibrated by inserting a reference electrode inside the battery. The decomposed electrode model shows high accuracy in predicting the cell terminal voltage and the anode potential under various current conditions. This model also has predominance considering both model simplicity and computational efficiency. An online anode potential observation algorithm is developed based on the DEM and the extended Kalman filter. A lithium plating-free fast charging algorithm is formulated further by integrating the closed-loop potential observer and the closed-loop current controller. The result indicates that the proposed decomposed electrode model is suitable for online applications in the BMS. • A novel decomposed electrode model (DEM) of lithium-ion batteries is proposed. • The DEM shows advantages in model accuracy, simplicity, and computing efficiency. • A high precision anode potential observation method is proposed based on the DEM. • A lithium plating-free fast charging algorithm is formulated with a PID controller.

Implementation of generative adversarial network-CLS combined with bidirectional long short-term memory for lithium-ion battery state prediction

• Combination of GAN-CLS and bidirectional-long short term (LSTM). • Battery data generation from images using GAN-CLS. • Bidirectional LSTM model training for predicting the battery internal state. • Provision of the reduction time, cost and a more accurate state estimation. This study newly introduces a complementary cooperative algorithm considering generative adversarial network (GAN)-Conditional Latent Space (CLS) combined with bidirectional long short-term memory (BLSTM) for improved and efficient lithium-ion rechargeable battery state prediction. The GAN-CLS algorithm, which is an advanced method of GAN, can generate corresponding images from an input label description. Long short-term memory (LSTM) is a specific recurrent neural network (RNN) architecture that can predict sequences more accurately than conventional RNNs. In terms of battery state prediction, the combination of two methods (GAN-CLS and LSTM) surely provides more improved and efficient rechargeable battery state prediction in contrast to conventional state predictors. The procedure of this study is as follows. First, we propose methods to enhance the data from battery charge/discharge by converting prepared data to images; then, the GAN-CLS method is used to generate corresponding battery data from previous images. Subsequently, the generated data is used to train the BLSTM model. Finally, the trained model is used to predict the battery state. By various experiments and verification, it is concluded that the proposed study can be a good solution for rechargeable battery state prediction (reduction of the time cost 50 times in modeling and 20 times in train/test, provision of a more accurate prediction mean square error (MSE) smaller than 0.0025 and the average MSE less than 0.0013).

An Algorithm for an Online Electrochemical Impedance Spectroscopy and Battery Parameter Estimation: Development, Verification and Validation

Abstract More advanced battery diagnostic approaches are required for a safer and more reliable operation of today's and future battery technologies. For the purpose of evaluating a battery's internal conditions, Electrochemical impedance spectroscopy has proven to be a powerful tool, but nowadays it is only used in laboratory setups. It could provide valuable information about the battery's internal states, if instead it is applied online in an actual battery application. Therefore, we have developed an efficient algorithm, which is designed to run on a battery management system continuously carrying out measurements of the electrochemical impedance by iteratively evaluating measurements of battery current and voltage. Furthermore, the algorithm adapts the parameters of an equivalent circuit model to best match the battery's impedance, hence providing characteristic measures of a battery's internal conditions. The algorithm is implemented in a generic form, which severs as a baseline that can be adjusted to more specific requirements and circumstances in corresponding battery applications. The scope of this work focuses on an introduction of the generic algorithm as well as a proof-of-concept. The later was carried out in two steps. First, the algorithm was run against a battery model. Subsequently, the algorithm was validated utilizing measurements from a real battery cell. In this case, laboratory electrochemical impedance spectroscopy measurements served as reference. The algorithm was able to estimate impedance with a high accuracy in both tests. A high accuracy was also achieved for the parameter estimation; however, its accuracy decreases with large superposed DC current rates.

Optimal Sensor Selection for an Electrochemical Li-Ion Battery Model

This work rigorously evaluates which sensor combinations are best for estimating lithium-ion battery internal states related to state-of-charge, state-of-power, and state-of-health. Lithium-ion batteries have emerged as an enabling technology for many industries that seek the benefits of electrification such as automotive, power systems, and consumer electronics. Central to the operation of lithium-ion battery technology is the battery management system (BMS), whose role is to monitor the status of and facilitate the charging and discharging behavior of the system. Fundamentally, the core challenges of a BMS are modeling, estimation, and control problems. To date, the vast majority of BMS technology and research operates based on the assumption of what is currently possible to measure in a battery system: current, voltage, and temperature. However, valuable advanced BMS capabilities have proven to be challenging to develop based on this sensor limitation.To systematically evaluate the value of different sensing technologies in BMS's, we formulate the sensor selection problem. In other research domains, the sensor selection problem is motivated by the goal of maximizing the usefulness of available sensor data for a given estimation or controls goal [1-3]. The research here examines the sensor selection problem from a mathematical point-of-view without limiting ourselves to the practicality of the sensing technology. That is, instead of asking if some existing sensing technology improves state observability, we ask what sensors are theoretically best for estimating internal states. We seek to motivate the pursuit of new sensing technologies or more rigorously justify the use of existing sensing technologies.We first present a methodology for evaluating the impact of different potential novel sensing capabilities based on an observability analysis for a reduced-order electrochemical lithium-ion battery model, specifically, the Single Particle Model with Thermal Dynamics (SPM+T) [4-5]. We demonstrate the impact of incorporating different sensors on observability of the reduced-order electrochemical model. We find that the inclusion of certain sensors has a greater impact on model observability than others. The result in Figure 1 for the SPM+T model proves that voltage and surface temperature sensing is, in fact, best for state observability. However, this result may change for more complex models, such as the SPMeT [6-7] or others that incorporate additional dynamics such as multiple materials, stress mechanics, etc.

Deep Gaussian process regression for lithium-ion battery health prognosis and degradation mode diagnosis

Accurate state of health estimation and end of life prediction is critical for safe and reliable operation of lithium-ion batteries. This paper proposes a deep Gaussian process algorithm for lithium-ion battery health monitoring. The proposed algorithm uses Gaussian processes to model mapping between the layers, and matrix-variate Gaussian distribution to model correlation between nodes of a given layer. Deep architecture of the proposed algorithm enables capacity estimation using the partial charge-discharge time-series data, in the form of voltage, temperature and current, eliminating need for input feature extraction. The algorithm also estimates statistical correlation between capacity and the elapsed time from the first cycle, which enables end of life prediction. Hidden layer output of the proposed algorithm correlates strongly with the battery internal states, enabling on-board diagnosis of battery degradation mechanisms. The paper demonstrates effectiveness of the proposed algorithm using aging dataset of batteries cycled at different C-rates, temperatures and usage profiles. The proposed algorithm predicts capacity and end of life with coefficient of determinant greater than 0.9 and mean absolute error less than 0.1, demonstrating high prediction accuracy of the proposed approach.